<%BANNER%>

Clearing a Path for Conventionalist Modal Semantics

Permanent Link: http://ufdc.ufl.edu/UFE0024369/00001

Material Information

Title: Clearing a Path for Conventionalist Modal Semantics
Physical Description: 1 online resource (240 p.)
Language: english
Creator: Butler, Jesse
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: analyticity, carnap, circularity, compositional, concept, davidson, de, dicto, direct, disposition, essentialism, extensional, intension, language, lepore, lewis, ludwig, mates, meaning, modal, modality, model, natural, quantification, quantifier, re, rigid, rigidity, semantics, theory
Philosophy -- Dissertations, Academic -- UF
Genre: Philosophy thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In this dissertation, I engage in a research project in modality and the philosophy of language aimed specifically at formulating and assessing the thesis that both de dicto and de re modal statements can be given a semantic treatment which shows that sentences whose primary operator is 'necessarily' can be understood to be true in virtue of the analyticity of the sentence following the modal sentential operator. I call this sort of semantic treatment 'analytic-deflationary'. Rather than defending an analytic-deflationary view outright, I take rather the preliminary step of assessing this analysis of necessity and trying to determine if the view is, after all, viable. My strategy is to argue that the conventionalist analytic-deflationary approach can clear some prima facie challenges to it by developing (at least the beginnings of) a semantical system taking inspiration from Carnap's work in Meaning and Necessity. Within this semantical system, I explain how to meet challenges to do with circularity, the problem of de re modality and a coherent treatment of quantification in (and into) both modal and non-modal contexts. My hope is that the semantical treatment I develop for the sentence operator 'necessarily' will be something which is of the right sort to serve as a small part of a larger project - a general semantical theory that is based on a Davidsonian interpretive truth theory.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Jesse Butler.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Ludwig, Kirk A.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024369:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024369/00001

Material Information

Title: Clearing a Path for Conventionalist Modal Semantics
Physical Description: 1 online resource (240 p.)
Language: english
Creator: Butler, Jesse
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: analyticity, carnap, circularity, compositional, concept, davidson, de, dicto, direct, disposition, essentialism, extensional, intension, language, lepore, lewis, ludwig, mates, meaning, modal, modality, model, natural, quantification, quantifier, re, rigid, rigidity, semantics, theory
Philosophy -- Dissertations, Academic -- UF
Genre: Philosophy thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In this dissertation, I engage in a research project in modality and the philosophy of language aimed specifically at formulating and assessing the thesis that both de dicto and de re modal statements can be given a semantic treatment which shows that sentences whose primary operator is 'necessarily' can be understood to be true in virtue of the analyticity of the sentence following the modal sentential operator. I call this sort of semantic treatment 'analytic-deflationary'. Rather than defending an analytic-deflationary view outright, I take rather the preliminary step of assessing this analysis of necessity and trying to determine if the view is, after all, viable. My strategy is to argue that the conventionalist analytic-deflationary approach can clear some prima facie challenges to it by developing (at least the beginnings of) a semantical system taking inspiration from Carnap's work in Meaning and Necessity. Within this semantical system, I explain how to meet challenges to do with circularity, the problem of de re modality and a coherent treatment of quantification in (and into) both modal and non-modal contexts. My hope is that the semantical treatment I develop for the sentence operator 'necessarily' will be something which is of the right sort to serve as a small part of a larger project - a general semantical theory that is based on a Davidsonian interpretive truth theory.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Jesse Butler.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Ludwig, Kirk A.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024369:00001


This item has the following downloads:


Full Text

PAGE 1

1 CLEARING A PATH FOR CONVEN TIONALIST MODAL SEMANTICS By JESSE BUTLER A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009

PAGE 2

2 2009 Jesse Butler

PAGE 3

3 To Kupusi Medonja, without whom, naught

PAGE 4

4 ACKNOWLEDGMENTS Let us begin at (least near) the beginning. I would like to thank Ben Hill Griffin, Jr. and Major Wilbur L. Floyd for giving their names to the building in which I studied philosophy for these past years. I thank my mother, Marsha Mc Govern, and my father, Arthur Butler, for their support, financial and otherwise, during my time at UF. No philosophical work whatsoever could have been done in Griffin-Floyd Hall if this building were not maintained and kept clean. I would like to thank the maintenance and housekeep ing staff at Griffin-Floyd Hall. Next, I thank all the faculty of the Philosophy Department that were not on my committee or directly connected to my research in any way but who contributed to the intellectual environment in which a dissertation like this could be comple ted: Dr. Auxter, Dr. Baum, Dr. DAmico, Dr. Copp, Dr. Haynes, the late Dr. Holly and Dr. Li u. Without the help of Virginia Dampier and Kenetha Johnson (and Noeleen Brophy before he r) the administrative goings on that are a necessary condition for any philosophical work would have ground to a halt, and I could not have completed this project. Another group that was helpful to the completion of this project were those graduate students who contribute d to the stability, normalcy and intellectual environment of the department: Ching-E Nobel A ng, Emil Badici, Carlos Bernal, Shawn Burtoft, Brian Coffey, Moti Gorin, James van Houten, Donovan Hulse, Evan Moore, Edward Perez, Kevin Savage, Holly Stillman and Casey Woodling. I am very grateful to the committee members who agreed to help me take on this pr oject: Dr. John Biro, Dr. Frederick Gregory and Dr. Gene Witmer. Without Dr. Kirk Ludwigs early and keen insight into the fundamental issues I take on in the following, unfailing attenti on and patience, and generous and insightful comments, this project could never have been completed (and probably could never have even been begun). I thank Dr. Ludwig. Fi nally, I thank my wife, Ivana Simi without whose help none of the work that went into this dissertation could have been started.

PAGE 5

5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ............................................................................................................... 4LIST OF ABBREVIATION AND SYMBOLS ............................................................................ 10ABSTRACT ...................................................................................................................... .............13 CHAP TER 1 INTRODUCTION .................................................................................................................. 14Our Project ..............................................................................................................................14Conventionalist Modal Semantics ................................................................................... 17Analytic-Deflationary Modal Semantics .........................................................................18Clearing a Path ............................................................................................................... .19Thorny Issues for such a Project ............................................................................................. 20Thorny Issue One: No Completeness Theorems Will Be Proved ................................... 21Thorny Issue Two: How Can a Model Th eoretic Treatment of Carnap Be Consistent with a Conventionalist Approach to Modal Semantics? ............................22Thorny Issue Three: Abduction versus Apodicticity ............................................... 24Thorny Issue Four: the Relationship of Language Possession to Concept Possession. ................................................................................................................... 27Thorny Issue Five: Our Analysis May No t Be Meaning Giving, but Rather Only Truth Functional ........................................................................................................... 282 SELECTIVE REVIEW OF THE SEMANTICAL SYSTEMS OF MEANING AND NECESSITY ............................................................................................................................31Introduction .................................................................................................................. ...........31Carnaps Semantical Systems and Modality .......................................................................... 33Semantical Systems S1, S2 and S3 ....................................................................................34Language of the Systems S1, S2 and S3 ...........................................................................35Rules of Inference ............................................................................................................37Designators and Extension .............................................................................................. 38State-Descriptions ............................................................................................................ 39L-Truth, Intensions and N ............................................................................................. 41Conclusion .................................................................................................................... ..........433 REWORKING AND GENERALIZATION OF CARNAPS SYSTEM WHICH MAKES EXPLICIT USE OF MODEL-THEORETIC TECHNIQUES ................................ 45Introduction .................................................................................................................. ...........45Carnaps Ideas Presented in, and Re vised in, a Model-theoretic Idiom ................................. 45Interpretations Can Provide Extension ............................................................................49

PAGE 6

6 Sets of Interpretations Can Provide I ntension .................................................................58Admissible Interpretations ........................................................................................... 60Conclusion .................................................................................................................... ..........634 OUR GENERALIZATION OF CARNAPS SYSTEMS LEADS TO A TREATMENT OF ANAL YTICITY THAT IS CONCEPTU ALLY PRIOR TO A TREATMENT OF NECESSITY ..................................................................................................................... ......66Introduction .................................................................................................................. ...........66On the Relationship of Possible Worlds, State-Descripti ons and Admissible Interpretations ............................................................................................................... ......68Overview of the Differences and Our Commitments as Things Stand Now .................. 68Birds eye view of the situation ................................................................................68View from the battlefield ......................................................................................... 71Differences in Ontological Commitment ........................................................................73Promissory Note for the Ways in Wh ich Interpretations Are Restricted ........................ 75On Conceptual Priority, Analyticity and Necessity ................................................................ 76Modal Realism and Truth-Making .................................................................................. 76Conceptualism and Truth-Making ...................................................................................79Conventionalism and Truth-Making ............................................................................ 81Can Conceptual Priority be Given to An alyticity so that an Account of Modal Semantics that is not Vicious ly Circular is Possible? .................................................. 84Conclusion .................................................................................................................... ..........845 CIRCULARITY AND REDUCTIVE ACC OUNT S OF MODAL SEMANTICS ................86Introduction .................................................................................................................. ...........86Some General Comments about Reduc tion, Modality and Analyticity ................................. 88Should We Rest Content Even If We Do Not Have a Satisfactory Analysis of Analyticity? .................................................................................................................. 89Necessity Reduced to Analyticity Reduced to Necessity Reduced to Analyticity Reduced to ................................................................................... 90What We Must Show for the Conventiona list Analytic-Deflationary Approach .... 93Three Separate, Yet Related, Projects to Investigate Modal Semantics and Specific Difficulties Faced by Reductive Accounts .................................................................. 94The metaphysical issue .............................................................................................94The semantic facts issue (again) ........................................................................... 95The reduction issue ...................................................................................................95Two Approaches to Reductive Accounts: Metaphysical Realist Approaches and Analytic-Deflationary Approaches .....................................................................................96Metaphysical Realist Reductive Accounts ...................................................................98Reductionist modal semantics la Lewisian possible worlds .................................98Reductionist modal semantics la Armstrongs states of affairs ............................99Difficulties for Metaphysical Real ist Reductive Approaches ...................................... 99Reductive Analytic-Deflationary Accounts .................................................................. 101Conclusion .................................................................................................................... ........103

PAGE 7

7 6 LOGICAL MANIPULATION OF THE INTE RPRETATION FUNCTIONS IN PREPARATION FOR A TREATMENT OF THE ADMISSIBILITY CRITERIA IN TERMS OF CONCEPTS ..................................................................................................... 109Introduction .................................................................................................................. .........109Beginning a Response to the Question over Ci rcularity: The Admissibility Criteria for Interpretations Must Be Presented by Wa y of How the Extensions of Terms Are Specified. .................................................................................................................... .......109Conclusion .................................................................................................................... ........1137 CONCEPTS UNDERSTOOD IN A PARTICULAR WAY AS THAT WHICH UNDE RWRITES I AND MAKES IT EPISTEMICALLY PERSPICUOUS ..................... 116Introduction .................................................................................................................. .........116Concepts ...................................................................................................................... .........121We Shall Attempt to Underwrite Me aning Talk with Concept Talk ............................. 122Making use of a traditiona l view: a predicate expre sses a concept under which things having a certain property ar e judged to fall by one who has the concept in question ............................................................................................. 122A prerequisite log ical framework ....................................................................... 131Aid from a compositional meaning theory? ........................................................... 132More aid than we thought? Does implic it knowledge of a truth theory for a language give us the entire pr erequisite logical framework? ............................. 133A promissory note for Chapter Nine ...................................................................... 133Now We Are in the Position to See Con ceptual Backing by Way of Concepts for Our Stitched Together Map of Intensions .................................................................. 133Conclusion .................................................................................................................... ........1358 TAXONIMIZING KEY (FAMIL IES OF) CONCEPTS ......................................................138Introduction .................................................................................................................. .........138Our Strategy: A Very Brief and Incomplete Survey of Concepts by Way of Concept Possession and Conceptu al Connections ..........................................................................139Survey of Different Sorts of Concepts: Abstract Objects ............................................. 139Survey of Different Sorts of Concepts: Logi cal / Abstract / Set-Theoretic Relations .. 141Survey of Different Sorts of Concepts: Physical Object ............................................... 143Survey of Different Sorts of Concepts: Feature / Aspect .............................................. 144Survey of Different Sorts of Concepts: Similarity ........................................................ 146Survey of Different Sorts of Concepts: Category ..........................................................147Survey of Different Sorts of Concep ts: Determinables and Determinates .................... 148Survey of Different Sort of Concepts: Primary Qualities ............................................. 149Survey of Different Sorts of Concepts: Secondary Qualities ........................................150Survey of Different Sorts of Concepts: Natural Kinds .................................................. 152Survey of Different Sorts of Concepts: Artifacts ..........................................................153Survey of Different Sorts of Concepts: Conclusion ......................................................154Conclusion .................................................................................................................... ........156

PAGE 8

8 9 LINGERING CONCERNS AND A PO SSIBLE DIRECTION FOR FUT URE RESEARCH ON A CLOSELY RELATED TOPIC (TWO-DIMENSIONAL SEMANTICS) ......................................................................................................................158Introduction .................................................................................................................. .........158Have We now Shown that We Can Prevent Vicious Circularity in the Deflationary Reduction if We Take this Approach? .............................................................................. 158How Far can the Reduction Go? The Ultimate Reductive Base and the Commitments this Strategy Incurs ............................................................................. 160A Final Word to Allay Fears about Disposi tions in Our Reductive/Explicative Base ..162Concepts Versus Quality Grounds of Chapter Seven .......................................................163Some Words on Two-Dime nsional Semantics ..................................................................... 164Conclusion: an Apodictic Approach to Modal Semantics versus an Abductive Approach ...................................................................................................................... .....16710 THE PROBLEM OF DE RE MODALITY ..........................................................................173Introduction .................................................................................................................. .........173Rigid Designation and Metaphysical Necessity ................................................................... 176What, exactly, are the Problems for Conve ntionalism? What is Unacceptable for a Conventionalist? ........................................................................................................ 177Does the Notion of Rigid Designation Presuppose the Existe nce of Essential Properties?..................................................................................................................178Possible Conventionalist Res ponses to the Concern over De Re Modality. .........................184Conclusion .................................................................................................................... ........18611 TECHNICAL APPARATI TO ENDORSE THE DE RE MODAL C LAIMS WE FAVOR, POSSIBLE OBJECT IONS AND RESPONSES ..................................................188Introduction .................................................................................................................. .........188Topological / Linguistic-U se Restrictions ............................................................................189Exploration of the Topological / Linguistic-Use Proposal ................................................... 198Can We Hold that Category Name s are Directly Referential? ...................................... 198Names of Fictional Characters ...................................................................................... 199Description Names (Such as the Numerals) ..................................................................201Conclusion .................................................................................................................... ........20612 SKEPTICISM THAT MEETS QUANTIFIED MODAL SENTENCE S, A PROPOSED CONVENTIONALIST TREATMENT OF THEM AND HOW OUR WORK MIGHT FIT INTO A GENERAL SEMANTIC THEORY ................................................................208Introduction .................................................................................................................. .........208Our Conventionalist Proposal for Sentences of the Form ( Q x ) ( ( x )) ............................. 208Kit Fines Assessment of the Prospects for Making Sense of Quantified Modal Sentences....................................................................................................................209There Are at Least Two Reasonable Ways of Making Sense of Quantified Modal Sentences....................................................................................................................209

PAGE 9

9 First option: logi cal satisfaction ............................................................................. 209Second option: essentially, esse ntialism or analyticity ..........................................210Our modest conventionalist desiderata and treatment of quantified modal sentences on the model of Benson Mate s treatment of quantified non-modal sentences ............................................................................................................. 213Fitting Things into a General Semantical Theory ................................................................. 216What We Have Done So Far ......................................................................................... 216Our Broader Goals .........................................................................................................217General Semantical Theories ......................................................................................... 218Compositional mean ing theories ............................................................................ 220An interpretive truth theory used in the service of a compositional meaning theory ..................................................................................................................221How What We Have Done Might Fit in ........................................................................ 224Problems for and Questions about the Appro ach We Have Tried to Clear the Path for ........................................................................................................................... ....225We have given a semantical (truthconditional) analysis, not a meaning giving analysis ..................................................................................................225Is I am here now analytic in English? If so, is it necessarily the case that I am here now? ............................................................................................................ 226Our account treats N as a (generalized) pr operty of sentences, rather than as a sentence operator per se ......................................................................................228Conclusion .................................................................................................................... ........229APPENDIX A OUR MODEL-THEORETIC REWORKIN G AND GE NERALIZATION OF CHAPTER THREE AND SYSTEMS OF QUANTIFIED MODAL LOGIC ..................... 230Outline of the Traditional Formal Approach ................................................................. 231How Our Model-Theoretic Reworking Can Support the Traditional Approach ........... 232The Approach of Hanson and Hawthorne in Validity and Intensional Languages ... 234The Relationship between R and R .............................................................................235B A PROPERLY SEMANTICAL DIFFICULTY FOR METAPHYSICAL REALIST REDUCTIVE ACC OUNTS THAT IS AVOIDED BY THE ANALYTICDEFLATIONARY METHOD .............................................................................................236LIST OF REFERENCES .............................................................................................................238BIOGRAPHICAL SKETCH .......................................................................................................240

PAGE 10

10 LIST OF ABBREVIATION AND SYMBOLS P1 0, P1 1, P1 2, 1-place predicate terms of the regi mented language of the model theoretic update of Carnaps semantical systems S1, S2 and S3. Pn 0, Pn 1, Pn 2, n-place predicate terms for n 0 of the regimented language model theoretic update of Carnap s semantical systems S1, S2 and S3. (If the number of places of the predicate term is clea r from the context the superscript may be omitted.) 1 Set of 1-place predicat e terms for this language: { P1 0, P1 1, P1 2, }. n { Pn 0, Pn 1, Pn 2, } for n 0. n, n 0, n 1, Metalinguistic variables ranging over n. a0, a1, a2, Individual constant terms of th e regimented language model theoretic update of Carnaps semantical systems S1, S2 and S3. Set of individual constant terms: { a0, a1, a2, .}. *, 0, 1, Metalinguistic variables ranging over 0, 1 Metalinguistic variables ranging over Carnaps designators: { n }. x0, x1, x2, Individual variable terms of th e regimented language model theoretic update of Carnaps semantical systems S1, S2 and S3. X Set of individual variable terms: { x0, x1, x2 } x x Metalinguistic variables ranging over X 0, 1, 2, Metalinguistic variables ranging over { X }. A metalinguistic variable rangi ng over strings comprising the concatenation of the elements of n-tuples of elements of X For example, might take the value x0x1x2 for n = 3. WFF A W ellF ormed F ormula a syntactical st ring of the languages we outline. Metalinguistic variables ra nging over the set of WFFs D Set of definite descriptions: WFFs of the form ( x )( x ). 0 1 Metalinguistic variables ranging over { D }. Set of sentences of the language of S1, S2 and S3.

PAGE 11

11 0, 1, Metalinguistic variables ranging over \ An interpretation of the language of S1, S2 and S3. An index set for admi ssible interpretations ( ) {\ } Set of admissible interpretations. A subset of the range of \ restricted to { D }. : The set containing all of the individuals in for each V0, V1 Metalinguistic variables ranging over {g, Y } (functional equivalents of truth values for a specific interpretation). c c c c 0 c 1 Concept (in Carnaps sense of individual concepts ) variables. c c *, c c0, c1, Concept (in the sense we shall sk etch in Chapters Seven and Eight) variables. These are respectively opening and closing quasi-quotations (see Quine 1976). We use these to indicate a stri ng of a particular type that is represented with both object la nguage symbols and metalinguistic variables. SD S tate D escription. A state description is a list of atomic sentences and negations of atomic sentences such that for every predicate letter n and all individual constants 0, 1, n-1, a state-description contains either n( 0, 1, n-1 ) or ~ n( 0, 1, n-1 ). L-truth A property of sentences defined in Meaning and Necessity A sentence is L-true if and only if it is true in every state-description. N A sentence operator defined in Carnaps Meaning and Necessity For sentence S, the sentence formed by prefixing N, i.e. N S is true just in case S is L-true, false otherwise. QML Quantified Modal Logic. Operator of QML and other simila r formal systems corresponding to the English word possibly. Sometimes used in formalization of the semantics of sentences involving the term possibly. Operator of QML and other simila r formal systems corresponding to the English word necessarily. Sometimes used in formalization of the semantics of sentences involving the term necessarily.

PAGE 12

12 I The map stitched together from {\ }. (See Chapter 6.) i This is the interpretation implica tion operator a metalanguage symbol informally defined in the following way. If an interpretation is such that it makes true then if that interpretation is such that the truth of semantically entails 1, we write i 1. There is more explication in Chapters Three and Six. I Uncurried I. (See Chapter 7.) Q A metalinguistic variable ranging over { }. Either ( x0) P1 0( x0) or ( x0) P1 0( x0) might replace (Qx0) P1 0( x0).

PAGE 13

13 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CLEARING A PATH FOR CONVEN TIONALIST MODAL SEMANTICS By Jesse Butler May 2009 Chair: Kirk Ludwig Major: Philosophy In this dissertation, I engage in a resear ch project in modality and the philosophy of language aimed specifically at formulati ng and assessing the thesis that both de dicto and de re modal statements can be given a semantic trea tment which shows that sentences whose primary operator is necessarily can be unders tood to be true in virtue of the analyticity of the sentence following the modal sentential operator. I call this sort of semantic treatment analyticdeflationary. Rather than defe nding an analytic-deflationary view outright, I take rather the preliminary step of assessing this analysis of necessity and trying to determine if the view is, after all, viable. My strategy is to argue that the conventiona list analytic-deflationary approach can clear some prima facie challenges to it by developing (at leas t the beginnings of) a semantical system taking inspiration from Carnaps work in Meaning and Necessity Within this semantical system, I try to explain how to meet challenges to do with circularity, the problem of de re modality and a coherent treatment of quantification in (and into) both modal and non-modal contexts. My hope is that the semantical treatment I develop fo r the sentence operator necessarily will be something which is of the right sort to serve as a small part of a larger project a general semantical theory that is based on a Davidsonian interpretive truth theory.

PAGE 14

14 CHAPTER 1 INTRODUCTION Our Project In this dissertation, we shall engage in a philosophy of language project in which we endeavor to show that a certain app roach to modal semantics is a viable one. In this sense, we are trying to clear a path for this sort of approach to modal semantics, rather than to defend this particular approach against all objections. But fi rst things first: what is modal semantics? And what is the approach to it for which we shall try to clear a path? In philosophy, semantics is the study of meaning of linguistic entities such as sentences (the cat is on the mat,) and subsentential parts out of which sentences might be construc ted such as predicate terms (is blue and is trapezoidal), names (Bobby and Oma r), logical operators (and, or, not), quantifiers (for all, there exists) and variab les (something, x). To provide more definition for the term semantics, we might think about what semantics is not (or at least what it is not required to be). The study of semantics can be thought of as distinct fr om the study of syntax. Syntax describes which strings of the vocabulary of a language ar e sentences. So one can use syntax to determine which strings of words are well-formed and which are ill-formed. For example, consider two strings of the same word s: a lumberjack quickly chops down a tree, and tree a chops a down quickly lumberjack. According to the rules of syntax for English the first is well-formed and the second is ill-formed. Only strings which are well-formed are candidates to be sentences, and only strings which are well -formed are those whose semantics we can investigate. A standard view is that sentences of a natural language like English are about something non-linguistic, and that there are word-world connections whic h secure this aboutness. For example, the sentence Bobby is trapezoidal is about the individual picked out by the name

PAGE 15

15 Bobby and makes the claim that that individual has a certain shape, specifically that individual is trapezoidal. So we see that th e study of semantics must be cl osely bound up with truth; if one understands the meaning of this sentence, then one knows the conditions under which it is true. Another standard view is that sentential mean ing (the meanings of grammatically complex expressions generally) is compositional: we can unde rstand the meaning of a sentence if we can understand the meaning of the sub-sentential parts of that sentence and understand the manner in which these parts are combined to form a syntactical string. So, according to these two received views, we can engage in an i nvestigation into semantics of sentences by studying the semantics of the sub-sentential parts. If we can come to understand how to understand the semantics of the name Bobby and predicate term is trapezoidal and can come to understand how to understand in terms of a semantical theory (or theory of meani ng) the manner in which these two terms are combined to form a meaningful sentence, then we can understand the meaning of the sentence. As an intuitive first stab at an account of the semantics of the sentence Bobby is trapezoidal, we might say that the sentence is tr ue if and only if that which is named by Bobby is among that class of things that are indicated by the predicate is trapezoidal. If the is trapezoidal picks out the class of things each of wh ich is trapezoidal, then the senten ce is true just in case that class includes Bobby. That is it is true just in ca se Bobby is trapezoidal. So far, so good, but what is meant by the modal in modal semantics? A modal is a qualifier for the truth of a sentence. In terms of our example, we might qualify the truth of the sentence Bobby is trapezoidal with the related sentence, Possibly, Bobby is trapezoidal or another related sentence Necessa rily, Bobby is trapezoidal. Th ese two variations are modal sentences because the truth of the original Bobby is trapezoidal is qualifie d. The first is true if and only if it could be the case that Bobby is trapezoidal, the second if and only if it must be the

PAGE 16

16 case that Bobby is trapezoidal.1 Clearly, to give an account of the semantics for these modal sentences, we need to consider something more than the actual class of trapezoidal individuals and whether Bobby is among its members or not. Ther e are other modals such as those expressed by (the temporal operators) it will always be the case that ., it will be the case that ., it has always been the case that ., it was the case th at ., (and the deontic operators) it is obligatory that ., it is permitted that . and it is forbidden that . But we will be focused only on the modals expressed by possibly and n ecessarily, and since th ese operators are duals of each other, that is, one can be defined in te rms of the other and not (Necessarily, Bobby is trapezoidal is true just in case It is not the case th at possibly Bobby is not trapezoidal is true), we will focus almost exclusively on necessarily. Understanding how to give an account of the semantics for sentences like these last two will occupy us for the next roughly 245 pages. I have said that we shall try to clear a path for an account of modal semantics of a certain sort. Of what sort is the account? The account we shall try to clear a path for is a conventionalist and analyticdeflationary. What do these terms mean? We can begin an answer by saying that the success of our work depends upon the notion of analyticity or, roughly, truth in virtue of meaning, a nd that truth in virtue of m eaning depends upon the linguistic conventions in force. More specifically, we formulate and assess the thesis that both de dicto and de re modal statements2 can be given a semantic treatment which shows that sentences whose 1 There is of course a standard epistemic reading of these English modal adverbs as well. We might say that on this reading, Possibly, Bobby is trapezoidal is true just in cas e it is conceivable or imaginable that Bobby is trapezoidal, and that on this standard epistemic reading Necessarily, Bobby is trapezoidal is true just in case it is in conceivable or unimaginable that Bobby is not trapezoidal. 2 Roughly, a de dicto modal statement can be understood to be about a sentence or about some word(s) ( dicta ), and a de re modal statement can be understood to be about an individual thing ( res ). For example, the following is a sentence that is ambiguous between a de re and a de dicto interpretation: Necessarily, the number of the planets is greater than seven. An extensive de re paraphrase of this sentence goes something like: The individual that numbers the planets, vis a number is such that necessarily, it, that is the nu mber itself, is greater than seven, and an extensive de dicto paraphrase of this sentence goes something like: It is necessary that the number of the planets is greater than seven. The de re interpretation is true because that individual that numbers the planets, the number nine

PAGE 17

17 primary operator is necessarily can be understood to be true in virtue of the analyticity3 of the sentence following the modal sentential operator, hence an analytic -deflationary approach to modal semantics. My inclination is to say that an analytic-deflationary semantics is the right way to go in an investigation in modality, but rather than defending such a view outright, we take rather the preliminary step of assessing this notio n of necessity and trying to determine just what would be required for this sort of view to be a live option. Conventionalist Modal Semantics To be such, I think the anal ytic-deflationary strategy m ust be at least as appealing as realist approaches to modality. We can get at what is meant by conventionalist approach to modal semantics by contrasting that sort of approach to a realist approach. A realist approach to modal semantics is one according to which we give properties qua abstracta a place in ontology and whose relationships are to secure the truth or falsity of modal claims or according to which possible worlds (concrete or abstract) are taken really to exist and to secure the truth or falsity of such claims. On a conventionalis t approach, the truth or falsit y of modal claims sentences involving the modal operators neces sarily or possibly are se cured by something other than mind-independent properties qua abstracta or possible worlds which serve as the truth-makers for our modal talk. Specifically, a conventionalist takes the truth or falsity of modal claims to be rooted in linguistic convention Typically, one who held such a position would hold roughly that all and only those sentences which are analytic express necessary truths, and so, as linguistic convention plays a key role in spelling out the usual notion of analyticit y, these conventions are one (but not the only ) key component of the beginnings of modal semantics. There are issues (or actually eight in 2009), is greater than seven of necessity, and the de dicto interpretation seems false because it seems that there might have been only five planets inst ead of nine (or eight). We shall say more about the de re / de dicto distinction and the corresponding issue at stake over the course of this document. 3 We will, of course, say much more about the notion of an alyticity as well over the course of the next few chapters.

PAGE 18

18 over whether something as seemingly contingent as linguistic convention could be the basis for the truth or falsity of sentences prefixed by n ecessarily, but such issues need not stymie a conventionalist view.4 For the sort of view for which we sh all try to clear a path, necessity will be explained in terms of analytic ity, a linguistic notion, but analyticity will, in turn, be explained in terms of the relations of concepts (on a spec ific understanding of thos e). Since the relation of concepts is at the root of this sort of modal semantics, on the f ace of things, we shouldnt see the contingency of linguistic conventions as a problem for the sort of conventionalism we try to make room for. That certain linguistic enti ties express certain con cepts as a matter of contingency is a side issue. Analytic-Deflationary Modal Semantics Since the linguistic notio n of analyticity is the only window we have into the relations of concepts to one another, we m ust pursue an a ccount of the sentence opera tor necessarily given in terms of analyticity: roughly, a sentence of the form Necessarily, S (where S stands for a sentence) is true just in case it is analytic that S, and a sentence of the form There is x such that, necessarily ( x ) (where ( x ) is a formula with only x free for example, x is a person) is true just in case ther e is a singular term a such that it is analytic that ( a). The account is in part entitled d eflationary because we try to deflate the sentence operator necessarily of its metaphysical stuffing. We shall endeavor to make no use of an ontology of concrete or abstract possi ble worlds or properties qua abstracta Rather, we will endeavor to keep our ontology as spare as we can. We may sp eak of possible worlds or properties as heuristics the cash value of which will be carefully explained, and any talk of which can be 4 For example (Sidelle, 2007).

PAGE 19

19 cashed out as soon as one would like after thes e two terms and their accompanying senses, as heuristics, play th eir functional role. Clearing a Path We shall not argue explicitly for an analytic -deflationary account of m odal semantics over other (realist) approaches, but e ndeavor only to show that the an alytic-deflationary approach can meet some of the challenges that face it. It may be that in trying to show that such an account can meet those challenges we expose problems for competing accounts of modal semantics, but we shall not explicitly argue for or against either a realist or conve ntionalist story. We shall simply try to prepare the way so the sort of generic conventionalist approach we sketch might more easily compete with realist approaches that sugges t that any attempt at understanding necessity in terms of analyticity cannot succee d. There are three main parts of the project of clearing a path. First, we must motivate the project by arguing fo r the initial plausibil ity of understanding the notion of analyticity without appealing to a modal notion of necessity or a closely related (family of) modal notion(s). To use the very notion (or notions closely related to the one) we set out ultimately to analyze in our work on analyticity would be to produce an uninformative, circular account. This is the work of Chapter Two through Chapter Eight. Second, we must show how the analytic-deflationary approach is able to endorse so-called de re modal claims. We may have the intuition that some singular terms are directly referring, ye t there are sentences in which those names appear that are true of necessity. If the senses as sociated with directly referring terms (if any there be) are insufficient to determin e their referents, then how could a sentence in which those terms occur be simply a matter of me aning? Would not the (n ecessary) truth of such sentences have to lie in the some feature or othe r of the actual individual picked out, not simply how we talk about it? Showing how the analy tic-deflationary account of modal semantics can endorse these claims is the project of Chapte r Ten and Chapter Eleven. Finally, in Chapter

PAGE 20

20 Twelve, we take on the closely related work of how to understand so-called quantified de re modal claims such as T here is an individual x such that, necessarily, ( x ) where there is quantification into the scope of a modal operator. In Chapter Twelve, we will have the opportunity to see just how the account of modal semantics we have developed fits in with a certain type of general semantic theory (interpretive truth theories as compositional meaning theories). Hopefully, we will see that there is space for model theoretic approaches, like the one we undertake, within the larger context of general semanti cal theories of the Davidsonian sort. We shall have succeeded if we have developed a generic analytic-deflationary account for which arguments can be made without the immediate blockages of circularity, problems over de re modality or issues over how to understand quantification. Of course, there may be other issues, lurking beneath the surface that are not re solved, and that is acceptable, given our goals for this project. If the initial hindrances are removed for our ac count, then it will only be a benefit to be in a position to assess these less ob vious difficulties for it. After all, we are in the business of assessing philosophical positions by a ssessing arguments for and against them: the more depth we can achieve in our assessment, th e better. Such depth is best had by bringing as many issues to light as possible, in as clear language as is possible. Thorny Issues for such a Project A wise m an5 once said that the vast majority of mi stakes in a philosophy paper are made at the outset, usually on the first page. Someone mi ght see the word conventionalist immediately preceding the phrase modal semantics and strai ght away think that something has gone wrong. More seriously, two major, contro versial assumptions have already been made in the page and a half since Chapter One began: th e separability of syntax and se mantics and compositionality in 5 Perhaps it was J.L. Austin originally, but I heard it firs t in the fall of 2 in Professor Ludwigs Proseminar.

PAGE 21

21 semantics. I believe that syntax and semantics s hould and can be separated and that doing so is essential for a fruitful investigation into modal semantics, and I hold the compositionality thesis I sketched earlier. If the reader is adverse to these theses, then the bumpy ride has already begun; progress of any sort is impossibl e if one waits to resolve all fundamental disagreements before one begins. To engage in a philoso phical investigation is to cri tically examine everything even the foundations upon which everything else rests a nd this sort of critical examination causes disagreements. The philosophical living room is an uncomfortable abode; a portrait of certainty has no place among the pictures on the walls, the furniture is constantly in danger of being rearranged (or removed altogether in preemptory fashion), and we are constantly trying to increase the size of the windows to make greater our ability to see by letting more light in. Of course, letting in more light means that folly within can be all the more easily observed. It is my wish for this document to be such that it lays its own weaknesses bare. I believe much more philosophical progress is made if one can clearly lay out an ac count with all of its possible benefits while at the same time making no e ffort to disguise its li abilities. Indeed, much more progress is made (and more easily made) when the proponent of a view points to its weak parts and to the controversial assu mptions that must be made in order for the view to get off the ground. Thorny Issue One: No Completeness Theorems Will Be Proved W e wil not propose a derivation system for the language which we develop. From the technical viewpoint taken by those who study philos ophical logic (an area wh ich this dissertation brushes up against), work in semantics may seem to lack credibility unless a completeness theorem is available to relate the formal sema ntics and formal derivation method for drawing inferences from a given set of sentences of the language/formal syst em under consideration. There are systems of modal logic for which pr oofs of completeness theorems exist, and the

PAGE 22

22 availability of these proofs will, to some exte nt, guide our investigation, but our efforts will not be to establish any original technical results (of the sort that Fitting & Mendelsohn6 or Hanson & Hawthorne7 do) along these lines or to develop any explicit method for drawing inferences in the language whose formal semantics we develop.8 Thorny Issue Two: How Can a Mode l Theoretic Trea tment of Carnap9 Be Consistent with a Conventionalist Approach to Modal Semantics? We develop a model-theoretic treatment of some aspects of modal semantics and the intensions of predicate terms. By intension of a predicate term, I wish to signal roughly that notion of the meaning of the term which is not entirely captured by, and outstrips, any understanding of the term which woul d be such that all and only the actual objects that fall under that term are described in a particular aspect by it. Placing the term intension in opposition with the term extension is helpful to the see what is to be signaled by the former. The extension of the predicate term blue is just the collection of all and only those things that are blue. But we should not claim that one understands the predicate term blue just if one is proficient at determining exactly those things th at are in the extension of blue. To say that one understands the term blue or knows what blue m eans is to say that one knows what the intension of the term blue is. To do that, one must understand, fo r instance, that the term is such that it might have applied to certain individuals which are not blue but which were such that if they had been 6 For all references to Fitting & Mendelsohn see (Fitting, M. & Mendelsohn, R.L., 1998). 7 For all references to Hanson & Hawthorn see (Hanson, W.H. & Hawthorne, J., 1985). 8 This is not quite accurate because we will try to show the semantic equiva lence (in a strictly, technical and nonphilosophical sense) of our modal language and a traditional system of QML developed by Fitting and Mendehlson (1998). From this semantic equivalence, we can see that there is a Henkin-style completeness proof of QML which we could use, given this semantic equivalence to show that a system of derivation based on their system of QML put to use for the language whose semantics we develop in this di ssertation is such that for an arbitrary set of sentences a conclusion is derivable from that set just in case that sentence follows as a logical consequence from that set of sentences. 9 For all references to Carnap see (Carnap, R., 1947).

PAGE 23

23 different in relevant ways (ways to do with how their surfaces reflected light in what we might call normal conditions) then they would be such that the term blue w ould correctly apply to them. To know the intension of a predicate term is to know how the term would be used appropriately in descriptions of novel circum stances. By definition, such a model-theoretic account is referential and extensional That is, the account we try he re to develop here is such that intensions of predicate terms will be defined in terms of various domains of discourse. Roughly, we try, first, to follow through on Carnaps characterization of in tension as a map from terms and state-descriptions to individuals in the domains of those state-descriptions. And so intension (or meaning) is exp licated in terms of individuals in the various domains of interpretations. Yet, as the reader recalls from just a few pages ago, we shall try to give an account of modal semantics that is ontologically spare in that it admits no possible worlds or properties qua abstracta How are both goals simultaneously ach ievable? I am uncertain whether both are simultaneously achievable, but I shall outline in the following, very briefly, what the strategy is. In Chapters Three, Four and Five, we generalize Carnaps treatment in Meaning and Necessity explicitly in model-theoretic terms while we try to get out on the table all the concerns over Carnaps original work that might plausibly be addressed in this idiom. In Chapters Six and Seven we try to show that with the generalization of Carnap into a model-theoretic idiom, we can change our understanding of this idiom in a way suggested to us by some fairly uncontroversial views on concepts and concept possession. Instead of relying on an ontological commitment to the individuals in the respective ranges of the maps that go proxy for Carnaps state-descriptions ( SD s), we shall come to understand these proxy maps (interpretations) in terms of the dispositional abilities of concep t possessors (or those who have conceptual mastery with regard

PAGE 24

24 to what is expressed by a certa in predicate). And so, if we can understand dispositions or dispositional abilities with recourse to only th e spare ontology required for conventionalism, then we shall have used the robustly model-theoretic re interpretation of Carnaps work merely as an intermediate step on the wa y to understanding modal semantics with a minimal ontology. Thorny Issue Three: Abduction versus Apodicticity I believe that m uch of the progr ess that was made in Kripkes10 Naming and Necessity was the result of a sort of inference to the best explanati on about essences and metaphysical necessity. I maintain that to hold the proposit ion expressed by the sentence water is H2O is metaphysically necessary but that it is epistemica lly possible that the sentence is untrue, one must hold that it is the deep stru cture of what we call water (in this world) that necessitates its superficial watery stuff characteristics OR th at it is the deep structure of something of a particular natural kind (whatever the superficial characteristics are had by a sample of it) that serves as that which determines whether a pa rticular sample of something falls under the predicate that expresses th at particular natural kind (water in this case). In either case, inference to the best explanation, or abductive reasoning, either about the relationship of deep to superficial characteristics or about correct use in fantastical counterfact ual scenarios (such as Twin Earth) is the driving fo rce for Kripkes conclusion. By way of full disclosure and at the risk of sidetracking us fo r just a few lines, I need to add that in this dissertation, I do not address expl icitly the issue over whether the account I try to clear a path for can endo rse the truth of (1) 1. Necessarily, water is H2O. 10 For all references to Kripke see (Kripke, S. 1972/1980).

PAGE 25

25 I think this account could plausi bly endorse such a sentence if one granted its logical form could be given by adverting to the following paraphrase (2). 2. Necessarily, for any amount of stuff wh ich is the individual referred to by if the referent of is water then the referent of is H2O. Such is roughly the strategy of Koslicki11. Of course, a philosopher taking the Kripkean line might deny that such a paraphrase was legitimate in holding that because that predicate terms like water and H2O are (directly) referri ng terms. This is the approach of Putnams (1975)12 as well as Nathan Salmon13 who undertakes to show how holdi ng this view that natural kind predicates are directly referri ng terms leads one inexorably to a thesis of metaphysical essentialism. (Much more on this later.) Suffice it to say that I do not find it at all consistent with the spirit of the conventionalist account to hold that natural kind predicates (or predicates of any sort for that matter) are referring terms. If one were to insist upon this sort of semantic treatment of natural kind predicates, then I fear anything I say in the following document will be in vain. I might only add, by way of enticement to a philosophe r of Kripkean bent, that from the truth of (1) follows the truth of (2), so to refuse the seman tic treatment of predicates I offer here is to be indisposed to the analytic-deflationary conventio nalist strategy at the outset as a matter of philosophical principle; nothing I can say or demonstrate will close this sort of gulf, save perhaps by showing that the way we clear a path for here has more pleasant consequences regarding other of our philosophical desiderata. A certain sort of inference to the best explanation, or abductive reasoning, is also at the root of the claim that a properly semantical assertion, such as that proper names are rigid 11 For all references to Koslicki see (Koslicki, K. 1999). 12 In addition to other philosophers of language of that particular era. 13 For all references to Salmon see (Salmon, N. 1981).

PAGE 26

26 designators, can lead us to a metaphysical conclusion such as the claim that Aristotle is essentially human. From the semantical claim, we must infer, given how rigid designation is spelled out14, that since the same individual is picked out in each possible world by the proper name Aristotle and that we have the (modal) intuition that anything which is not, or was not, human cannot be Aristotle, then we must conclude that Aristotle is human in each possible world (if we affirm our intuition). We must conclude therefor e that Aristotle is essentially human. We infer a metaphysical conclusion on the basis of a semantic fact because the metaphysical conclusion seems to be that which best explains the semantic fact; a textbook case of abductive reasoning. (Of course, there is a host of tangles to do with the very notion of rigid designation and whether we have already committed ourselves to too much if we have even taken this notion on board while at the same time trying to enga ge in an analytic-def lationary, conventionalist path-clearing. More on this later as well.) I shall argue that an approach which is at least as productive is one in which we engage in a sort of apodictic reasoning; th is is a sort of reasoning where we reason from star ting points to a conclusion in a deductive manner. (Alonzo Church15 adumbrates the need fo r abstract entities in semantic analysis, the need of which is seen by reasoning abductively, but on pain of philosophical apostasy, I would assert that a certain particular admonition of his16 should not be 14 I try to take the most doctrinaire approach and claim, by way of explication that a term is a rigid designator just in case if has a referent at an arbitrary possible world W1, then if has a referent at a different possible world W2, the referent of at W1 is the same as the referent of in W2. On the received view of rigid designation, proper names, like Aristotle, are rigid designators. 15 For all references to Church, see (Church, A., 1951). 16 In his (1951), Church writes on page 104: To those who object to the introduction of abstract entities at all [in semantic analysis] I would say that I believe that there are more important criteria by which a theory should be judged. The extreme demand for a simple prohibition of abstract entities under all circumstances perhaps arises from a desire to maintain the connection between theory and observation. But the preference of (say) seeing over unders tanding as a method of observation seems to me capricious. For just as an opaque body may be seen, so a concept ma y be understood or grasped. And the parallel between the two

PAGE 27

27 followed blindly.) Our starting points are wh at I understand to be certain uncontroversial features of meaning as use. Our conclusion will be the (form of) a theory which gives an account of semantical notions such as intension so as to provide an explicati on of the truth of modal claims (sentences prefixed with necessarily or possibly). Of course, we must engage in some sort of abductive reason ing ourselves, as I believe that ev ery philosophical theory that poses something by way of ontology must. So it seem s that the real difference between the metaphysical/more heavily abductive theories of modal semantics and th e less heavily abductive theory we try to clear path for is what we take to be the more ba sic methodological starting points. Do we, for example, take intuitions about utterances of particular sentences as more basic starting points or do we take a systematic approach that emphasizes compositional semantics and an intelligible epistemology? The question is, of course, rhetorical We purse the latter. My hope is that this approach can do without the ontology and handle most of the intuitions or explain them away. Thorny Issue Four: the Relationship of Language Possession to Concept Possession. The account of m odal semantics we try to cl ear a path for is one which is properly linguistic (hence conventionalist in the sense of linguistic conventions ), yet one for which we use concepts or conceptual mast ery in explaining linguistic co mpetence. Conventionalism about modal semantics is a view according to which all necessity is linguist ic necessity, and so according to this view epistemic access to modal tr uths is guaranteed only for those beings who cases is indeed rather cl ose. In both cases the observation is not direct but through intermediaries light, lens of eye or optical instrument, and retina in the case of the visible body, linguistic expressions in the case of the concept. Rather than be concerned strictly with the desire to maintain the connection between theory and observation, we might wish to bar from our ontology concepts by claiming, for example, that to say that a conceiver grasps or possesses a concept is simply faon de parler for our claim that a conceiver has conceptual mastery (a complex dispositional ability) with a certain predicate. I tentatively asse rt that the burden is on Church to show that we need to admit into our ontology something (and if so, what exactly) to account for this dispositional ability.

PAGE 28

28 speak a language. However, one might hold that non-linguistic beings, such as higher animals, do have concepts and so are therefore capable of belief. One might further hold that animals are capable of having epistemic access to necessary truths if one were to hold th at the relationship of concepts (perhaps in the case of animals concepts that are not e xpressed by a language terms) to one another was the seat of necessity. The acc ount we clear a path for must deny that nonlinguistic beings can have access to the truth or untruth of modal claims. This may be a thorny issue; discussion of concepts and their relation to linguistic entities is the subject of Chapter Seven. Thorny Issue Five: Our Analysis May Not Be Meaning Giving, but Rather Only Truth Functional Toward the very end of our investigation, we sh all try to fit our progres s in together with a larger, m ore general theory of meaning. Specifica lly, we shall try to situate what we have done into the context of a Davidsonian interpretive trut h theory used in the co ntext of a compositional meaning theory. Such a theory will have meaning theorems or M -sentences of the following form, S in L means that p where for S we substitute the structural description of a sentence (i.e. we mention a sentence by way of a description of it) of the object lan guage L, and for p we substitute a metalanguage sentence whose meaning is the same as that denoted by the description that replaces S. Since we shall focus extensiv ely on the sentence operator necessarily and try to show how it can be understood in terms of anal yticity, we shall try to show that sentences of the following form are indeed M-sentences of a Davidsonian inte rpretive truth theory, Necessarily, S in L means that it is analytic that S. While we might be able to argue (of course, if the reasoning preceding Chapter Twelve goes through) that Necessarily, S is true just in case it is analytic that S, it seems flatly false to claim that Necessarily, S means the same as It is analytic that S given that the phrases necessa rily and it is analytic that cannot, at least at

PAGE 29

29 first glance, be substituted one for another in ar bitrary sentences in whic h they occur. An analogy may be helpful here to see why I claim that these two terms cannot be the same in meaning. Consider the predicates trilateral and tria ngle. The two do not mean the same, as each term has to be with a different feature of straight-sided plane figures, be anything which is a trilateral is a triangle of necessity and a nything which is a triangle is a tr ilateral also of necessity. The analogy with necessarily and is analytic that is not a perfect one: to be so necessarily would have to do with a different feature of that to which it might apply (sentences or propositions) that does the phrase is analytic that. We will build th e case in this dissertation that necessarily will be a generalized property of sentence as is is analytic that, that they are necessarily coextensive, and that we can analyze the concept of necessity in term of (something like) the concept of analyticity, but there are still differe nces in connotation (and differences in what the folk meaning of is analytic th at and the account of analyticity that we provide hereafter) that prohibit us from claiming that necessarily means the same as is analytic that. Given this difference in meaning, our analysis cannot be meaning-giving, but can serve to explicate the concept of necessity making use, inter alia of the concept of analyticity. In particular, we want to show that there is an account of modal seman tics on which there is a necessary equivalence between th e truth of the senten ce necessarily, S a nd the truth of the sentence it is analytic that S (modulo some eme ndations we offer for the notion of analyticity in this context). This may be a thorny issue for some who want more out of the sort of investigation into modal semantics than we get from that in which we are engaging. I submit that given our goal of trying to understand necessity in terms of analyticity, and our desire for providing a truth conditional treatment of meaning, this sort of ex plicating, yet non-meaninggiving analysis is the

PAGE 30

30 best we can hope for. We discu ss this issue at greater length following the work we undertake in Chapter Twelve on trying to situate things into the interpretive truth theory.

PAGE 31

31 CHAPTER 2 SELECTIVE REVIEW OF THE SEMANTICAL SYSTEMS OF MEANING AND NECESSITY Introduction In Chapter One, we gave a rough, infor mal ch aracterization of an analytic-deflationary strategy for an account of modal semantics for ce rtain sentences and termed the category of approaches to modal semantics to which it bel ongs conventionalist. I promised to spell out more thoroughly a specific anal ytic-deflationary stra tegy soon and, in the process of providing this spelling-out, to set the stage for pointing out an immediate problem this account of modality faces if the account is to avoid vicious circularity. (We will explicitly present and address this problem in Chapter Five and Chapter Eight.) I believe we can look to Carnaps work on semantics and modality in his Meaning and Necessity to provide a firm base for the development of a conventionalist approach. A selective review of so me of Carnaps more salient themes will be our present work. We shall present the basics of Carnaps sema ntical systems in order to build up to his proposed account of a modal sentential operator N. I aim to provide a faithful characterization of his semantical systems, but I do not wish to undertake a scholarly stu dy of Carnaps work. Instead, I hope that if we get the fundamentals right, we can do Carnap justice while using his system as the basis for a model-theoretic rework ing and generalization of Chapter Three. With this model-theoretic reworking, we will be in a position in Chapter Four to have an understanding of analyticity at least for a formal system that partially models our intuitive notion of meaning (intension). With this development of this formal notion of analyticity, we can see more clearly how the conventionalist position could be an attractiv e one. Carnap has gotten us most of the way there; the reworking of his funda mentals should make the urge to understand necessity in terms

PAGE 32

32 of analyticity even more compelling. Of c ourse, once the machinery that allows for interpretations of different sets of atomic sent ences and negations of atomic sentences of the language to provide for intensi on is laid bare, it is obvious th at we must be careful to acknowledge how exactly we choose to accept or re ject such interpretations according to the purpose we have for them. As a look ahead to a bit of technical terminology, we say that an interpretation (in the model-theoretic sense) of the sentences of a Carn apian state-description (essentially a description of the state of the universe by way of a set of atomic sentences or negation of atomic sentences) is admissible if the interpretation is such that predicate terms are evaluated so as to be in line with what a cognizer who has th e concept expressed by the natural language analogs of those terms has in mind for th e meaning of those terms. (I ask the reader not to be alarmed. This is only a warm-up. We have much more explanati on to get through. This introduction is only meant to set down some broa d outlines.) The admissibility requirement is important for the reasons we have just hinted at: an account of semantics for modal claims is not acceptable if it is viciously circular that is, if the analysis of modal notions (such as that expressed by the sentence operator necessarily) is such that the analysans make use (perhaps implicitly) of the very same notion (or a closely related notion) that occurs in the analysandum If, in analyzing necessity in terms of analyticity, we must make use of the notion of necessity (or closely related notions) to give a reasonable ch aracterization of analyticity itself, then our analysis is unsatisfyingly circular. Of course, there are already idealizations of language which incorporate modal operators and which are not subject to objections about circul arity. In particular, I have in mind systems of quantified modal logic (hereafter abbreviated QML). The semantics for these systems are given traditionally in terms of possible worlds. In part because they are idealizations, these

PAGE 33

33 formal systems are well behaved in that ther e is no concern over semantically defective predicates or other natural language difficulties. In addition, it is usually the case that formal languages themselves along with their semantics are taken to be models for how we might understand the symbolic modal operators or in terms of a ( given ) class of possible worlds the domains of which are provided explic itly along with an accessib ility relation borne by pairs of those worlds to each other1. So these formal language idealizations do not provide exactly what we desire from a conventionalist account. But, I believe our enterprise is strengthened if we can show th at the model-theoretic reworking we provide here is capable of supporting the formal language idealizations that are thought to approximate the modal operators. If we can show that our reworking of Carnaps system supports a system of QML, then I think we will have demonstrated that this sort of approach to modal semantics is in no worse shape than any account based upon the idealizatio ns of these formal languages and their traditional possible world semantics. In Appendix A, we try to show that we can give the semantics for the language of QML with the modeltheoretic reworking of Carnap we provide in the second main section of this chapter. There are technical differences, but from the work of Hanson and Hawthorne2 we see that systems with semantics suggested in this chapter are well behaved and have the same technical utility as the traditional approach to semantics for QML. Carnaps Semantical Systems and Modality In Meaning and Necessity Carnap is concerned w ith deve loping what he calls semantical systems essentially artificial languages (of first and higher order) with formal syntax whose 1 Or, conversely, what the ordered pair consisting of (1) a class of possible worlds and (2) an accessibility relation would consist in given prior knowledge of truth-values of sentences in which or occurred. 2 For all reference to Hanson and Hawthorne see (Hanson, W. H. & Hawthorne, J., 1985)

PAGE 34

34 semantics are given intuitively without strictly fo rmal characterization. In this section, I present the generic fundamentals for each of the semantical systems S1, S2 and S3 together with some features specific to S2 (whose language includes the modal sentential operator N): their languages, (very briefly) their rules of inference, the interpretation of the languages of these systems in terms of extension (for both singular and predicate terms), and the interpretation of the languages in terms of intension (for which we must review state-descriptions and the L notions). Semantical Systems S1, S2 and S3 3 The semantical systems each have an arti ficial language with a common subset of vocabulary: variables, singular te rms, predicate terms of first order, logical terms such as connectives and quantifiers, and the definite de scription and the predicate abstraction formula operators ( and respectively). And, for S2, the artificial language has a sentence operator N (we will define it sh ortly for the present we can think of N for N ecessarily ). The syntax and semantics of these languages is similar to that presented in a textbook on first-order predicate logic. There are also variable s, singular terms and predicate terms of higher-order in these languages, but we wont do an y exposition of how the semantics or rules of inference work for formulas containing these higher-order terms. (These semantics and rules of inference for these terms are analogous to the first-order te rms, but there are complications to do with consistency of the systems with higher order terms and variables even before one notices that any system with a usual sort of interpretation in which quantificati on over functions and predicates is possible cannot be complete because of Gdels first incompleteness theorem. John 3 Actually, these are not quite Carnaps systems. For exampl e, I do not have the same lin e up of logical connectives that Carnap does. I would like to indicate here that I de part in some respects from Carnap, but not in respects essential for understanding his proposal.

PAGE 35

35 Myhill4 has written a paper that is an excellent en tre into further discussion of the difficulties Carnaps systems face if they are to include higher order terms and variables. Early work by Donald Davidson5 on Carnaps method of extension and intension is also helpful in regard to related issues.) Language of the Systems S1, S2 and S3 We give the vocabulary of the language of these semantical systems. There is a denumerable infinity of variables: x0, x1, x2, . There is a denumerable infinity of singular constant terms (i ndividual constants): a0, a1, a2, There is a denumerable infinity of one and more place (first-order) predicate terms: P1 0, P1 1, P1 2, (one-place predicate terms indicated by the superscript) and P2 0, P2 1, P2 2 (two-place predicate terms), and so on. There are the usual first-order lo gic connectives and quantifier: ~ and the definite description iota operator the predicate abstraction lambda operator and the grouping and formation symbols (, ), and ,. The formation ru les for formulas follow directly and we provide the (informal) se mantics for the well-formed form ulas (termed WFFs) in this section. A completely formal treatment follows in the second section in we which we provide our modeltheoretic reworking of Carnaps systems. WFFs are defined recursively as follows. The base case is an atomic formula: 1( ) 6 is an atomic formula (recall that 1 is a metalinguistic variable ranging over one-place predicate terms P1 0, P1 1, P1 2, etc. and is a metalinguistic variable ranging over the union of 4 For all references to John Myhill see (Myhill, J., 1963). 5 For all references to Donald Davidson see (Davidson, D., 1963). 6 Recall that we use the characters and to represent respectively opening an d closing quasi-quotes see the list of abbreviations on page 4.

PAGE 36

36 variables and constant terms), similarly 2( 0, 1) is an atomic formula and, in general, the base case is given in sentences (1) and (2). 1. n( 0, n) is an atomic formula 2. Any atomic formula is a WFF. The recursive clause is complicated, but starts in sentences (3)-(5). For any WFFs and variable x and metalinguistic variable ranging over strings comprising concatenations of ntuples of variables7, 3. ( ) is a WFF 4. ~( ) is a WFF The following further recursive rules (6)-(8) require some work-up. WFF contains n variables just in case there is an n-tuple of variable terms such that each of the elements of the ntuple is a substring of If contains variable x then x is free in if there is a WFF that is a substring of and contains x and there is no WFF which has ( x )8 as a prefix of which is a substring. 5. If each x that is a member of the n-tuple the c oncatenation of each member of which is is free in WFF then is a WFF (which has the same free variables as as is 0 m-1 for m n. If m < n, then, 0 m-1 has each of { xm, xm+1, xn-2, xn-1} free. 6. If WFF has single free variable x then ( x )( ) is a WFF. The set of all WFFs with this form make that which is referred to by D. (Think the set of all D efinite D escriptions.) 7. If WFF has a free variable x and ( x )( ) is a WFF then the string which results from substituting ( x )( ) for every occurrence of x in is a WFF. The free variables of are those of except for x (it does not occur in as all instances we re replaced). 7 For example, a specific n-tuple of variables is { x0, x1, xn-1}; in this case a specific value for is x0x1xn-1. 8 One might think that we should include x and ( x ) in the list of variable binding prefixes, we do not do so at this particular juncture as we are defining recursively WFFs in clauses and the clauses which explain the behavior of the predicate abstract operator and the definite description operator are yet to come.

PAGE 37

37 8. Finally, if the language of the semantical system contains the symbol N, and is a WFF that is not a member of D, then N is a WFF. We can define sentences (members of ) in the following way: if is a WFF and is not a member of D9 and has no free variables, then is a sentence. One point of interest is that sentences which in clude the modal operator N can be either of a de re or de dicto variety as for a sentence and formula with only x free, both N (de dicto ) and ( x )N ( de re ) are sentences. Rules of Inference The only locus of substantial talk of rules of inference for th e semantical systems of Meaning and Necessity comes in Carnap has in mind the usual axiomatic development for these systems. For such a development, we might have either a finite set of axiom schemas (for which there will of course be avai lable an infinity of actual axio ms) along with rules of inference like modus ponens and perhaps universal generalization or a sort of natural deduction system in which there are several (intuitively validity pr eserving) rules of in ference (and perhaps no axioms at all). It is interes ting that not much emphasis is placed on the actual method of deduction for the formal systems. Instead th e actual method of deduction is assumed as unproblematic and much more emphasis is placed on the actual semantical interpretation of the languages of the formal systems. This cavalier approach may seem less than cautious at first, but I think the emphasis on semantical interpretations of the languages of the formal systems S1, S2 and S3 may be eventually vindicated (to a lesser extent) by the modeltheoretic reworking we provide of Carnaps notions in this chapter along with and (to an even greater extent) by some work of Hanson and Hawthorne to do with th e a new approach to intensional languages. 9 We must make this restriction because a defi nite description, that is, a WFF of the form ( x )( ) (where has only x free) has no free variables, but is not a sentence, as we can see by noting that the English language definite description The tallest mountain is not a sentence.

PAGE 38

38 Designators and Extension Obviously, Carnap is developing a semantical r ather than merely syntactic system the languages of the semantical systems are supposed to be about something. To develop the semantics for the languages in question, we can begin with the notion of a designator of which there are two fundamental kinds: si ngular (referring) terms and predicate terms. Informally, the terms Sir Walter Scott and The author of Waverly both designate individuals and so are singular referring term designators.10 Formal analogs of such terms, an individual constant for the former and a definite de scription formed from the operator, are each used to pick out unique individuals (though either may fail to do so). Predicate terms are designators which serve to pick out sets of i ndividuals (extensions). We provide only an informal treatment of Carn aps original semantics, and then sketch how the formal semantics might go based on informal treatment. Hopefully, this will be enough to set us on the right track and to motivate our wo rk in Chapter Three. We will provide a formal treatment of the semantics in Meaning and Necessity with the use of explicitly model-theoretic techniques. We can say that a name like Sir Walter Scot t might have as its formal analogue an individual constant such as a2 and a definite description like The author of Waverly has as its formal analogue something like ( x0)( P2 99( a12, x0)) if we pretend that P2 99( x1, x0) is the formal analogue of the relation e xpressed in English by x0 is an author of x1, and a12 is the formal language analog of Waverly The expression ( x0)(P2 99( a12, x0)) is read the unique individual such that that indivi dual is an author of Waverly 10 Of course, on the assumptions that there is an individual corresponding to the first name and that Waverly has a unique author.

PAGE 39

39 Analogously, but perhaps artificially, pr edicate terms are sa id to designate11 sets of such individuals in the domain the la nguage is supposed to speak about. To give a flavor for the semantics of predicate and predicate abstract terms as we did for singular terms, we might represent is blue formally as P1 0, is green as P1 1 and is cold as P1 2 and so with predicate abstracts we can formally represent is blue or green as x0.( P1 0( x0) P1 1( x0)) 12 and is blue and is cold as x0.( P1 0( x0) P1 2( x0)) .) With these basic notions, we can define extension implicitly. If two singular terms designate the same individual, then those two terms have the same extension. If two predicate terms designate the same set of individuals, then those two terms have the same extension. The extension of a sentence is its truth-va lue. There is room for disagreement13 about what exactly the extension of a designator is (e specially for singular terms), but since our interest here is not scholarly study of Carnap but rath er to use the basic notions of hi s work to serve as the basis for our investigation, I will pass over these worries a nd take the intuitive notion of extension as acceptable. In our modeltheoretic reworking, we w ill give a formal characterization that can be the subject of (perhaps more exacting) scrutiny. State-Descriptions Even though the question over what is to be, exactly, the domain of interpretation for the languages of his semantic systems is not given a definitive answer in Meaning and Necessity it is clear that the atomic sentences of these languages are such that they can be used to provide the 11 To say that predicates designate may seem an odd choice of word, but I am trying to follow Carnap in his assertion that predicators (a general term meant to including predicates) are designators (1.9) 12 Where (P1 0( x0) P1 1( x0)) is an abbreviation for ~(~ P1 0( x0) ~ P1 1( x0)). 13 For example, see (Davidson, 1963)

PAGE 40

40 state of the universe of individuals about which they speak. Carnap refers to a specific class of atomic sentences which describe the state of the universe as a state -description in A class of sentences in S1 which contain for every atomic sentence either this sentence or its negation, but not both, and no other sentences is called a state-description in S1, because it obviously gives a complete descript ion of a possible state of the universe of individuals with respect to all properties and relations e xpressed by predicates of the system. Thus state-descriptions represent Leibnizs possible worlds or Wittgensteins possible states of affairs. (9) Whatever the languages of semantical systems like S1 are supposed to be about, the various statedescriptions (hereafter on occasion abbreviated SD) in those semantical systems indicate the predicates that hold of the individuals designated by individual constants and the relations that hold among individuals so designated, and do so as exhaustively as is possible given the predicate, relation and singular term s for the language in question. Something else thats interesting to notice from Carnaps initial presentation of statedescriptions is the assumption that the atomic sentences are pairwise independent. From the presentation were given of statedescriptions in there seems to be no formal restriction about which atomic formulas are allowed given the incl usion of any other. For example, for predicate terms P1 3, P1 5 and two-place relation term P2 4 and singular terms a0 and a1, a statedescription that includes the sentences P1 3( a0) and P1 5( a1) might include either P2 4( a0, a1) or ~ P2 4( a0, a1). This situation seem s unexceptionable unless P1 3 and P1 5 were interpreted such that two sentences P1 3( a0) and P1 5( a1) together entailed ~ P2 4(a0, a1). (We have a clear example of this if P1 3 is to be interpreted as is exactly three meters long and P1 5 is to be interpreted as is exactly five meters long and P2 4( x0, x1) is to be interpre ted as the length of x0 is greater than x1.) In this situation, any state-desc ription with both of the former atomic sentences could not include P2 4( a0, a1) on pain of contradiction. Since Carnap means to be providing semantical systems, it seems that he must at least implicitly require that the set of

PAGE 41

41 sentences that is a state-descri ption is consistent. What is ha ppening here? Why were explicit restrictions not placed on the co llections of atomic sentences (and negations of atomic sentences) to disallow such contradictions? It may be th at the atomic sentences were only supposed to include basic properties, such as the exact length of individuals, from which parasitic, relational properties and re lations, such as is longer than co uld emerge, but not themselves be included in the state-description. This speculation seems misguided because it seems that unless a formal analogue of a0 is taller than a1 is among the atomic sentences of a part icular language, it is difficult to see how any sentence which expresses this situation could be included in th e language at all. More likely, it seems that Carnap assumes that there would be an implicit interpretation for the predicate and singular terms of the language for his semantic al system. Since the sentences of the statedescription are to describe th e properties and relations which hold of and among particular individuals in a certain state of the universe and on any reasonable assumption about any particular state of the univer se it cannot be the case that a0s length is 3m and a1s length is 5m but a0 is longer than a1 on the usual meaning of the numeral s, length and longer than, given the implicit interpretation we have for the terms of the language, a state-description wouldnt include any pair of sentences which are inconsistent We will argue later that it is helpful to make these assumptions explicit. With our modeltheoretic update, we will be able to do this and explicitly disallow the situation in which a stat edescription (or our in terpretation proxies for them) is inconsistent. L-Truth, Intensions and N Since a state-description is supposed to provide the state of the univers e of individuals that are nam ed by the individual constants of the language (to the extent that th e state of this universe can be described with the vocabular y of the language), the collecti on of all state-descriptions is

PAGE 42

42 supposed to delimit the way that the universe might have been. With the notion of the collection of state-descriptions and ranges, we can in troduce the notions termed Ltruth and L equivalence and use them to define intension implicitly. Briefly, if a sentence is included in each state-description (in case is an atomic sentences or is ~ where is an atomic sentence) or is tr ue according to each state-description (on the usual recursive rules for truth for predicate logic), then is Ltrue For predicate terms (or predicate abstract terms) and if (and only if) the sentence ( x0)( ( x0) ( x0)) 14 is true according to each state-description (4), then ( x0)( ( x0) ( x0)) is Ltrue and and are Lequivalent For singular terms and if (and only if) in each st ate-description, the identity relation holds between and or both have no denotation, then and are Lequivalent. For any two (predicate or singular) te rms, if these terms are Lequivalent then they have the same intension .15 In general, intensions might be thought of as functions either fro m state-descriptions to individuals (in the case of singular terms including those formed with the -operator) or from state-descriptions to sets of individuals (in the ca se of predicate and predicate abstract terms). So intuitively, two terms have the same intension i ff they pick out the same individual (singular terms) or set of individuals (predicate terms) in each state-description. Finally, we can define the semantics for th e modal operator. For Carnap, N creates intensional contexts contexts in which co-denoting terms might not be substitutable salva 14 This is, of course, an abbreviation for ~( x0)(~(~( ( x0) ~ ( x0))(~ ( x0) ( x0)))). 15 More work is done on an explicit formulation of intension for designators. Ultimately, the intension of a predicate term is claimed to be a property and the intension of an individual expression (individual constants and individual descriptions those formed with the iota operator ( x )(. x .)) an individual concept I will not reiterate here Carnaps explanation of intensions in -5; rather, Ill hold off until we develop our model theoretic reworking of the theory of these sections. After we reformulate Carnaps basic notions, we will be in a position to see that the intensions of predicate terms and indivi dual expressions can be given a purely se t-theoretic (and I hope just as clean and intuitive a) treatment.

PAGE 43

43 veritate For any predicate (or predicate abstract) term and singular term (either constant or definite description) to assess the truth of N( ( )) we must consider the intensions of and Specifically, if ( ) is Ltrue, then N( ( )) is true, false otherwise. If N( ( )) is true, then the truth of ( ) is independent of how the world turned out (assuming that the class of statedescriptions tells us somehow exactly how th e world could have turned out). Similarly, N(( x )( ( x ))) is true iff ( x )( ( x )) is Ltrue. In an intensional context, variables free fo r that context (but pe rhaps bound outside it) range over individual concepts functions from state-descriptions to individuals. In such contexts, we must consider the intensions of th e predicates terms that occur. Keeping this in mind, if we consider the de re sentence ( x )( N ( ( x ))), and take the intuitive semantics for we see that it is true if there in an individual concept which could be substituted into the following formula N ( ( c )) such that the resulting sentence is true. This sentence is true just in case for every SD s the substituend for c evaluated at s is such that it is in the extension of at s But in this case, the sentence N (( x )( ( x ))) is true, as this sentence expresses the Ltruth of the informal something is So on Carnaps view, from the truth of the de re ( x )(N ( ( x ))) follows the de dicto N (( x )( ( x ))).16 Conclusion In this short chapte r, we have tried to ma ke clearer some of the salient notions of Meaning and Necessity Doing this is required for the next step we shall take in Chapter Three: we shall rework and generalize Carnaps basic ideas in a model-theoretic idiom. Doing so will highlight the need for more qualification to be made about Carnaps claim that the sentences of an SD 16 There cannot be something like an iff here because even though if N (( x0)( ( x0))) is true there will be some function (whose name can be substituted in for c ) from state-descriptions to individuals such that in an intensional context c is P is true, were not guaranteed that there is an individual concept that names this function.

PAGE 44

44 must be pairwise independent. It may be that Carnap has in mind languages which are such that it reasonably be assumed that the sentences of an SD are pairwise independent, but for the purpose to which we shall try to adapt Carnaps work we cannot reasonably assume this, and we shall not do so. The model-theoretic machinery will allow us to see some of the assumptions that seem to have gone into Carnaps work and appreciate how these assumptions give rise to a fundamental problem for the approach Carnap take s. Briefly, Carnap take s the collection of all SDs to tell us something about m odal truths (with the N operator) and something about the meaning of predicate terms (after all intension is defined as a map from SDs to extensions). In the model-theoretic update, I hope we shall be able to observe th at such an approach is not workable unless conceptual priority is given to meaning notions of intension and analyticity In other words, we must use the basic framework developed by in Meaning and Necessity to give an account of the intensions of predicate terms, and hence an account of analyticity for de dicto sentences, and then move on to giving an account of the sentence operator necessarily. If we do not proceed in such fashion, I argue that an an alytic-deflationary story about modal semantics will fall victim to a sort of vicious circularity.

PAGE 45

45 CHAPTER 3 REWORKING AND GENERALIZATION OF CAR NAPS SYSTEM WHICH MAKES EXPLICIT USE OF MODELTHEORETIC TECHNIQUES Introduction Carnap has articulated a powerful idea: that a class of linguistic entities can provide a plausible treatm ent of modal semantics. This no tion is at the very core of the conventionalist analytic-deflationary approach to modality, I believe there are so me difficulties with Carnaps development of and arguments for this sort of lin guistic approach to necessity. In this chapter, we will try to expose some of these shortcomings and show what it would take to hold a conventionalist view in the face of them. To do this, I will rework and generalize Carnaps semantical systems with the use of model-theoretic ideas. Once this is done, I hope we shall be in a position to see some of the weak aspects of the presentation of Meaning and Necessity and to see what we might be forced to commit ourselves to if we wish to continue on the conventionalist path. Carnaps Ideas Presented in, and Re vised in, a Model-th eoretic Idiom We have seen that, because state-descriptions (as certain se ts of atomic sentences and negations of atomic sentences) are supposed to desc ribe the state of the universe of individuals which the languages speak about, the language s of the semantical systems are to be interpreted. In this section, we aim to show that the formal semantic notion of an interpretation as a map from certain expressions of a formal language to individuals or sets of individuals in the domain of discourse can provide Carnaps notio n of extension, and that we can approximate Carnaps notion of intension if we consider a cer tain class of interpreta tions for the languages of S1, S2 and S3. In a sense, our use of in terpretation might clear up what may have seemed obscure according to Carnaps presentation of formal semantics. Soon, we will be in position to see how we might understand analyticity at the end of our reworking.

PAGE 46

46 Hopefully in our presentation and reworking of Carnaps id eas with the tools of modeltheoretic formal semantics, we shall be able to detect with more easily places where Carnaps proposal is vague or less than robus t. Specifically, our translation of his ideas into a specifically model-theoretic idiom will allow us to move off the implicit view (of Carnap) that the truth of atomic sentences of the SDs are independent of one another. Once we begin thinking of the interpretation of sentences of an SD rather than simp ly thinking of those sentences as syntactic entities, we will see that an upper bound on the size of the class of SDs can be placed with the use of the notion of consistency, which, because the sentences of an SD are to be interpreted is a properly semantic rather than merely syntactic issue. Of course, by using model-theoretic techniques to explicate and generalize Carnaps work we run the risk of losing a main initial attraction of his approach. Carnap was able to dispense with an ontological commitment to possible worlds as physical or abstract entities because SDs were to represent, in as much detail as they were capable of, what these possible worlds would be like were there to be any Because SDs were merely syntactic no issue of what their sentences were to be interpreted over would ever come up. Once we start using model-theoretic formal semantic techniques, we are requi red to provide a domain that se ntences of an SD are to be interpreted over. In other words, for the model-th eoretic update to work, the sentences of an SD must be about something, and we must know what that something is. We will move away from the term SD in favor of talk of an interpretation (we shall use the symbol \ to indicate an interpretation). For any SD, ther e is to be a corresponding interpre tation; the interpretation is to provide all the information that was provided by the SD. But as th ings stand over the course of the next few chapters, an interpretation will pr ovide much more information than the SD to which it corresponds; and this exces s of information is not a good thing. The excess information

PAGE 47

47 is, of course, that the domain of interpretati on is something we must have an ontological commitment to if were to do a model-theoretic reworking of Carnap and stop there. For a model-theoretic treatment to even get off the ground, we must acknowledge an ontological commitment to the domain over which the sentences of an SD are interpreted. And so, we should give at least a preliminary charact erization of what we are, as a consequence, committed to. Now, if we are to make any pr ogress in understanding analyticity for a formal language which is some simplified approximation of our own natural language, then the most likely candidate for those things which SDs are about are the very possible worlds that SDs were to describe. The SDs were to represent after all possible configurati ons of the universe as described by the atomic sentences of the la nguage of the SD. But in curring an ontological commitment to any sort of mind-independent po ssible worlds as truth makers for the modeltheoretic reworking we provide fo r SDs is really the last thing we want, as the conventionalist modal semantics for which were clearing a path is to be deflationary and so as ontologically as conservative as possible. I argue that we will not have to admit possibilia into a domain with respect to which interpretations are defined, even though it seems as if we will with the modeltheoretic update we are about to engage in. To show why, I shall lay out the strategy we will employ for the remainder of this chapter and the next five. First, in the remainder of th is chapter, we will show that an interpretation, thought of as a map from individua l constant terms, predicate term s and sentences to members of a domains, sets of members of a domain and trut h values, respectively, can provide at least as much information as a corresponding SD does. Wh at are the domains of interpretation that includes those individuals which individual constant terms are interpreted to be? For the sake of this chapter, we can allow that each domain (of interpretation) comprises just the set of

PAGE 48

48 individuals in the possible world described by the SD to which an interpretation is to correspond.1 The members of each domain populate universes that are as richly detailed as an imaginer might imagine given as long as it might take to do so. So far, a rather heavy ontological commitment has indeed been incurred. We shall fi nish this chapter by claiming that there is a class of admissible interpretations which roughly correspond to th e class of SDs of Meaning and Necessity In what follows, we shall demonstrate how from this class of admissible interpretations we can think of these as just functions from individual constant terms and predicate terms to individuals and sets of indivi duals at a possible world (as it is imagined) (one function interpretation per world), we can construct a single function I from indices (each of which is a member of an index set for the set of all admissible interpretations) and singular and predicate terms to individuals in a possible world and sets of individuals in a possible world respectively. Then we can generate a function I which takes as input a singular or predicate term, an index and an individual which is a member of the domai n of the interpretation which has that index and returns 0 or 1: 0 if the indivi dual is not that picked out by th e singular term, or not among those picked out by the predicate term and 1 if the indi vidual is that picked ou t by the singular term or is among those picked out by the predicate term. We shall then argue that this function is exactly analogous to one which characteri zes congnizers abilities to sort given conceptual competence with concepts expressed by the predicate terms that are among the functions arguments. Our only commitment will be to that which we mu st be committed to by a traditional view of concepts (as concept possession). And so what se emed to be our original heavy-duty ontological 1 At this point, Im agnostic on what individuals there are. In particular, I dont mean to take a stand on the question of (modal) actualism: an actualist would say that the only individuals there can be in possible worlds are those individuals that are in the actual world.

PAGE 49

49 commitment to the ranges of our interpretations (the so-called domains of interpretation) was really just an intermediate step in passing from talk of possible worlds to talk of concept possession. The road is a long one, and our route may b ecome obscured along the way. I will offer sign posts to help us understand where we our along our journey. It may seem that we spend too much time meticulously grooming that part of th e path that has been (hopefully) cleared and defining its precise edges over the co urse of the next five chapters, but I think this is not the case. I believe it is important to remember that once we have updated Carnaps system with the aid of model-theoretic ideas and then di spensed with what must underwrite a model-theoretic treatment (a commitment to the domain of interpretation) in favor of talking about the epistemically and ontologically respectable notion of conceptual mast ery, if we have done our job well, we will be in a good position to see worries over what have been seen as insurmountable obstacles for conventionalist approaches such as the problem of de re modality and quantifying into opaque context simply melt away. If we havent been careful with what we have said before we get there, then the melting will seem magical, but I assert, as forcef ully as I might politely do, that the melting away is not magical, and if we have done our job, we will have earned it. Interpretations Can Provide Exten sion We have already given the vocabulary of th e formal language. Let us consider a map, \ from certain expressions of the language to memb ers, sets of members of a domain of discourse or truth values. \ is called an interpretation for our language. If we let denote the set of individual constants D the se t of WFF formed with the operator, 1 denote the set of (oneplace) predicate terms, 2 denote the set of two-place pred icate terms, (and in general let n

PAGE 50

50 denote the set of n-pla ce predicate terms), denote the set of senten ces of the language and denote the set of individuals in th e universe or domain of discourse, then schematically, we have: 1. \ : { } 2. \ : n 2n, (\ maps n-place predicate terms to sets of n-tuples of individuals, in particular, \ : 1 2, that is, one-place predicate terms are mapped to sets of individuals.) 3. \ : n( x0, x1, xn-1) =\ ( n).2 4. \ : { D } such that \ (( x )( )) is the sole member of \ ( ) iff \ ( ) is a singleton and is undefined otherwise. 5. \ :{( xmxm+1. xn-1 .( n( 0 1 m-1 xm, xm+1, xn-1))} 2nm such that \ : ( xmxm+1. .xn-1 .( n( 0 1 m-1 xm, xm+1, xn-1)) = { m m+1,. n-1 | (\ ( 0 ), \ ( 1 ), \ ( m-1 ), m, m+1, n-1 \ ( n)}.3 AND \ : {( xmxm+1. .xn-1 .(( x0x1. xm-1)(n( x0, x1, xn-1))} 2nm such that \ : ( xmxm+1. .xn-1 .(( x0x1. .xm-1)(n( x0, x1, xn-1)) = {m m+1, n-1 | there are some 0 1 m-1 and (\ ( 0 ), \ ( 1 ), \ ( m-1 ), m, m+1, n-1 \ ( n)}.4 6. \ : ~( ) = (\ ( ))c (where is a WFF and \ ( ))c denotes the set complement of \ ( )) an individual is in \ ( ))c just in case is it not in \ ( ).) 7. \ : (( ) = (\ ( ) \ ( ))(where and are WFFs) 2 This is a bit of technical detail to make sure we get the right result for predicate abstract terms in (5) and (8)-(10). As an example, for a one place predicate term P1, \ ( P1) = \ ( P1( x0)). Which is, informally, the set of all things to which is P1 rightly applies under \ 3 This looks to be a complicated ch aracterization, but a simple example will make things clear. The formula ( xy .( P( x ) & R( x y )) is satisfied by ordered pairs of individuals su ch that the first falls in the extension of is P and such that the first bears relation is R to the second. So in terms of our model-theoretic treatment \ (( xy .( P( x ) & R( x y ))) = the set of ordered pairs of objects such that the first is in \ (P ) and the ordered pair is in \ (R ). 4 Again, this looks overly complicated, bu t an example helps make sense of it all ( x .(( y )(R ( x y ) & Q ( x y )) is satisfied by individuals which are such that there is another individual to which they bear relation R and to which they bear relation Q. In our model theoretic terms, \ (( x .(( y )( R ( x y ) & Q ( x y ))) = the set of individuals such that there is some constant term a such that ordered pairs the first member of which is a member of that set and the second is \ ( a ) such that these ordered pairs are members of both \ (R ) and \ ( Q )

PAGE 51

51 8. \ : ( x0x1. xn-1 .( i+k( xi+0, xi+k) j+h( xj+0, xj+h)) (where 0 i j n-1, and i+k, j+h n-1) = ({ 0 ... n-1 } | i+0 ... i+k \ ( i+k) and j+0 ,..., j+h \ ( j+h)). 9. \ : ( x0x1. xn-1 .(~( n( x0, xn-1)))) = ({ 0 ... n-1 } | 0 ... n-1 (\ ( n))c). 10. \ : ( x0x1. xn-m-1 .(( x0x1. .xm-1)(n) = ({ 0 ... n-m-1 } | there are 0 1 m-1 and (\ ( 0 ), \ ( 1 ), \ ( m-1 ), 0, 1, n-m-1 \ ( n)). 11. \ : N( n) =\ ( n)5 12. \ : {g Y } (\ maps sentences to values of g (true) or Y (false)) The last clause needs explanation and expansion. The rules for truth under an interpretation are given recursively. The base cl ause for atomic sentences is given first. The recursive clauses follow. 13. For any n and 0 1 2 n-1 (recall that { D }), \ (n( 0 1 2 n-1 )) = g iff \ (( 0 1 2 n-1 )) \ ( n).6 14. For 1 if 1 is ~ 2 for some 2 \ ( 1) = g iff \ ( 2) = Y 15. If 1 is 2 3, \ ( 1) = g iff \ ( 2) = \ ( 3) = g 16. If 1 is ( x ) ( x ), \ ( 1) = g iff there is some individual constant such that \ ( 2) = g where 2 = ( ).7 17. If 1 is .( )( 0 1 2 n-1 ), \ ( 1) = g iff there \ (( 0 1 2 n-1 )) \ ( ). We can now claim straightforwardly th at the denotation of a singular term is \ ( ) and that the designation of a predicate term is \ ( ) and so any two designating terms 0 and 1 are 5 This is a stub for the moment. We shall provide the truth conditions for sentences of both de re and a de dicto form which include the N operator, but for the time being we n eed to be able to show that completely general WFFs with free variables can be interpreted over a domain. 6 Rules for the truth of a sentences of the form x 0( x ) (( x )( 1(x ))) where 0 has only x free and 1 has only x free can be given a straightforward recursive treatment also. We shall not do so here. 7 The set of all individual constants ( ) may have to be expanded to include if it does not already. This move follows Mates. For all references to Mates see (Mates, B., 1972).

PAGE 52

52 co-extensive iff\ ( 0) =\ ( 1). This all seems exactly in line with what Carnap lays out in the sections about extension. Also, we see that given that the interpretation for the language can provide an implicit treatment of extension, an interpretation can endorse a sentence which is included in an SD in the sense that for if is included in an SD, then an interpretation \ can be such that \ ( ) = g. Since this endorsement is possible for each sentence of the SD, we might say that a certain interpretation can be such that it endorses the entire SD, or serves as a proxy for a statedescription: an interpretation, \, is a proxy for an SD, s1, just in case for every sentence included in s1, \ ( ) = g. Apart from simply providing proxies for statedescription, an interp retation can forestall some of the difficulties that we canvassed earlier. Specifically, we saw that, informally, we might have a situation in which each of these sentences are included in a particular state-description: a is exactly three meters long, b is exactly five meters long, a is longer than b, and so the statedescription would be inconsistent, according to any expected understanding of the terms involved. This situation seemed to be something Carnap didnt want, and perhaps something he thought wouldnt arise given how he thought about the interpreta tion of the languages of his semantical systems, but which was nevertheless not explicitly disallowed by his presentation of state-descriptions. With interpretations serving as proxies for state-descript ions, we can explicitly disallow such behavior. We do this, in part, with the following sort of restrictions. We give the formal presentation first and then an explication of the int erpretation entailment relation denoted by i. Let V0, V1 {g, Y }. For any two members of a state-description 1, 2, if\ ( 1) = V0 and \ ( 1) = V0

PAGE 53

53 i \ ( 2) = V1, then \ ( 2) = V1. In general for any n members of a state-description 1, 2, n, if \ (~ 1 ~ 2 ~ n1 ) = V0 and \ (~ 12 n1 ) = V0 i \ ( n) = V1, then \ ( n) = V1. Since, it can be the case that is (~ 1 ~ 2 ~ n1 ), a more general, and simpler, formulation of the interpretation entailment is to say that for sentences 1 and 2, if \ ( 1) = V0 and \ ( 1) = V0 i \ ( n) = V1, then \ ( 2) = V1. The interpretation entailment relation ( i) is such that given a partial interpretation of 0 and 1 (an interpretation restricted only to 0 and 1), for singular terms and ( 0( ) & 1( )) i 2 2( ) iff the predicate 2 is such that given its understood meaning, and must bear 2 2 given that is 0 and is 1. Again, we could go through the tedious, yet straightforward way to explicitly define i recursively, but we shall no t do so. (In fact, doing so will be redundant given the content of Chapter Se ven.) The important thing to remember is that we are asserting that we can le t interpretations go proxy for interpretations, and we can restrict these interpretations such that when so restricted they respect the intuitive meaning connections between the natural language pred icates our artificial language predicate terms were to model. For instance, we want the interpre tations to be such that if an individual falls under the extension of the artificial language predic ate meant to model our natural la nguage predicate scarlet then the interpretation should be such that that thing also falls under the extension of the predicate term mean to model our natural language term red. I hope I have demonstrated, at least in principle, that with the notion of the interpretation entailment relation that our interpretations can be restricted so as to maintain what we think of as the analytic conne ctions between predicate terms. Later on, in Chapter Seven, we will add even more substance to this thesis. We will show that the interpretations are restri cted by the conceptual repertoire of a conceiver who has all the

PAGE 54

54 appropriate conceptual competences. The present discussion is meant to show only that there are formal restrictions available to us which can be used to simu late the analytic connections between natural language predicate terms in the c ontext of the formal language we develop in this dissertation. One might fear that since were trying to produce a r ough and ready definition of analyticity in the reworking of Carnap in this chapter, that we shouldnt be making use of the phrases like the understood meaning of 2 2 for fear of circularity. Such a fear might seem appropriate now, but once we put th e interpretations we develop in this chapter on a more firm conceptual footing in Chapter 7, that fear will be soothed. Since we do not have any guarantee that the atomic sentences are independent of each other (unless theres a background assumption on Ca rnaps behalf about th e interpretations the predicate terms are to receive), it seems reasonable to restrict our interpretation proxies with i. An interpretation \ restricted by i will provide all the informa tion that the state-description that it is a proxy for was meant to provide withou t the possibility of (unforeseen and unintended) inconsistencies given the intended meaning of predicate terms. Two concerns for interpretations as proxies for SDs approach : Before we proceed, I would like to address a worry ove r whether the enhanced interpre tations we have developed in this section are of the right sort to serves as proxies for Carnaps state-descriptions. Our concern over this issue will pursue and expand upon the propos al at the end of the last short section to insure that Carnaps state-descriptions were consistent. Whereas state-descriptions are specified enti rely syntacticallyfor each predicate term and each individual constant term of the language a state-de scription cont ains either or ~ and this is the case regardless of any interpretation thats provided for any predicate or

PAGE 55

55 individual constantan interpreta tion, that is to provide the sa me information, seem to involve more than just syntax. A closely related worry is over whether our semantic proxy for statedescriptions can maintain the pr oper independence of atomic senten ces. We have seen that the formal apparatus is available to guarantee that th e interpretations that se rve as proxies for statedescriptions are such that consistency-given-the-intended-meani ng-of-terms can be maintained. And we have suggested that i should be used to restrict our interpretation proxies. Are our interpretations too restrictive to serve as proxi es for Carnaps state-descriptions? The atomic sentences of state-descriptions we re to be independent of each othe r, for instance, whether or not a state-description contains P1 1( a0) it may contain P1 14( a0) or ~P1 14( a0). But an interpretation might be such that \ (P1 1) = \ (P1 14), so the situation in which \ (P1 1( a0)) = g and \ (~P1 14( a0)) = g is impossible. In that inte rpretation, the two atomic sentences are not completely independent of each other.8 There are two immediate responses to this so rt of worry. First, even though they are provided purely syntactically, we have already s een that it is obvious that state-descriptions do describe something in that one such gives a complete description of a possible state of the universe of individuals with resp ect to all properties a nd relations expressed by predicates of the system(9). Carnap has the reasonable assu mption in the background that a universe of individuals cannot be inconsistent. That is to say, for ex ample, that for a universe of individuals it cannot be the case that, in our terms \ (~ P1 14( a0)) = \ ( P1 14( a0)) = g or in Carnaps terms a state-descriptions includes both ~ P1 14( a0) and P1 14( a0). 8 This situation might arise without being immediately obvious if predicates are defined in terms of others with the -operator. For instance, if the predicate abstract x ( P1 2( x ) & ~ P1 3( x )) is named P1 213 for short, so that, P1 213( a ) is true just in case P1 2( a ) & ~ P1 3( a ) is, then a state-description might include both P1 213( a ) and P1 3( a ), but an enhanced interpretation \ could not be such that \ (P1 213( a ) & P1 3( a )) = g

PAGE 56

56 On the other hand, it doesnt seem at first blush, that Carnap would like to disallow a particular state-description in which the extension of P1 14 is the same as the extension of P1 1 and that this state-desc ription includes both P1 14( a0) and ~ P1 1( a0) indeed this was one result of his assumption that for any two atomic sentences of the state-de scription, each of the pair is independent of the other. But a state-description that incl uded two such sentences should not be possible. Since the extension of P1 14 is exactly the same as P1 1, the set of sentences this statedescription comprises should not contain both P1 14( a0) and ~ P1 1( a0), as P1 1( a0) makes the same claim as P1 14( a0).9 The independence of atomic sentences cannot be, for Carnap, absolute. What should be Carnap s implicit restriction on state-de scriptions that describe only consistent states of the universe can be and is reflected in the interpretations we have provided as proxies. Another situation that would be disallowed if we consider only consistent universes is the following. If the extension of th e singular referring term a0 is the same as the extension of the singular referring term a127, then a state-descripti on cannot include both (say) P1 1( a0) and ~ P1 1( a127), otherwise the set designated by P1 1 would both include and not include that which is designated by a0 (and a127 since they designate the same individual). The enhanced interpretations were considering as proxies for state-descriptions do not admit this situation either because if \ (a0) = \ ( a127), then, if \ (a0) \ ( P1 1) (that is \ ( P1 1( a0)) = g ) then \ (a127) \ (P1 1) (that is \ ( P1 1( a127)) = g ), otherwise \ ( a0) \ (P1 1), a contradiction. The second response addresses th e concern over whether more information is sneaked in by the interpretations than was originally present in the state-descriptions. Now it may seem at first that we could be able to determine some analytic connections among certain different 9 Again, the same holds for the situation in which such inconsistencies occur less obviously with predicate abstracts.

PAGE 57

57 predicates in the context of an interpretation that we could not determine from the mere syntactic presentation of a state-description One might think that, for example, there is analytic connection between is red and is scarlet to be seen in virt ue of how these predicates are interpreted, and that this connection does not emerge from the bare state-descriptions themselves which are supposed to indicate exactly which individuals are red and which are scarlet. I think that given the previous discussion about what the state-de scriptions are to represent, we should be able to see that th e only analytic connections to be discerned from interpretations are those that could be determined from the statedescriptions. In the case of is red and is scarlet, one could see from a state-description of a consistent universe that if that statedescriptions contains the sentence (a0) then the state-description must contain the sentence (a0) (where represents something like the informal is scarlet and represents something like the informal is red) if the statedescription is to accurately represent the state of the universe made up of the individua l of the domain of discourse. All scarlet things are, after all, also red things. This equivalence of information present in st ate-descriptions and in terpretation proxies can be seen clearly when we consider the formal nature of the language at issue. The sentences of a state-descriptions each of wh ich contain a predicate term along with the desi gnation of each of the individual constants of th e language, explicitly provide th e individuals of the domain of discourse to which the predicate applies. To find out if a certain individual named by a0 say of the domain is we check the state-descriptions members until we find either the sentence ( a0) or ~ ( a0). We can find out just as much, but no more, with an interpretation proxy. Either \ (a0) is a member of the set picked out by \ ( ) or it is not. On the basis of the

PAGE 58

58 interpretation, we have no other information about the relationships of the interpretations of predicates other than this. We should remind ourselves why this is so. As per usual with model-theoretic treatments of semantics, an interpretation \ is a map defined only over individual and predicate constants and sentences of the language for which it is an interpretation. The values \ takes over sentences of the language can be determined recursively given only the values of \ on the predicate and individual constant terms of that language. The map \ is not defined over expressions of the language such as ( P1 1 = P1 3) for or ( a1 = a3) and so no information is provided other than what sets and individuals are designated respect ively by predicate and individual constant terms. We will argue later that any analytic connections between predicates (such as whether P1 1 has the same intension (to be defined soon) as P1 3) will be a result of certain properties of a certain class of interpretations we consider rather than a certain specific one. Sets of Interpretations Can Provide Intension In the last section, we have s een how an interpretation as we have defined it can be used to serve as a proxy for a state-description: the inte rpretation endorses as true all and only the sentences of state-descriptions while at the same time providing no more information than what was explicit or implicit in the st ate-description. Since we have the notion of a class of statedescriptions simply a class of sets of atom ic sentences and the negations of the atomic sentences, we have the notion of the correspondi ng class of interpretations simply a class of functions as earlier defi ned that serve as proxies for the resp ective state-descriptions. As Carnap uses the notion of the class of state-descrip tions in his explication of the Ltruth and L

PAGE 59

59 equivalence and his implicit defi nition of intension, can we use the class of proxy interpretations to spell out this notion. If we use as an index set for the class of st ate-descriptions, then the class of interpretations (\ ) which are the respective proxies of these state-descriptions is {\} I (think I ntension) is a map such that : 18. I : (such that, for any I ( ) = \( )) 19. I : n 2n (such that, for any I ( n) = \( n)) 20. I : {g, Y } (such that, for any I ( ) = \( ))10 This gets the right result in terms of a modeltheoretic reworking of the semantical systems as far as predicate and singular terms are concerne d. First, Carnap does claim explicitly that the intension of a singular term is an individual concept which is a function fr om state-descriptions to individuals. Second, recall that intensions of predicates we re defined with Ltruth and L equivalence: predicate terms 0 and 1 have the same intension iff ( x )( 0( x ) 1( x )) is Ltrue and two singular terms have the same intension i ff they are Lequivalent (that is, the functions that are the individual concepts of these respective terms are id entical). Third, I think we might cautiously generalize and claim that the intension of a predicate term is a function from statedescriptions to extensions, and th at two predicate terms have the same intension iff the functions that are the intensions of these respective terms are identical. Finally, I am not sure if Carnap makes any comment about the intension of sent ences, but it seems that it should be something like a formal analogue of meaning as understood independently fr om a specific extension. And, interestingly, the notion of inte nsion we have provided here could be understood as a function 10 I need have as its domain only what is outlined in (18)-( 20) because, even though much more complicated expressions involving predicate abstraction and definite description term may be said to have intensions, the WFFs which occur in such expressions are reducible to expressions of the terms of (18)-(20) with the use of the recursive machinery that is anal ogous to the numbered sentences (5)-(10) of this chapter.

PAGE 60

60 which picks out the situations in which a sentence is true.11 This seems in line with commonplace claims that if one knows the meaning of a sentence (of course, to do this, one must have, at a minimum, the concepts whose appl ication conditions are partially modeled by the intensions of the semantical constituents of the sentence) then one knows its truth conditions (that is, the circumstances in which the sentence is true ). Intensions, so understood are thinner than meaning, but to know meaning one must know intensions. Admissible Interpretations The issue of exactly which class of s ets of atomic sentences and negations of atomic sentences is to be considered state-desc riptions is not addr essed directly in Meaning and Necessity but perhaps it should have been.12 We have already surmised that since Carnap is developing systems whose languages are provided with formal semantics, the consistency of those systems is important. The languages of the systems are to be about something because we are to be able to construct state-descriptions fr om certain kinds of sentences of those languages. This assumption points to some restrictions on the class of state-descriptions, and we have suggested in the previous sect ions how some of these might be realized in terms of the interpretations that are to be proxies for state-descriptions. Ve ry briefly, I would like to expand upon what we hinted at earlier. Since the notion of interpretation we have developed in the preceding sections was to be a substitute for the notion of state-de scription for any statedescription, there is a interpretati on proxy for this interpretation that on which is true all and only the atomic sentences and negations of atomic sentences that were members of that state11 Since interpretations were, after all, to serve just as proxies for state-descriptions. 12 Carnap does, of course, provide a synt actical criterion that gives the complete class of SDs for his languages, but this syntactical criterion is so permissive that it allows every syntactically consistent (i.e. having both ~ and is disallowed) set of atomic sentences and negations of atomic sentences. I will argue that such a criterion is not restrictive enough because it cannot preserve, in a robust, epistemically perspicuous way, the analytic connections between certain predicate terms.

PAGE 61

61 description any restriction on interpretations will be a de facto restriction on the sort of statedescriptions there are. Since I believe the restriction we sugge st would be welcomed by any reasonable investigation of modality, we w ill not spend too much time arguing for them. Earlier, we tried to make it the case that inte rpretations were such that they maintained consistency for the semantical system whose la nguage they interpreted. Let us say more about how we must explicitly require any interpretatio n of the language of these semantical systems maintains consistency. For example, if the langua ge contains the two-place identity predicate (say it is P2 0) that hold of all a nd only ordered pairs of identical objects, then the interpretation \ must be such that it endorses each of \ ( P2 0( a0, a0)) = g = \ (P2 0( a1, a1)) = \ ( P2 0( a2, a2)), but that if (say) \ ( a0) \ (a1), then it must be that \ (~ P2 0( a0, a1)) = g Other such examples are possible. Also, to reiterate what we stated be fore, we must also require that if \ is such that, for any two predicates and \ ( ) = \ ( ), then for any singular term \ ( ( )) =\ ( ( )). And, in general, interpretations must be such that the restrictions outlined formally at the end of the section An Interpretation Can Provide Extension (and in the section following it) are enforced. But it seems that aside from these unobjectionable restrictions, the class of interpretations must likely be limited even further, if were to try to apply our investigations of the formal systems to the study of modal semantics for natural language. If the class of interpretations is to ground the truth of analytic statem ents (as the class of state-de scriptions grounds the truth of sentences which include the modal operator N), then, on a conventionalist view of modal semantics at least, this class of interpretations must take some sort of stand on controversial modal statements.

PAGE 62

62 For example, if we were to take a conventi onalist approach to modal semantics and assert that necessity can be explained roughly in terms of analyticity, then we would want this approach to account for the truth of statements such as Necessarily, water is H2O and Necessarily, Aristotle was not a tea pot. These statements do not seem to be such as to be endorsed according to a notion of analyticity which is grounded by a class of interpretations which is restricted only by the sort of consistency worries we have addre ssed in the previous paragraphs. To endorse the intuitive truth of these modal st atements, the class of interpreta tions must be whittled down yet further. I think such whittling is possible, and that we can indi cate how to shape up the class of interpretations in such a way as to explic ate the previous modal claims according to a conventionalist view, but I will not do so yet. We will leave that projec t for the next several chapters. At present, I want to only to draw our attention to the fact that the class of interpretations must be restricted in certain ways if were to get anything useful from the notion. I would like to coin the term admissible interp retation to apply to a ll and only those members of the class of interpretations prop erly restricted (whatever the prope r restrictions tu rn out to be). Analyticity for atomic sentences of L and N : Once we have the notion of an admissible interpretation, we can finally make a proposal for what analyticity (relative to some formal language) comes to. Not surprisingly, analyt icity is exactly analogous to Carnaps N Formally, we say that, relative to the language (L) of the semantical system were considering: 21. is analytic in L iff for each admissible interpretation, \, \( ) = g An alternative formulation is (22): 22. is analytic iff for each admissible interpretation, \, I(\, ) = g. Specifically in terms of the semantics wed developed in our update of Carnaps work, we have: 23. If 1 is N( 0) and \( 1) = g just in case for all I(\, 0) = g.

PAGE 63

63 We might informally spell analyticity out in the following way. Our notion of intension I was to spell out, in terms of all the way things might have turned out, how we correctly use designator terms. If a sentence is such th at the sentence is true on every ad missible interpretation, that is, every correct way of speaking about a particular actual or counterfactua l situation, then the sentence is true simply in virtue of how we use the terms in questi on. This is just to say that the sentence is analytic. There is of course a remaining bit of business to clear up with this so rt of explanation of analyticity. Recall that Carnap gave the semantics of a sentence like ( x )(N ( ( x )) by adverting to the notion of an indi vidual concept over which x ranged because N created an intensional context. It seems that we must make an analogous move in terms of defining analyticity (in L) here, for how are we to make sense of the quest ion of whether a formul a with a free variable ( ( x )) is analytic? The natural move to make (whi ch is the move we make) is to say that a de re sentence informally given as There is something x such that it is analytic that x is is true just in case there is an individual constant a such that a is is analytic.13 We take this issue up in exhaustive (exhausting?) detail in Chapter Eleven. Conclusion In this chapter, we have m ade use of the m odel-theoretic notion of an interpretation as a map (i) from individual constant s and definite descriptions of a language to individuals in a domain of discourse, (ii) from nplace predicate terms to n-tuples of individuals of a domain of discourse, from (iii) sentences of a language to a functional equivalent of truth values. We have 13 It is interesting to notice that it is analytic that may serve to create a meaning context for variables bound outside its scope just as N creates an intensional context for such variables. Just as an intensional context forces us to consider individual concepts over which the variable ra nges, the meaning context may force us to consider the counterfactual situations in which the individual constant (or name) might be used rather than just how the individual constant (name) is used in the actual situatio n.) We will spell out in detail how to understand quantified sentences on the analytic-deflationa ry view in Chapters 10 and 11.

PAGE 64

64 begun our update and generalizati on of Carnaps project by constr ucting these interpretations so that for any one of the SDs of the sort described in Meaning and Necessity there corresponds exactly one interpretation. Our move is possibl e because interpretations are such that one could straighforwardly make true all a nd only those sentences of an SD.14 In the course of showing how this is possibl e, however, we have noticed that the modeltheoretic techniques we have us ed raise interesting questions about the supposed independence of the sentences of as SD. Of course, Carnap may have had something different in mind in his original notion of an SD (perhaps the pred icates were to be such as to describe prima facie independent physical properties of an object like temperature and co lor), but I claim that we can use the notion he has developed in the service of an account of in tensions for a formal language that is supposed to roughly appr oximate a natural langua ge like English. But to do this, we must acknowledge that the sentences of an SD are not independent of each other. Ive argued that the interpretations (one per SD) are such that they can reflect the appropriate dependencies. We started using the term as an index set for the class of SDs, and then made an implicit, unmarked slide into using it to indicate an inde x set of the class of co rresponding interpretations. From now on we will be speaking about the interp retations that were originally supposed to be proxies for SDs. The once-merely-proxy interpreta tions will, no doubt, take on lives of their own and will take on properties that were not specifically bestowed upon the SDs in Meaning and Necessity One specific aspect of this new life that we will see over the next fe w chapters will result from our attempts to delimit, in the least problematic manner possible, the class of interpretations we allow. We have referred to the properly delimited class as the class of admissible 14 I stress that one could do so because we will actually wind up with a smaller class of (interpretation proxies for) SDs, because Carnap did not rule out SDs that were not possibly true because of lexical meaning connections.

PAGE 65

65 interpretations. More work must be done on ju st how this class shoul d be carved out of all possible interpretations of th e sort we have suggested. Another major concern looms so far unaddre ssed in the background. The model-theoretic techniques we have used so far depe nd upon the existence of underlying sets ({ }) each of which is a model of the sentences each of whic h an interpretation makes true. And, as things stand now, it seems that the propert ies had by the members of each of and relations borne by members to each other are what allows for the dependencies among sentences of the SDs to be accounted for. If were committed to these underlyi ng sets, then it seems that were committed to something like a class of possible worlds, and as we are supposed to be clearing a path for a deflationary, ontologically parsimonious account of modal semantics, this commitment is undesirable perhaps even intolerable. I do not think we will be forced into such a commitment, but until we get more clarifica tion and background out on the table, we must sit in the less-thancomfortable position in which we must hold for the time being that there are the underlying sets which are the models for each one of our interpretations.

PAGE 66

66 CHAPTER 4 OUR GENERALIZATION OF CARNAPS SY STEMS LEADS TO A TREATMENT OF ANAL YTICITY THAT IS CONCEPTUALLY PRIOR TO A TREATMENT OF NECESSITY Introduction To begin, let us review our progress so far. In Chapter Two, we rehearsed key elem ents of Carnaps proposal in Meaning and Necessity In Chapter Three, we made explicit and extensive use of model-theoretic techniques to update and generalize his approach and to provide the groundwork for carving out an accep table class of admissible in terpretations. The tension between our review of Carnap in the former and the explicitly model-theo retic generalization of the latter should be obvious. Carnap is trying to squeeze modality out of meaning without resort to what is spoken about. We have claimed that to make sense of this idea, we must back the meaning notions with domains of discourse. It seems that we have repaired Carnaps original idea so well that it no longer functions as it is su pposed to. Since we do want to clear a path for the view according to which modality is squeezed out of meaning, we must return to Carnaps original insight that meaning and necessity can be brought together, but th ere are detours to be taken in the new route to the ultimate destination. In this chapter, some stock-taking is in or der. We need first of all to clarify and differentiate the notions of possi ble worlds, state-descriptions a nd admissible interpretations and then to do some work to clarify the relationship of each to the others. What ontological commitments are incurred if we use possible worl ds as the ground for the truth of modal claims? What commitments are there for state-descriptio ns as such? What commitments are there for a class of admissible interpretations as things stand now? We will try to answer these questions and from our answers it should be obvious that more must be said and more work must be done in order to build on the progress we have made in Chapters Two and Three to see how the path

PAGE 67

67 clearing we promised for an analytic-deflationary account of model semantics to be accomplished. I assert that we want a meaning notion of an alyticity that is con ceptually prior to the modal notion expressed by the sentence operator necessarily. What does this mean? Roughly, I would like us to develop a notion of analyticit y that can be underst ood without a previous understanding of the modal notion expressed by n ecessarily as a sentence operator. This may seem odd as our purported goal is to analyze necessa rily in terms of analyticity and so on that score it may seem that the two notions are concep tually linked. What I am advocating here might best be put in terms of an analogy with arith metic and modular arithmetic. One might understand arithmetic principles and perform arithmetic operations without any knowledge of modular arithmetic, but one would be unable to perform m odular arithmetic operations (for an arbitrary modulo) without prior k nowledge of arithmetic. I believe that we are in a similar situation re garding analyticity and necessity. We shall try to show that analyticity can understood without an explicit knowledge of the modal notion expressed by the sentence operator necessarily. And then, we sha ll have shown, if all goes well, by the very end of this dissertation, that the semantics for sentences of the form N and (Qx )N( ( x )) can be provided with the more basic notion of analyticity. Of course, doing so requires th at we take quite a few thi ngs on board. For instance (and this might serve as a bit of long-range look-ahead), we might to forced into (i) a (perhaps reluctant) acceptance that any treatment of modal semantics which provides a workable epistemology of modal truths cannot be completely reductive1 and (ii) a certain view of concepts (more likely a deflationary view of concepts as well best expressed by the locution conceptual 1 See Chapter Five.

PAGE 68

68 mastery)2. The path-clearing for conventionalist modal semantics comes at a price. Is the price low enough that we are willing to pay it? Whethe r we wish to buy or not, we should be in a position to say whether the goods are worth their price. In order to be in such a position, we must know the hidden costs of the path -clearing. I shall try to highlight these as clearly as I can. On the Relationship of Possibl e W orlds, State-Descriptions and Admissible Interpretations Now that we have finally given an initial ch aracterization of analyt icity (for sentences whose primary operator is not a quantifier that is sentences in which quantification is not into an opaque context) in a langua ge comes to in terms of admi ssible interpretations, a bit of clarification is possible, and in order to help separate the notions of possible worlds, statedescriptions and admissible interp retations. Carnap introduced stat e-descriptions as (a certain kind of) sets of (a certain kind of) linguistic entities which were to represent possible worlds. Of course, his investigation is aime d at universes of indi viduals that can be adequately described with the formal languages he considers, so theres some distance between the possible worlds described by state-descriptions and the possible worlds that provide truth makers for modal statements in natural language. But the conn ection between possible worlds of David Lewis3 sort and what is represented by the state-descriptions of Meaning and Necessity is apparent. Overview of the Differences and Our Commitmen ts as Things Stand Now By clarifying the relationship between possibl e worlds, state-descript ions and the class of admissible interpretations, we can see what our commitments are as things stand. Birds eye view of the situation So where exactly do the adm issible interpretations fit in? Recall from the last section that an admissible interpretation is a member of a cl ass of interpretations, and that this class is 2 See Chapters Six, Seven and Eight. 3 For all references to David Lewis see (Lewis, D., 1986).

PAGE 69

69 restricted in certain ways. (The restrictions will be made exp licit in Chapter Seven.) But each admissible interpretation is to be a proxy for state-description.4 From these requirements on admissible interpretations, we can observe someth ing about their features which may be helpful in understanding what admissible interpretati ons are not, and this observation deserves articulation. An admissible interpretation is suppose d to provide all the information that a statedescription does, but not necessarily more. Admissible interpretations are functions from linguistic expressions to individuals, sets of i ndividuals and truthvalues which are supposed to imitate correct linguistic behavior (o r semantic use, formally speaking) rather than to describe situations in which we use the terms of th e language differently than we actually do. For example, consider two different members, and of the index set of admissible interpretations, such that \( ) \ ( ). Now in this situation, we do not want to assert the following. For an arbitrary member of \( ) (call it ) and an arbitrary member of \ ( ) (call it ), that lacks the feature or features on the ba sis of which we would, given the usual meaning of our predicate terms, cl aim that it falls under the predicate or that lacks such a feature or features, and so claim that \ and \ simply represent different ways we might use the predicate What we wish to say, rather, in this situ ation is that we hold fixed the ways we use across every member of : the two interpretations are suppos ed to represent two different situations in which, given our usual meanings of the term the set of things which are is different; the set of individuals which are in is not the set of individuals which are in 4 From these two assertions about admissible interpretations we see that were committed to the restriction of the class of possible worlds in some ways, but this is unobjectionable: the class of worlds which serve (in part) as the truth-makers for modal statements in Lewis theory are rest ricted in at least one obvious way these worlds include only those which are possible rather than all worlds possible and impossible alike.

PAGE 70

70 .5 Different admissible interpretations are to represent different scenarios in which language is used in the same way. The function of admissibl e interpretations fits in with the notion of intension in the following way: the notion of inte nsion we have developed in this dissertation is supposed to model (albeit only partially ) our intuitive notion of meaning. Since a necessary condition on knowing the meaning of a predicate term is knowing when to correctly apply the term (and of course this knowledge requires that one who knows the meaning of the term would be able to correctly apply it in counterfactual scenarios), the different admissible interpretations are meant to provide counterfactual settings in which language can be used and show how the terms of the language would be used in these differe nt situations if we were to use these terms to describe aspects of these situations. So in a sense, admissible interpretations might be claimed to do double duty: to be proxies for, and descriptions of the way we speak with respect to, state-descri ptions. One might argue that this double-task is too large: an interpre tation cannot serve as a pr oxy for a state-description (that was in turn to represent a possible world) while exhibiting correct use of designating terms in the various counterfactual s cenarios without the appearance of some sort of unpleasant circularity. I believe that the double-task for the class of admissibl e interpretations is not too big, but that the task must be precisely of this size and nature to provi de a satisfying account of modal semantics. In so claiming, we call upon a fundamental tenet of the conventionalist approach: that meaning and modality must be intimately linke d and that modality cannot be understood as conceptually prior to notions of meaning, intension or concep t possession, but rather that the latter is conceptually prior to the former. We will have to wait until subsequent chapters to see the full argument for this assertion. Ultimatel y, to advocate a conventionalist modal semantics, 5 There is, of course, a notion of constant domain versus variable domains here that must be addressed.

PAGE 71

71 we must hold that meaning and modality are not conceptually separable, but that the former is prior to the latter. To do so, we must remain calm when confronted by the size or nature of the task of the class of admissible interpretations: to serve as proxies for state-descriptions and at the same time to provide a description of correct semantic use. The class of admissible interpretations will serve to provide descriptions of correct semantic use because they serve as proxies for the state-descriptions. For an arbitrary predicate term the set of admissible interpretations is, inter alia to provide exhaustively the c onditions under wh ich the use of is acceptable in describing arbitrary individuals. Hopefully, we will be in a position to see how modal semantics (for each of the sentence types were concerne d with) can be provided given our account of the class of admissible interpretations. View from the battlefield Once we step away from these h igh-view, stra tegic concerns, we come quickly to low-tothe-ground, tactical issues. An immediate worry is over whether everything we would like to speak about in these counterfactual scenarios mu st be named. We have the intuition that on the one hand if is physical object, then, necessarily, has a spatiotemporal location, but on the other that theres no requirement that there must be some singular expression in the language of the semantical system such that on some interpretation \, \( ) = but it seems that there must be a name for (and indeed for every individual about which we make de re modal claims) if were even to be able to attempt the sort of c onventionalist strate gy that we have been trying to lay the ground work for. Theres more to be said about this issue, but I will not say much more in this dissertation.6 6 A brief rough and ready suggestion for how to deal with this problem is to claim that any results that follow for the particular generic formal language we have developed an d continue to develop hold for another generic language just like the one we shall have developed in this dissertation except for the fact that the new language contains one

PAGE 72

72 Perhaps a deeper worry is over whether we have actually come to have any more insight into the status of modal statements from this so rt of treatment this concern came up at the end of the last section on Admissibl e Interpretations. Do es describing correct semantic usage help us at all in our understanding of modal claims? If so, how? To reiterate, Ive hinted that the truthvalue of N( ) ultimately depends upon which statedescriptions there are just as according to another sort of account of modal semantics the truthvalue of of ( ) depends on which possible worlds there are. We have trie d to place a few restrictions on the admissible interpretations (mostly restrictions aimed at maintaining consistency of the semantical systems), but it doesnt seem that these restrictions ar e of the right sort to make the admissible interpretations such that they cl early endorse the truth of the clai ms that assert certain analytic connections that hold between certa in predicate terms in virtue of the intuitive meanings of those terms. And the restrictions we have suggested are certainly not of the right strength to ensure the truth of substantive modal claims such as necessarily, water is H2O, and necessarily, Aristotle was not a teapot. One important difference between possible-worlds approaches and the sort of approach we have developed here (and will continue to develop in the next section) is that whereas there is hope to restrict the admissible interpretations in such a way that the claims we want to be endorsed are endorsed, and that we ca n make the restriction in a way that doesnt make explicit appeal precisely to modal notion of necessity, restricti ng the class of possible worlds in a manner that makes no use of modal notions seems more difficult. If one cannot more semantically primitive singular referring term that term can be used to denote the individual that was unnamed in the original generic language. And the extensions of pr edicates for any admissible interpretation for that language can be adjusted accordingly to endorse the truth or falsity of any sentences in which thos e predicate are asserted to hold or not hold of the new individual so named. The same strategy can be used to expand the language we develop in this dissertation to include new predicate terms. The strategic notion is that anything or extension can be talked about with the appropriate language; we expand the language in obviously accep table ways when we wish to talk about something as yet unnamed, or when we wish to make claims about the relations between sets of individuals which are not as yet the extensions of certain predicates under some admissible interpretation.

PAGE 73

73 restrict the class of possible worlds in such a non-modal manner, then any hope for an informative reductive analysis of modal statemen ts with these possible worlds which shows how modal knowledge is possible is dashed either by the viciously circular nature of such an analysis (if the class of possible worlds is restricted with appeal to moda l notions) or the failure of such an analysis to provide insight into our knowledge of modal statements (if we simply take the class of possible worlds as theoretically prior to our investigation into modal semantics). That we do take the class of possible worlds as pr ior to any philosophizing about modal semantics, and simply focus on the utility in explication of modal statements that this class provides is suggested by Ted Sider.7 Differences in Ontological Commitment As things stand, there should be serious worries over whether we can even claim to give an extensional account of intension Ive proposed without immediate and serious regress and circularity problems. The set of admissible interpretations was to spell out meaning facts, but it looks as if we need meaning facts to classify a particular interpretati on as admissible or not. I mean to resolve this tension over the next few sec tions (and in chapters af ter this one), but it is beneficial to hold with the te nsion and see what, precisely is making us nervous about our present situation. By working out the exact problem in detail, we will see a way to a resolution. We can begin to focus our concerns by noting what the ontological commitments of a modal realist approach (like a Lewisian possible worlds approach) versus a Carn apian state-description approach, versus the admissible inte rpretation approach we are trying to use in the effort to clear the path for conventionalism. 7 For all references to Ted Sider see (Sider, T., 2003).

PAGE 74

74 Ive claimed that admissible interpretations do a double duty by providing proxies for state-descriptions while simultaneously demonstr ating how designating terms would be used in presenting those state-descrip tions. Of course, one may doubt whether this strategy (using admissible interpretations to give an account of modal semantics) can be successful. But even if we could see that it is be vi able, one might be dissatisfied with such a strategy because, according to this approach, the truth of modal statements depends upon how designating terms of a semantical system would be used to describe a count erfactual situation were that situation to obtain. If were to understand ad missible interpretations as pe rforming the double duty, it is difficult to see how we could eliminate the subj unctive would be from the last sentence. The fact that (for in stance) a predicate would apply to if some situation were to obtain indicates a fundamentally dispositional character in the base in terms of which modal statements are analyzed.8 On the other hand, if one were sanguine about ineliminable dispositional nature of the reductive base of the admissible interpretations strategy, he might wonder whether this strategy incurs fewer ontological commitments than a possible worlds strategy. If we take one aim of Meaning and Necessity to be a reductive explanation of the modal operator N such that its application conditions are given by certain features of all of the members of a certain class of st ate-descriptions, then we have an ontological commitment to the class of state-descriptions give n that we desire a firm reductive base. In other words, on the assumption that our account of the modal operator is to be reductive, if we want to claim that N ( ) is true because the truth of is entailed by each state-description, then it seems we must 8 A kind of semantic entailment may ensure that we could infer the correct application of predicates to individuals for most predicates which bear rich an alytic connections to others. Specifically in terms of an example, we could infer that the predicate triangular app lied to any individual to which each of the predicate plane figure, straightsided and three-sided applied. So in this case, no fundamental appeal to dispositions must be made. But in the case of so-called basic predicates predicates which ar e such that there application is not entailed by analytic connections in the way that triangular is, then it seems that a fundamental appeal to the dispositions of cognizers is required for the analytic-deflationary path to be pursued.

PAGE 75

75 admit that the state-descriptions into our ontology, rather than sa ying state-descrip tions represent situations which merely could have obtained. We can this commitment as one to two sorts of abstracta : sets and sentence types (atomic sentences and the nega tion of atomic sentences). We incur a slightly different commitment with our modeltheoretic reworking. Since interpretations (functions from expressions to indi viduals, ordered tuples of individuals and truth values) served as proxies for state-descriptions and intensions were also explained as a function (from interpretations and expressi ons to individuals, ordered-t uples of individuals and truth values), we incur whatever commitments we ta ke on board when we commit ourselves to the existence of these functions. Furthermore, since were committed to intensi ons only insofar as they partially model our use of language, it seems that ther e may be room (somewhere down the road) to argue that we do not really incur the commitment to the functions th at are interpretations or intensions as these are only meant to approximate the way we use language. As a preview, I will a ssert in Chapter 7 that we need the notion of concept possession to restrict the admissible interpretations in a plausible way I do not think this commits us to accepting concepts into our ontology, but the explanation of concept possession (in the way we will spell it out) seems to be fundamentally dispositional in character. Promissory Note for the Ways in Wh ich Interpretations Are Restricted We have already placed som e restri ctions on interpretations (recall the i operator of Chapter 3). We did so under the assumption that we knew what the terms were to mean, but we are using interpretations to give an extensional treatment of intens ions of predicate terms. If we can underwrite this delimitation in a responsible way, then we can cl aim that all these restrictions hold and that there is no commitment to a domain of objects which the sent ences are about (a set

PAGE 76

76 of possible worlds for instance). This will be our ev entual goal, but as things stand in this section of this chapter, we are committed to the existenc e of those individuals in the domain of discourse of each \, and so committed essentially to { } and some sort of partitioning of this set into discreet domains, one for each interpretation. Later, we will argue that we can make use of these interpretations without commitment to th ere being these individua ls. We must first get clear on conceptual priority, m eaning notions and modal notions. On Conceptual Priority, Analyticity and Necessity To illus trate the need for the conceptual pr iority of analyticity (to necessity) for a conventionalist analytic-def lationary view, it he lps to contrast this view with other competitors with respect to truth-making. I will consider a modal realist Lewisian view (views like Michael Jubiens9 are similar in this particular regard that is, with regard to the fact that modal claims are made true in virtue of extra-linguistic / extra-conceptual entities this is not to say that Jubiens view is anything like Lewis regarding any other pa rticulars), a conceptualist view as presented by (but not necessari ly advocated by) Amie Thomasson10 and finally a generic conventionalist view. Modal Realism and Truth-Making I believe th at David Lewis position on modality hardly requires exposition as it has been so thoroughly examined in countless articles and philosophy seminars, but briefly Lewis postulates a metaphysical multiverse which consis ts of completely distinct entire worlds (complete universes) neither spatially nor temporally re lated to each other. If we call the multiverse M then we say that for a sentence S It is possible that S iff for some member of 9 For all references to Michael Jubien see (Jubien, M., 2009). 10 For all referenes to Amie Thomasson see (Thomasson, A.L., 2005).

PAGE 77

77 M S is true. So, for example, if It is possible that there is a building a mile high is true then in some member of M there is a building that is a mile high. The sentence operato r Necessarily (or It is necessary that) is defined as the dua l of it is possible that. Since the members of M are called possible worlds, we often hear the following slogan th at encapsulates this realist approach to modal semantics It is possible that S iff S is true in some possible world. So we might claim (with tongue a bit in cheek) that trut h-makers reside in possible worlds for Lewis. The statement corresponds to a certain f act (that there is such a building some where (?)), and it is in virtue of this correspondence that the statement is true. On a different view of modality, truth-makers for claims might be the relations borne by properties thought of, in a property-realist way, as ab stract objects. On Michel Jubiens view (if I understand his thesis in its broadest terms) a modal statement is true because of certain relationships borne one to another by those pr operties which are instantiated by those things which are constituents of the proposition expressed by the sentence. So, for instance, a de dicto modal claim like Necessarily, every square is a r ectangle, is true becau se the property denoted by the predicate is recta ngular is such that it, in some se nse contains the property denoted by the predicate is square. In Jubiens termi nology, the property of being square entails the property of being rectangular. Just as on Lewis view, theres trut h-making at work (albeit of a different kind). If there really are possible worl ds as Lewis describes, then if they are to be the ground for the truth of modal claims, and they themselves, ar e to have no modal properties (and so the sort of analysis he offers is reductive that is, it aims to redu ce the modal to the non-modal11), then 11 We shall take up the topic of reduction and reductive analys es in the next chapter. It is enough to say here that modal semantics accounts for which a correspondence theory of truth is assumed are such as to be reductive in nature. That is, accounts of modality which assume that the truth of a sentence is had in virtue of its correspondence

PAGE 78

78 they must be conceptually prior to every modal notion or related notions. The reason is that these worlds are what ground, non-circ ularly, all modal talk. If th e possible worlds were not conceptually prior to modal notions expressed (for exam ple) by the sentence operator necessarily, then it might very well be that this modal notion was such that the class of possible worlds was delimited someway or other with the aid of this notion. One might say, for instance, that a certain world could not be among the clas s of possible worlds because it was necessarily the case that such a world did not exist. If su ch were the case then a modal notion would be involved in the decisions about which possible worl ds were allowed. But since we were trying to use the class of possible worlds to explain in some significant way what makes modal statements true, then, if we used modal notions to delimit this class, we would clearly be offering a viciously circular explanation, as the expl anation of what makes modal st atements true would rest of modal notions. If Lewis view is right, then we cannot even understand any philosophical talk of modal properties, necessity or possibility, unless we fi rst grasp the notion of possible worlds. The same goes, mutatis mutandis, for Jubiens view, a version of Ne o-Platonism. He proposes an ontology comprising a certain kind of abstract object (prope rties) and concrete part iculars. He colorfully describes the division between th e two ontological categories in terms of A Great Line of Being: concreta reside below it, properties above. For an indi vidual of either category to fall under a certain predicate is for that individual to bear what Jubien calls th e instantiation relation to the property ( by definition, a resident above the Great Line of Being) the predicate picks out. If one property is su ch that an instantiati on of it requires the inst antiation of another property, then we say that the first entails the first. On a certain conception of how we think to something are likely to be such as to attempt to explain the modal in terms of that which is non-modal, i.e. they attempt to reduce the modal to the non-modal.

PAGE 79

79 about the lay of land above the Great Line of Being, one might say th at the second property contains the second. Of relevance to our discussion of modal semantics is the observation that in terms of explanation of the truth or untru th of modal claims, our underst anding of the properties residing above the Great Line of Being and their beari ng certain containment relations to each other must come first, then an unders tanding of modal semantics. The properties and the relations they bear to each other must be taken as already existing and making true our modal claims if Jubiens analysis is to be a re ductive one. And so, these properties and the relations they bear to one another must be taken to be primitive and con ceptually prior to the tr uth of the modal claims that follow. Just as on Lewis vi ew, there is truth-making at work (albeit of a different kind than does the work for Lewis).12 Conceptualism and Truth-Making On the other hand, one m ight hold that relati onships borne to each other by concepts ( qua constituents of thoughts contents that are common to thoughts of different thinkers) are the truthmakers for modal claims. Whether this view is substantially different from a property realist view depends upon how we understand the ontological status of concepts. On one hand, concepts may be understood as mind-independent abstracta the relationships between which are what the truth of modal claims consists in. On this view, modal claims have truth-makers, so a correspondence theory of truth is at work: a modal claim assert s a certain relation that holds between the concepts expressed by the predicate te rms of the sentence that expresses the modal claim, if the sentence corresponds to the relation borne by certain concepts to each other, then the 12 Does the use of truth-makers in an account of modal se mantics force one into some broad region of logical space as far as a theory of truth is concerned? My hunch is that if there must be something to which a modal statement corresponds for the statement to be true i.e. a truth-maker, then one must go in for some sort of correspondence theory of truth. Professor Ludwig observes (correctly I be lieve) that in general, simply providing an account of the truth conditions for a claim is not to assert anything about the concept of truth, but only to use it.

PAGE 80

80 modal claim is true, false otherwise. This positio n seems very close to a property realist version of modal realism. And so, on this version of conceptualism, the existence of concepts and the relationships they bear to each other must be co nceptually prior to any notion of analyticity, a notion specifically to do with linguistic entiti es. No wonder, given that this version of conceptualism is backed by a sort of correspondence th eory of truth. A dilemma for modal conceptualism : On one hand there is the concept realist view of concepts we just canvassed: according to this view the existence of concepts, the relations they bear to one another and their role as thought constitu ents is conceptually pr ior to modal claims as the former is required to make sense of the latter. On the other hand, one who wishes to hold a conceptualist view might take a sort of concept anti-realist st and on concepts. Concepts might be initially characterized as c onstituents of thoughts and then on ce the observation is made that two thinkers might be thinking the same thought and that thoughts are somehow compositional (made up of discreet re-combinable subparts), one might reason, by a principle of abstraction, that concepts were these subparts which might be shared among thinkers. On this view, concepts come close to being the meanings of semanti cally primitive terms, where meaning is understood in terms of certain repetiti ve, regular patterns of use. On the conceptual realist view one might wonder whether we have epistemic access to all the concepts there are. Is every concept such that it has been, is or will be a constituent of the thought of someone? Prima facie it doesnt seem so. Might not we have had a concept we actually do not? I assert tenta tively that the concept realis t view collapses into an abstracto realist view of some sort; one according to which mind independent abstracta are the things that make true our modal claims. In any case, on the conceptual-realist view, it seems that the existence of concepts must be conceptu ally prior to a notion of analyticity.

PAGE 81

81 On what might be called the c onceptual-antirealist view, if we assume that concepts can be shared among thinkers only insofar as co ntents of thoughts can be communicated through language and that thoughts, and so the sentences that express those thoughts, are compositional in nature, then I believe that we can get away from a corresponde nce theory of truth, and give conceptual priority to analyticity. Of course, we do not want to abandon the notion of truth on the conceptual-antirealist view even though we w ill claim that a sentence is not made true by a correspondence to something or other. What is to underwrite our claim that a sentence is true according to such a view? One thing we certainly do not wish to claim is that there is no relationship to anything nonlinguistic that makes a sentence true on the conceptual-antirealist view. We can hold this view and still believe that word-world relations are, in part, that wh ich guarantee the truth of certain sentences. According to this view, language is about something, often things which are not any sort of linguistic entities. It is the fact that language is about something combined with the fact that we use linguistic entities with certain regular, repeatable meaning constitutive patterns that ensure the truth of sentences. I urge us to consider whether the conceptual-antirealist view collapses into a healthy and moderate sort of conventionalism. I will try to sketch this view in the next few sections. Conventionalism and Truth-Making If we say that true sentences are true (at leas t in part) in virtue of our m eaning conventions, things are not as crazy as they sound. This view can be taken to be equi valent to denying that there is anything a true sentence corresponds to th at makes the sentence true. Sentences are true in virtue of meaning, and meanings might be determined by convention, but, on this view, it is not the case that true sentences correspond to conventions and th ese conventions (by themselves) are what make true sentences.

PAGE 82

82 To see how this view might reasonably be made sense of, we might consider a deflationary view of truth. To put things in slogan form, we might hold that an arbitrary sentence like Snow is white is true if and only if snow is white. In general, the sentences of a deflationary theory of truth are of the form 1. S is true in L if and only if p. where for S, we substitute a structural description of an object language sentence13 that is a translation of the used metalanguage sentence substitu ted in for p. (Senten ces of the form of (1) satisfy Tarskis convention T.) There need be no thing that our true sent ence corresponds to in virtue of which it is tr ue, but given the work we have done in the previous chapters, we have a reasonable handle on how this sort of deflationa ry view might go in terms of the simplified characterization we have given of intensions for a formal versi on of a language like English. My hope is that a deflationary view of truth captures the correspondence intuition that a true sentence is true in part because it is about something (or so me things), but that there need be no one thing to which a true sentence corresponds in order for its truth to be guaranteed. Much later (in Chapter Twelve), we will try to fit what we have done (and hopefully will have done) in this dissertation into a larger gene ral semantical theory of the sort developed by Donald Davidson in his work on truth-theo retic semantics, and expanded upon recently by Lepore and Ludwig (2005, 2007). But to get there, I argue that we will need to have done the following: (1) Provide the form of a theory whic h gives us an acceptable notion of intension for predicate terms (which we have already done), (2) expose exactly what we are committed to given that we desire to fill into that form the details of a theory which would provide us with a sort of extensional treatment of intensions for predicate terms (we are doing this in the present 13 If is a variable ranging over sentences, then could serve as a structural description of a sentence which might be substituted for

PAGE 83

83 chapter), (3) then argue that we can make good on this theory without commitments to abstracta to which our epistemic access is dubious. (We will do this over the next few chapters.) It will be easier to do (1)-(3) if we can make use of a deflationary theory of truth. I do not intend (nor do I believe we need) to investigate co mpeting theories of truth over the course of th is dissertation, but merely make use of one that best fits our purposes. Deflationary theories of truth and the need for the conceptual priority of analyticity (intensions) to properly modal notions: For a deflationary theory of truth to provide us with knowledge of modal claims expressed as sentences of an object language for which we endeavor to provide the semantics, we must understand the meanings of the sentences of the object language for which we are trying to provide the theory. I argue that getting things right both in terms semantics and modality will require that we provide an account of understanding of the intensions of predicate terms. In order for the in terpretive truth theory (into which we shall try to situated our work) to be usable for an analysis of necessarily as a sentence operator, we must have an account of our knowledge of the intension of predicate terms. And so in this sense, we need an account of analyticity th at is conceptually prior to an account of properly modal notions. We will have such if we can give an account of epistemic access to the intensions of predicate terms, inter alia If we can do so (and there will be much more to come on this topic in Chapter 6, Chapter 7 and Chapter 8), then we can app eal to a deflationary vi ew of truth to give a univocal account of the truth of sentences of an object language which may or may not include modal operators. We endeavor to show that th ere can be truth without truth-makers, and so demonstrate that a deflationary view of modality is a viable option.

PAGE 84

84 Can Conceptual Priority be Given to Analytic ity so that an Account of Modal Semantics that is not Viciously C ircular is Possible? I hope and believe so, but there are immediate difficulties for this particular project. A careful look at and discussion of such difficulties is the goal for Chapter 5. Conceptual priority can be given to analyticity if we can show that epistemic access to intensions of predicate terms depends upon an actual ability that the speakers of a language have (i.e. conceptual mastery). We will attempt to use concept mast ery talk to show how knowledgehow can be used to build up a class of admissible interpretations if we allo w dispositions (to sort individuals according to conceptual mastery) in the base of our reduction. The resulting analysis will not be completely reductive as there may be some sort of moda l elements (i.e. fundamentally dispositional elements) in that which the semantics of the ope rator necessarily is reduced to. We shall have worked out a notion of our knowledg e of intension that is conceptu ally prior to the modal notion expressed by necessarily and we shall be in a position to see how any arbitrary de dicto modal claim is true on a conventionalist approach. All that will remain is a treatment of de re claims and quantification. Conclusion In this chapter, we have acknowledged that our reworking, clarifica tion and generalization of Carnaps sem antical systems and account of the semantics for N has not come without a price. By doing what I think ha s been some constructive reparatory work, we have uncovered a lacuna in the foundation that underlies the conve ntionalist contention th at necessity can be reduced to analyticity. To give an extensional / model-theoretic treatment of intension that is worthy of the name, we must, at least temporarily, assume that th ere are (sets of) objects picked out by the terms in the language for which we are trying to provide the semantics. Ive tried to clarify the commitments we have made by our choice of this sort of treatment in the hopes that

PAGE 85

85 each one of the commitment that are unpalatable can be dispensed with once we have made our way further down the path we will be clearing. We are in a bit of an uncomfortable position at present, but please hold tight we will work our way out of it. To carry out the project of cl earing a path for a conventionalist modal semantics, we need to show that an analytic-defla tionary account of a sentence oper ator like necessarily can be such that it is not viciously circul ar. In particular, we need to s how that a satisfactory account of analyticity can be given which does not make use of the very moda l notions that analyticity was meant to analyze. A challenge is to demonstrat e that we can ensure th at our knowledge of the intensions of predicate terms (a nd so a notion of analyticity for de dicto sentences) can be understood as conceptually prior to the moda l notions expressed by the sentence operator necessarily. Only if this concep tual priority is possible, can th ere be a conventionalist analysis that is not viciously circ ular possible. This conceptual priority is possible if we take on board a deflationary theory of truth so as to do away with a need for truth-makers (and so any sort of correspondence theory of truth). Turning to a deflat ionary theory of truth highlights the need for an account of the epistemology of the intensions of predicate terms and serves to anticipate the sort of general semantical theory that our work on the sentence operator necessarily might eventually be fit into. Indeed, c onventionalism, a deflationary theory of truth and a use theory of meaning seem to line up.

PAGE 86

86 CHAPTER 5 CIRCULARITY AND REDUCTIVE ACCOUNTS OF MODAL SEMANTICS Introduction If a reductive account of modal semantics is to be su ccessful in the sense of providing us with insight into how to understa nd the sentence operator necessarily, the account must not be viciously circular. To see this, suppose that a pr oposed account aims to explain the semantics of necessarily by reducing modal talk to some reductive base in terms of which we are to understand the truth conditions for sentences prefix ed by this operator. If, in this account, the reductive base were such that its characterization required the same sort of (or even, in fact, very similar ) modal notions as the very same which were to be accounted for to begin with, then it wouldnt be successful. It would provide only the illusion of understanding rather than any real insight. In this chapter, we explore issues to do with reduction, modality and analyticity. Our broader concern is, of course, to clear a path for an analytic-d eflationary approach to modal semantics of a conventionalist flavor. One of the prim e motivations for an approach of this sort is specifically epistemological; we wish to give an account of the senten ce operator n ecessarily which makes plain a plausible route to a speakers knowledge of modal truths. Such a promise will be honored only if we clear a path for an ac count of modal semantics that is not viciously circular. I believe that as thi ngs stood at the end of Chapter Fo ur, the danger of circularity loomed (among other dangers) for the sort of appr oach we are trying to clear the way for. What was owed to a discerning and skeptical, yet no t antagonistic critic was an account of how to characterize intension (and so sp ecifically analyticity) in terms of an extensional or modeltheoretic treatment that did not commit us to ad mitting into our ontology those individuals that we took to be in the domain of interpretation for the singular and predicate terms of the

PAGE 87

87 simplified formal language for which we were trying to provide semantics. We will provide such an account (or at least give it ou r best shot) in Chapters Six, Seven and Eight, but before we do so we must spend this chapter understanding what sort of analysis will be satisfactory for us. Unless we spend a few pages now on this back ground issue, the solution we propose in the subsequent chapters may seem deficient in that the analysis will include modal elements (more precisely elements fundamentally dispositional in nature perhaps it is an open question whether dispositions can be characterized only in terms of non-categorical pr operties), and so the analysis we wind up proposing will not reduce the modal to the non-modal. In this chapter we shall discuss other approaches to modal semantics that are specifically not deflationary. These approaches take the trut h-makers for modal clai ms seriously and admit into their ontology those things which make true modal claims. In particular, we consider David Lewis possible worlds and Armstrongs1 states of affairs. But we do so not to consider the advantages and disadvantages of these views vi s--vis an analytic-def lationary conventionalist view (even though such advantages and disadvantag es may become apparent adventitiously), but rather to highlight the problem of circularity that haunts reductive accounts of modality. By seeing how circularity can threaten these realist views, we shall be able to see more easily how it also threatens (and perhaps even more potentially devastatingly) a view of the sort we are trying to make viable. To help keep the dialectic clear, I shall say th at my hunch is that we face a deep seated difficulty in the project to understand modality if we desire each of the following (all at the same time): (1) an account of modal sema ntics that reduces the modal to the non-modal, (2) an account of modal semantics that is not viciously circul ar (in the sense that the account uses the same 1 For all references to Armstrong see (Armstrong, D., 1997).

PAGE 88

88 notion in the analysans that was meant to be analyzed in the analysandum ), (3) an account of modal semantics that makes modal truth epis temically accessible in a straightforward way without postulating that speakers have direct epistemic access to abstracta or other entities (such as Lewisian possible worlds or Ar mstrongs states of affairs) that are causally inert with respect to those speakers. I believe we cannot have an a ccount of modal semantics that satisfies each of (1)-(3) simultaneously, and I hope that my reasons for holding this view will emerge over the course of this chapter. If my reasons for beli eving so are good ones, then we can see that one who holds a view on modal semantics must give up one of (1)-(3). A proponent of the analyticdeflationary view we are trying to clear a path for must give up (1). I think that someone who holds a Lewisian possible worlds view on modal semantics must give up (3). Obviously, no one wants to give up (2). My feeling is that it is bette r to give up (1) than (3) because we do want a story about modality that makes modal knowledge possible b ecause it does seem that we have such knowledge. Some General Comments about Reduc tion, Modality and Analyticity On the face of things, difficulties of this so rt m ight seem to loom for a conventionalist approach. The conventionalism we outlined in the Ch apters Three and Four was after all to be a deflationary approach in particular we try to make sense of the sentence operator necessarily without resort to any metaphysically robust notion of modality, without even resort to the notions of concrete or abstract possibl e worlds or various relations th at might hold between Platonic properties and without reso rt to the doctrine of essentialism (that individuals have some of their properties essentially and others only contingently). The goal of a conventionalist semantics was to understand necessity as analyticity so that the sentence Necessarily, S is true just in case it is analytic that S. One might wonder if the conventionalist project we outlined in Chapter Four was

PAGE 89

89 meant to be reductive; if necessity is analyzed in terms of analyticity ( reduced to analyticity?) then one might have a further concern over whether there were circularity dangers for the conventionalist account. Specifically, if necessity is reduced to an alyticity, and if we must use the very modal notion of necessity in our char acterization of analyticity, then we might be tempted to think that we hadnt given a satisf actory analysis of nece ssity to begin with. Should We Rest Content Even If We Do Not Have a Satisfactory An alysis of Analyticity? Of course, one might argue that if we could show that we provide a satisfactory semantics of sentences of th e form Necessarily, S by evaluating the whether S was analytic whatever analyticity itself came to then we could rest content. On this view, necessity would have been reduced to analyticity on this account, and whether or not analyticity could be spelled out without modal notions similar to t hose involved in our understanding of necessity or possibility would be a separate question, to be answered in another inquiry. We might say, for example, that a sentence is analytic if it is entailed by true meaning sentences and leave it at that. I am encouraging us to press further because I be lieve that through our reworking of Carnaps treatment in Meaning and Necessity we might make a proposal about how to understand analyticity. If we do so, we may realize that our understanding of analyticity involves certain modal notions. If the modal notion involved in analyticity could be only exactly that of necessity (which wed set out to expl ain), then the conventionalist approach might be less than satisfactory. On the other hand, if there were so me modal notions involve d in the analysis of analyticity, but that these modal notions were not exactly the same as that of necessity, then our version of conventionalism might be informative, yet not complete ly reductive. That is, in the

PAGE 90

90 base upon which the semantics for sentences invo lving the sentence operato r necessarily rests might be some modal notions (like those involving certain dispositional aspects2, for example). Necessity Reduced to Analyticity Reduced to N ecessity Reduced to Analyticity R educed to Theres another problem for the analytic-deflati onary approach if it so happens that we are unable to give an analysis of analyticity without the use of exactly the same notion of necessity wed set out to give an account of. If such is the case, th en in the reductive base of analyticity sits (this same notion of) necessity, which was to be explained in terms of analyticity so it seems that theres a deep, vicious circularity in the pr oposal to use analyticity to explain necessity because we are unable to spell out analyticity itself non-circularly. It is mu ch to our advantage to make an effort to assess the prospects for anal ysis of analyticity by considering some worries over circularity in the general area of reductive accounts. These general worries over whether analytic ity can be accounted for non-circularly can be spelled out in terms of a specific issue regard ing Carnaps proposal fo r the semantics of N Briefly, whether N applies to a sentence involved which state-descriptions there are, but it seems that to determine which state-descriptions there are involves the very modal notion of what is possible (or necessary, since the two are interdefinable). Since we have reworked statedescriptions as interpretations, and based our account of analyticity on Carnaps N if modal notions must delimit that set of state-descriptio ns (which indirectly provide the semantics for N ), then since interpretations (as reworked st ate-descriptions) provide for the analysis of analyticity, if meaning notions must delimit the admissible interpretations then it looks like a 2 Since dispositions are in the reductive base, we will not analyze them. My hope is that even though it may seem that dispositions may involve a modal element, this element is not exactly that which we express with the words necessarily and possibly. Remember ou r analysis is not meant to be reduc tive, only informative. I am arguing that if we take certain dispositions as brute, then we can make a proposal for how to understand analyticity and from there we can understand the semantics of the sentence operator necessarily.

PAGE 91

91 similar sort of worry over circularity holds for our characterization of analyticity. For how do we determine which interpretations are allowed other than by using what the terms (of the language) themselves mean to delimit the class of admissible interpretations? We might simply claim that the semantic facts determine which interpretations are to be allowed. And this might be a good solution. This is essentially the strategy Carnap takes in appendix B of Meaning and Necessity when we develops the noti on of meaning postulates. He proposes that we can present the analytic conn ections that hold between predicates by endorsing postulates such as (x)(B(x) ~M(x)) where we think of B e xpressing the informal predicate is a bachelor and M expressing the informal predicate is married, and requiring that those postulates are true in every state description. (One might think of these postulates as axioms in a system of derivation for the language whose semantics Carnap develops in Meaning and Necessity were any effort taken toward spelling out such a system of derivation.) As we discussed in Chapter Four, the notion of meaning postulates goes a distance towards providing something like our intuitive notion of what we mean when we use a certain predicate on a certain occasion, but one who takes up Carnaps meaning pos tulate approach would lack resources at the disposal of one who advocated the model-theore tic approach. In particular, one who advocates the model-theoretic approach can say something about what a predicat e term like B means by way of specifying what is in the extension of B in a certain total circumstance. (Actually, we will claim something different, but equivalent, in Chapter Six a nd Chapter Seven: that we can specify if, in a certain total ci rcumstance, a certain individual fa lls in the extens ion of B or not.) We can see a particular weakne ss of Carnaps meaning postulate s approach if we consider Hilary Putnams arguments based on the Lwe nheim-Skolem Theorem in his (1980). He argues

PAGE 92

92 that by using the sort of techni ques this theorem makes available to us, we can show that any consistent countable set of sentences of first order logic is not suffi cient to ensure an the intended interpretation of the lang uage of those sentences.3 In light of Putnams initial arguments, the outlook seems bleak for Carnaps proposed meaning postulates as the basi s of an account of analyticity in the context of the modal systems developed in Meaning and Necessity But we do not need Putnams heavy-duty logical arguments and apparatus to show that Carnaps meaning postulates are not enough to secure the intended interpretation of the la nguage. Think about the situation informally in the following way. The set of sentences of an SD, together with meaning postulates, form a consistent set (S) of sentences of a first-order language, so, by the (upward and downward versions of the) Lwenheim-Skolem Theorem S can be interpreted over a model whose domain is the natural numbers Even though the sentence (x)(B(x) ~M(x))) was meant to be about the relationship of bachelors to those who are married, there is always an interpretation for them according to which, B is not interpreted as is a bachelor and M is not interpreted as is married because they are ju st interpreted as sets of natural numbers. Interestingly, neither Putnams nor our more pedestrian observation, become an immediate problem for the model-theoretic approach we develop in this dissert ation; the basis of admissibility for the interpretations (which are to be proxies for Carnaps state-descriptions) has ultimately to do with how the predicates and singular referring terms, rather than sentences, are interpreted. Requiring that the interpretation of predicate term s and singular referring terms is the operative notion will allow to us claim that th is interpretation is provided, if not for free at 3 In brief, Putnams strategy is to observe that Skolems Paradox (which arises because that the Lwenheim-Skolem theorem shows us that there can be a countable model which makes true a formal language version of the sentence the power set of the natural numbers is uncountable ) shows us that any consistent set of formal language sentences meant to express not only axioms of ZF or any other theory of sets but also to express empirical features of the world and operational constraints on how we take measurements is not enough to give us the intended interpretation of the word set, that most basic of terms, because this theory admits both of an interpretation on which all sets are constructible and of an interpretation on which there is a non-constructible set.

PAGE 93

93 least at a reduced cost, by the conceptual repert oire of competent speaker s of a natural language of which the formal language we develop here is meant to be a simplified model. Specifically, if P1 21, is to be the formal language analog of th e natural language pred icate is a tree, then whether a particular interpretation is admissi ble will depend in part upon if it makes true sentences in which P1 21 occurs given that those with concep tual mastery regarding that which is expressed by is a tree would assent to those sentences. In other words, our admissibility criterion will ultimately spelled out with the help of th e conceptual abilities of speakers competent with the predicate and singular terms, ra ther than with only the austere tool of logical consistency as applied to a set of meaning postulates together with some set of sentences meant to express empirical claims.4 Another issue, unrelated to Putnams concerns, also comes into view for the semantic facts approach. One should bear in mind that on this suggestion, semantic facts (perhaps expressed by meaning postulates) would underwrite modal clai ms (on the conventionalist approach). One might worry over what would be the ground for se mantic facts and whether this ground involved some modal element or other (just as dispositi ons might involve some modal element of other). What We Must Show for the Convention alist Analytic-D eflationary Approach Given all this, some of our time is well spent thinking about whether ce rtain approaches to modal semantics can be both reductive and informa tive. I believe that there are difficulties for approaches to modal semantics that aim to reduce the modal to the non-modal (that is, which purport to show how to understand modal semantics in terms of a non-modal reductive base in other words, a base that can be characterized without recourse to modal discourse). In order to do a satisfactory job in clearing a path for the co nventionalist position we tr y to develop, we must 4 This observation is exactly in line with Putnams at the end of his (1980).

PAGE 94

94 show that such difficulties are avoided by our approach this will involve showing that the analytic-deflationary approach doesnt attempt to reduce the modal to the non-modal. We will see more clearly the problems that we avoid by considering two reductive realist approaches to modal semantics that face problems over circularity. Three Separate, Yet Related, Projects to Investigate Mod al Semantics and Specific Difficulties Faced by Reductive Accounts Now, having said all this, let us set the stag e for our demonstration that reductive accounts of modality face serious difficu lties and that since the analyt ic-deflationary account is not (completely) reductive it need not fa ce these problems. There are at least three separate projects involved in the effort to disent angle the circularity worries over the delimitation of the class of state-descriptions or admissible interpretations and a reductive account of modality. To get a clearer sense of the project we pur sue in this chapter and in the re mainder of this dissertation, we will say a bit more about each of the th ree and use them to outline our course. The metaphysical issue The firs t has to do with the metaphysical question of how a class of state-descriptions or whatever is to play the functional role of (Leibnizs) possible worlds or (Wittgensteins5) states of affairs is to be delimited. If we held that there were real possible wo rlds, and that those could help us reductively explain the tr uth or untruth of the modal claims we were interested in, then we may be (I say should be ) concerned with the worries Shalkowski6 raises which we will get to in a few pages. 5 For all references to Wittgenst ein see (Wittgenstein, L. 1961). 6 For all references to Shalkowski see (Shalkowski, S. 1994)

PAGE 95

95 The semantic facts issue (again) The second issue has to do with an analogous concern for the anal ytic-deflationary approach : can we simply claim that semantic facts delimit for us the interpretations which were to serve as proxies for Carnaps state-descriptions, or should we try to say more about how the class of admissible interpretations is delimited? Depending on whether one takes a deflationary or a realist approach to an analys is of modality, one of these first two questions will be privileged over the other. For instance, a possible worlds theo rist (a modal realist) keen to give a reductive account of possibility would take the pressing issue to be giving a non-circular account of how to reduce modality to a completely non-modal base, that is, the class of possible worlds delimited non-modally. The metaphysical issue takes preceden ce. On the other hand, if one argued for a deflationary approach to modality in which, for exam ple, necessity is to be analyzed in terms of analyticity, then semantic issues would be more pressing. Specifically, if a linguistic community has come to use words in a certain way, so that there can be claimed to be facts about the correct (canonical) use of these words, that is, semantic facts, how do those semantic facts determine which interpretations are to be allowed? And can we explain this without appeal to modal notions? The reduction issue Now there r emains the question over whether the analysis of modality is reductive (and if so, to what extent). Is the an alysis such that the modal notio n of necessity (or alternatively possibility) is explained in terms of non-modal notions? We have already hinted that there are troubles raised for the possible worl ds theorist if he expects his an alysis to be reductive. We are now in a position to address the third issue by adverting to the following question. Can an analytic-deflationary acc ount be such that it makes use of no modal notions in the account it provides of analyticity? I believe that the anal ytic-deflationary account of analyticity for which

PAGE 96

96 we are trying to make room rests ultimately upon certain dispositions of concept possessors. I am not certain if dispositions ar e modal in nature, but they do seem such that they can be characterized only in terms of counterfactual situa tions (or subjunctive conditionals). Two Approaches to Reductive Accounts: Metaphysical Realist Approaches and AnalyticDeflationary Approaches In our ass essment of circularity worries for modal semantics, we will consider two main types of accounts of modal seman tics: metaphysical realist acc ounts and analytic-deflationary accounts. We have seen that possi ble worlds, state-descriptions a nd interpretations (of the sort we have developed in Chapter Two) are closely related; before we address each type of account specifically, I would like to demons trate explicitly that worries over circularity are a trouble for both of these two approaches. To do so, let us consider a simplif ied class of state-descriptions. Recall that each member of whic h is to represent a distinct po ssible world on Carnaps view, and that for this class of state-desc riptions there is a class of prox y interpretations. Even though this proposed class is extremely small and could never do the work that is required of the class of state-descriptions or possible worlds, by assessing it we should be able to see clearly a problem of circularity in reductive accounts of modal semantics for this small class that can be readily generalized in such as a way as to become a difficulty for the actua l class of state-descriptions or possible worlds. Let our simplified cl ass of state-descriptions be {sd1, sd2, sd3} where: 1. sd1: {~ P1 0( a0), P1 0(a1), ~ P1 1( a0), P1 1( a1), P1 2( a0) ~ P1 2( a1)} 2. sd2: { P1 0( a0), ~ P1 0( a1), P1 1( a0), ~ P1 1(a1), ~ P1 2(a0) ~ P1 2(a1)} 3. sd3: { P1 0( a0), P1 0( a1), P1 1( a0), P1 1( a1), P1 2( a0) ~P1 2( a1)} Now we have interpretations ( \1, \2, \3) corresponding to sd1 sd3: 4. \1: \1(a0) \1( P1 0), \1(a1) \1(P1 0), \1(a0) \1(P1 1), \1( a1) \1( P1 1), \1(a0) \1(P1 2), \1(a1) \1(P1 2); 5. \2: \2(a0) \2( P1 0), \2(a1) \2(P1 0), \2(a0) \2(P1 1), \2( a1) \2( P1 1), \2(a0) \2(P1 2), \2(a1) \2(P1 2);

PAGE 97

97 6. \3: \3(a0) \3( P1 0), \3(a1) \3(P1 0), \3(a0) \3(P1 1), \3( a1) \3( P1 1), \3(a0) \3(a1) \3(P1 2); And we see that there interpretations are proxies for the state-descriptions because \1(~ P1 0( a0)) = \1(~ P1 1( a0)) = \1(~ P1 2( a1)) = g \1(P1 0( a1)) = \1( P1 1( a0)) = \1(P1 1( a1)) = \1(P1 2( a0)) = g (exactly what we expect from a proxy for sd1); \2( P P1 0( a0)) = \2( P1 1( a0)) = g \2(~ P1 0( a1)) = \2(~ P1 1( a1)) = \2(~ P1 2( a0)) = \2(~ P1 2( a1)) = g (exactly what we expect from a proxy for sd2); and finally, \3(P1 0( a0)) = \3( P1 0( a1)) = \3(P1 1( a0)) = \3( P1 1( a1)) = \3(P1 2( a0)) = g \3(~ P1 2( a1)) = g (exactly what we expect from a proxy for sd3). Given this class of state-descriptions, we see that according to Carnaps view, the sentence N (~ P1 2( a1)) is true because every st ate-description (there are only three here) contains ~ P1 2( a1). Also, N ( P1 0 P1 1) is true because in each state-de scription every individual that is P1 0 is also P1 1 in other words, P1 0 and P1 1 have the same intens ion. According to our proposal for analyticity in Chapter Two, the following sentences are analytic: ~ P1 2( a1) and ( x )(P1 0( x ) P1 1( x )). It is plain to see that on Carnaps view what is necessary depends upon which statedescriptions there are. This de pendence remains even if one takes the suggestions from Chapter Four for limiting the sentences of a state-description (by making certain restrictions on the admissible interpretations that are proxies fo r the state-descriptions) because even on the assumption that the sentences of a state-descriptio n are all pairwise independent, it seems that a state-description that is not among the class of SDs might have been among. This would-be member of the class might make it the case that the truth-value of a sentence prefixed by N might change. A related point is that even on the unrealistic assu mption that the sentences of a

PAGE 98

98 state-description are pairwise independent, we do not want to allow every specifiable statedescription as that would leave nothing necessary other than identity statements such as a0 = a0, and this result runs c ounter our intuitions. Metaphysical Realist Reductive Accounts I hope we can see that in term s of this toy example that the statedescriptions there are determine respectively which sentences are with N as a prefix are true and which sentences are analytic as we have defined it in Chapter Two. This demonstration is a clear case of some much more general observations made by Shalkowski. Before we cons ider his general objection to reductive accounts of modal semantics, I would like to get out (extremely) bare bones version of two other approaches of the reductive sort: thos e of Lewis and Armstrong. Reductionist modal semantics la Le wisian possible worlds Carnap has taken his state-descriptions to represent (as well as can a formal language) Leibnizian possible worlds, and so taken at least one step away from the realist view that the possible worlds (or residents of them) are themselves the truth-makers for modal statements. The movement away from the realist position is of course a featur e of the analytic-deflationary approach of conventionalism; but one might also be tempted rather toward a metaphysical realist position as an approach to modal semantics. One pos ition in the realist sector of this particular logical space regarding m odal semantics is that of David Lewis. (Recall from Chapter Four that Lewis postulates a metaphysical multiverse which c onsists of completely distinct entire worlds (complete universes) neither spatially nor temporally re lated to each other. If we call the multiverse M then we say that for a sentence S It is possible that S iff for some member of M S is true.)

PAGE 99

99 Reductionist modal semantics la Armstrongs states of affairs Ar mstrongs approach is closer to Carnaps than Lewis. Modal semantics are explained in terms of states of affairs. In a sense, Ar mstrongs states of affairs become modal semantic proxies for possible worlds. States of affairs are in turn built by conjoining primitive states of affairs. For example, F ( a) (a is F ) represents a primitive state of affairs (as does ~ F ( a) a is not F ) such primitive states of affairs are conjoined with all others such to form maximal sets of primitive states of affairs (simply states of affairs). I understand Armstrongs approach to modal semantics as endorsing the following general principle: Possibly S is true if S is true in some state of affairs. Difficulties for Metaphysical R ealist Reductive Approaches I only m ention these approaches as they will help us see the difficulty for the analyticdeflationary approach. Shalkowskis objections: Shalkowski maintains that there are two main desiderata for an account of modal se mantics (p. 669): The first concerns the foundation or ontologi cal ground of modality: What are the truth conditions of necessary truths? The second concerns how we can come to have justified beliefs about modally qualified propositions: What is our epistemic access to necessity? An adequate theory of modality must an swer both of these questions. Neither the foundations of nor our knowledge of m odality should be an utter mystery. Given these desiderata there are (at least) two main objections to the Lewisian and Armstrongian approach. If an account of modal semantics is to be reductive then the truth of modal statements is to be ontologically grounded in non-modal facts. In this sense, the approaches of both Lewis and Armstrong are prima facie reductive attempts. Shalkowski argues that these two approaches (and reductive approaches in general) fail to satisfy both desiderata. He asserts that reduc tive accounts can fail in e ither one of two ways.

PAGE 100

100 First, if the ontological grounds of modal statements are to lack all sort of modal character (including a modal dimension in th eir characterization), then it doesnt seem that these grounds are such that they can be char acterized in a way that is satisfying from an epistemological standpoint. For example, for Lewis, the class of objects7 that provide the ground for modal statements must be such that only possibilia (as opposed to im possibilia ) are allowed as members of these objects: no obj ect can include a round square. One who takes this position faces a dilemma: either this class of objects (possible worlds) exists prior to our inves tigation of modal semantics, or our modal intuitions are taken to be prior to the characterization of the class of objects (possible worl ds). If one grabs the first horn, it is puzzling why we have any modal knowledge at all: how are we acquainted with the mysterious class of objects that are the truth-makers for our modal claims? If we grab the second horn, it seems that our intuitions of whats pos sible must somehow circumscribe the class of objects that contain the truth-make rs, and so the account is a fa ilure as a reduction because the ground cannot be specified in a way that makes no use of modal notions. What Shalkowski sees as the second failure (what I will call the bottle caps in Hackensack objection) has to do with the relevance of the ontological ground to the actual modal properties that are to be accounted for. We can put the objection in the form of a question: what is the relevance of Socrates counterpart in some possible world being a carpenter to the claim that the actual Socrates might have been a carpenter? To put a fine point on it, we could say that perhaps the collection of all the bottle caps in Hackensack (and a particular relation on these bottle caps) is (are) such that they could be used to represent exactly the class of objects 7 The objects are possible worlds. Shalkowski uses this term so as not to be prejudicial.

PAGE 101

101 (and the accessibility relation on these objects possible wo rlds) that we take to provide the ground for modal statements. Would facts about this collection of bottle caps be the ri ght sort of thing to give us information about modal statements? If all the in formation presented by the class of objects that are to provide the ground for modal semantics is presented by the bottle caps in Hackensack and the relation they bear to each othe r, then it is hard to see how the answer could be no, but it doesnt seem that we want to say that the bottle caps in Hackensack are the right sort of thing to ground our modal knowledge. Reductive Analytic-Deflationary Accounts The analytic-deflationary account w e are tryi ng to clear a way for here is not really affected by the bottle caps in Hackensack objection the interpretations that are to be the proxies for the state-descriptions are about the things of which we make modal claims. But the first of Shalkowskis objections that any hope for a reductive account which respects our epistemological desideratum is dashed because the objects that are to serve as truth-makers for modal claims must be delimited in a modal way if we are to have knowledge of possibility and necessity does apply to the anal ytic-deflationary account we have developed so far. We recall that the interpretations we constructed in Chapte r Two were to be proxies for state-descriptions; if state-descriptions are to re present possible worlds, then diffi culties for possible worlds as a reductive account of modal semantics will be di fficulties for the interp retation proxies also. The difficulty with circularity for analytic-deflationary re duction spelled out: The dependence of what is analytic upon which interpretations we allow is apparent. If it is analytic that, say, ( x )(P1 0( x ) P1 1( x )), we see that this is the case only because of the features of the interpretations we do consider. If we thought that the form al notion of analyticity we outlined in

PAGE 102

102 Chapter Two bears similarity to the noti on of truth in virtue of meaning for natural language we might be concerned for reasons parallel to Shalkowskis first objection (how to delimit and still reduce). If analyticity for a na tural language is defined in term s of a natural language analog of intension (recall an intension is a map from inte rpretations and terms to extensions), the notion seems to depend upon the (possibly arbitrary) ch oice of which interpretations there are. One might fear that the choice of which interpretatio ns we consider depends upon some intensional or modal notions. We might hold th at certain interpretations are allowed because terms so interpreted are interpreted correctly or have their usual meanings But this would be to admit as Shalkowski observes (see the quote below) that meaning is modal in nature. To use a notion (meaning) which modal in nature in the same respect as that which it is meant to explicate (modality) is clearly a specimen of the sort of vicious circularity we have admonished against. On the other hand, we might try to invoke a modal notion to say which interpretations are to be considered, but if we are to use the notion of an alyticity to analyze the modal notion of necessity then clearly this move is also viciously circular. Indeed, Shalkowski picks up on this consideration toward the e nd of his paper (p. 686): Theories framed in terms of linguistic usage automatically satisfy the possibility condition8 in an inoffensive way, but they can meet the exhaus tiveness constraint9 only by admitting that meaning is modal in nature, since there obviously could be more linguistic conventions than there are. That an expressi on means what it does involves not merely the fact that the expression has been or is being used in certain ways but also the fact that it is permissible to use it in novel circumstances in some limited ways. That meaning is projectible, but restricted, is ju st the fact that it is possible to use the expression in certain ways and not in others and still accord with the conventions of a given language. Expressions with the same previous usage but different projections ont o novel cases differ 8 Endorsing only those modal claims that we hold pre-philosophically to be true. 9 Endorsing all those modal claims that we hold pre-philosophically to be true.

PAGE 103

103 in meaning. Thus, the story of meaning is, in the final analysis, a m odal story and not the proper basis for the foundations of modality.10 If we wish to explain the natural language sentential operator necessarily in terms of analyticity, then the dependence of the allo wed interpretations upon the modal notion of possibility might seem to pose a pr oblem. We set out to analyze n ecessarily in terms of what is analytic, yet if the notio n of possibility (or the interdefinable notion of necessity ) is required to explain analyticity, then we are using the notion of necessity to analyze the operator necessarily. Our efforts would have led us in a circle, and we wouldnt know more than when we started. In sum, the circularity comes if we assume if we expect meaning to be both defined in terms of the admissible interpretations and to delimit what the admissible interpretations are. Conclusion Shalkowski m akes a strong case that accounts of modal semantics cannot be both reductive and satisfactory in terms of epistemology, and they persuade me. But he s uggests also that what he calls theories framed in linguistic usage are not of the right sort to provide a proper basis for the foundations of modality, an d I do not agree with this point. I want to finish this chapter with a coda that recalls the a ssertion I made in the introduction. Recall that I claimed that one who held a coherent view of moda l semantics could not take that view to be (simultaneously) (1) an account of modal semantics that reduces the m odal to the non-modal, (2) an account of modal semantics that is not viciously ci rcular (in the sense that the acc ount uses the same notion in the analysans that was meant to be analyzed in the analysandum ), (3) an account of modal semantics that makes modal truth epistemically accessible in a straightforward way without postulating that 10 Of course, I disagree with the last sentence of this quote but I think the source of this disagreement is that Shalkowski seems to hold on independent grounds that me taphysically realist approaches to modality (what we might call modal semantics) are preferable to deflationary approaches. Also, Kirk Ludwig observes that some of the bite could be removed from Shalkowskis criticism if the meaning of terms is fixed by communal intensions with respect to the use by members of the community of those terms.

PAGE 104

104 speakers have direct epistemic access to abstracta or other entities (suc h as Lewisian possible worlds or Armstrongs states of affairs) that are physically causally inert with respect to those speakers. Perhaps the reasons the mutual incompa tibility of (1)(3) have become clearer in our rehearsal of Shalkowskis arguments. I hope so, but in case they havent I would like to try once again to show the incompatibility of these thr ee desiderata. It will help things to recall and reconsider some of the ground we covered in Chapter Four. Recall that we suggested there that accounts of modal semantics that we re specifically not deflationary, i.e. accounts that took modal objects seriously such as Lewisian possible worlds, Platonic properties residing above the great line of being and the like, were such as to be compatible, in a very easy and natural way, with a correspondence theory of truth. According to one of these views, the sentence expre ssing a modal claim is true because it corresponds to something either a feature of some possible worl d or the relations of some Platonic properties. Given a correspondence theory of truth we can re asonably talk about the truth-makers for modal claims. If a non-deflationary view of modality is to avoid vicious circularity (the use of identical modal notions in analysans and analysandum ), then no modal characterization of which possible worlds are to be allowed or which relations among Platonic pr operties are to be allowed is possible, otherwise the account is viciously circular. For example, if one claims that there is no possible world in which time runs backwards beca use it is simply not possible that time can run backward, then the use of possible worlds as a reductive base of modality is viciously circular. Possible worlds must be conceptually prior to m odality on this view; the same goes for Platonic properties or states of affairs. Now, the truth-makers for modal claims ca nnot bear any physical causal relation to the speakers who utter sentences that express those claims at least on the Lewisian approach or the

PAGE 105

105 Platonic properties approach. On the former, tw o worlds can be distinct only if they are completely spatio-temporally distinct from one a nother. On the latter b ecause Platonic properties would drop below the great line of being if they bore any physical causal relation to any physical thing and theyd cease to be the right sort of things to be the basis for modality. But a thinker might nevertheless have epistemic access to these truth-makers, but only if that thinker had perceptual abilities that outstrippe d any of the five senses, that is apprehension of those things which have no physical presence in the universe in which the thinker exists. On the other hand, if one takes a deflationary view (most likely an analytic-deflationary conventionalist view), then one holds that moda l truths are epistemically accessible because on this view sentences which expre ss modal truths are just sentences which are analytic or whose truth can be shown to follow from an analytic sentence. So according to my thesis that it is not the case that each of (1)-(3) can be satisfied and if we do not want our analysis to be viciously circular, we must give up th e view that the modal can be reduced to the non-modal. Why? Consider what would happen if on the analytic-deflationary view, the modal were reduced to the non-modal. Doing so would mean that there was no modal dimension at all to the class of admissible interpretations, but rather that the class of admissible interpretations was considered primitive and prior to any conceptual abil ity had by users of a language. I ar gue that there are two ways we might understand the class of admi ssible interpretations as prior to any modal notions, both of which are unacceptable for us if we are partial to a parsimonious approach to modality which makes for a workable epistemology. The first way: to take seriously the class of admissible interpretations, we must admit into our ontology a class of domains of interpre tation each of which includes the members

PAGE 106

106 (individuals) of the domain of interpretation. On th is first way of doing things, we must admit the members of each domain of interpretation into our ontology because the admissible interpretations were to be such that they sp elled out in an extensi onal manner the notion of intension for predicate terms. If we try to reduce the modal (nece ssity) to the non-modal (a set of interpretations11 that is specified with no recourse th e words necessity, p ossibility or the notions underwriting our unde rstanding of these term s), then at a minimum we must be able to appeal to the supposed reductive base. That is, we mu st be able to claim that there are, in fact, those things to which we have reduced the moda l. Carnaps original suggestion could not quite carry this project out, unless ther e was some prior grasp of the inte nsions of the predicate terms, which, of course, seemed impossible given that pr oviding this notion of intension seemed to be at least a secondary goal of Carn aps work. To follow through with the first suggestion, we must in effect claim that there is something like a class of possible worlds (or at least a class of things one for each admissible interpretation which is described in exhaustive detail by that interpretation). To do so, there can be no appeal to our prior held conceptions of necessity and possibility, and so no epistemic access is guarant eed to the domains of each interpretation, as they are in no way in causal interaction with us (If they were they would be disqualified as candidates for modal features, as they would be part of the actual physical world.) The second way: we could claim that the ranges of interpretations are sets (perhaps pure sets or sets of natural numbers) and then introduce another function (a so-called embedding function) which takes elements of those sets to individuals in the worl d. Such a strategy would, prima facie make a commitment only to sets qua abstracta and would have the added virtue of 11 Interpretations in this sense are simply functions from one set (say Dom) to another set (say Rng). To have the proper sort of understanding of such functions, we must co mmit to the existence of the elements of the sets Dom and Rng.

PAGE 107

107 being a proposal for providing the intended inte rpretation of a modal la nguage with a decidedly actualist flavor (as only those individuals in the actual world are candidates for falling in the extension of a predicate). This sort of strategy is that taken by Christophe r Menzel as explicated and adapted with a slight nominalizing modification by Greg Ray12. I believe that this sort of approach either doesnt make modality completely epistemically available (on Menzels original approach) or is if not viciousl y, at least perceptibly less than virtuously, circ ular (on Rays adapted approach). Let me say briefly why. To make sure that predicate te rms are such that they have the same meaning across each interpretation, Menzel argues th at each particular predicate term must be mapped to a single relation-in-int ension and then embedd ed into the world. Ray changes things up a bit by observing that the m eaning of predicate terms can be accounted for essentially pragmatically so there neednt be a ny requirement for Menzels use of the notion of relations-in-intension as far as the argu ments master structure is concerned. On Menzels approach, establishing the in tended interpretation of a modal language depends upon our commitment to a class of rela tions in intension that can only be understood on the model of Platonic properties. Since these relations in intension are to be an essential part of the non-reductive base to which modal semantic s is reduced and can bear no physical causal relation to us, we are not guaranteed epistemic acce ss to modal truths on this approach. On Rays adaptation, the intended interp retation of a modal language is essentially grounded on a explanatorily prior, pragmatically explicated, not ion of knowledge of meani ngs or intensions of predicate terms. Ive argued that meaning is essentia lly modal (or at least dispositional) in nature and that something like a class of possible worlds (class of admissi ble interpretations) is need to make sense of it. If this is right then Rays analysis is subtly but undeniably circular at worst and 12 For all references to Greg Ray see (Ray, G., 1996).

PAGE 108

108 less informative than it could be, at best. I argue that it is much better to use an analog of the class of possible worlds a cla ss of admissible interpretations to explain meaning (and so let it be that meaning is conceptually prior to modality ) and then show how modality can fall out of meaning. We shall pursue this topic fu rther in Chapters Seven and Eight.

PAGE 109

109 CHAPTER 6 LOGICAL MANIPULATION OF THE INTE RPRETATION FUNCTIONS IN PREPARATION FOR A TREATMENT OF TH E ADMISSIBILITY CRITERIA IN TERMS OF CONCEPTS Introduction This short c hapter is essentially a warm-up for what comes later in Chapter Seven. To focus the warm-up, we should recall that we are s till under the threat of ci rcularity and still under threat of ontological commitment to the ranges of each interpretation in the class of admissible interpretations. We will address these difficulties in Chapters Seven, Eight and Nine. To be in a position to do so, we must carry out a bit of l ogical manipulation of th e functions which model our meaning notions which we used to generalize Carnaps treatment. Beginning a Response to the Question over Circularity: T he Admissibility Criteria for Interpretations Must Be Presented by Way of How the Extensions of Terms Are Specified. Let us take a few paragraphs to develop some notions closely related to intensions as we defined them in Chapter Two. Our development may help assuage worries over the circularity problem for the analytic-deflationary account we have just canvassed. We have defined interpretations as maps from singular terms and predicate terms to individuals and sets of individuals in a domain of discourse.1 These interpretations were to be proxies for statedescriptions and so were taken to be a set-theoretic way of specifying the more general notion of intension a function from terms and interpretations to extensions Essentially, intensions were functions created by stitching t ogether various interpretations: the intension of a term was a function from interpretations to ex tensions (themselves a part of th e domain of discourse of these interpretations) such that for an arbitrary interpretati on, the intension assign ed the extension of that term in the interpretation to that interpretation. In specific terms, the intension of is the 1 Interpretations are defined over sentences of the formal language also, but I dont consider this part of the their domain here.

PAGE 110

110 map that assigns the set of all that is under interpretation \ to the interpretation \. So in the way it was constructed, the map I was defined in terms of the various interpretations of {\ }. If we could provide intensions in a direct way in a manner not dependent on the individual interpretations stitched together to form inte nsions then we coul d use the collection of intensions for each of the terms of our language to create the in terpretations themselves, and so use these intensions to define proxies for state-descriptions.2 We might do this in the following way. Recall from Chapter 3 (18)(20) that intensi on was a map from interpretations and terms to individuals or sets of individua ls. Clearly, calling such a function an intension was prejudicial, but helpful to understand what the function I is actually meant to do. In the following, since we know which notion I was meant to capture, we will not use the word intension but rather make use of only various formal devices. So consider the function named I defined in the following way with assistance from I (where represents the domain of discourse of interpretation \ and represents where is an index set for the interpretations): 1. I : {0,1} s.t. for and I ( ) = 1 iff I(\, ) (=\( )) = 2. I : 1 {0,1} s.t. for and 1, I ( ) = 1 iff \( ) = I(\, ). 3. I : nn {0,1} s.t. for d n and n n, I ( ,d, ) = 1 iff d \( n) = I(\, ). Essentially, I is a map from interpretations, a super domain of discourse and (singular and predicate) terms to yes (1) and no (0) that in dicates which individuals of those domains either (1) are the denotatum of the singular term or (2) fall under the predicate expressed by the predicate term in question. 2 If we then assumed that the sentences of natural lang uage are compositional in nature the assumption that a sentences semantic value (roughly meaning ) is dependent upon the semantic values of its constituent parts (their meanings ) and their mode of combination, then we might be able to determine quite generally the intensions of sentences as those interpretations on which the sentences were true.

PAGE 111

111 At first blush, one may wonder why the domain of I needs to be { } {1} rather than just { } {1}. In particular, why must one dimension of I be a particular interpretation whose index is a member of ? The short answer is that I is to capture all the information present in \ for each if we consider the restriction of I to { } { 1} for a specific then exactly when I ( ) = 1 is \( ) and exactly when I ( ) = 1 is =\( ) and so, with this restriction, does I present the same information as is presented by \. A more intuitive answer is that \ was to be a proxy for a stat e-description (which was in turn to represent a possible world) and so I must have capability to represent each of those proxies. To elaborate a bit, if we have the individuals, 0, 1, 2, then given the singular term and one-place predicate term 1, I indicates that, gi ven that each of 0, 1, 2, are part of the same situation or scenario (that is, they were to be part of the same proxy for a state-description), which of 0, 1, 2, is the designation of and which fall under the extension of For instance, if, in the situation (call it ) and I ( 0, ) = 1 and I ( 0, ) = 0, then 0 is in and the individual (object) 0 is in the extension of but is not the individual (object) designated by In this way, we can specify the quality of situation in terms of distributions of properties and relations across objects and indications of which objects are the designata of singular referring terms if we are provid ed with a domain of individual objects to begin with. Finally, we can attempt to s how how certain features of I might be used to construct interpretations and how these features of I might be used to allow and disallow certain interpretations (and so lead to a class of admissible interpretations). I might be such that, for

PAGE 112

112 instance, from I ( 0, )=1, it follows that I ( 1, )=0 or that from I ( 0, )=1, it follows that I ( 1, )=0 or from I ( 0, )=1, it follows that I ( 1, )=1 or from (I ( 0, )=1 together with I ( 1, ) = 1) it follows that I ( 2, ) = 0 or any other number of complicated relationships between certain values of I In this most general way, we see that by providing I with a certain structure (or in other words, rest ricting it in certain ways) makes it the case that only certain interpretations are allowe d given that the restrictions on I are restrictions on I and that together with the domain for each interpretation of {\ }, I can completely determine the behavior of each of \ for .3 Given (= ) we can directly constr uct interpretations given I : we first simply choose a subset of and then choose an interpretation whose range is a countable subset of 2 (the set that is the union of and the set of subsets of ) in accordance with the restriction imposed by I (and so by I).4 According to this strategy, the allowed or admissible interpretations are those whose ranges are chosen from and whose assignments of memb ers and sets of members of those ranges to singular and predicate terms do not contradict the features or restrictions placed (by whatever means) on I Of course, to make the whole strategy plausible, we must produce a reasonable way to stru cture and restrict I this project will be taken up in Chapter Seven. After we do some work to provide a way to understand I we will be able to say more about how we might go about restricting I and we will be able to sa y a bit more about how to 3 Recall also that there were already some consistency re strictions (see Chapter Two, the sections entitled and An Interpretation can Provide Extension Two Concerns for Interpretations -as-Proxies-for-St ate-DescriptionsApproach and Admissible Interpre tations for details) on each of \ these restrictions ar e naturally preserved by the structure and restrictions on I 4 Actually a countable subset of { 2 22 23 .} to handle generally n -place predicates, but we will just deal with one-place predicat es for discussion here.

PAGE 113

113 understand the domain of I Hopefully, after some very basic and fairly non-committal work with concepts, we will be able to demystify this function. Conclusion In this brief chapter, we have put ourselves in a position to address som e of the concerns raised in Chapters Four and Five by providing the technical apparatus to encode each of the admissible interpretations in a single function I We can transition between I I and \ in the perfectly straightforward way spelled out in Chap ter 3 (18)(20) and (1)(3) of this chapter. Since we will be able to make transitions of this sort between I I and \, in the following, we may spell out our technical developments with an y of these three technical devices (most likely in terms of either I or \). Recall that we seek the even tual goal of underwriting the criteria for admissibility of interpretations in terms of conceptual possessio n (or conceptual mastery). How has our technical development of the relevant notions helped us in doing this? On one way of thinking about concepts, we might consider one who has concep tual mastery with the concept expressed by the predicate to have the ability to sort those things which are called from those things which are not called With I we give the same information presented by {\ } in such a form that one who has I can immediately and directly read off whether an individual, in a certain universe as described by an interpretation falls under a certain predicat e or not. There still should be a bit of concern over circularity b ecause we are still using the notion of an interpretation (state-description proxy) to give the meaning or intension of a predicate term. Specifically, the function I is to be used as a sortal for which individuals fall under a certain predicate, but the function I does so by using a class of interpretations which can we can only make sense of if we can somehow give the m eaning or intension (even in terms of sorting

PAGE 114

114 ability) of predicate terms directly. We shall try to do this in Chapter Seven. In particular, we use Christopher Peacockes5 study of concepts to show how we might provide a base level grounding for the sorting ability that conceptual mastery come s to without recourse to specifically linguistic knowledge-that. Using concepts in this manner will go some way toward soothing our fears over ontological commitments made in our model-theoretic rework ing and generalization of Carnaps semantical systems. Conceptual mastery might be char acterized as a dispositional ability: one has conceptual mastery regarding the predicate just in case one is disp osed, in the right conditions, to sort s from nons. Of course this characterization is rough, ready and most likely circular, but it is enough to point us in the directi on we will be heading in Chapter Seven. The characterization is circular because I which is to be an account of the meaning or intension of a predicate term, does so only by tak ing as input indices of interp retations which themselves are to be proxies for SDs which are supposed to be descriptions of complete universes in which predicate terms are used to pick out extensions in those described uni verses with the usual meaning. Yet still I argue that with I we have gotten something cl ose to the right form to characterize conceptual mastery: I is a function which takes as parameters a predicate term, an individual and an interpretation i ndex and returns essentia lly yes or no (1 or 0). The output is of the right sort for a function to characterize a disposition to sort in dividuals; but we are still left with the fact that I operates on a domain of individuals in order to dispense with the ontological commitment we have incurre d we must explain how to understand I without a commitment to such individuals. We try presently to do so by review of a fairly noncontroversial position on concepts (Peacockes). One interesting development for this chapter 5 For all references to Christopher Peacocke, see (Peacocke, C., 1992).

PAGE 115

115 and all subsequent is the relativ e closeness of the sort of theo ry that used to provide the conceptual backing for our proposal for th e intension of predicate terms and the general semantical theorya compositional theory of meaninginto which we will much later try to situate our work. The notion of concept position we need to make our generalization of Carnap work in some sense depends upon the features of what are prerequis ite to understanding a language on a particular view of meaning. My hope is that it will be comforting to see that the use of a conservative compositiona l theory of meaning very nicely lines up with the sort of model-theoretic update and genera lization we have provided of Carnaps work. I remain hopeful as well that we might go some distance toward responding on Davidson s behalf to Dummetts criticism that a theory of meaning should be a theory of understanding. (M y hope is that we are filling in the very place where Du mmett pointed out what may have been understood as a lacuna in Davidsons work.)

PAGE 116

116 CHAPTER 7 CONCEPTS UNDERSTOOD IN A PARTICULAR WAY AS THAT WHICH UNDE RWRITES I AND MAKES IT EPISTEMICALLY PERSPICUOUS Introduction In this chapter, we try to show how the m ap I which, if we have been convincing in Chapter Six, was of the right form to be what gives a rough an d formal characterization of intension of predicate terms, might be underwritten by a fairly uncontroversial view of concept possession. I shall present the case as using concept talk to underwrite meaning talk By way of introduction, I should say what so rt of concepts I have in mind for the underwriting process. It should be no surprise that we have in mind exactly those concepts whatever we eventually come to settle on fo r what the word concept means which are expressed by predicate terms. For example, the concept expressed by the predicate is a tree or is alive are the sort that we will claim underwrites our use of I There are surely concepts that are grasped when one knows the meaning of the terms addition, inflation and transcendence, but these are not the sort of concep ts we shall discuss in this chapter. Perhaps, in the fullness of time and in the ripeness of philos ophical investigation one might propose how to understand the meanings of such terms in terms of concept possessi on or possession of a number of concepts which bear particular (conceptual) relations to one another, but we will not do so here. We were set in motion in Chapte r Three by the wish to update and generalize Carnaps semantical systems in the service of attempting to use his work in modality to provide an analysis of the sentence opera tor necessarily. Carnaps SDs are meant to describe possible worlds in terms of some set of basic predicat e terms. We do not have in mind something aimed at the foundations of physics quite as much as Carnaps work was, but nevertheless we are trying to give an account of the intensi ons of predicate terms for those terms that could be used to give

PAGE 117

117 a bear-bones description of a possi ble world. It might be that in the description of a possible world, one need not resort to term s like inflation or adjudicati on, but the application of those terms might be appropriate when speaking of the possible world that has been described in more basic terms. Indeed, such an outcome is one promise of the philosophical method of conceptual analysis: given that we describe a possible wo rld in which people engage in such-and-such trading behavior with each othe r and use thus-and-such a currency to trade with, and if the situation arises in that world in which more a nd more currency is paid out and more and more currency is required for trades th at required much less currency before, then we can claim in that possible world that for those economies in which tr ading has been thusly affected that there is inflation. Our claim is made possible because we can hope to give a conceptual analysis of that which is expressed by the term inflation. So our job here should be only to show how certain basic terms can be underwritten w ith concepts of a certain form. I have spent a fair amount of time worrying abou t the threats of circularity for an analyticdeflationary conventionalist account of modal sema ntics and the threat of a commitment to the existence of truth-makers for modal claims, for example a commitment to entities like Lewisian possible worlds, Platonic properties qua abstracta etc. My hope is that in this chapter we can show that a view of concept possession can simultaneously ea se both of these worries. My fear is that the way in which this view of concept po ssession allays these worries will be unacceptable given the usual demands on an account of modal semantics. Worries over circularity will be eased because our explications of the intensions of predicate terms will be grounded out in the dispositions of concept possessors, underst ood as a sort of knowledge-how instead of knowledge-that, rather than in a ground that is characterized only in strictly speaking modal terms, such expressed by necessarily or possibly. Our strategy for a treatment of the modal

PAGE 118

118 might be given schematically with the following where e is interpreted as explicated in terms of: 1. Modal Terms e Intensions of Predicate Terms e Dispositions of Concept Possessors It is true enough that dispositions might be moda l in nature, but the notion expressed by the term necessarily is not identical to the notion of a disposition. The two are no doubt conceptually connected, but I believe that we can gain insight and understanding into the former with the use of the latter and that we can have an intuitive, pre-theoretical understand ing of the latter because it seems that we are possessors of concepts, give n that we are disposed to sort individuals correctly into, say, tables and non-tables (and so have the concept expressed by the predicate is a table1). In sum, it seems to me that claiming that we, as speakers, do have a capacity for sorting which can be reasonably characterized in a normative fashion is entirely plausible. Indeed, radical skeptical scenarios aside, one woul d have to be irrational to deny that we can and do make judgments about whether certain individuals fall under ce rtain predicates or not and speak intelligently and intelligib ly with each other about whether these individuals do so fall and for the most part agree about our judgments. If we can proceed from this unobjectionable assumption, codified as concept possession and then explain the semantics for modal claims, then we have made progress. 1 Kirk Ludwig observes that if for a conc ept expressed by the predicate (say) is C1 then if there is another concept expressed by the predicate is C2, and the extension of is C1 is the same as the extension of is C2 in all actual an counterfactual situations, then the ability to sort what is C1 from what is not C1 and the ability to sort what is C2 from what is not C2 is not enough fix precisely the concept deployed. For one could be deploying in this circumstance either C1 or C2. This observation is not merely formal as i s triangular and is trilateral are two such concepts. We see that there is more to be said about th ese two concepts in particular and about necessarily coextensive concepts in general once we realize that is trian gular and is trilateral do not appear to be basic. Are there basic concepts which are necessarily co-extensive? Perhaps, and an investigation into whether there are or not may be an interesting project in its own right, but for our purposes in this dissertation, we need not concern ourselves with this problem. All we need for the conventiona list thesis is that to grasp a concept is to have some certain knowledge-how concerning the ability to sort individuals.

PAGE 119

119 Because concept possession is a dispositional characteristic, we see how to ease any worries over the sort of ontological commitment I had asserted might be required to make sense of the model-theoretic update of Carnap. We had been worried that to give an extensional account of the intensions of predicate terms, ther e must be objects that are members of the sets that predicate terms were mapped to. We shall see here that a commitment to these objects is not required if we claim that to po ssess a concept is to be disposed to make a certain kinds of assertions about individuals be they actually presented or presented only by a certain mode of presentation in thought of representation strictly in thought. Of course, there may be worries over the commitments we are forced into to make sense of the similarities of individuals one to another or the similaritie s of modes of presentatio n of individuals (or of entire scenarios) one to another. Would we be committed to the notion of sets qua abstracta in this case? I am not certain, but I do hope and believe that worries over the ontolo gical commitment required to account for similarities of these sorts is a differe nt issue and one that might become less pressing once we realize that we are able to characterize, and speak ab out, similarities of individuals and modes of presentations of indi viduals. One guiding principle for the sort of approach we are trying to clear the path for in this dissertation is that we engage in a sort of bottom up strategy for explaining modal semantics. That is, we star t by taking for granted abilities we actually have and then showing how we can use an understanding of those abilities to gi ve an explication of the semantics for necessarily. This approach is opposed to what I call the scientific method approach to philosophizing which I discus in Ch apter Nine, and which I think is a method that does not give satisfactory result s, as following it has led many in to countenancing a robust notion of metaphysical necessity.

PAGE 120

120 To follow through on the promise of starti ng from the bottom up, I believe we must ultimately move toward a use theory of m eaning. When making a non-modal claim in which some aspect of the world is reported to be a certain way, such as when I say, It is not raining anywhere in Gainesville, FL at 3:04PM Thursday May 15, 2008 such a claim is true just in case it is not raining anywhere in Gainesville, FL at 3:04 Thursday, May 15, 2008 and so in this sense the claim is made true by a correspondence w ith some aspect of the world. To conclude on the basis of this reasoning that a modal claim such as the one expressed by Necessarily, all green tetrahedrons are te trahedrons, is true because it corr esponds to some situation obtaining in all possible worlds (for example) is to partake in a sort of infe rence to the best explanation. One who takes this sort of line has assumed from the sort of correspondence that makes true nonmodal claims together with the assumption that th is modal claim is true (and so there are some true modal claims) that there must be somethi ng to which the true modal claims correspond and in that correspondence lies the truth of those modal claims. I argue that such an approach is not the right sort of approach to take. Rather we ha ve tried to, and shall continue to try to build a theory of modal semantics (or at least provide the form of such a theory) out of basic primitives. We have tried to build up the theory rather than proceeding as the correspondence theorists do in the fashion of the scientific method. To make progress, we mu st abandon any sort of reliance on the correspondence theory of truth and indeed turn our backs on this sort of scientific method philosophizing. More on this in Chapter Nine. Finally, we shall notice a co mfortable snugness with which our proposed underwriting of meanings with concepts fits with another much more comprehens ive, broad reaching and general project in the philosoph y of language that of general se mantical theory, specifically an interpretive truth theory as compositional meaning th eory. We try to use talk of concepts of the

PAGE 121

121 sort that might be expressed by predicates (is blue or is a house) to underwrite the function I that was to provide directly the intensions of predicate terms. It seems reasonable to hold that there are at least some prerequisites to having a c onceptual repertoire at all: one must have some sort of prior conceptu alizing capacity to have any c oncepts of this sort at all. It is interesting that all the prerequisite conceptual izing capacity would be had by one who possessed a language. In other words, one who understands a language has enough conceptualizing power to have satisfied the conditions for the having of the con cepts that are those that underwrite the intension of the predicate terms we have been so concerne d about. This is interesting because much later, when we try to fit our work into a larger projec t of general semantical th eories, the most natural candidate will be an interpretive truth theory as compositional mean theory. (And, I think, that for one who holds a Davidsonian interpretative truth theory as a compositional meaning theory, the sort of approach to modal se mantics that we have tried to cl ear the way for here is the best candidate for providing an analysis of the sentence operator necessa rily in the context of that meaning theory.) On this sort of compositio nal meaning theory, one who knows a language already has enough conceptual ability and material to be in a position to have the sort of concepts that underwrite meanings. The analysis of necessarily we have been undertaking here and the interpretive truth theory (and the deflationary theory of truth) line up together nicely, and, I would argue, this lining up is further evidence that an analytic-deflationary conventionalist approach to modal semantics is a viable one. Concepts But we m ust return to the situation on the ground as we left it at the end of Chapter Six. Do we have a reasonable way to structure / restrict I while at the same time making the case that we incur no ontological commitment to elements in the ranges of each of the admissible

PAGE 122

122 interpretations? I think we do and I believe the way we can do this ( no surprise here) is to appeal to concepts as expressing a dispositional sorting ability. We Shall Attempt to Underwrite Meaning Talk with Concept Talk We take the uncontroversial view that a speak ers linguistic com peten ce with the predicate term is underwritten by the grasping of the concept expressed by and his knowledge that the predicate term expresses the c oncept in question. I begin by cons idering a view of Christopher Peacocke and then continue by trying to adapt th at view for my specific purposes. Then I address the foundational issue concerning what sort of cognitive abili ties a thinker must possess to grasp any concepts at all. Fina lly, I assess whether being able to speak and understand a language gives a speaker enough cognitive material to be in a pos ition to have concepts. Making use of a traditional view: a predicate expresses a concept under which things having a certain property are judged to fall by one who has the concept in question We understand what is m eant by concept in the way suggested by Christopher Peacocke toward the beginning of his A Study of Concepts On pages 7 8, Peacocke gives the possession conditions for the concept red. The concept red is the concept C to possess which a thinker must meet these conditions: 1. He must be disposed to believe a conten t that consists of a singular perceptualdemonstrative mode of presentation m in predicational combination with C when the perceptual experience which makes m av ailable presents its object in a red region of the subjects visual field and does so in conditi ons he takes to be normal, and when in addition he takes his perceptual mechanisms to be working properly. The thinker must also be disposed to form the belief for the reason that the object is so presented. 2. The thinker must be dispos ed to believe any content of any singular mode of presentation k not meeting all the conditions on m in (1) when he takes its object to have the primary quality ground (if any) of the dis position of the objects to cause the sort of experiences of the sort mentioned in (1). To give a gloss on Peacockes treatment of the possession conditions for the concept of red, we must begin by noticing that the concept in question is certainly a perceptual one. To spell

PAGE 123

123 out the possession conditions of red Peacocke makes use of C as a variable that includes the concept red in its range red could have been used, but the use of C highlights that the account is not circular. Even though red is the present in (1) and (2), it designates something other than what is picked out by red, namely red picks out a certain phenomenal property or sensation that is caused by red objects on normally functioning perceptual mechanisms in normal conditions. Now according to (1), the thinker (let us call him Thomas for convenience), if hes to possess C, must be disposed to believe a propos ition (or content) that consists of a singular perceptual-demonstrative mode of presentation m such that m is C when the perceptual experience which makes m availabl e presents its object in a red region of the subjects visual field in normal conditions. What does this m ean? If Thomas possesses C, then when he is presented (when he takes himself to be in norma l conditions and his perceptual system to be working normally) with an object that causes red se nsations, then Thomas will come to believe a certain proposition or content. What is the conten t? The content consists of a visual presentation m that is a mode of presentation of the object in question in predicationa l combination with C, roughly that expressed by the se ntence that which is presented by m is C. The content is a perceptual-demonstrative mode of presentation because a specific object is picked out (or demonstrated) the mode of presentation is of a specific object and, of course, the content is perceptual in that it is visual. When will Thomas come to believe such a content? Exactly when the perceptual experience he has which is the mode of presentation of m is such that it presents m in a red (again red represents the phenomenal property wh ich sensations as of those caused by red things in normal conditions) pa rt of the visual field. Furtherm ore, Thomas must form those beliefs about the object presented by m because of the character of m. (It is not entirely explicit in Peacockes presentation whet her with m he intends to indicate a kind of mode of

PAGE 124

124 presentation or whether he means m and k to be used as variables which are to range over modes of presentation all of a certain kind. He does seem to use m to indicate a mode of presentation of a certain kind a perceptual-demonstrative mode of presentation but it is implicit that there might be another mode of presentati on of the same kind, call it m which is such that Thomas is not disposed to believe the si ngular content expressed by m in predicational combination with C. Similarly for k and k of the same kind, but different in that Thomas is not disposed to believe that si ngular content expressed by k in predicational combination with C.) But (1) characterizes only the aspect of possessing the concept that accounts for instances when Thomas is actually pres ented with a red object. Thomas must also be able to make certain judgments about red things when those things are not visually presented to him or are so in other than normal conditions. In such cases, according to (2), if Thomas is disposed to belie ve propositions or contents consisting roughly of k is C (where k is any singular mode of presentation not meeting all the conditions on m) if k is of an object which he takes to have the primary quality ground that makes such that it would satisfy (1) if it were presented in the manner outlined in (1). In othe r words, if Thomas is somehow presented with an objec t or represents an object to himself (perhaps even in conversation, remembering or in some other refl ection or imagination), then if the manner of presentation of the object is k and the object pr esented by k is such that Thomas believes the object to have the feature or qual ity that makes it the case that an object which has that feature or quality appears to be red in normal conditions, Th omas will be disposed to judge warrantedly k to fall under C. Conversely, if Thomas is presented with an object or represents an object to himself and the manner of presentation of the obj ect is k and the object presented by k is such that Thomas does not believe the object to have th e feature or quality that makes it the case that

PAGE 125

125 an object which has that feature or quality appears to be red in normal conditions, Thomas will be disposed to judge warrantedly k not to fall under C, even if the object does have the feature or quality that would cause it to appear red in normal conditions. Peacocke provides us with a prima facie non-circular, worked-through analysis for the possession of the concept red. A first thing to notice is that possessing C gives Thomas at a minimum the ability to distinguish (o r sort) thing he believes to be red things from things that he does not believe to be red in actual (clause (1)) and counterfa ctual (clause (2)) circumstances (given that hes not mistaken or in error) in that possessing the concept C disposes Thomas to judge warrantedly that an object presented by m or k is C given that Thomas believes that the object presented by m causes a deployment of red with respect to m or that Thomas believes the object presented by k has the feature or quality th at makes it the case that such as object would cause a deployment of red in appropriate circumstances. If an object is presented by a mode of presentation m (of the same type as m but such as to be different from m with regard to the appropriate respect on the basis of which Thomas in is an epistemic position to judge that which is presented by m to be C) such that m does not meet condition (1) or k (of the same type as k but such as to be different from m with regard to the appropriate respect on the basis of which Thomas is in an epistemic position to judge that which is presented by k to be C) such that k does not meet condition (2), then Thomas would be di sposed to withhold the judgment that the object presented by m or k is C given his beliefs about that which is presented by m or k Now, with Peacockes analysis as a model, I w ould like to try to sketch very briefly some general conditions on concept pos session (or conceptual mastery). But first, I will offer a few general words about the notion of concept as I use it here. The related notions of concept, concept possession and conceptual mastery ar e inextricably bound up with the notion of

PAGE 126

126 judgment (by a cognizer who possesses the appropria te concept or has ap propriate conceptual mastery). In particular, I claim that one who (alternately) posse sses the concept expressed by the predicate is F or has conceptual mastery with th at which is expressed by the predicate is F has the ability to judge correctly wh ether an individual named by a is such as to fall under the concept expressed by is F. In other words, to have conceptual mastery with is F is to be able to judge correctly, in appropriate circumstances, whether a is F is true or is untrue. Moreover, to have conceptual mastery with that which is ex pressed by is F is have the disposition to make such judgments ( correct judgments) on the basis of certain feat ures or distinctive characteristics had by the individual named by a. Finally, these certain features or distinctive characteristics must be those very features on the basis of wh ich the cognizer who has conceptual mastery with the predicate is F is disposed to judge correctly that a is F is true or is not true. If a reader were left nonplussed by Peacockes talk of modes of presentation, especially in light of the ambiguity over whet her the m and k were to be us ed to stand for different kinds of modes of presentation or si mply variables ranging over mode s of presentation, I would share that readers perplexity. Specifical ly, I would claim that even in th e absence of any lack of clarity to do with the exact function of m and k, there is a bit of obscuring done by the phrase mode of presentation itself. To do a bit more explicat ion of the notions of c oncept, concept possession and conceptual mastery, I believe it helpful to try to understand this curious phrase. What exactly is a mode of presentation supposed to be? Since we are trying to sketch out the conditions under which a competent cognizer will co rrectly judge an individual to fall under a certain concept, and the cognizer must consider, in some manner or othe r, the individual about which a judgment is to be made, it seems that a mode of presentation of that object will be a particular manner in which that cognizer thinks about, imagines, represents to himself or otherwis e is presented with the

PAGE 127

127 object either by apprehending that ob ject with the senses or by considering the object in a merely imagined situation. There must be some conceptu al space between the individual (which may or may not fall under a certain concept) that a cognizer is presented w ith or represents to himself and any particular concept that that individua l might fall under; we are after all trying to separate, conceptually, that which might fall und er a concept (the indi vidual) and that under which the individual might fall (the concept). Bu t doing so is often exceedingly difficult in the abstract, especially if we are trying to give a characterization of concept possession for concepts we might call basic, that is, concepts which can not be analyzed further. I have more to say about this in Chapter Eight, but for the time being I would like to illustrate the difficulty we have for giving an acceptable characterization of concept possession in the abstract in virtue of the sheer variety that one finds in the types of modes of presentations. It certainly seems that an individual might be presented (o r represented by himself) to a cognizer by way of a description of that individual. So a description, perhaps gi ven by the understood utterance of a sentence in a language that the cognizer unders tands, is certainly a legitimat e mode of presentation. And a description of any indivi dual involves the attribut ion of features to that individual the having of which may be grounds for the correct judgment that individual falls under certain other concepts the falling under of which may or may not be re levant to some questions about whether this object falls under other concepts, and so on. The we b of relationships borne to each other by the concepts possessed by a sophisticated cognizer is most definitely an intricate one. My hope for this short chapter of this dissert ation is not to map the infinitely complex inter-looping tangles of a web of conceptual relationships, but rather to argue that a competent co gnizer does have a set of exceedingly complicated multi-track disposi tions which allows that cognizer to sort

PAGE 128

128 individuals with regard to, and because of, the f eatures had by those individuals into the set of things that fall under a certain concep t or the complement of that set. Having made these general remarks, let us re turn to Christopher Peacockes account of a certain concept to do primarily with visual modality and to our adaptation of his account to our purposes in the remainder of this document. The account from Peacocke above was specifi cally of a concept to do with visual modalities; when I try to give the more genera l account, we might be in danger of having to accommodate so many other sorts of concepts th at we wind up with onl y a necessary condition on the possession of a concept (or the having of conceptual master y regarding what is expressed by a predicate term). But of the range of diffe rent concepts this sketch is supposed to accommodate will be restricted to those which, to use Peacockes phrase, can be placed in predicational combination with singular constituen ts of the propositions or contents. Despite the fact that this account may only be enough fo r a necessary condition on concept possession (mastery), I believe that will suffice for the role we need concept possession to play in a larger story. As a warm up, I offer the following. Suppose we want to offer a very primitive necessary condition on the concept expressed by the pred icate is a dog. We could roughly say that a thinker possesses the concept expressed by the pr edicate is a dog if th at thinker can, when presented with individual objects (either by being in the physical presence of those individuals or being given descriptions of thos e individuals), make warranted judgments about which of those things were dogs and about which of them were not dogs and do so on the basis of the features had by those individuals. Now we have just tried to give a necessary condition on concept possession of the concept expresse d by the predicate i s a dog and we have used the very predicate we have just mentione d. Is the proposal circular? No, b ecause the predicate is a dog is

PAGE 129

129 mentioned in the analysandum but used in the analysans Of course, there are concepts which are not expressed by predicates, but to try to give a necessary condition of the possession of those concepts would be exceedingly difficult because there would be no predicate available to be used in the analysans. At any rate, in this dissertation we are concer ned with underwriting the intensions of terms of a language with conceptu al competencies, so we need not be concerned with concepts which are not expressed by predicate terms. With th is warm-up, let us move ahead to a general necessary co ndition on concept possession. The concept expressed by the predicate is F is the concept C to possess which a thinker must meet these conditions: 2. (1 .) He must be disposed to believe a conten t that consists of a (singular) mode of presentation m in predicational combination with C when the condition, circumstance or situation which makes m available presents its object as having the certain features F1, F2, Fn. The thinker must also be disposed to form the belief for the reason that the object is so presented. 3. (2 .) The thinker must be disposed to believe any content of any singular mode of presentation k not meeting all the conditions on m in (1 ) when he takes its object to have features F1, F2, Fn. 4. (3 .) An individuals having the features F1, F2, Fn is considered by the thinker an adequate distinctive characteristic (or quality in Peaco ckes terms) ground for that individual to be F (that is, such that C correctly applies to it).2 Now the first question we should ask is whether th is account is circular. I maintain that it is not immediately circular the symbol F does appear in both the analysans (the concept expressed by the predicate is F) and the anal ysandum (adequate ground for that individual to be F) but is mentioned in the analysans and is us ed in the analysandum. So in terms of the form of the account (or necessary condition), the circularit y is no more than to say: snow is white is 2 I do not mean (2)-(4) to be a characterization of a necessary condition on the possession conditions of just perceptual concepts (as Peacocke has done for red), but rather a general condition on concept possession in general.

PAGE 130

130 true iff snow is white.3 Even so, one may wonder whether the account is informative. I argue that it is because from it we see that how the thinker is able to judge warrantedly, on the basis of the presentation of a certain individu al as having certain features ( F1, F2, Fn), a certain content consisting the concept C in predicational combination with the mode of presentation of an individual. In terms of how we have accounted for the possession of the concept C it doesnt matter that it is expressed by th e predicate is F. All that matte rs is that one who possesses the concept can warrantedly judge a ce rtain content to be true on the basis of whether the individual (which is a constituent of the proposition that is the content) is presented as possessing certain features. We must also make th e unobjectionable claim that certain predicates are satisfied by objects with certain specific features. Also, we make the further unobj ectionable claim that predicate terms and concepts can be related by the expresses relati on. Specifically, if an individual has features F1, F2, Fn, then the predicate is F applies to and if that predicate expresses the concept C then the possession conditions are exactly those which are given by 1 and 2 above. Of course, it is a contingent matter which predicate expresses the concept C but once a predicate does, we can understa nd linguistic attributi ons as conceptual attributions. 3 One might worry over whether I have used a description (the features F1, Fn) to denote the concept and that description is used in the characterization of the concept in question, and so object that the necessary condition I have in fact offered is, after all, circular. This interlocutor might further propose that I should merely drop (4) to eliminate the circularity. The situation is complicated perhaps a bit clarification would help. In (2)-(4), I have tried to characterize the following : if a thinker possesses C then the thinker will believe that m is C if m is presented to the thinker as having certain features and the thinker comes to believe that m is C on the basis of his believing it to have those features (similarly for k ) and that the having of those features is adequate grounds for thinking that the predicate is F applies to th at individual. The features F1, Fn are not meant to serve as a description of C they are not even in general such that a thinker can articulate th em. They are rather merely t hose features on the basis of which the thinker comes to have beliefs involving the concept C I aimed at no more than the spelling out of the claim that thinkers deploy concepts on the basis of featur es had by the individuals under consideration for whether a concept applies to them or not.

PAGE 131

131 A prerequisite logical framework A question that has a risen is whether there is a basic set of fundamental cognitive abilities the having of which is required to possess any co ncepts at all (given our approach to the problem). We should address this question because if our particular a pproach requires basic, fundamental cognitive abilities that an individual is unlikely to ha ve even when we intuitively claim that this individual posse sses concepts, then our approach should be rethought. If on the other hand, these basic abilities are such as to be likely had by one wed intuitively attribute concept possession to, then the approach we have sketched is a viable one. So, what representational cognitive abilities ways of think about indivi duals must one have in order to possess any concepts at all? Here are some (I hope) non-controversial proposals. 5. Any potential concept possessor must have the ab ility to think about t hose things that may fall under a concept or not. Those things mi ght be called individua ls, entities or subjects. In other words (a nd not to use the following term with any metaphysical loading), the potential concept possessor must be able to think of individuals as property bearers or property havers. 6. Any concept possessor must have the ability to consider in some generality a feature ( characteristic or quality ) on the basis of the having of which an individual might be judged to fall under a concept. In other words (and not to use the following term with any metaphysical loading), the potential concep t possessor must be able to think of determinable properties that might be had by individuals. 7. Any concept possessor must also have the abili ty to think about in a similar amount of generality a specific respect (or aspect) which a thing can have a feature. Respects in which a thing can have features may well be indepe ndent of each other. A thing might have a specific feature (being spherical) with regard to a certain respect (shape in the this case), this feature is independent of features relative to other respects of the thing 8. Any concept possessor must have the notion ex pressed by the logical ~ sentence operator (alt. some notion equivalent to logical nega tion) in order to thi nk about the candidate entities (see (5) above) as not falling under the concept. Now of course, there are others such as SOME, ALL, and AND.

PAGE 132

132 Aid from a compositional meaning theory? If we hold that a m eaning theorist can use a meaning theory to represent a language speakers competence with the use of words, th en we may get some basic logical framework material and structure simply in virtue of this kn owledge. To help get this point out, consider, for instance, a section from Lepore s and Ludwigs (2007 Chapter 1, .2.) in which they offer an interpretive truth th eory (entitle truth0) for a very simple language. I relate here a recursive axiom for truth0 and the rule of inference for the truth0 theory that intuitiv ely captures our notion of universal quantification. RC2 (and). For all formulas and ( and ) is true0 if is true0 and is true0. Universal Quantifier Instantiation: For any sentence variable v and singular term Inst( v ) may be inferred from UQUANT( v ) (Where Inst( v ) is read as the result of replacing all instances of the free variable v in with the singular term and UQUANT( v ) is read as The universal quantification of with respect to v If RC2 and Universal Quantifier Instantiat ion represent a speakers competence with words, the speaker has in his logical conceptual prerequisite tool kit a notion analogous to that which is expressed by the first order logic sentence operator & and that which is expressed by the first order logic quantifier ( x). In other words, a competen t speaker has gotten (for free, just by knowing the language) something in his ba sic conceptual tool-kit the notion of and and for all. From these together with RC1 (the truth0 recursive axiom for not), we get the notion of some. Perhaps from these basics we have enough material to claim that a cognizer with these basic concepts has the primitive notion of a collection all the things that a certain predicate is true of.

PAGE 133

133 More aid than we thought? Does implicit know ledge of a truth theory for a language give us the entire prerequis ite logical framework? To claim that a speaker knows a language must we claim that he grasps (albeit perhaps incompletely) at least one concept expressed by a pr edicate term? I believe th e answer is yes. If so, then to be this sort of minimal speaker, one must have the prerequi site logical framework, because to grasp that concept the speaker must have the notion of a thing that may fall under a concept, the notions of a feature with regard to a certain respect the having of which is the warrant for claiming that the predicate that expresse s this concept correctly applies to that thing. A promissory note for Chapter Nine A conventionalist claim s that th e truth of modal claims lies in linguistic convention. Havent we seen here that it is the relationship of concep ts (whatever they are) rather than sentences as used to convey meaning that lies at the root of m odal semantics? I will argue later that this is not the case. Now We Are in the Position to See Concep tual Backing by Way of Concepts for Our Stitched To gether Map of Intensions Given our account of (at least a necessary condition on) the concept C I want to suggest a formal approximation for con cept possession. Consider the map con such that for ` the set of (re)presentations of entire worlds, ` the set of individuals of those worlds, andV, the set of concepts: 9. con : ` ` V {0, 1} where for m ` c *V ` `, con ( m `, c *) = 1 iff one who possesses c is disposed to warrantedly judge true the content (or proposition) consisting of c in predicational combination with m where m is of `. Given that our account of con cept possession is successful, all con gives us is a generalization of this notion to arbitrary concepts, individuals and representations. LetV 1 be the set of concepts that are expressed by predicates (recall that 1 was to stand for the set of one-place predicates).

PAGE 134

134 Now we can see an isomorphism between I restricted to { 1} and con restricted to {` ` V 1}: if m is a (re)presentation of the world which corresponds to index and the predicate expresses the concept c *, then con ( m `, c *) = I ( ). We now have the appropriate conceptual backing of I restricted to { 1}. A similar backing is possible for I restricted to { n n} for n 1 with the appropriate substitution of ` n for ` and V n for V 1 in the right places. It is interesting to note that while there is a sort of implicit restriction on the nature (or perhaps size) of a (re)presentation m* for the 1-place predicate case, there can be no such restriction for the general case of an nplace predicate. We think of a representation of an individual as a representation of that individual in the larger context perhaps of an imagined scenario and so we think of the representation of that individual as only a small part of an imagined counterfactual scenario or possible world so conceived. In general, a repr esentation of an n-tuple of individuals for an arbitrary n 1 cannot be small in this sense. In the most general case, an arbitrary representation must be such th at it represents entirely a comp lete imagined scenario or counterfactual situation because it must be capable of representing an n-tuple of individuals for arbitary n. This does seem like a lot to swallow, for how could a finite cognizer possibly imagine a completely detailed counterfactual situation given the cognizers finiteness? More needs to said about this possibility later, but I think we can satisfy ourselves until we say more about this possibility by noting that even though no finite cognizer could imagine th e presentation of an infinite universe, we can get at the notion of what is conceiva ble in an ideal sense by thinking about what a finite conceiver might be able to present or represent to himself if given an infinite amount of time. Admittedly, the notion of a comp letely detailed representation of an entire counterfactual situation is fantastic on its face, but I believe we can understand what this means

PAGE 135

135 if we consider how finite cogni zers represent to themselves pa rts of a possible world (perhaps only the parts that present a sing le object) and then think how they might imagine entirely the whole world in which the indivi dual theyve presented to themselves was situated. In addition to this evidence, I believe that the notion of a comple tely conceived entire counterfactual world is more plausible, given our actual imaginative pow ers, than either Lewisian possible worlds or a region above the Great Line of Being copiously filled with Platonic properties. Conclusion In this chapter, we have tried to give a so rt of (ultim ately) non-linguistic basis for our knowledge of the intensions of predicate terms. We have app ealed to the notion of concept possession to show how the map I might be understood to give the extension of predicate terms directly in a non-circular, yet not completely reductive way. The notion of concept possession rests on the notion of dispositions to make certa in judgments on the part of cognizers. And so, one who requires a completely redu ctive analysis of modality, that is, an explication of the modal entirely in terms of the non-modal would be diss atisfied with this approach. I shall argue in Chapter Nine that the desire for a completely reductive account of modality is motivated by the adherence to the correspondence theory of truth and the background assumption (perhaps implicit or unacknowledged) that philosophizing should follow an abducti ve, scientific method approach. As Ivana Simic has put it, the desire fo r a reductive story about modality is an implicit desire for an explanation of modal facts rather than a desire for an explication of the truth of some sentences which express modal claims. The latt er desire is had by a theorist who wishes to start from basic principles, such as that we employ words to indicate objects, and use certain meaning constitutive patterns of use, and show how an account of modal semantics can be had

PAGE 136

136 from these basic assumptions with little use of ab ductive reasoning. This is a sort of apodictic approach to philosophizing that I believe to be just as respectable as the abductive approach. In Chapter Eight, we shall engage in a very rough and ready effort to provide a taxonomy of concepts of particular impor tance to the path clearing for c onventionalist modal semantics. I believe our efforts will pay a dividend in the demonstration of how members of families of concepts and their relationships to one another are on all fours with our notions of analytic connections between certain me mbers of families of predicate terms. I hope that we will accumulate more evidence for the claim that the relations of concepts mirror the relations of understood meanings of predicate terms and that this conceptual structure makes obvious an epistemology of modal claims: we come to know modal truths by co ming to possessing the concepts the predicates of our language expre ss and seeing the conceptu al connections between those concepts. Later we will argue that we can di spense with the notion of concept as something we must admit into our ontology, but for the ti me being its important to see the epistemic deliverances of concepts and their connections. Our taxonomizing will also help us to s ee how we might very reasonably place unobjectionable restrictions on the map I in order to ensure that it endorses just those de re modal claims that we pre-theoretically hold to be true. By observing how conceptual connections can be used to provide information about a nd a certain level of structure for the map I we should be able to warm ourselves up to the idea that just as the map can be structured and restricted in terms of the set of individual it assigns to predicate terms, the map can also be structured and restricted to the individuals assigned to singular referring constant terms relative to the assignments made to predicate terms. Such restrictions will allow us to claim that certain de re modal claims are true or false without a co mmitment to any sort of metaphysical thesis

PAGE 137

137 about the nature of those indivi duals that are referred to by those singular referring constant terms. Some may take the fact that our treatment of de re modal claims is thus mute on substantive metaphysical issue as a liability, but I believe one who takes seriously the analytic deflationary conventionalist approach will see this possibility of sile nce as a virtue; we shall have made modal semantics safe, in a modest sense, for the absence of metaphysical assumptions about essence. That we can give an account of modal semantics without a commitment to those theses that the abductive method seems to require is further evid ence that this approach is a viable one.

PAGE 138

138 CHAPTER 8 TAXONIMIZING KEY (FAMILIES OF) CONCEPTS Introduction Our taxonomy is, of course, by no m eans meant to be exhaustive, but rather only meant to show that the analytic connections between pr operty terms can be backed up in a plausible manner. If the approach we are clearing the way fo r here can be shown to be a viable one, then perhaps this sort of taxonomizing can provide the framework fo r more lengthy investigations into the relations borne to each other by concepts among certain families. At the risk of providing a possible spoiler fo r what follows, I should say that our initial examination of our concepts, concept families and th eir relationships will be used as a lead-in to our investigation of the problem of de re modality. Since we have plac ed the class of admissible interpretations on a firm if dis positional footing, we can use thes e functions from word to object with relative impunity and profligacy. In this chapte r, we shall endeavor to show that conceptual connections understood in an informal pre-theoreti cal way can be understood to place restrictions on the images under our interpretations of predi cate terms relative to one another. For example one who is competent with the concepts expr essed by the terms is red and is scarlet recognizes the conceptual connec tion between the two; namely a connection we can express with the claim that anything scarlet is red. Similarl y for the concepts expre ssed by the terms has a color and is red; a connection between the two can be expressed with the claim that anything that is red has a color. We will use our intuit ive notions of conceptual connections to place restrictions on the admissible interpreta tions of the following sort. For all and one-place predicate terms and \( ) \( ) and \( ) \( ) if for is substituted is scarlet and for is substituted is red and for is substituted has a co lor or is colored

PAGE 139

139 Our Strategy: A Very Brief and Incomplete Survey of Concepts by Way of Concept Possession and Conceptual Connections We have suggested that the notion of concept possession can provide the right sort of backing for I and with such backing we can see a way to give a non-circular acco unt of modal semantics that is conventionalist in that it uses (essentially linguistic ) interpretation proxies for statedescriptions. We should do a bit to survey the territory in order to get a feel for how the conventionalist modal semantics We are trying to clear a path for might be underwritten by concept possession and conceptual connections spelled out in terms of concept possession: by looking at a few different sorts of concepts, we will be positioned at least to say how the possession conditions of one concept may be related the possession conditions of others. Survey of Different Sorts of Concepts: Abstract Objects One obvious way to begin a discussion of the concept of ABSTRACT OBJECT1 is to note that no physical object can be an abstract object: physical objects are contingent and have a spatiotemporal location abstract objects are necessary existents and are not spatiotemporally located The class of physical objects is completely di stinct from the class of abstract objects. One might object with the observation that there ar e certain kinds of abstract objects, sets in particular, that might include physical objects as members. Is the set whose members are the chairs in the Griffin-Floyd Philo sophy Library at 1PM on April 7th, 2009 an abstract object even though its members are contingent pa rticulars? I am not sure what to say a bout this particular issue, but for the meanwhile I hope we can be satisfied with the observation that the philosophical work done by abstracta is different than the philosophical work by physical objects. Since these two sorts of things perform different theore tical functions, we should admit 1 Ill use italicized 10-point font for words which designate the concepts of that which are expressed by those words (DOG will name the concept of dog) but some times, for emphasis, Ill use concept of X (concept of DOG) to indicate these concepts.

PAGE 140

140 both into our ontology and would do well to hold that th ere is no overlap be tween the abstract and the physical. Given that what we have just said is palatable, we can notice another difference between abstract objects and physical objects by examining the rle the type / token di stinction plays for each of these two broad categories. Consider the number one (that named by ). There seems to be only one number one the one that exists necessarily in every possible world. So anything that is of the type of the number one will be the number one the only number one. Since there is a type of the number one and only (necessarily) a single token of that type, the type / token distinction is certainly not as usef ul as the type / token distinction for physical objects, or at least its uses are different. The same goes with other abstract objects like th e property of being red. The property of being red is a necessary existent, so it exists in every possible world. There is only one property of being red. But presumably, there is type that the proper ty of being red is of. The situation looks to be an alogous with the number one. To explain the possession conditions of ABSTRACT OBJECT we must invoki ng the notion of necessary existence and so involve modal notions Also to understand th e notion of abstract object as opposed to physical object one must understand the type / token distinction something that is useful for understanding physical objects, but not for ab stract objects (or at least useful in a different way). Another prima facie difference between abstract objects a nd physical objects is that at least for abstract objects which are us ed in mathematics or other te chnical disciplines, the modal properties of these objects are ex hausted by their relations spelled out in terms of the theory in whose sentences their names are constituents (or to put it another way which is about these abstract objects). For example, we might use the numbers (as the referents of the numerals) to

PAGE 141

141 explain the truth of a mathematical statement like > 7 and since the true statements about the numbers are true of necessity, it seems that modal properties (not including t hose had in virtue of their being abstract objects) of these abstracta are completely exhausted in terms of the functional role they play in the techni cal disciplines in which they are used. One might even make the case that abstracta such as the numbers are the truth makers for statements which are true in virtue of meaning: we choose to the num erals and etc. to spell out a theory of arithmetic (for instance). That > 7 is true is simply a matter of how we choose to use these symbols in th e context of that theory, and what statements and methods of inference we sanction within that system. So to understand how the numerals are used, what statements we take to be true made with the nu merals and related notions in the practice (for the sake of the discussion) of arithmetic, is to know something of what is true of those individuals which the numerals refer to (that is, the numbers). That is to say the rules for making assertions (inferences or axiomatic claims) are completely spelled out for the terms whose referents are abstracta like the numbers (or sets, functions, etc. ) in terms of the theory for which the relationships of the referents of the singul ar terms of the theory are truth-makers. Survey of Different Sorts of Concepts: Logi cal / Abstract / Set-Theoretic Rela tions Another concept closely related to ABSTRACT OBJECT is the concept of ABSTRACT RELATION. We can begin by noting that abstract relations ho ld between certain abstract objects, and so a cognizer (let us call him Ral ph) who possesses a concept whic h is a determinate of the determinable of the concept ABSTRACT OBJECT, could correctly token the concept of a specific abstract relation when two abstra ct objects did, in fact, bear a cer tain relation to each other. For example, if Ralph possessed the concept of SET MEMBERSHIP, then for any individual (or set) and set A Ralph could correctly determine (assuming he has enough information) whether or not

PAGE 142

142 is a member of the set A. A similar, analogous story can be told if Ralph has the concept IS GREATER THAN. What, specifically, is required fo r the possession of one of this sort of concepts? A necessary condition on having a determinate concept of the determinable ABSTRACT RELATION is possession of the concept(s) that are of the type of which the relata of the concept in question are determinates. For example, if Ralph possesses the concept of SET MEMBERSHIP, then Ralph must have the concept of SET and the related concept of ELEMENT ( OF A SET ). It doesnt seem that Ralph must possess the concept of the determinable category of which the specific concept he possesses is a determinate that is, Ral ph does not need to possess the concept ABSTRACT RELATION in order to have the concept of SET MEMBERSHIP. And, of course, Ralph must have the crucial bit of knowledge how he must be disp osed, under certain conditi ons and given the right amount of information, to judge warrantedly when the set membership relation holds between two individuals (sets can be considered individuals). It is interesting to observe th at Ralph could be such that he learned about set theory in a strictly formal sense: Ralph only knows about sets by way of learning about Zermelo-Frankel set theory (ZF), say. In this case, it might be that Ralph has only a formal notion of SET, ELEMENT ( OF A SET ), and SET MEMBERSHIP. Ralph still has the concepts in question, but his grasp on these concepts is had only by his lear ning of the formal definitions, properties and behaviors of the abstract objects whose interacti on is outlined by the formal theory which hes come to know. In this rather odd situation, the possession conditions of Ralphs concep ts are entirely spelled out in terms of the axioms and rules of inference of ZF, and so the notion of set membership and the meaning of is an element of set (as taken to express the concept of SET MEMBERSHIP) are provided by this formal theory. In this case, the possession of the concept of SET MEMBERSHIP

PAGE 143

143 can be determined by verifying Ralphs knowledge of the formal theory in which these notions are explicitly and implicitly defined. I take this to be evidence that, at least for some concepts that are determinates of the determinable ABSTRACT RELATION, the possession of those concepts can be had in virtue of knowing a formal theory which provides an explicit or implicit definition of the meaning of the predicates (again of th e formal language) which expresses the concepts under consideration. Survey of Different Sorts of Conce pts: Physical Object The most basic category of concepts under which fall the inhabitants of the world around us is that of physical object. What preci sely is involved in the possession of the concept of a physical object? Quine (p. 171, 1960) has offered a very liberal proposal for understanding of what constitutes a physical object: a physical object comprises simply the content, however heterogeneous, of some portion of space-time, however disconnected and gerrymandered. I encourage us to help ourselves to Quines propos al, and after we become accustomed to it that we offer a slight modification. His proposal is satisfying, on one hand, beca use things which we prephilosophically consider physical objects are physical objects; the old saw, chestnut, armchair and table of the philo sophers drawing room are physic al objects. But, on the other hand, his proposal for physical object also has the (at first strange) conse quence that a region of spacetime might not be contiguous, and so a re gion of spacetime might include exactly the armchair and the table; and so what one might call the armchair andtable is also a physical object. This result seems unobjectionable after a minute: if we tried to individuate physical objects along the lines of our convention about them, we would alrea dy have prejudiced our concept talk in favor of a certain metaphysical vi ew about the individuatio n of physical objects. On Kirk Ludwigs suggestion, I would proffer one modification of Quines proposal for what constitutes a physical object, so as to be more in line with our ordinary notion. It seems

PAGE 144

144 reasonable to think that physical objects persis t through time, so they are probably not the Quinian occupiers of spacetime, but rather f our-dimensional spacetime worms which are such as to be continuous (in some appropriately loose understanding of that term) regarding their three-dimensional spatial location with respect to time. I hope that such a modification of Quine retains some of the flexibility of his original account, but captur es a bit more of our ordinary notion of physical objects. So it seems that to possess the concept of physi cal object a cognizer must have the yet more basic concepts of REGION, SPACE, TIME (or SPACETIME), and MATTER (or MATTER/ENERGY). Possession of each of the concepts requi res the possession of the concept of SHAPE, LOCATION (or POSITION) and CONSTITUTION. I am tempted to say not much more about these concepts, as they may be basic (or close to basic) and only (inter)definable in terms of each other. For example, it seems right to say that any physical ob ject must have a location in spacetime, but that individuals which are not physical objects (if any there be) such as numbers, properties or relations (abstract objects) or jealousy and bitterness (mental obj ects) cannot have a spatial (or spatiotemporal) location. By way of noticing another difference between the physical and the abstract, we see that physical objects are also such that they are not types, but tokens. There are types of physical objects (such as spherical objects), but an in dividual that is a physic al object is a token. Survey of Different Sorts of Concepts: Feature / Aspect There are, o f course, certain wa ys individuals can be; and the way an individual is in a certain respect may or may not have a bearing on the wa y an individual is in other respects. For example, an individual (a tree, say) may have br ight green (as opposed to dark green) leaves, but whether the tree is tall has or not need not have any bearing on th e color of its leaves. There are several locutions that express the notion of the ways individuals can be: an individual a can be a

PAGE 145

145 certain way, a can have a certain property, a can have a certain feature, and so on. The phrase ways a thing can be seems too imprecise; and the invocation of property talk seems too fraught with metaphysical supposi tions and provocative, so to talk about the notion that is expressed by each of these, I will us e feature. To speak of the certain respect in which an individual is a certain way or other or has a certain feat ure which may or may not be independent from other respects in which the i ndividual is a certain way, I will use the term aspect. So, we could say that whether a has feature F is a question of a certain aspect of a, this question of the certain aspect of a as F -ness may or may not be independent from another aspect of a whether or not a has feature G ( as G -ness). For example, a rock might be dark gray or light gray and might be igneous or sedimentar y the rock has different features relative to certain aspects. In this example, the rock might be a particular shade of gray which is just to have a certain feature relative to a certai n aspect of the rock (its color). The rock might be of a certain formation type, igneous or sedime ntary, which is to have a certain feature relative to another aspect of the rock (how it was formed). Since a rocks color is related to its formation process, these two features of different aspects are not independent. There are, of course, features with respect to different aspect which are independent; the rocks size is independent of its color because rocks of any color can be broken so as to be of a whole range of sizes. If we try to generalize these observations and think about what would be required for possession of certain concepts that express the noti ons of features that can be had by individuals and the aspects of the individuals that those features describe, we might propose the concept of FEATURE / ASPECT. What are the possession cond itions for the concept of FEATURE / ASPECT? The cognizer who possesses the concept of FEATURE / ASPECT must know that individuals can be certain ways, that is have certain feat ures, and that these ways of being or features are such that

PAGE 146

146 only a certain respect or aspect of individual is described or made determinate by the having of feature. For example, a cognizer might come to know that the physical object he is presented with is spherical. He can know th at the object is spherical and th ink of the object as spherical and also know that the objects shape is i ndependent of other of the feat ures of the object such as the objects size or color because he possesses the concept of FEATURE / ASPECT, and knows that concepts such as SPHERICAL, SMALL, and GREEN are such that if the locutions is a feature / aspect, being spherical, being small and being green express the obvious concepts or name the properties that are picked out by the obvious c oncepts, then sentences like being spherical is a particular feature / aspect, being small is a particular feature aspect and being green is a particular feature / aspect are tr ue in virtue of the conceptual connections between the concepts at issue. Survey of Different Sorts of Concepts: Similarity Even with o ur initial and incomplete sketch of the concept of FEATURE / ASPECT, we can understand the possession conditions of a concept that is closely rela ted to the notion of feature / aspect, the concept of SIMILARITY. As a first cut, we can say that a cognizer has the concept of SIMILARITY if one understands how two or more indi viduals can share a common feature to do with a single of their aspects. More precisely, if one posse sses the concept of FEATURE / ASPECT, then one may realize that (say) tw o individuals each have some f eature that determines a certain of their aspects, and that this shared feature causes the individual s to resemble each other in this particular way. For example, the cognizer who has the concept of FEATURE / ASPECT might realize that while individual a is red and large and b is green and small, both a and b are spherical and so share a feature and resemble each other with regard to a certain feature that determines an aspect of a and b. One who possesses the concept of SIMILARITY will also be aware (given that this cognizer possesses other releva nt concepts) that cert ain features of two

PAGE 147

147 individuals a and b may be similar but not be the same feature. For example, a may be spherical but b may be ovoid but nearly spherical and so a and b may be similar but not share exactly the same feature, but merely share features that are such that the having of th ose features results in certain kind of resemblance between a and b. Possession of the concept of SIMILARITY may also require possession of a relational concept (IS SIMILAR TO) which is correctly applied to two entities which fall unde r the concept of FEATURE / CONCEPT such just in case these entities bear a relation of similarity to each to other and th ese entities determine th e same aspect of the individuals which fall under th ese concepts respectively. Survey of Different Sorts of Concepts: Category If one has the concept(s) of SIMILAR / SIMILARITY, and the concept of SET (and related notions) one has met the prerequisites to possess a particular concept of CATEGORY. A cognizer possesses the concept of CATEGORY if he can group individuals into sets based on their similarities and dissimilarities. For example, if individuals a and c both have feature F but individual b does not, then if a cognizer possesses the concept F then the cognizer is in a position to think of a and c belonging to a category (perhaps th e category of things which are F ) to which b doesnt belong. The cognizer notices that a and c are similar to each other in a way in which b is not similar to either a or c If b and c both have feature G but individual a does not, then if a cognizer possesses the concept of G then the cognizer is in a position to think of b and c belonging to a category to which a doesnt be long. Just like the last case, the cognizer notices that b and c are similar to each other in a way in which a is not similar to either b or c Since We are leaving concerns over vagueness aside in all of our considerations here, we can say that for any set of individuals a single cate gory (of the sort we ha ve been considering) partitions the set into two distinct subsets a su bset of individuals who belong to that category (perhaps empty) and a necessarily di stinct subset of individuals who do not belong to that

PAGE 148

148 category (also possibly empty). But it may also be the case that a collection of three or more categories partitions a particular set without remainder; for example the categories indicated by ( 0], (0, 1], (1, + ) partition without rema inder the real numbers. There are infinitely many ways to exhaustively partition the real numbers, as there are fo r any infinite set of individuals. Survey of Different Sorts of Concepts: Determinables and Determinates In philosophical discourse, we speak often of determ inables and determinates: we say that red is a determinate of the determinable color ; scarlet is a determinate of the determinable red ; and scarlet17 (just to give it a name) is a determinate of the determinable scarlet. What can we say about the concept of DETERMINATE and the concept of DETERMINABLE? First, it seems that if one has the concept of DETERMINATE then he must also have the concept of DETERMINABLE given that they are defined in terms of each other. Perhap s, theres only a single concept maybe the concept of (for lack of a different phrase) DETERMINABLE/ATE. What, intuitively, is going on here? Regarding de terminates and determinables, we have the idea of a broad category which applies to, in virtue of a set of general features had by, a class of individuals under consideration. The category marked out by these general features is the determinable under which all of these individuals fall. In this partic ular category are more narrow subcategories which apply to, in virtue of a more specific set of features had by, and as a consequence increasing similarities (with respect to some feature or other) shared by, a class of individuals each of which already fall under the larger category. For example, individuals which have a color (have the determinable property of having a color) are some color or other (have a determinate color); individuals which are red (a determinable of which there are determinates) are some shade of red or other (have a determinate shade of red) ; individuals which are scarlet

PAGE 149

149 (again, a determinable of which there are determin ates) are some shade of other of scarlet (have a determinate shade of red). So to have the concept of DETERMINABLE/ATE one must have the noti on of (a certain kind of) category (categories) into which into which indi viduals are placed on the basis of similarity, and in which there are further categories into which individuals can be placed on the basis of more fine-grained similarities. On e who possesses the concept of DETERMINABLE/ATE, must know that individuals can be grouped according to similarity of a certain sort or other, but individuals which can be so grouped and be such that they have features which allow for further grouping (subgrouping) on the basis of si milarities of the same sort that allowed for the original grouping to be made. Po ssessing the concept of DETERMINABLE/ATE requires at least possession the concepts of SET / SUBSET, FEATURE / ASPECT and SIMILARITY is required for the concepts of NATURAL KIND and ARTIFACT (among the many others we do not canvas here, of course). Survey of Different Sort of Concepts: Primary Qualities Let us consider various concepts of the so -called prim ary qualities. The hallmark of a particular primary quality is the independence of the qualitys existence from any particular observations of an individual which has the partic ular quality. The determinate qualities of the determinable feature of having a shape are primary qualities; so if an individual is square, then its quality of squareness is a primary quality. What are the possession conditions for a primary quality like squareness? One who possesses the concept of SQUARENESS must possess various other concepts of the features that are had by in dividuals who have the pr operty of being square: to name a few the concept of a PLANE / GEOMETRICAL FIGURE, the concept of RIGHT ANGLE, perhaps the concept of LINE, perhaps STRAIGHTNESS and so forth. Perhaps one who has the concept of SQUARENESS must also have the more ge neral determinable concept of SHAPE.

PAGE 150

150 There are other primary qualities that we might consider such as number or configuration. But we can assert that having any specific primary quality concept such as SQUARENESS does involve other more basic concepts we have al ready canvassed such as concepts of PHYSICAL OBJECT and FEATURE / ASPECT. To be a physical object seems to requi re having a spatiotemporal location as well as a certain shape; to have a primary qua lity such as a certain shape requires that the a certain aspect of an individual ha ve a certain determinate feature. Survey of Different Sorts of Concepts: Secondary Qualities We have surveyed at bit of the ter ritory regarding the concepts of various primary qualities. It would be beneficial to our survey to consider a representative few of the concepts of the socalled secondary qualities. Of course, traditionally the having of a specific color or other is to have a secondary quality a quality or propert y the having of which is somehow dependent upon the observer of that very quality or property. So what are the possession conditions of a concept like RED? We can start with some observations about the fundamental conceptual repertoire required to identify an individual as (having the property of) being red. Fo r a cognizer to rightly think about an individual as havi ng the property of being red, one must first of all have the ability to understand that individuals can have an appearance that is perceived visually; one will most likely be capable of having visual percepti ons and will be able to see. We should be reluctant to claim that a cognizer without the ability to have visu al experiences of certain sorts (those experiences that are as of having a visual perception) now or in the past could have the concept of RED or would at least have a con cept different from the concept RED than a cognizer who could have (had) such experiences would have. The cognizer without the capability for visual experiences might understand enough about th e physical world to real ize that light waves can be reflected off of the surfaces of objects and that light waves are of certain frequencies and that the perceptual mechanisms of sighted creat ures are such that li ght waves of different

PAGE 151

151 wavelengths are perceived in di fferent ways, but this does not seem like enough for the sightless cognizer to have the same concept that is had by the sighted cognizer. And the experientially capable cognizer must realize at least a few of these details to count as having the concept RED; he must realize that only indivi duals which have visi ble surfaces (or surf aces which are, in principle, capable of being visible with his no rmal visual perceptual apparatus) are those qualified to be such that th ey can fall under the concept RED. In the recognition that only individuals with visible surfaces are such that they can fall under the concept RED, theres already quite of a bit of conceptual repert oire in play. One who possesses the concept RED must realize that those individuals that fall under it must be physical objects with facing surfaces that are (at least in principle) able to be visually perceived. Also, it seems that one would have the concept of FEATURE / ASPECT because a red square is different from a red disk in that it is differently shaped, it is color is similar. Perhaps it is not necessary for one to possess the concept of SIMILARITY that we have outlined before specifically with regard to the secondary qualities We can illustrate this with the following thought experiment; it is logically possible that everyt hing in a particular cognizers environment could have been the ex act same shade of red. This unfortunate knows that things seem a certain way to him, and may even have a way of describing what their appearance is (even though this seems unlikely), but does not realize that they could look any other way. Since he does not realize that things could look another way, there is not (yet) any specific notion of similarity among any of the sec ondary qualities that are color qualities. If he were to see something of a color other than the sh ade of red he is seen for his whole existence, then he might come to have the notion of diffe rence and similarity along the dimension of the secondary quality of color. It is interesting also that a cognizer neednt have linguistic capacity

PAGE 152

152 for sorting the color concepts which he posse sses. An artist has certainly many more color concepts (understood as the ability to make color discriminations) than she has words for colors. Survey of Different Sorts of Concepts: Natural Kinds The notion of a natural kind draws on m uch of the conceptual material that we have surveyed in last few short sections. If a kind K is such individuals which are of that kind (that is, are K) are distinguishable from individuals that are not K in a way that conforms with a distinction of the natural world, then K is a natural kind. For example, th e distinction between inanimate and animate objects is such that animate object can be considered a natural kind term. Those individuals to which the term applies (like th e oak tree on the other side of the apartment complex or the neighbors dog Rex) are such th at their structure and function is markedly different in specific ways from individuals to wh ich the term does not apply (like the computer I am typing on right now or the couch I am sitting on) and that these specific differences are such that the constituents of the world can be categoriz ed with these terms and such categorization is independent of the particular de sires and intentions of the c ognizers who use these natural kind terms. The possession of concepts that are of na tural kinds is very demanding a cognizer must have an extensive conceptual re pertoire together w ith the proper conceptual connections among the various members of that repe rtoire to possess natural kind concepts. To possess a certain specific natural kind concept K, seems to require at least having the following concepts. He must have the concept of PHYSICAL OBJECT because those things that fall under natural kind concepts are physical objects, and one must realize this to have the concep t in question. He must certainly have the concept of SIMILARITY given that members of the natural kind bear similarities this is how the kind is marked off). He must perhaps also have the concept of DETERMINATE/ABLE; members of certain natural kinds are often members of other broade r natural kinds for instance a specific species of tree might form a natural ki nd, any member of this particular natural kind

PAGE 153

153 will also be a member of the broader natural kind formed by plants, terrestrial beings, living beings, etc. Perhaps he must even have the (previously unca nvassed) concept of INDIVIDUAL; we saw from our example of the natural kind formed by a specific species of tree that the members of that natural kind are marked out by the fact that they are individuals, th at is, certain specific trees of that species are member s of the natural kind because me mbers of the kind have certain characteristics had in virtue of their struct ure, function and functional organization. These characteristics are such that only individuals separate organisms as differentiated by these sorts of specific structure and function and functional organization coul d have these characteristics. One who has a natural kind concept will likely have the concept of CATEGORY as well given that it is often the case that natural kinds E F and G are such that any member of any one of these kinds is a member also of natural kind K and so E F and G might be thought to be categories of the kind K Survey of Different Sorts of Concepts: Artifacts Finally, we spend som e time thinking about what the possession conditions are for a concept of something that is an artifact. Let us consider specifically the concept of EYEGLASSES for the sake of our overview. I choose this specific type of artifact because, ev en though it is certainly logically possible that an object with an organi zation and constitution identical to a certain pair of eyeglasses could come to exist even if there ha d never been any people to make artifacts, it is not prima facie ridiculous to claim that we might not refer to that individual as a pair of eyeglasses, simply because it wasnt created in th e right way and does not play the right sort of functional role in the activitie s of humans. Of course, thats c ontroversial, but let us limit our discussion of eyeglasses by saying that a cognizer has the concept of EYEGLASSES only if the cognizer applies this concept to those things whic h are indeed artifacts.

PAGE 154

154 One who correctly applies the concept must ha ve the capability of understanding (at least) two broad notions one captured roughly by the concept of MANUFACTURED OBJECT, which applies to those things that are constructed, manufactured or made by a creature capable of manipulating it environment to certain complex effects and the other roughly captured by the concept of PURPOSE the use to which an object is put With these two notions in mind, one could understand how a specific physi cal object, like one which is a pair of eyeglasses, could have a teleology and functional role such that is could rightly fall under the concept EYEGLASSES. Of course, as with the concepts of the natura l kind terms, a huge prerequisite conceptual repertoire is required along with the panoply of conceptual conn ections between the members of that repertoire. To recognize the commonality be tween any two different pairs of eyeglasses, a cognizer must have the concepts of SIMILARITY, CATEGORY, DETERMINATE / ABLE, FUNCTION, FUNCTIONAL ORGANIZATION, and INDIVIDUAL among a host of others. Survey of Different Sorts of Concepts: Conclusion Now I hope we will see that we have com e to the place at which we wanted to arrive. To possess the concept C is to possess a dispositional so rting ability. If the concept of C is expressed by the predicate is C, then a c ognizer who possesses it has the appr opriate dispositions so as, in the right conditions and with adequate information, to be able determine whether an individual is C or is not C. Of course, one can possess the concept C without knowing that the predicate is C expresses the concept in question. In fact, it could be the case th at a cognizer possessed a concept that was not expressed by any predicate of th e cognizers language (o r any language for that matter). In such a situation, I believe it would be difficult to characterize that cognizers sorting ability in a non-circular way. But we need not fear. To give a non-circular account of the possession conditions for this (a s yet unexpressed) concept, we should consider a language exactly like the cogni zers except that it contains an additional predicate term say. (In terms

PAGE 155

155 of the system we have set up we can easily do so since we model natural language with a formal one in which there are a denumerable infinity of predicate terms.) Then we say that a necessary condition on possessing the heretofore unexpressed concept is to be able to sort *s from non*s. The predicate terms in the account of concept po ssession is doing no work other than to provide some linguistic handle for th e concept in question. In this se nse, the predicate term is not essentially built in to the account of concept possession. We can simply assume outright that on the view we are advocating for concepts (of a certain sort2), they are sortals: a n ecessary condition on possessing C is to be able (given enough information about the individuals in question and the situations in which those individuals are embedded) to sort individuals into two groups those which fall under C and those which do not. We have seen that concepts may be such that they can be used to create different classes of three or more categories into which one who possesses those concepts which create the categories can group individuals. For example, if T, U andV are categories such that if an individual is of the right sort to belong to one of these categories then if it falls under the concept A then the individual belongs to categoryT, if an individual falls under the concept B then it belongs to categoryU, and so on. Then one who posse sses each of the concepts A, B and C can sort the individuals (given enough information of course about the individuals and the situation in which it is embedded) that are of the ri ght sort to belong to one of th ese categories into these categories without remainder; given enough in formation about an individual I1 and the situation in which I1 is situated, the possessor of the concept of A can determine whether I1 falls under the concept A or not, if so I1 belongs to category T, if not I1 belongs either to categories U or V or is not the 2 We have been considering explicitly only those concepts that can be expressed by predicate terms such as is in sentences like is There are other concepts expressed by terms such as & which are not obviously sortals, but rather properly logical. We have not been concerned with such concepts in this chapter.

PAGE 156

156 right sort of thing to belong to either of these categories. If I1 falls under B, then it belongs to category U, if not then it belongs either toV or is not the sort of thing to belong to either T, U orV. Finally, if I1 falls under C, then it belongs to category V. If concept possession is characterized, very roug hly, by the ability had by the possessor to sort individuals into two groups (giv en that the conditions are right and various skeptical scenarios are ruled out), those who fall under the concept a nd those who do not, then we should be able to represent the relations between concepts with bi nary trees. So perhaps (and this is merely a suggestion for future research) binary trees c ould be used to represent the structure of I Conclusion And finally, we can see how we can m ake us e of the relationship of concepts (the possession of one of which is thought of as an ability of a certain sort) to restrict the members of the class of admissible interpretations. 1. For the predicate terms and (of arbitrary number of places ), if the concepts expressed by and are such that one who has conceptual mastery with regard to both of the concepts expressed by these resp ective terms has also the dis position to assert (under the appropriate conditions3) that any individual which he judges to fall under also falls under then for all \( ) \( ) and is warranted in his judgment by the conceptual competences in question. If what we have said earlier in this chapter, then with repeated applic ation of this principle for the (families of and members of those familie s of the) concepts expressed by the predicates we have surveyed in this chapter w ill impose the sort of structure on {\ } that reflects our intuitions about the connections between concep ts. My hope is that by working our way down from the most general terms ABSTRACT OBJECT to the least general (we have surveyed) such as 3 Of course, much will have to be filled in here as appropr iate conditions is just about as expandable placeholder as can be. I do believe that enough could be packed into to get things right.

PAGE 157

157 ARTIFACT, we can provide a detailed structure for the class of admissibl e interpretations, and do so in a way that requires only the basic notion of con ceptual mastery. Of course, the problem of de re modality still lingers; no matter how much structure we place on the predicate terms of our language by ensuring th at the class of admissible interpretations mimics the connections we take th ere to be between the concepts expressed by the predicates of the sentences of a state description, unle ss the a predicate app lies only to a single individual, so far we have no way to restrict the members of {\ } to reflect the intuition we might have the a certain individu al falls under a certain predicate as a manner of meaning. This issue may at first seem to be a troubling one b ecause whereas conceptual relationships can be understood in terms of the charac teristics of features had in common by objects (and so whether or not these objects fall under certai n predicates on the basis of thos e characteristics or features), when we speak about de re modal claims, we do not necessarily speak of the characteristics or features had in common of objects what is under consideration is a single object, the res or thing, that the claim is about. Or at least so things seem before we begin a more comprehensive, thought out and subtle inves tigation into the issue. We will address the so-called problem of de re modality in Chapter Ten. In the next, Chapter Nine, we will return to some matters that might not have quite been resolved yet.

PAGE 158

158 CHAPTER 9 LINGERING CONCERNS AND A POSSIBLE DIRECTION FOR FUT URE RESEARCH ON A CLOSELY RELATED TOPIC (TWO-DIMENSIONAL SEMANTICS) Introduction We have provided the form of the theory wh ich an analytic-deflati onary conventionalist approach to modal sem antics might take. We ha ve also gone a little way toward showing how some actual flesh might be placed on the skeletal form. There are questions that still remain and objections to be anticipated and for which repl y must be begun. In Chapter Nine, we try to respond to two issues of importance. First, I bring up (again) what I believe to be an important feature of the theory whose form we have tried to give. There may still be worri es over circularity, and even if those who worry about vicious circularity have been persuaded by the previous chapte rs, I feel there may still be a bit of concern over the non-reductive nature of our account. I address these worries in the following section. Second, theres an 800 lb. gorilla in the room any time we speak of modal semantics which goes by the name Two-Dimensional Semantics. Toward the end of this chapter, we shall try to engage this beast so as to have a reasonable a nd rational discussion with him. My hope is that our project need not be seen as incompatible with the Two-Dimensional framework and intuitions. Have We now Shown that We Can Prevent Vicious Circu larity in the Deflationary Reduction if We Take this Approach? We have argued that the omnibus I can be used to provide the set of admissible interpretations each one of which is supposed to be a proxy for a Carnapian state-description. One of the difficulties for other approaches to modal semantics was that the class of possible worlds or states of affairs was such that it could only be delimited in a manner which provided

PAGE 159

159 satisfactory epistemological results by making us e of the very modal no tions for which it was meant to provide the semantics. Why does not the approach based on I face the same sort of difficulty? We claim that the structure of I could be provided if we ha d a detailed and specific account of concept possession conditions and the conceptu al connections between the members of our conceptual armada Since the fulfillment of the obliga tion incurred by our promissory note on the structure of I would be secured if we provided such an account of concepts and their connections, we can say that the aim of our analytic deflationary approach to modal semantics is not a completely reductive one. This is so because it may be the case that concept possession can be explained only in terms of certain dispositions of a possessor of the concept. Even if there is some sort of ineliminably dispos itional element to the story about the concepts that provide the structure of I we are not in the same situation that the Lewisian or Armstrongian is in. First off, we have not claimed to provide a reductive acco unt of modal semantics. Second, it is unlikely that the modal notions we set out to provide the semantics for are precisely the same that turn up in the account of dispositional features of concept possessi on. The modal notion expressed by necessarily is, as we have spelled things out, a linguistic one; to be able to understand this notion one must be able to understand a language of which it (or a translati on of it) is a term. The most fundamental notion for the conventionalist account (t hat of concept possession) need not be an ability which the cognizer must have a language to possess. For example, some sort of cognizer of a very primitive sort, might have th e capacity for sorting squares from non-squares, but might not have any language capacity at all. Conversely, anyone who is actually able to speak a language must have the capacity to sort on the basis of at least one predicate (see Chapter Seven, Aid from a Compositional Meaning Theory (An Interpretive Truth Theory)?), but this

PAGE 160

160 is enough to show that the notion expressed by nece ssarily is distinct fro m that of a cognizers dispositions to sort (his sorti ng ability) in the most basic se nse. Does this show that our understanding of dispositions does not rely on a prior understanding of nece ssity and possibility? Timothy Williamson1 argues that our knowledge of count erfactuals expressed by subjunctive conditionals (statements of the form if it were the case that r then it would be the case that s ) is a specific cognitive capacity which we exercise in a priori and a posteriori contexts and is what provides for our knowledge of the truths of modal statements. He writes, In some loose sense, we may well have a spec ial cognitive faculty or module dedicated to evaluating counterfactuals. It would have significan t practical utility. If we wanted, we could call it intuition, alt hough it would not in general be a priori. What seems quite unlikely is that we have a special cognitive f aculty or module dedicated just to evaluating counterfactuals whose antecedents are incompatib le with their conseque nts: the case is too special. Yet that is the crucial case for the meta physical modalities. It is far more likely that the general cognitive capacities that enable us to evaluate counterfactuals whose antecedents are compatible with their c onsequents also enable us to evaluate counterfactuals whose antecedents are incompa tible with their conse quents, and therefore the metaphysical modalities. This is not to say that we can reduce modality to something non-modal. Our offline capacity to evaluate counterfactual conditionals is modal in the sense that it is an ability a multitrack disposition. Such multitrack dispositio ns can only be reduced to the non-modal if there were some categorical base in terms of which they could be reductively explained. How Far can the Reduction Go? The Ultimate Reductive Base and the Commitments this Strategy In curs This sort of account blocks the kind of vici ous circularity that would result from using Carnaps intensions to completely reductively ex plain a natural language analog of the sentential operator N. On the account we have develope d so far, interpretati ons are classified as admissible on the basis of the whether a co mpetent semantic user who possesses concept C 1 For all references to Timothy Williamson see (Williamson, T., 2005).

PAGE 161

161 would find acceptable atomic sentences of the form ( ) where and are predicate and singular referring terms of th e language, respectively, and expresses C. Granted, there is dispositional character to this (or any) ability, so if there is a modal aspect to dispositional properties, then the account does not even purpor t to offer a completely reductive analysis. It seems that there is an inescap able appeal to the dispositional character of concepts, but if Williamsons point goes through, then we can explain modal knowledge in terms of knowledge of a certain kind of counterfactuals even if we cannot provide a reductive account of modality. There may, however, be another way to approach the problem in which we appeal only to the notion of semantic entailment rather than to the use of subjunctive conditional statements to express counterfactuals. We take to be basic knowledge of meaning in the sense of competen ce. Of course, when we talk about knowledge of m eaning and what it implies, we use language, and what the language we use means determines what follows from someones knowing the language. It follows, inter alia that if that pe rson believes that has certain features and considers whether is he will come to believe that is assuming that he believes the having of the features that does are conditions sufficient for the app lication of the concept expressed by is and that he considers the question whether the concept expressed by is applies and so comes to believe it does. From this it follows that if he were to come to believe all of the above, then he would come to believe that is By walking through this process, we have shown that we have derived our result from just an underlying semantic entailment: an individua ls having of certain features semantically entails that that individual is In sum, wherever we would have appealed to subjunctive conditionals such as, if x were the case, y would be the case, we can instead appeal to the claim, that x is th e case entails that y is the case.

PAGE 162

162 A Final Word to Allay Fears about Disposition s in Our Reductive/Explicative Base Even though the base which the modal operator necessarily is reduced to is dispositional in our account of modal seman tics in analytic-deflationary style, I do not think we should despair. I do not think the abil ity of one to who has the concep t expressed by the predicate is needs to be accounted for with full-blown modal re alism. As I have tried to show, all we really need is an account of idealized total representations (imagined counterfactual scenario). True, there is quite a bit of idealiza tion in our account: a completely imagined counterfactual scenario is such as to be impossible for a finite conceiver given a finite time, as is the notion that a finite conceiver in a finite time could ev en identify, in the context of th is sort of imagining, specific, arbitrary individuals presented in this imagining. I grant that it is all rather far-fetched, but not so far-fetched as to be something of no value: a fi nite conceiver could not do those things just mentioned, but a finite conceiver, just like one of us could do so if give n arbitrarily long and sufficient memory resources. And then again, we are engaged in a project of analytic philosophy idealization is our mothers milk. In the face of all these implausibilities, I stand firmly behind the assertion that what we have done in the for going is at least as plau sible than metaphysical realist suggestions for modal semantics. Everyt hing we have suggested is something an ideal cognizer could do; for Lewisian possible worlds or Platonic properties I am uncertain how any sort of epistemic access to modal knowledge is possi ble. Since we do believe that we have modal knowledge, I think our non-reductive, yet epistemi cally perspicuous account of modal semantics is a better alternative even though we are committed to some admittedly wildly fantastical (from where a philosophical layman sits) notions in our account. Our notions are tamer than what must be countenanced by a metaphysical realist, and better in terms of epistemology, too.

PAGE 163

163 Concepts Versus Quality Grounds of Chapter Seven Should we include the generalized concept possession condition num ber 3 (numbered sentence (4) in Chapter 7) in our analysis of concept possession? If we do include it, one might wonder why we are so obsessed with concepts in stead of certain qualiti es or features which might be had by each one of a class of individuals: if these qualities or f eatures are really what cause individuals to be sorted by what we ha ve been calling concepts why cannot we simply speak about a class of properties as reified quali ties of features that objects might have on the basis of which they might be sorted into the groups that we think of as be ing those sets of things which fall under certain concepts. Taking this sort of reified qual ity / feature approach might be attractive with regards to the traditional analyt ic project of getting to how things are in themselves, but it has an immediately distastefu l consequence. Recall that it was the cognizers epistemic relationship to the feat ures or qualities ha d by certain individuals that was the key aspect of our account of concept possession ; if we drift away from this epistemic relationship toward a more ontological focus on properties qua these reified features, we risk pairing with our account of modal semantics an obscure epistemology. Cognizers may have epistemic access to an individual with certain features, but, once we m ove to considering in full generality a class of properties as reified qua lities, we are no longer guaranteed epistemic access to those properties. To be of any use at all, this class of properties must include all properties, even ones that correspond to features that no cogni zer will ever recognize in any individual, even ones that are such that the features they correspond to will ne ver be causally interactive with any cognizer. So, for consistency, this class of properties must be thought of as abstract and not causally interactive at all with cognizers. On this approach we have rejected desideratum (3) of the conclusion of Chapter Five, as the properties qua reified features/qualities collaps es into a Platonic account of

PAGE 164

164 modal semantics, and so this approach would ma ke epistemology of modal truths much less than transparent. Conventionalism versus conceptualism redux: the worry over wh ether the qualities should be the ground for the intensio ns of predicate terms rather than concepts the possession of which allows us to sort objects on the basis of those qualities leads us to another puzzle that comes up in the path clearing for conventionalis m. Shouldnt modal semantics ultimately be grounded in relations of concepts rather than simply linguistic convention? Whereas concept possession is characterized by the ability of cognizers to character ize correctly individuals on the basis of their features or qualities, and so one concept (perhaps as a faon de parler if the underlying notion is to be that of conceptual master y which of course is just this sorting ability) can be characterized as distin ct from another on the basis of what kind of sorting the two concepts actually do, linguistic c onvention seems arbitrar y. Could not cat have meant what is meant by bat? The concepts on th e basis of which a cognizer sort s are intimately related to the very job in which they assist, the meanings of terms in a language are just arbitrary matters of convention so to speak. Since meanings are in this sense arbitrary and concepts do the actual work, why should we be trying to clear a way fo r conventionalism rather than conceptualism? Our previous response was that if our notion of conceptualism were such that concepts were considered to be abstract entitie s such that it might be that there was a concept that was never grasped by any cognizer, then the view collapsed into a sort of Platonism and faced the troubles that the Platonistic view faced. Some Words on Two-Dimensional Semantics And now to the 800lb gorillas in the room that goes by the nam e Two-Dimensional Semantics. We should have at l east something to say about this view, given that the view we have developed in this disse rtation is not one that is prima facie compatible with a two-

PAGE 165

165 dimensional approach. We shall consider, very brie fly, what I take to be a typical, mainstream two-dimensional view and show how it is in fact compatible with the analytic deflationary view. David Chalmers2 writes that a primary intension is a function from scenarios to extensions, a secondary intensi on is a function from possible worl ds to extensions, and a twodimensional intension is a function from whic h can be recovered a primary and secondary intension. Let us focus on the primary and secondary intensions by way of a familiar example. The primary intension of water, in the mouth of the speaker who is at the center of the scenario, is watery stuff, the stuff that plays the usual water role in the contexts in which We are speaking (nonscientifically) or the stuff with the superficial features had by water in the actual world. The secondary intension of water is H2O. In an arbitrary speaker-centered world (alternatively, scenario, or even perhaps sp eaker-centered counterfactual circumstance), the extension determined by the primary intension of water is the st uff whose superficial characteristics are those had by wa ter in the actual world. Primary intension is supposed to track epistemic possibility (given a certain way we ha ve of speaking) we have automatic epistemic access to the superficial features of water given th at we are competent with the term water. In an arbitrary possible world (we let speaker-cente ring drop out of the picture in the case of secondary intensions because we are trying to get at metaphysical possibility something that is, on Chalmers view, not necessarily epistemically accessible), the extension determined by the secondary intension of water is H2O. Whether something falls in the extension determined by a secondary intension is not to depend upon sp eakers and their epistemic access given that secondary intension is supposed to track features of individuals (or kinds of individuals) independent of how cognizers th ink about those individuals or kinds. That is, the secondary 2 For all references to David Chalmers see (Chalmers, D., 2006).

PAGE 166

166 intension is supposed to track metaphysical n ecessity. Primary and secondary intension are not thought to coincide because of the intuition that it is epistemically possible that water could have turned out not to have been H2O, but it is metaphysically necessary that water is H2O. As the two-dimensional framework that Chalmers has set up takes seriously possible worlds to explain secondary intension3, we cannot immediately fit our sort of semantic approach into the Two-Dimensional framework, but if we assu me that an interpretation (in our sense of the word we have developed herein) can play, in a satisfactory way, the functi onal role of a possible world, we might say that the secondary intensions of terms is that which places some of those restrictions which form the cr iterion of admissibility for an interpretation. Specifically, the secondary intension of is wate r is a function from possible worlds to everything which is H2O in those possible worlds; we use this secondary intension to place the following requirement on any admissible interpretation \ of index : \(water) is all the H2O and only H2O at circumstance In accord with the role it is to play in Chalmers Two-Dimensional framework, secondary intension can be unde rstood to correspond roughly to th e semantic facts that place appropriate restrictions on our in terpretations. Similarly, primary intensions can be thought of as reflecting a particular speaker s knowledge of m eaning (or lack thereof). Put somewhat artificially with the use of the terminology we have developed so far, the primary intension of is water might be thought as what a passable, bu t not completely competent, and unreflective speaker believes implicitly, that \(water) is. To be explicit, an uneducated and unreflective speaker or merely an unreflective one living before 1750 CE might believe that \(water) is just the watery stuff he finds in the situation A more reflective and circumspect speaker might 3 I believe there are serious problems with doing this as I have mentioned in Chapters Five, Six and Seven, but I shall not rehearse these criticisms here.

PAGE 167

167 hold rather that \(water) is stuff in situation that has a certain property (perhaps unknown to him, but discoverable through empi rical investigation) and is su ch that it satisfies a certain description associated with the term water. In this case, the associated description might be something like the watery stuff around here or a sentence or two th at describes waters superficial characteristics. If this speaker were even more thoughtful (and had some facility with reasoning and argumentation), he might come to believe that he didnt have the concept expressed by the predicate is water at all, bu t rather only knew the associated description satisfied by anything having the property had by everything falling under the concept expressed by is water. According to this line of reasoning, a speakers know ing the primary intension of is say, can be thought of as that speakers knowing the associated description satisfied by those things in a certain circumstance which are in the extension of the secondary intension of is in circumstance .4 Conclusion: an Apodictic Approach to Modal Semantics versus an Abductive Approach By way of c onclusion, I would like to say more about the distinction I have alluded to, but never spelled out in its entiret y, over the previous sections an d chapters. The distinction is between what I have called (I hope not inoppor tunely) the abductive / scientific method approach and the apodictic / axiomatic method approach. The names for the opposing sides of the distinction come from what I see as an appr oach to philosophizing in which, in accord with the first side entities or relati onships are postulated to explain, in a metaphysically robust way, the truth of claims that we hold intuitively (p re-theoretically) to be true. On the opposing apodictic side, an idealized (for malized) account of the actual abil ities (and presumed epistemic 4 I follow Kirk Ludwigs argumentative strategy here in .6.3 of his (2003).

PAGE 168

168 access to the intensions of predicate terms) had by speakers is used to build-up a philosophical view that provides the form of a theory in which an account of modal semantics can be fashioned. Of course, the apodictic method makes modal semantics epistemi cally available at the price of lacking a robust metaphysical story that explains moda l properties and identities in terms of the way things are in themselves without be ing conceptualized by c ognizers. I would assert, but will not offer further argument for the thesis here, that for an account of modal semantics one can have either a metaphysical r obustness that explains (or at le ast purports to) the way things are in themselves without a guarantee of epis temic access (this is the abductive method) or a guarantee of epistemic access with no claim whatso ever of metaphysical r obustness (this is the apodictic method). A possible philosopher (let us call him Phil) who will one day become a Lewisian possible world realist might hold that the sentence expressing a certain modal claim is true. For instance, he or she might claim that (13) is true and that (14) is a fa ithful paraphrase of (13). 1. There could be a six-legged, four-eared dog. 2. It is possible that there is a six-legged, four-eared dog. Phil wonders why this sentence is true and reasons in the following way. Non-modal sentences such as the cat is on the mat at time t0 and place p0, are true just in case the cat at place p0 is on the mat at time t0, and so, since the truth of a n on-modal sentence is explained by its correspondence to a state of affairs or situa tion, Phil reasons, the truth of the modal must be explained by a correspondence to a state of affairs, that is, there is a tr uth-maker for all truths non-modal and modal alike. The difficulties over what sort of things the truth-makers for modal sentences are is what prompts postulation of possi ble worlds and propertie s as reified features

PAGE 169

169 and members of ontology.5 We should keep in mind that the postulation of these sort of entities and relations as truth-makers is infere nce to the best explanation, that is, abductive reasoning. I believe, as I have claimed earlier in Chapter Four that modal r ealism in the form of Lewisian possible world theories and prope rty realism line up in that they are all essentially abductive approaches to modal semantics. In the specific context of two-dimensi onal semantics, one might use the abductive approach in the explanation of the metaphysical necessity of st atements whose negations seem epistemically possible. The example we discusse d in the preceding section was similar to the claim that water is H2O. The claim is metaphysically ne cessary (according to the twodimensionalists), but that water is not H2O is epistemically possibl e. How to explain the metaphysical necessity if we have no guaranteed epistemic access to the secondary intension of water? We might posit either (1). That the deep structure of what is called water around here (this universe) is the seat of th e fundamental determiner of what counts as water, rather than the superficial features of what is called water around here, and so the secondary intension of water is determined by abductiv e reasoning. Or (2), we might hol d (another posit) that the deep structure of a quantity of matter is that which is responsible fo r superficial features of that 5 One might wonder whether the analytic-deflationary conventionalist account of modal semantics we have developed appeals to a correspondence of the following so rt: Necessarily, S is true because there are certain facts about meaning that the sentence corresponds to in virtue of which it is true. Perhaps we could say that meaning facts make it the case that it is analytic that S, and this is the correspondence that makes true the claim Necessarily, S. I think this characterization gets things backward. A more profitable way to think about things would be the following. We engage in certain meaning constitutive patterns of use of predicate terms, but our patterns of use are not simply syntactical; we use words to semantic effect. That is, there are word-worl d connections. These meaning constitutive patterns of use gu arantee that some sentences (say S* among them) are true in every circumstance in which they could be uttered. In other words, these sentences are analytic roughly true in virtue of meaning. From this we reason, that, given the analysis we have proposed for necessarily, Necessarily, S* is true. Do we say that our meaning constitutive patterns of use ar e the truth-maker for Necessarily, S*? It sounds odd to claim this, but if we persist in doing so, we must realize that to do so is not to say that there is a single fact in virtue of which the sentence is true, but rather that our customary us age, along with a compos itional semantical theory, explains why the sentence is true. On the analytic-deflationary approach, we start with assumptions about meaning and show how we can argue that certain modal claims ar e true. On a modal realist approach, we begin with the hunch that a certain modal claim is true and then theorize about what it is in virt ue of which the claim is true (alternatively, what is that fact without which it would be the case that the claim would be false).

PAGE 170

170 quantity of matter and then assume that upon which the superficial features supervene (or course, as a matter of necessity) is the property which is picked out by the secondary intension of a natural kind predicate term. The fi rst is a semantical assertion, the second a metaphysical thesis. Either way, we must engage in a so rt of inference to the best expl anation if we are to satisfy both of our intuitions about water. On the other hand, lining up with the approach to modal semantics we have been pathclearing for is the so-called apodi ctic or axiomatic approach. W hy do we use these terms? We do so because in this method, we start from a basis and reason from this basis to generate the form of a theory. We start from the following premises and try to work toward a theory of modality reasoning in deductive fashion from these pr emises. One premise we start with is that competent speakers know the intensions of predi cate terms of their language, and that this knowledge is essentially knowledge -how: knowledge that allows th e speaker to use terms to indicate individuals of a certain sort in actual or counterfactual situations. Another premise (that will become more obvious toward the end of this dissertation) is that language is compositional in nature and that the meaning of a sentence can be calculated from the meanings of its constituents and their mode of combination and that speakers have the dispositional ability to imagine counterfactual scenarios and sentences which might be uttered in those imagined circumstances. We try to reason from these starting points to a conclusion which is the framework for theories about modal semantics. This framework is meant to be a structure which can show how modal semantics is possible and might be carried out given our desire not to make any more ontological commitments than necessary and what we take to be bedrock assumptions about how we use language to communicate.6 6 One could argue that the apodictic ap proach could very well be such that an advocate of it may eventually use possible worlds (or some other modal realist tool) in order to explicate semantics. I have tried to show that even

PAGE 171

171 One might have wondered whether any philo sophizing about metaphysics in general, ontology in specific, requires an abductive approach. After all, any time we philosophize about what there is and come to a conclusion, however tentative it is, that we have reasoned using inference to the best explanation. With regard to the external world (that presumably exists independently from us cognizers) there is al ways a distance between perception and reality, hence the sense of the term ver idical applied to perception and chance for skepticism to get started. I hope we have not been openly hostile to metaphysics in favor of epistemology, but it is my wish that we have engaged in a minimum of abductive reasoning about what there is in the effort to carry this project through. My desire ha s been to admit into our ontology only what is required to make sense, in an acceptable, non-circ ular fashion, of the word s of our language. We, too, much engage in abductive reasoning, as mu st any philosopher; I hope we can do so in a manner than has beneficial results regard ing an epistemology for modal semantics. We conclude our arguments to clear a path for analytic-deflati onary conventionalist approach for statements whic h are not explicitly of the de re variety. Chapter Ten and Eleven are devoted to showing that difficulties fo r such a treatment in dealing with de re modal claims are not insurmountable. In Chapter Ten, we lay out the problem for the conv entionalist and try to prune off some branches of possible solutions fo r the conventionalist in handling the problem of de re modality. In Chapter Eleven, we propose a technical apparatus fo r dealing with modal claims that allows us to endorse everything we want to without making a commitment to essentialism. Of course, in Chapter Eleven, we do not get something for nothing : we get no profound and substantive insights into the Truths of High Metaphys ics; the only reason that our proposed semantics endorses de re modal claims is that the use of certain classes of singular though such an advocate could do this, that nobody pursuing the analytic-deflationary approach must make use of modal realist notions (such possible worlds).

PAGE 172

172 referring constant terms is restricted in certain ways such as to make those de re modal claims come out true according to this theory. This is not to say that these term s are such that their associated senses are sufficient to secure their respective references; rather these terms are object introducing7, and so could be given reference clause s in an interpretive truth theory as compositional meaning theory for the language for wh ich we are trying to give an analysis of the sentence operator necessarily, but are such that they can legitimately be used to refer only to objects which fall under various predicates in various counterfactual situations. Then, much later in Chapter Twelve, we will try to fit everything we have done together with a general semantical theory after we explain how a conventionalist approach can accommodate quantified into sentences. 7 See Ludwig (2007).

PAGE 173

173 CHAPTER 10 THE PROBLEM OF DE RE MODALITY Introduction Any sort of approach to modal sem antics th at seeks to understand necessity in terms of analyticity faces the problem of de re modality. Briefly, the difficulty for such a view is that while analyticity is a semantical or meaning (and more generally a conceptual ) notion, some sentences seem necessarily true, but not so in virtue of meaning. On the face of things, a conventionalist who wishes to assert that necessarily, S is true must claim it is analytic that S and so faces a difficulty: if it s eems to us that necessarily, S is true, but S is not the sort of sentence which could be analytic, the conventiona list view is not satisfactorily comprehensive because it cannot give the righ t result for this sentence. In this section and the following two, we sketch out the proble ms a conventionalist approach faces over sentences of a certain form wh ich seem to be true of necessity, but not true in virtue of meaning, and in the remainder of the chapter, develop a re sponse to these problems on behalf of the conventionalist using the framework we have begun in th e preceding chapters. By way of introduction to this set of issues, let us first note that there are, of course, sentences of the form necessarily, S in which S is obviously analytic, thes e are not the sort of sentences that pose difficulties (at least of the de re variety) for the conventionalist. For example, we can say that the following sentence is analytic: 1. If something is a closed trilateral plane figure with straight sides, th en it is triangular. because of the respective meanings of the predicates is a closed figure, has straight sides, is trilateral and is triangular and the manner in which the sentence is composed by the combination of these predicates. We say unproblem atically in this case that prefixing this sentence with necessarily results in a true sentence by the lights of the forgoing chapters.

PAGE 174

174 But there are sentences whose form is not that of universal quantification, a subset of these is a problem class for analytic-deflationary modal semantics speci fically sentences of the form is where for a singular referring constant term is substituted and for a predicate term is substituted. On the face of things, if we held a particular view about how the referent of a singular term is secured, then it is easy to see how we might have trouble understanding how such a sentence could be analytic. In particular, if we hold that at leas t some singular referring terms are directly referential (let us say that the term a is among those), then it seems that the sentence a is F could not be analytic, as there could not be the right sort of semantic content associated with a to allow even for the possibility of the analyticity of a is F Let us say a bit more about why this is so. An oft-repeated way of characterizing the view that at least some singular referring terms are directly referential is to say that directly referring terms are those that serve to contribute only their referents to the proposition expressed by the sentence in which they occur. So, if we advert to the previous example, on the assumption that a is directly referring and the referent of a is (the non-linguistic individual) Abe (whatever that is), then in the proposition expressed by a is F a contributes only Abe. Assumi ng that no meaning or conceptual content is associated with non-linguistic entities (like Abe), there simply is not enough of such content to allow for the possibility that a is F is analytic (assuming that it is not analytic that everything is F ). There cannot be conceptual material associated with the directly re ferring singular term a as it serves (semantically speaking) simply as a pointer to its referent. The problem for the sort of analytic-deflationary account of modal semantics we are developing is that, pre-philosophically we do hold that certain sentences of the form necessarily, is where a directly referring sing ular term is substituted for are true, and prima facie it

PAGE 175

175 seems that the conventionalist position cannot endorse such sentences because we cannot understand how is could be analytic give n the difficulties we have just canvassed. For a specific example, if We are pers uaded by Kripkes intuition pumps, we hold that the following sentence is true: 2. Necessarily, Aristotle is human. If, in this sentence, the only semantic functi on Aristotle serves is the contribution of a referent to the proposition the se ntence expresses, how can it be a matter of meaning alone and hence analytic that Aristotle is human? The notion of direct reference is not the only ingredient in this recipe for trouble for the conventionalist. To show us how what is picked out by a directly referring singular term might have a certain property essentially Kripke introduces the notion of a rigid designator The term can be explained in the following way. If we us e possible worlds as a helpful heuristic for making sense of modal discourse and assert that the claim 3. Aristotle might not have been the teacher of Alexander. is true just in case in some possible world, Aristotle was not the teacher of Alexander, then a singular referring term is a rigid designator just in case it picks out the same individual in each possible world in which is denotes anything at all. According to Kripke, proper names are rigid designators, and so Aristotle picks out the same individual in each possible world (however it is we are to understand those, and however we are to understand the not ion of sameness across possible worlds). Now we can glimpse why we might th ink that (2) is true, but how it cannot be the case that Aristotle is human is analytic and so see how difficulties arise for conventionalism. If we hold that Necessarily, S is true for sentence S just in case it is true that S in each possible world and

PAGE 176

176 that the sentence is true in each possible world, and, in addition, S is a is F where a is a directly referring rigid designator with no associated semantic cont ent, then the referent of a must be F (on the view of modality we have assumed for the sake of argument), but it is not analytic that the referent of a is F because there is not enough semantic content associated with the term to make the statement a is F true as a matter of meani ng alone. The conventionalist seems stuck in an impasse. Rigid Designation and Metaphysical Necessity In sum if we assume a direct reference thesis for semantically unstructured singular referring terms1, that proper names are semantically unstructured and that they are rigid designators, then the proper name Aristotle pi cks out the same individua l, without the benefit of semantic content, in any counterfact ual circumstance in which it designates. If we also understand the truth of the sentence, necessarily, Aristotle is a person in terms of possible worlds, then the sentence is true just in case in every possible world P the referent of Aristotle, if it exists in P is a person. In this case, Aristotle is essentially human. And in general, on these assumptions, if there is a true se ntence of the form necessarily, a is F in which a is a proper name, then the referent of a is F in each possible world in which the referent of a exits, and a is essentially F 1 We can continue to play fast and loose with what were actually committed to by holding this thesis, but at this point Ill suggest that instead of simply holding that direc tly referential singular terms serve only to contribute their referent to the proposition expressed by the sentence in whic h they occur, we might assert that within the context of a compositional meaning theory based on an interpretive truth theory like the one spelled out in Lepores and Ludwigs (2007) a directly referring term is one whic h receives a reference axio m in the meaning theory. Specifically, for a singular referring term if ref( ) = O is the reference axiom for then the term is directly referring. A better term for the category of such terms is object introducing as such an appellation avoids the confusion that the directly of directly referring might incur; a term might be object introducing but there may be conceptual content associated with it. Such terms could still be given the reference axiom treatment in an interpretive truth theory, but there may be certain restrictio ns on how these terms are us ed to introduce object, i.e. restrictions on what sort of objects they might introduce.

PAGE 177

177 What, exactly, are the Problems for Conventionalism? What is Unacceptable for a Conventionalist? If such is the case, what exactly is unpalatable to a conventionalist? Briefly, if the referent of a is F in each possible world in which it exits and a has no semantic content, then, on this folk way of understanding modality, necessarily, a is F is true, but a is F cannot be analytic as there is no semantic content to a other than its non-linguistic re ferent. Now, if some singular term could pick out the same individual in ev ery possible world where that individual exists without the aid of any sort of f eature had by this individual, or any sort of descriptive content associated with the singular term itself, and this individual had some property in each of these possible worlds (other than proper ties which apply to all objects like the property of being selfidentical), then it does not seem that the ha ving of this property by the individual could reasonably be ascribed to any of our conventions about how to refer to this individu al. Indeed, it does not seem that this individuals having of this property would be analytic (a matter of semantical assignments alone), yet it does seem that the having of the property would be necessary, given that, by the set-up of the situation, this individual (when it exists) must have the property. So the conventionalist cannot accept that we can use a singular referring term to pick out the same individual across possible worlds unle ss some relevant feature (or features) of that individual is (are) requ ired to secure the referent or there is semantic content somehow associated with the name (perhaps not enough co ntent to secure the re ferent of the name). The problem of Essentialism and what wo uld be required for conventionalism to avoid it: as we have suggested a rela ted problem for a conventionalis t approach to is that of metaphysical essentialism. According to the example we have sketched so far, if, in fact, (2) is true, then we can claim that Aristotle is esse ntially human. This claim is tantamount to saying

PAGE 178

178 that there are modal features2 of certain individuals in this case the individual picked out by Aristotle that can evade semantic characteriza tion. This is so because a particular individual can be picked out with a direc tly referring term and a true modal claim can be made of that individual using that term. The truth-maker for th e modal claim must reside in the individual so picked out rather than in any semantic feature of the name used to refer to the individual in discourse because the semantic c ontribution of the directly referri ng term is just the contribution of the referent to this discourse. For a conventionalist account of modal semantics to succeed, one who holds it must be able to endorse, in a manner that is not ad hoc the truth or falsity of each modal claim that is intuitively true or false respectively (or show why We are mistaken to hold pre-philosophically those claims true or false). Does the Notion of Rigid Designation Presuppo se the Existence of Essential Properties? In preparation for showing how conventionalis m can endorse sentences of the type we want it to, let us take a closer look at the notion of rigid de signation on the assum ption that reference is direct for some singul ar referring terms. I want to suggest that the drawing of the metaphysical conclusion that esse ntialism is correct on the basis of the semantic phenomenon (rigid designation) can only be the result of begging the question for essentialism or begging a closely related question: one ove r the issue of how to understand the phrase same individual in any possible world in which th e term designates anything. To see this, we will continue to make use of the possible worlds heuristic, but we will get away from Kripkes examples about objects that fall under familiar kinds (which I believe to be 2 If an individual has the pr operty of possibly being green or has the property of necessar ily being green, then it has a modal feature or property.

PAGE 179

179 prejudicial in favor of the conclu sions he draws). So let us consid er the matter purely formally in terms of a simplified example. Consider a directly singular referring term c and the map, ref from singular referring terms and possible worlds to referents, such that ref ( c w ) is the referent of c in w Consider four possible worlds w0, w1, w2, w3 and assume that ref ( c w0) = ref (c w1) = ref ( c w2) and ref ( c w3) is undefined. Since, according to the our definition of the map ref the referent of c at each of these possible worlds is the same individual, except in that world in which there is not the individual ref ( c w3) (because ref is not defined for this argument), and by stipulation, c is a directly referring term, by Kripkes lights c must be a rigid designator. But, simply on the basis of the foregoing together with the notion of rigid designator, on the face of things, nothing prohibits us from claiming that at w0, ref ( c w0) has only intrinsic properties P0, Q0 and R0, at w1 3, ref (c w1) has only intrinsic properties P1, Q1 and R1, and at w2, ref (c w2) has only intrinsic properties P2, Q2 and R2, and for i j {0, 1, 2} and i j any merelogical combination of {Pi, Qi, Ri} is completely distinct from any merelogical combination of { Pj, Qj, Rj}. On this example, there is no property that is essential to the individual picked out by c And so, if everything in this example is workable, we can c onclude that just because an individual may be picked out by a rigid designato r, that individual need not have any essential properties. To try to assure ourselves that the example is persuasive, we should consider the places where one might object. Should we be permitted simp ly to stipulate (as we have done) that the referent of c (ref ( c )) is the same individual at the various possi ble worlds We are taking into account while at the same time stipulating that ref (c w0) has no properties in common with 3 In addition, of course, to those properties which are had by every individual the property of being self identical, for example. Properties had by every individual arent usually candidates for essential properties of an object.

PAGE 180

180 ref ( c w1) or ref (c w2) (and similarly for the referent of c at w1 and w2). How can what is referred to with c be the same across a range of possible wo rlds if the individual has completely different properties in each world of this range? This situation seem s to fly in the face of how we use actual names: the thing we mean to pick out with the name Bobby might have been slightly different (Bobby might have had curl y, red hair instead of straight, black hair or he might have been much smarter than he is), but to imagine a possible world (or counterfactual situation) in which we refer to a certain volcano with the term Bobby seems bizarre (to say the least). Agreed, this situation does seem vastly at odds with how we actually use proper names, but, unless some restrictions are spelled out how to understand the same of th e definition of rigid designation, it is no t disallowed given our provisions for directly referring singular constant term rigid designator and possible world So how are we to understand this the same? We might claim that an individual can only be considered one and the same in different possible worlds if, at each possible world, the individual has some set of propertie s or other. But to do this would be to claim that for a directly referring singular constant term to be a rigid designator, that is, for the term to refer directly to the same individual in any possible world in whic h it refers to anything, the term must pick out an object which has a certain set of properties. If an individual ha s a certain set of properties in each possible world in which the individual exists then, by definition, that individual has those properties essentially. And since this commitment to essentialism is required for an object to qualify as the same individual across possible wo rlds, this formulation of rigid designator requires a commitment to essentialism. The doctrine of essentialism is not argued for with the help of this notion of rigid designation, only reasserted in somewhat different guise.

PAGE 181

181 But, of course, it could be the ca se that some rigid designator, d, say, simply happened to be such that for each possible world wi either ref (d, wi) is not defined or ref ( d, wi) has property expressed by is P In this case, necessarily, d is P is true in the absent any prior assumption about essentialism. We shall see later on in this chapter that the conventionalist will face difficulty endorsing the truth of this senten ce unless we make some other assumptions about the function of directly referri ng singular terms. Alan Sidell e sketches the assumptions a conventionalist must make if he is to hold on to the notion of rigid design ation on page 67 of his (1989), If transworld identity is not a matter of mind-independent modal fact, a term cannot be both rigid and purely ostensive (which is the dou ble duty [most] rigid designators are supposed to serve in most treatmen ts). For the conventionalist, transworld identity (or any modal property, for that matter) is not to be a matter of mind-independent modal fact (a condition which could include on a broad understanding the case in wh ich transworld identity will be explained in terms of semantic and conceptual facts, rather than strictly in terms of what might be called metaphysics proper the truths of which are altogether independent of any semantic or conceptual facts) and so a term cannot be both rigid and purely oste nsive (that is, se rving to pick out a referent with no semantic or meta-semantic4 content whatsoever) because to allow this is to provide for the possibility of tr uth of a sentence like necessarily, d is P without the possibility of a conventionalist explanation of its truth. A related tangentepistemic access to modal truths and modal seemings in the context of realist versus conventionalist approaches: while We are on the topic, let us pursue a brief aside and consider how allowing for the truth of a sentence like the preceding (necessarily, d is P ) leads us to modal skepticism gi ven the account of modal semantic s that endorses this claim is 4 This may be a good term for the content provided by the competence one has with wh at Ludwig calls category names.

PAGE 182

182 to be of the properly metaphysical stripe and reductive.5 To avoid circularity, the class of objects (possible worlds) that provide truth-makers fo r modal claims such as the preceding must be ontologically independent of our conceptualization. This means that if such an account of modal semantics is to be noncircular a nd reductive, we are not (indeed must not be ) guaranteed epistemic or conceptual access to these objects. But if this is the case, and some rigid designators are purely ostensive ( purely referential in Kit Fines6 terms who follows the use of Quine (1976)), then theres no way, in general, to know whether what is picked out by d has a certain property or other in a certain possible world. And so, as a consequence of this situation, our knowledge of the truth of the sentences of the form necessarily, is in which any purely referential rigid designat or is substituted for is not guaranteed. If we pursue this line we must be comfortable with modal skepticism, at least for some de re modal claims. In this dissertation, We are trying to clear a way for a theory of modal semantics according to which we are not forced to be comfortable with this sort of modal skepticism. Just to tie up a bit of one loose end, re call that I said that we were not (and cannot be) guaranteed epistemic access to the class of objects (possible worlds) which are the reductive grounds for our modal claims because a guarantee of such epistemic access would be tantamount to a concession that the class of objects to be the reductive grounds was not mind-independent. In particular, we cannot be guaranteed epistemic access to those individuals picked out in the class of possible worlds by dire ctly referring terms. However, it may be that we do have epistemic access to these individual s by some one off freak accident or ability. Even if such were the case, I do not think that such a situation shou ld be comforting to one who holds the view that 5 Shalkowskis and others admonishments of reductive accounts of modal semantics are canvassed in Chapter Three, Chapter Four, Chapter Five and Chapter Six. 6 For all references to Kit Fine see (Fine, K., 2005).

PAGE 183

183 a class of mind-independent objects can be the re ductive ground for modal claims given that this person is not happy to hold a view which may lead in a few short steps to modal skepticism. Even if we have epistemic access to the particul ar individual so named, theres likely to be another individual for which we do not have epistemic access after all we are not guaranteed access. One who holds the conventionalist view, on the other hand, attempts to treat the problem of de re modal claims in such a way that the kno wledge we believe ourselves to have is guaranteed, and in so doing attempts to give an account on which we are guaranteed to have the knowledge of de re modal claims that we believe ourselves to have. Regardless of whether one holds the conventio nalist view or a realist view, we have intuitions that certain de re modal claims are true and that we know this. On the realist view, we are forced to hold that we are not guaranteed knowledge of the trut h of these claims. It is my hope that the conventionalist view will be able to endorse the clai ms we believe are true, and will be able to show that, given that we know a langua ge in which these sort of claims are made, our knowledge of these claims is guaranteed. If one did not have any intuitions about the truth of certain de re modal claims, then he would not feel the pull of any sort of explanation of their truth either realist or conventionalist. And it seems likely that for claims about which we have no intuitions, we would not be tempted to claim th at we had some sort of epistemic access to the truth-makers for those claims. For if epistemic access is some kind of vi ew into the realm of metaphysics proper (some sort of faculty for the a pprehension of Platonic properties or some sort of epistemic access to the situations on near a nd distant possible worlds), then how might we have this sort of knowledge without having the hu nch that these claims are true? The situation would be similar to knowing a theorem of ma thematics, but not having the hunch that the sentence that expressed the theorem was true. Su ch a situation would be very odd indeed. In any

PAGE 184

184 case, as a look-ahead, we can comfort ourselv es with the goal of a conventionalist modal semantics regarding de re claims: the conventionalist will seek only to provide a semantics for de re sentences such that it endorses the intuitions we have about the truth or untruth of such sentences. Now we return to the difficulty of de re modality for a conventionalist account. The problem of providing an endorsement of de re modal claims that are prima facie true is a pressing one for the conventionalist. I believe that we can accommodate the notion of rigid designation within the c onventionalist, Neo-Carnapian framework we have developed in the Chapter Two and Chapter Three and possibly use this notion to affirm most of the de re sentences we consider whose primary operator is necessarily. (But, to an ticipate our approach, I think the notion of rigid designati on will not be useful in giving a conventionalist account of the semantics of de re modal claims. In particular, the notion of rigid designation together with an explication of the semantics of the modal de re sentences we are c oncerned about can be subsumed under a more general thesis about how we should circumscribe the use of directly referring singular terms in the natural language we partially model with our set of admissible interpretations.) Possible Conventionalist Responses to the Concern over De Re Modality. What are the options for the analytic-deflati onary account of modal semantics? A first cut might be to reformulate the notion of rigid designation in terms of our conventionalist framework. The reformulation will likely be long and arduous. First, note that we can spell out rigid designation using only the sentence operator necessarily without the notion of possible worlds. To warm up, and as a reminder of what has gone before, heres a formulation with possible worlds:

PAGE 185

185 4. A c is a rigid designator iff for any individual x if c refers to x then for each possible world w if x exists in that world, then c refers to x in w and for any individual y if y exists in w and y is not identical to x then c does not refer to y in w Let us try to do the same thing w ith only the operator necessarily: 5. c is a rigid designator in a language L iff for any individual x if c refers to x then necessarily if x exists, then c refers in L to x and for any individual y if y exists and is not identical to x then c does not refer in L to y One hurdle has been jumped: possible worlds talk is not necessary, only the sentence operator necessarily is need ed. Now, it may be that we could carefully formulate a version of rigid designation within the framework we have developed in preceding and see what we could do to show that the analytic-def lationary account handles all that we want it to, but given the doubt we have over whether there are any apparen tly essentialist conseque nces that result from the truth of de re modal claims in the absence of background essentialist assumptions in the formulation of rigid designation, I discourage us from doing so. Instead, we will try to show how the analytic-deflationary approach can endorse de re m odal claims without making use of any notion of rigid designation. To th is end, we have the following. A preliminary proposal: one might hold7 that there are certain properties that are had essentially. This suggestion is not on its face, tantamount to essentialism8 the notion that some individuals have certain properties essentially because the current proposal is about the features of properties rather than features of individuals9. Specifically, if an object O has the property 7 Thanks to Chris Lubbers for this proposal. 8 As an aside, we note that there are some properties that are had by all individuals (such as the property of being self-identical) but our commitment to this fact is not a commitment to essentialism. To hold an essentialist view, one would have to believe that there was an individual which had a property the lacking of which would constitute its failure to remain that same individual AND that this property was NOT one that was had by every individual. For example, an essentialist might think that the individual who is Aristotle must have the property of being a person if that individual is to (continue to) be identical to Aristotle, but must also hold that there are individuals which do not have the property of being a person essentially. 9 Such a claim is, on the face of things, de qualitas (of a property) rather than de re

PAGE 186

186 expressed by is F and this property is one of the special cla ss of properties, then O has this property necessarily. If a directly refers to O then sentence necessarily, a is F is true. No notion of rigid designators or essentialism seems to be required to endorse the truth of the modal sentence. But whats really at work here? If O has the property expressed by is F and this property is such that those individuals wh ich have it have it of necessity, then does not that mean that those individuals which happen to have this property are such that (to dip into the possible worlds heuristic for illustration purposes) ther e is no possible world in which one of those individuals does not have it, that is, each of those individuals has it essentially ? This solution may mark out a class of properties as different an d so may purport not to be essentialism, but it seems that essentialism is a consequence of this sort of view, and We are at pains not to accept essentialism as the consequence of any appro ach we may take toward clearing a path for conventionalist modal semantics. Conclusion Even though the (unsatisfactory) proposal does have essentialism as a consequence, we do have the intuition that drives us to this sort of proposal. Indeed, if we were constrained to a sort of material mode of philosophizi ng, we would wish to say that since we do use the name Bob to refer to a person, and we have the intuition th at Bob must be a person, else he would not be so-called. This intuition leads us on the material mode of thinki ng, to the failed proposal, that is, into thinking that for some properties (of whic h the property of being a person is one) anything which has that property has it necessarily. But there is another way of thinking about this intuition if we switch to the formal mode of philosophizing. We might think that there is something about the name Bob which requires that it be used to pick out objects of a certain sort. Is this tantamount to making the controversial claim that

PAGE 187

187 proper names have senses? Yes and no. On the suggestion we offer in Chapter Eleven, proper names will have associated senses in that they can be used only to refer to objects that fall under certain predicates, but, and this is a big but, th e conceptual content associated with proper names (for example) will not be enough to secure the referent of the name.

PAGE 188

188 CHAPTER 11 TECHNICAL APPARATI TO ENDORSE THE DE RE MODAL C LAIMS WE FAVOR, POSSIBLE OBJECTIONS AND RESPONSES Introduction We can use restrictions of ex actly the sort m entioned in the conclusion of Chapter Ten that is, explicit restrictions on how proper names are used to refe r to individuals in a language to provide an analytic-deflationary conven tionalist approach with a way to endorse de re modal claims. In this chapter we shall try to capture th e intuitions that drove the failed proposal to the effect that de re claims were essentially de qualitias claims, by switching to formal mode and claiming that the use of names is restricted in cer tain ways. Before we dive into this, we should take a moment to recall the relationship of the th ree sorts of maps we have used to give our model-theoretic generalizati on of Carnap. The set of ad missible interpretations, {\ }, was to be such that, given that Carnap s state-descriptions are restricted by concerns over consistency and concerns about the analytic relationships of certain predicat es to certain other predicates, each member of {\ } is a proxy for a Carnapian state-description. The map I is built from {\ }, so that an index and term are arguments to I and the result is an individual or set of individuals that are picked out by (in the case of singular terms) or fall under (in the case of predicate terms) the term in question. We could say that I presents the information found in each of {\ }, in a different, perhaps handier, fo rmat. (Of course, the existence of I depends upon a definitive characterization of the index set .) Finally, the map I presents all the information of I (and hence each of {\ }) in yet a different format. The map I takes as parameters a term, an index and an individual in the range of \ and returns either a yes or no just in case either (for a singular referring term) the individual is picked out by the te rm at that index according to \ or (for a predicate term) the individual is among the set of individuals picked out by \ The

PAGE 189

189 map I was supposed to put things in the right form at for understanding intensions in terms of conceptual competence. With the use of {\ } we can understand how we might think of the possible world indices that are the members of : each member of is something like an entire universe as imagined by one with comple te competence regarding all the predicate terms of the language we are dealing with. We have just explaine d in relatively few words the relationships borne by any of \, I, or I to each other. We can develop our theory for the semantics of de re modal claims with regard to any one of these (sets of) maps and easily generalize the theory to the other (sets of) maps. Now we dive in. It is interesting to note th at while we have taken considerable pains to delimit the class of admissible interpretations with regard to how we specify the extensions of predicate terms at various indices and what the (set theoretic) relations between extensions of predicate terms are which bear certain meaning or analytic relations to each other, we have made no restrictions on singular referring constant terms across different admissible interpretations. Doing so will be our project in this chapter. Hopefully, we shall see that some very natural restrictions can be placed on singular referring constant terms and that those restrictions can be exactly the one s that endorse all and only those de re modal claims that we hold pre-theoretically to be true. Topological / Linguistic-Use Restrictions Even though the last proposal of Chapter Ten fails to satisfy our requirem ents, theres a useful kernel in this way of approaching the problem: we can largely adapt the suggestion that some properties are such that th ey are had of necessity to the Neo-Carnapian framework we have developed in previous chapters by imposing certain strictures on the semantical system which is to model, partially, our notion of intension. The ba sic idea is to restrict the interpretations which

PAGE 190

190 were the constituents of the map I of Chapter 3 with the use of a three-place relation of predicate and singular terms (call it e ). As a preliminary, note that no ontological commitment is incurred by e it is merely an explicit way of repr esenting the manner in which we would like the map I to restrict implicitly its as signment of directly referri ng singular terms to individuals relative to its assignment of sets of individuals to predicate terms. Let us provide some motivation for the relation before we spell out the technicalities. The intuitive idea behind e can be illustrated in the following. Say we pick out a certain individual with a directly referring singular term ( a) and the sentence, a is red is true (because the referent of a is red). It seems intuitive that the (thing itself which is named by) ref( a ) must be a physical object: it makes no sense to claim that this individual is red unless that objec t is indeed physical. It is odd to say that, for example, ref( ) is red. It is important to no tice here that the intuitions we are trying to pump here are de re in1 in the following way: given that the thing picked out by the object introducing term a, that is, ref(a), we are asserting that it makes little sense to claim that ref( a ) is anything other than a physical object. To attempt to use the semantically primitive a to denote an abstract object runs counter our intuitions about the correct way to use the term a. I would like to underscore here that we are making a claim about the relationship (relative to our correct use of that term) of the semantically primitive term a and those individuals which might be picked out by that term. We are not making the weaker, de dicto claim, It is necessary that if a thing is red, then it is a physical object. 1 It might be just a bit awkward to call the claim were making here de re because we are actually making a claim about a certain class of semantically prim itive singular referring terms, so maybe de relatio in denotatio is perhaps more accurate (yet considerably less catchy). The claims we make will be such that they make true certain de re claims we wish to endorse.

PAGE 191

191 Similarly, if we pick out an individu al with the directly referring term b and the sentence b is a successor ordinal is tr ue (because the referent of b is a successor ordinal) then ref(b) must (at the very least), given our customary way of using singular re ferring terms, be an abstract object: it is nonsense to claim ref(Ernie) is a successor ordinal, given that we normally use the semantically primitive term Ernie to pick out human beings. The same goes for this example as for the previous: we are not making the de dicto claim, It is necessary that if a thing is a successor ordinal, then it is an abstract obj ect. but rather something much more like a de re claim about how the semantically primitive singular referring term b is correctly used. The intuition about a rather gene ral feature of language that I am trying to highlight with these examples can be put in the following way. I believe that we use singular referring terms, like proper names, in a specific way. When we use such a term to refer to an actual individual, we are bound, by our normal use of this term a nd terms like it, to refer only to individuals of certain kinds with that term when we speak co unterfactually about how things might have been. Given that we use a name like B oots to refer to my actual cat, I assert that we use the name Boots to refer only to individuals of a certain kind when we speak about counterfactual situations which describe the way the world might have been. I am not exactly certain where to draw the line about just how much freedom there is for what type of indivi dual this is, but I think we can safely say that this line is between the fo llowing extremes. Given th at we refer to my cat with the name Boots, then we might speak abou t a counterfactual situa tion in which Boots has ginger fur instead of black and white fur and use the term Boots to refer to my cat. And given that we refer to my cat with the name Boots, then we cannot use the term Boots to refer to anything other than a physical object. It just wouldnt make sense to say that we could conceive of a situation in which Boot s referred to the 118, 219th prime number while claiming that we

PAGE 192

192 were using all of our singular referring terms in an acceptable way our use of Boots in this case wouldnt be in lin e with our general prac tices for using names. The proposal is that our use of proper names is such that their use is restricted in certain ways when we speak about counterfactual situati ons about how the world might have been. In other words, there are meaning facts or use facts about certain semantically primitive singular referring terms that are sp elled out in terms of patterns of meaning constitutive use of these terms. We will spell out a way to model thes e restrictions given the formal model we have set up in the previous chapters over the next few paragraphs. I be lieve one virtue of the way we set things up is that we do not have to take a stand on the precise restrictions for how these terms function with regard to our formal m odel; we show merely that our model can reflect such restrictions. This sort of appr oach is different from both Ludw igs (2007) approach to handling de re modal claims and different from Sidelles (1989) approach. Our approach provides a generalization of Ludw igs suggestion of category names, in that the present approach shows how th e use of singular terms might be restricted in more general and flexible manner. Whereas a category name mu st refer to an object of certain kind in any discourse; our method of restricting admissible inte rpretations allows for a name to refer (in a counterfactual situation) to an object of different (but likely si milar) kind than the one of the individual it actually refers to. We have enough flexibility to f ill in the detail later about just what the exact restrictions are. Our approach is different from Sidell es in that our truth-makers for de re modal claims are not the conventions we actua lly have, but rather can be selected from among certain ways we might have used (in accord with some set of use norms) singular referring terms. I believe this approach allows for a bit more generality and flexibility than Sidelles account.

PAGE 193

193 The big picture representing this sort of approach is that usin g the structure that we have created as a generalization of Carnaps work, we can capture formally the manner in which our intentions, norms and habits with regard to semantically pr imitive singular referring terms shape our use of such terms. The explicit topological restrictions of the omnibus function I can capture the implicit restrictions there are on the use of such terms relative to the manner in which they are correctly used. Having given some background, let us flesh in the details. A technical presentation will make things easier. The relation e provides the means to formalize the ways in which we normally use directly referring terms. (There are, of course, de re modal claims which we might wish to endorse which require an even tighter restriction on I s assignments of directly referring singular terms relative to it is assi gnment of certain sets of indivi duals to certain predicate terms. For example, we might want our semantic theory to endorse the truth of our old friend, the sentence: Necessarily, Aristotle is a human being. We can use the relation e to enforce these sort of restrictions also. We see this after the technical presentation of the relation.) 1. Let the relation e ( 11 ) be such that for any predicate terms and and singular referring constant term IF e ( ), THEN, if there is an 2, such that \ *( ) \ *( ), then for each other \( ) \( ) if \( ) is defined.3 By substituting is red for is a physical object for and a for we get the first intuitive result of the preceding. By substitu ting is a successor ordinal for is an abstract object for and b for we get the second intuitiv e result of the preceding. 2 For a review of the precise characterization of I and its relation to the set { \ }, see Chapter Six. 3 There are easy generalizations of R to triples the first tw o members of which might be of arbitrary arity, but these generalizations may be of only marginal interest for our purposes. For example, let e n( n, n, ) be such that for any n-place predicate terms n and n, IF ( e n( n, n, )), THEN if there is an such that \ *( ) is included in a member of \ *( n), then for each other \ ( ) is included in a member of \ *( n), provided \ ( ) is defined.

PAGE 194

194 So what about that old standby, Necessar ily, Aristotle is a human being? We can accommodate what intuitions we have here by substituting is a person for both and and Aristotle for and holding that e ( ). Specifically, we hold that e (is a person, is a person, Aristotle), and so, as we have defined it, we have: if there is a \ such that \ *(Aristotle) \ *(is a person), then for each other \,\(Aristotle) \(is a person) if \(Aristotle) is defined. This is tantamount to restricting I so that anything that it assigns to Aristotle in a specific scenario considered counterfactual circumstance is such that that individual is included in the set assigned by I at that scenario (or mode of presentation) to the predicate is a person. We can now state explicitly the conditi ons under which sentences of the form Necessarily, ( ) are true on the conventionalist approach of understanding necessi ty as analyticity given our development of the relation e: a sentence of the form N( ( ) (a formal language approximation of Necessarily, ( )) is true in L (a generic language of which the features had that class We are investigating in the dissertation see Chapter Two) just in case for each \( ) \( ) if \ is defined for ; which is true just in case e ( ). If we require I s assignments to directly referring singular terms re lative to its assignments to predicate terms to conform with e, then we have a way of restricting I so that specific de re modal statements are endorsed. Is the truth of the de re modal statements we want to come out true a matter of analyticity or meanings al one? Not quite in the same way that true de dicto modal claims are a matter of meanings alone, but we will see in the following that features of the use of language (as partially modeled by I ) lead to the endorsement of the de re modal claims.

PAGE 195

195 Some comments are in order. The first is an ack nowledgement of debt to the insightful, but ultimately unsatisfactory solution of Chapter Ten. The suggestion there was that certain properties are such that they are had essentially: if individual ref(a) (the semantically primitive singular referring, object introducing term a picks out this individual) happens to have the property expressed by is P then ref( a) is P necessarily.4 This basic idea is one that we try to preserve in the restrictions we place on I by insisting that it conform to the restrictions in force because of e. The problem with that unsatisfactory so lution was that it made modal properties (that were the truth-makers for de re modal claims) inherent to individuals, independent of how we refer to them. In contrast, the present proposal aims to endorse the same claims but seeks to do so by stipulating how the singular terms (names) th at refer to the individuals are to be used relative to how certain predicate terms are to be used We should also note that the present proposal ha s been fashioned to be mostly of a piece with the strategies of Ludwig (2007) and Sidelle (1989) in their respec tive dealings with the problem of de re modality in articulating parts of a conservative or conventionalist modal semantics. Consider Ludwigs proposal of category names as part of a solution to the problem of de re modality. In the context of a compositional meaning theory, a ca tegory name is a directly referring singular term whose reference axiom is such as to ensure that the name picks out an individual of a certain kind. (Category names may be so called because they are used to refer only to individuals of a certain kind or category.) For example, Aristotle is a category name given the following reference axiom: 2. ( C ) For any x if x = A and x is a person, then re f(Aristotle) = x .5 4 To be clear, as I understand it, the suggestion was not de dicto about the saying a is P, nor exactly de re but rather de qualitas about the property P. 5 (Ludwig, 2007) page 6.

PAGE 196

196 Where A is directly referring singular term that is not a category name whose referent is Aristotle. On this view, anytime a competent spea ker uses the name Aristotle the speaker refers to an individual which is a person. Since the re ference axioms are to govern our use of names even when we speak of counterfactual situat ions about the way things might have been, even in modal contexts a competent speaker uses the name Ari stotle to refer only to an individual which is a person. I assert that holding e (is a person, is a person, Aristotle) and insisting that I conform to the restriction from e forces the same result on us. If this is right, then it seems that we have th e tool to capture generally the characteristics of category names with the relation e. Presumably, strings like Joe Billy and Ned are also category names which are used to refer to persons; let us call the set of category names used to pick out persons Cp (so Aristotle Cp Joe Cp ). Now then, we can hold that for each Cp, e (is a person, is a person, ). This claim should be such as to endorse all the de re modal claim that would be endorsed by holding each of Joe, Billy, Ned Aristotle, etc. as category names in the context of a compositi onal meaning theory based on an interpretive truth theory because in any interpretation \ {\ }, \ ( ) \ (is a person). We turn next to Sidelles treatment of de re modal claims in the context of a defense of conventionalism. He asserts on page 77 that, The conventionalist is claimi ng that we cannot make any sense of modality, of essential properties, or of identity acr oss possible worlds independently of our conventions. So it is not as if, as is required for this [ contra conventionalist] realist worry to get going, there are facts about whos who in various possibl e worlds and our conventions then merely determine which of these things are to be called by the same name or fall under the same predicate, but rather that th ese decisions (or at least some of them) determine whos who. If a name is used rigidly, th e things to which it applies are thereby identical. We may explain how we can generate truths de re then, by saying either that our conventions do not merely regulate how we talk, or by sa ying that the metaphysical facts on which the possibility of de re truths depends are not separabl e from how we talk. However we describe it, the conventi onalist is able to produce de re modal truths because, on this view,

PAGE 197

197 our conventions cut a lot deeper than our [r ealist] opponent (above) gives them credit for, and they can do so because it is not merely the modal facts that result from our conventions, but the individuals and kinds that are modally involved. (original emphasis) Sidelle is going further than I wish to both strategically and tactically Strategically, he goes further by saying that we may not be able to understand modal features (modal facts, modal properties and transworld identity) as having their origin in anything other than our conventions. I do not say that we cannot understand modal facts as having their origin in anything other than our conventions. We might be able to understand m odal facts as having thei r origin in modal and essential properties. I claim that it suffices for us to make sense of the semantics of the de re modal claims to make use of the generalization we have carried out of Carnaps work together with the de re restrictions we place on {\ } with the relation e. If, as we have suggested, we can make sense of the semantics of those sentences in the way we have proposed in this chapter and Chapter Ten, then realist explan ation for the origin of modal facts seems explanatorily otiose and epistemologically suspec t. And he goes further t actically, by trying to give a satisfactory account of rigi d designation in a conventionalist milieu I doubt we need to do so (as I have indicated earlier in Chapter Ten). But he is br ushing up against the notion that the intentions with which we use a term are important in restricting what sort of individual is picked out by the term in a modal context. If Si delle found our approach in the previous chapters appealing and in line with his aims here, th en I think he would find the restriction of I by means of holding that certain predic ates and singular terms bear e to one another to be compatible with his approach to the requis ite conventionalist endorsements of de re modal claims that are intuitively true. Finally, in order to allay worries that may have come up over whether we have actually said enough about which specific predicates and singular terms are to bear relation e to each

PAGE 198

198 other, I would like to reiterate the modesty of the scope of our project here. Unlike Sidelle, we are trying simply to clear a path for conventiona list modal semantics and show that such an approach is viable among other possibly realist approach es to modal semantics. I argue that we have shown how certain modal de re sentences of traditional interest and puzzlement could be reasonably endorsed in the context of the theory we have developed in the preceding chapters. We havent (nor should we have) undertaken to give a detailed tr eatment of exactly which (sorts of) predicates and (sorts of) singular terms bear e to one another; simply to have shown that I can be restricted to get what we desire out of our semanti cal theory is enough. Exploration of the Topologica l / Linguistic-Use Proposal Of course, there are questions of, challenges for, doubts about, and possible extensions and refinem ents of the approach we have outlined. I will consider three in this section. First, we will consider whether a direct reference theory is re ally compatible with th e restrictions placed on I by taking seriously e. Then, we will consider how effectively this approach can deal with names (like Sherlock Holmes) which denote fictional characters. Finally, we will consider what been recently called description names6 as another possibility for dealing with certain de re modal claims. Can We Hold that Category Names are Directly Referential? Let us m ark a distinction by the use of another term for certain singular referring terms. If such terms serve the function of introducing into the proposition expressed by the sentence in which they occur and the terms are semantically primitive, in the sense that one could not understand such terms by understanding sentences in which those terms did not occur, let us call those terms object introducing following Ludwig (2007). Such terms may have an associated 6 (Ludwig, 2007) pages 3-5.

PAGE 199

199 sense (such as a category), but because they are semantically primitive in the forgoing sense, this associated conceptual content is not sufficient to determine the referent of such a term. Names of Fictional Characters There are tw o broad strategies available to one who holds this view with regard to the names of fictional characters lik e Sherlock Holmes: pragmatic and semantic. On the pragmatic side, one could hold that fictional discourse is to be understood in roughly the same way that non-fictional discourse is but that we hold that such discourse is not to taken seriously in the same sort of way that non-fictional discourse is. Such is John Searles7 line. On this view, we need not say much more because the modal seman tic theory we develop is not that which does the work of explaining how we understand proper na mes as used in fictional discourse. If an opponent were to challenge our semantical stor y on the basis that it doe s not afford us an appropriate way of dealing with na mes of fictional characters, yet sh e held a Searlian view of the logical status of fictional discour se, then we do not have to seri ously consider (that particular aspect of) her criticism. More likely, one who ch allenged our view would hold that a theory of semantics should be that which explains how we are to make sense of names of fictional characters. We turn presently to this concern. On the semantic side, one would try to account, in terms of a general semantic theory, for fictional names. There are two sorts of categor ies under the heading of semantic treatment of fictional names. The first is a sort of complex logical form with which we might give an account of the truth of the sentence Sherlock Holmes is a dete ctive by understanding the sentence in the context of, or in relation to, some work of fi ction relative to which the truth or falsity of the sentence should be assessed. More specifically, suppose that we are give n a body of discourse in 7 For all reference to John Searle see (Searle, J., 1975).

PAGE 200

200 which the name Sherlock Holmes features, fo r instance this body might be the text of Sir Arthur Conan Doyles The Hound of the Baskervilles Now our general semantical theory (especially the one we have been boosting here a Davidsonian interp retive truth theory as compositional meaning theory) is supposed to in dicate to us how to understand the meaning of sentences given that we understand the mean ings of their constituent words and the (grammatical) mode of combination of those wo rds. Given that we understand the meanings of the sentences that form this body of text, we could respond affirmatively to the question, Is Sherlock Holmes a detective given what youve read in The Hound of the Baskervilles ? This specific case suggests a general treatment in whic h determining the truth of Sherlock Holmes is a detective should take the following approach: the sentence is true just in case, if we use B as a variable to range of bodies of text (narratives), and the IN to stand for the th ree place relation that holds between bodies of text, semantically primitive terms and predicat e terms such that IN holds of B1, N1, 1 just in case N1 is a(n) 1 is true relative to B1 8 then ( B )( IN ( B Sherlock Holmes, detective) In this case, the sentence does not look to be de re after all, or if it is de re ( de Fabula specifically), then, it is rather about (the contents of) a body of text (hence Fabula ) instead of about what might have been named by Sherlock Ho lmes. So, on this sort of approach to the names of fictional characters, we mustn t modify our account of modal semantics. 8 One who is able to understand the sentence N1 is a(n) 1 must be in a position to know that N1 is an object introducing term which is strictly empty. The sentence Santa Claus is fat, is strictly speaking meaningless because the semantically primitive singular referring term Santa Cl aus is empty; since it serves a meaning function of being an object introducing term, yet doesnt introduce any obj ect into the proposition expressed by this sentence. We understand the semantic role played by Santa Claus as being the same sort as pl ayed by George W. Bush. Understanding the semantic role played by semantically primitive object introducing terms, understanding the role of predicate terms like is a detective and understanding the grammatical mode of combination of those two sorts of terms are all that is required to understand the sentence Sherlock Holmes is a detective.

PAGE 201

201 On the other side, we might deal with fic tional names as names of a special sort. Now either, fictional names are such that they actually have referents, just not actual referents (referents of a different ontological status that which is named by George W. Bush or ), or fictional names are such that they work, not as object introducing terms, but rather as terms which signal that they are significant in some so rt of meta-fictional way. On the first option, we would hold that a sentence such as Sherlock Ho lmes is a detective contains an ordinary predicate is a detective it is just the case that this predicate applies both to physical objects and objects that have the ontological status of fictional characters This approach would require that we take the domain of a specific interpretation with index to contain the individuals denoted by proper names of actual people such as George W. Bush and Socrates and individuals which are denoted by proper names of fictional characters such as Sherlock Holmes. The important observation to make is that whatever sort of tack we take in addressing this problem, it seems that the framework we have de veloped in previous ch apters (and the beginning of this one) will be suitable for that particular tack: if we choose pragmatics, then we need do nothing, as these pragmatics allow us to remove the explanation of the semantics of Sherlock Holmes is a detective from those sentences we need be concerned about; if we choose a properly semantical tack, then such a sentence is not even de re ; on the special names / ordinary predicates tack, we need simply expand the domain (= ) to include fictional entities that are the referents of fictional names. Description Names (Such as the Numerals) Finally, we m ight gain insight into the relativ e amount of satisfaction we should take from the use of e as a way to ensure that the analy tic-deflationary account endorses certain de re

PAGE 202

202 modal claims by contrasting it with another wa y they may be handled. Category names are not the only tool developed by Ludw ig in his 2007; he also uses description names to explain how a conservative, epistemologically responsible appr oach to modal semantics could account for the truth of certain de re modal claims. Description names are introduced to show specifically how we may understand de re sentences in which quantification is into the scope of a modal operator (sentences of the form ( x ) ( x )) where we take this sentence to be a typical formalization in the usual idiom formalization idiom of a natural language sentence involving the sentence operator necessarily). Even though we do not take up this issue until Chapter Twelve, we should assess the strategy we developed so far for de re modal claims by comparing our technique to one that made key use of description names. Briefly, the idea is that if conceptual content were present in virtue of how each of a class of singular referring terms provided its referent, then those terms c ould be directly referring, but, because of this conceptual content, we could se e the analyticity of certain sentences in which these terms occurred. A description name is so-called because it provides a definite description which picks out an individual.9 If, in the context of a compos itional theory of meaning for a specific object language, we can give reference axioms for singular terms, and if those reference axioms are such that they induce certain pr operties or relations on or among the referents indicated by the axioms, then we can claim that these properties or re lations follow from how these terms secure their respectiv e referents as a result of facts about the meaning theory itself 9 Such names might do so in virtue of their syntactic features rather than any conceptual content associated with their semantic features (as names, rather than definite descriptions, they are semanti cally unstructured). We can advert to the numerals for an example. The string of characters that is a numeral reveals the relative position in the number line of that which it refers to. A cognizer competent with the numerals need appeal to no other conceptual content than what is encoded by syntactic features to understand what each numeral refers to.

PAGE 203

203 specifically, features of certain of the reference axioms of that meaning theory. It sounds complicated, but an example helps explain. Ludwig uses the numerals and numbers as an example of how to understand the quantified sentence ( x ) ( x > 7). In providing the semantics fo r such a sentence, we have reference axioms for each numeral , given in terms of the successor relation (and the addition relation, the multiplication relati on and a concatenation function) that might go like this For any numeral n, if 3. (a) n= then for any x if ~( y )(successor( y )= x ) & ( z )(successor( x )= z ), then ref() = x 4. (b) n= then for any x if x is the successor of 0 (that is x =successor(0)), then ref() = x 5. (c) n= then for any x if x is the successor of 1, then ref() = x 6. (k) n n n n then for all j if L( n, j ), then the x such that x = SUM(0, j ref( ni) 10i) is such that ref( n) = x .10 Since we have, by the meaning of the successor relation a nd the greater than relation, successorm( n) > n (for any m > 0), it is analytic (or at least a matter of the application of meaning statements alone) that successor2(7) > 7, that is, > 7 is analytic. And so, on the conventionalist reading of (9 > 7) is true also. Since the sentence has a de re form, the sentence > 7 is analytic, a nd these names refer directly, it seem s that there must be conceptual content associated with the names and it is had in virtue of the way in which the referents of these names are fixed. 10 Where in (k), L( n j ) is read as n is the concatenation of j numerals each of which are assigned a reference axiom of (a) (j) (let us call th is class of special numerals the 1-placers ), and SUM(0, j ref( ni) 10i) is read as the sum of ref(n0) 100, ref( n1) 101, ref( nj) 10j where n0 is the 1-placer suffix of n n1 is the 1-placer suffix of the numeral which, if prefixed to n0 would result in n n2 is the 1-placer suffix of the number which, if prefixed to n1^ n0 would result in n etc. Description names are given much more thorough treatment in (Ludwig, 2007). I just wanted to get out the gist here so we can see the main ideas of how the argument goes.

PAGE 204

204 In general, it seems that the manner in which we use numerals to refer to the numbers provides us with the sort of inform ation that allows us to see the analyticity of a certain class of sentences in which the numerals occur. We see, by understanding how the numerals work, that > 7 is true in virtue of semantic assignm ent alone. So at least for the numbers, names do provide some content that allows us to detect an alyticity in certain cases on the basis of how we use those names to refer to individuals. It is obvious that description names are a s ubspecies of category names the category that the numerals belong to is given implicitly in these axioms with our use of the successor function. The successor function is defined only for the natural numbers. But the numerals, and description names in general, are certainly a special subspecies of category names. To be competent with the numerals is to know a great deal (an infinite amount, actually) about the numbers and their modal properties. Indeed, one might very plausi bly argue that the numbers modal properties are exhausted by the conceptual material present in the numerals reference axioms. In other words, one might plausibly claim that the only modal properties had by the numbers can be reduced to the truth or falsity of de re modal claims involving the greater than, lesser than and equal to relations. Given the strength of this position, then one might wish that we could assimilate all category names to the treatment we have provide d for description names. To see if such is possible, we should take a moment to see what is added to the knowledge one has if one is competent with a class of mere category names if one is, in f act, competent with description names. The description names are such that the reference axioms determine a referent no matter what the context is in which they are used. This is likely because the numbers are abstract objects necessary existents whose prope rties are had necessarily. Our use of the numerals to refer to

PAGE 205

205 the numbers is completely stipulative, and that whic h is a referent of a numb er like such as is an abstract object and so in virtue of so being has all of its (non-relational) properties of necessity (and has none accidentally). If the conc eptual content presented with the reference axioms for the numerals is sufficient to provide one who is competent with the numerals with all the modally relevant facts about the numbers, pe rhaps such is the case because the numbers are abstracta and our use of the numerals is completely sti pulative. It is the conceptual content that one who is competent with those names, and that is presented in the reference axioms for those names, from which all of the modal properties of the referents follow. It is not immediately obvious that category names of other sorts (lik e Bob and Ned) are such that one who is competent with those names knows all of the moda lly relevant properties about the referents of those names. Perhaps we have this intuition because the re ferents of Bob and Ned are contingent entities with what we might call accidental featur es. But we do have the intuition that certain de re modal claims expressed by sentences that in clude category names are true (Necessarily, Aristotle is human.) The important thing to notic e is that in this chap ter we havent taken a metaphysical stand on whether or not Aristotle is essentially human, but rather developed the part of semantical theory on whic h we restrict names such as Ari stotle so that they can only be used to refer to individuals of a certain kind (i n the case of Aristotle human beings), and so enabled ourselves to endorse the de re modal claims that we find intuitively true. Now the conceptual content had by being competent with category names such as Aristotle is not enough to uniquely determine its referent (becau se it is not enough merely to know that the referent of Aristotle is a human being in order to know which human being is the referent of the name), but whether the conceptual material associat ed with those category names is such that all

PAGE 206

206 the modally relevant properties are known by one w ho is competent with the name is certainly an open question. And whatever do turn out to be a ll of the modally relevant properties of the referents of the category names (if there are any others at all), it is quite easy within the framework we have developed here to let e be such that it places the appropriate restrictions on the names in question. To do so, we would require there to be Ludwig ian description names of the sort we have described for (contingently existing) concreta as well as (necessarily existing) abstracta as we wish to make de re modal claims about the former as well as the latter. For the approach to be fully general, we must be guaranteed that such names would always be available for any modal claim the truth of which we wish to explicate, but there seems to be at least prima facie doubt as to whether we could have such a guarantee. Research into the av ailability of description names is a starting point for future work. Conclusion We have seen that there are resources for one who holds the analytic-deflationary account to deal with the problem of de re modality. By generalizing the intuition that some category of object to be denoted is associated with some names, we can restrict the map I so that it mimics our use of such names. The possibility for a more convincing treatment exis ts in the description names, but I caution that we should be judicious in claiming that there are enough of these names to go around in the modal discourse wed like our theory to explicate. We have yet to deal with quantification into modal contexts, and we should f eel urgency over this issue, as we have tried to understand necessity in terms of analyticit y. How are we to even understand the question of whether an open sentence could be analytic relative to an assi gnment? This is one topic of Chapter Twelve. After we have de alt with quantification, we shall endeavor to fit our work in

PAGE 207

207 with a larger project of a more general nature. We shall try to place what we have done with the context of a compositional meaning theory.

PAGE 208

208 CHAPTER 12 SKEPTICISM THAT MEETS QUANTIFIED MODAL SENTENCE S, A PROPOSED CONVENTIONALIST TREATMENT OF THEM AND HOW OUR WORK MIGHT FIT INTO A GENERAL SEMANTIC THEORY Introduction So far, we have addressed all the is sues that we laid out fo r ourselves at the beginning of our path clearing save two, one specific the other ve ry general: first, the semantics for quantified sentences in which quantification is into a m odal context, and, second, how to situate the work that has been as our fairly narrow focus in this dissertation into the broader philosophy project of a general semantical theory. We address first the more specific issue and then take on the more general one. After doing this, we sh all fashion remarks to conclude this investigation and gesture toward directions for feature research. Our Conventionalist Proposal for Sentences of the Form (Qx) ( ( x)) .1 We have focused on the how to understand what it means for universally quantified sentences of the form ( x )( ( x ) ( x ) to be analytic and de re sentences of the form ( ) to be analytic, and so argued that we can clear a path for a conven tionalist reading of the sentence operator necessarily for sentences of that fo rm. It is no surprise that for a sentence S of either form, we try to clear a path for showing that Necessarily, S is true just in case S is analytic. Specifically, in the first case, ( x )( ( x ) ( x ) is true just in case ( x )( ( x ) ( x ) is analytic (as we have spelled that notion out in Chapter Thr ee through Chapter Eight); in the second case ( ) is true just in case it is analytic that ( ) (as we have spelled this out in Chapter Ten and Chapter Eleven). In this chap ter, we shall demonstr ate how a conventionalist 1 In the following, we use to denote a quasi-formal language analog in a philosophers shorthand of the sentence operator necessarily in natural language sentences.

PAGE 209

209 has tools for understanding the semantics of sentences of the forms ( x ) ( x ) and ( x ) ( x ). I will call sentences of these forms quantified modal sentences. Kit Fines Assessment of the Prospects for Ma king Sense of Quantified Modal Sentences Of course, we wish our sketch of a theory of modal semantics to accommodate sentences of this form also, but prima facie the situation seems grim for a conventionalist approach. Our difficulty can be seen by reviewing the skepticism with which quantification into a(n) (opaque) modal context has been regarded. To lay out the pitfalls of the territory we must negotiate in order to provide a treatment of quantified moda l sentences in which we understand necessity as roughly analyticity, I rehear se Kit Fines arguments. There Are at Least Two Reasonable Ways of Ma king Sense of Quan tified Modal Sentences Fine suggests that quantified modal sent ences, that is sentences of the form ( Q x ) ( x ) can be intelligible to us in one of two ways. A prerequisite for understand ing Fines claim is the notion of a substitution instance If ( x ) is a formula with only one free variable (or open sentence), a substitution instance of ( x ) is the sentence that results when we write the formula and substitute for every occurrence of x an occurrence of some constant (say) a. We indicate the sentence that results from so substituting a for x by ( x / a). First option: logical satisfaction The first way accord ing to which a sentence of the form ( Q x ) ( x ) might be intelligible is if the formula ( Q x ) ( x ) can be logically satisfied.2 There are, in turn, two ways this might happen. First, the formula (with only x free) ( x ) might be such that ( x / a) is a (classically) valid sentence: for example, if ( x ) were x = x F ( x ) ~ F ( x ) or ( y )(F( y ) (F( y ) F( x )). Second, the predicate substituted for the metalinguistic variable of 2 I borrow Kit Fines terminology here.

PAGE 210

210 the original sentence could be i s self-identical or a nother such predicate that is satisfied by every individual.3 We shall not give any more consideration to th is first sort of satisfa ction as sentences of this sort do not pose a difficulty for the conventi onalist, but we must consider another way in which quantified modal sentences might be intelligible so as to be able to make sense of all the sentences which involve the sort of content in which we are interested in this project. Second option: essentially, es s entialism or analyticity To explain the second way quantified into sentences might be satisfied, we need some terminology. The quantifier in the sentence ( x ) Fx is objectual if we understand the proper suffix of this sentence ( Fx ) to name a propositional function, relative to the la nguage of which this expression is a formula, from objects to propositions expressed by sentences that result by substituting a purely directly referring singular terms for x in the formula. This general strategy is laid out in 1. 1. FxOQ 4: {objects} {propositions expressed by F ( x / a1), F ( x / a2), } (where a1, a2, have no associated conceptual content and are obj ect introducing (in Ludwigs (2007) terms) or are pure ly directly referentia l (in Fines (2005) terms) to members of {objects}.) On the other hand, the quantifier in the sentence ( x ) Fx is autonomous if we understand the proper suffix formula ( Fx ) to be a function from expressions types5 to a certain class of expression types (sentence types). 3 There is a problem with this formulation because the individual constant would have a bearer and so we could infer from the sentence, Necessarily, a is a that something exists. I shall not dwell on this issue. 4 The functions subscript OQ should make clear this function is one we take Fx to name when objectual quantification is in force. 5 Autonomous quantification is best understood as a genus of which there may be several species. In a particular species of autonomous quantification, the domain may be rest ricted to a certain subset of expressions. Substitutional quantification is a species of autonomous quantification.

PAGE 211

211 2. FxAQ 6: {expression types: 1, 2, } {sentence types F ( x / 1), F ( x / 2,) } (Just to be clear, a token of type F ( x / 1) is of the sort to be true or false if understood when uttered or read on a specif ic occasion because it is a sentence token.) Semantic uniformity is a relation that can hold be tween a quantified sentence and a substitution instance of that sentence. There is semantic uniformity between ( x ) Fx and F ( x / a ) just in case the term a plays the same semantic rle in the latter as does the variable x in the former. Specifically, in the case of objectual quan tification, there is seman tic uniformity between ( x ) Fx and F ( x / a) just in case ther e is a specific object the denotatum of a where a is a purely directly referring singular term (that is, a referring singul ar term with no associated senses of any sort) such that the propositional function FxOQ applied to this object yields a proposition that includes the denotatum of a. (This sentence (type) that is the result of the propositional function FxOQ applied to the object that is the denotatum of a is expressed by the sentence (type) F ( x / a ).) On the other hand, under the assumption of autonomous quantification, there is semantic uniformity between ( x ) Fx and F ( x / a ) just in case the string (= a) is such that F ( x / ) (= FxAQ( )) is an expression type th at is a sentence type. A proper substitution instance F ( x / a) of ( x ) Fx is one in which there is semantic uniformity between the latter and the former for either reading of the existential quantifier. In a similar fashion, we can apply the sa me terms to senten ces that include In particular, on an objectual read ing of the existential quantifier, there is semantic uniformity between ( x ) Fx and F ( x / a) just in case there is a purely directly referring singular term a such that the propositional function Fx applied to the denotatum of a yields a proposition that 6 The functions subscript AQ should make clear this function is one we take Fx to name when autonomous quantification is in force.

PAGE 212

212 contains this object (that is expr essed by the sentence necessarily, a is F ). And, in case of autonomous quantification, there is semantic uniformity between ( x ) Fx and F ( x / a) just in case there is a string (= a) such that F ( x / ) is a grammatical expres sion that is a sentence. (This happens when the (autonom ous quantification) function Fx is defined on a.) Fine asserts that th e truth condition of ( x ) Fx on the objectual readi ng of the existential quantifier is different from the truth condition of ( x ) Fx on the autonomous reading of the quantifier and vice versa To repeat in other words, the truth-maker for ( x ) Fx on an autonomous reading of the quantifier is distinct from the truth-maker for ( x ) Fx on an objectual reading of the quantifier. The quantified sentence ( x ) Fx is true on an objectual readi ng of the quantifier iff there is some object, the denotatum of a such that necessarily it is F This way of understanding ( x ) Fx is to understand it in the strictest de re sense; the truth of the sentence depends upon the object denoted by a That the denotatum of a is so denoted is of no real consequence to the truth of the sentence F ( x / a). On the other hand, ( x ) Fx is true according to the autonomous reading of the quantifier iff there is a string a which if substituted into the formula F is such that the resulting sentence F ( / a) becomes analytically true, that is, just in case there is an re lationship between the conceptual material associated with the term a and the concept expressed by the predicate F which guarantees the truth of F ( / a). The sentence ( x ) Fx could be true on one reading of the quantifier but not on the other because on the first, objectual, reading of the quantifier, a must be a mere tag for it is denotation; the truth of the se ntence on this reading presumably has something to do with the properties of the denotatum of a, and on the second, autonomous reading of the quantifier,

PAGE 213

213 there must be conceptual content associated with the expression (that is the name) a of the right sort to guarantee the truth of F / a. Our modest conventionalist de siderata and treatment of quantified modal sentences on the model of Benson Mates7 treatment of quantified non-modal sentences According to the account we have provide d in Chapter Ten and Chapter Eleven, semantically primitive singular referring terms are object introducing : they serve to load objects into the propositions expressed by the sent ences in which they occur. These terms are also such that there is conceptual material associ ated with each name. (That is, there is associated conceptual material if we think that the restrictions placed by e on the sort of objects semantically primitive terms can be used to refer to in each of \ associate conceptual material with these terms.) If an interlocutor were to hold us to the standa rd of strictly objectual quantification in Fines terms, then he would be dissatisfied by what we will propose here (and will probably also be dissatisfied with the treatment we offered in the previous chapters). We desire something different of our treatment of quantification. What we desire something along the lines of what Kaplan (1968) has developed. What we desire from our treatment of quantification is not that names are pur ely directly referring in Fines sense, but (1) that quantification be univocal in both modal and non-modal contexts and (2) that we be able to see that the truth of sentences of the form ( Q x ) ( x ) follows from the truth of sentences which themselves are true in virtue of meaning. Si nce we should agree with Fine that quantified sentences are intelligible if there is a single pr oper substitution instance, a univocal treatment of quantification will require that variables play the same semantic rle in both sentences of the form ( x ) Fx and of the form ( x ) Fx 7 For all references to Benson Mates see (Mates, B., 1972).

PAGE 214

214 To set things up, let us adve rt to the treatment Benson Ma tes provides on his page 60 for truth under an interpretation for existentially quantified sentences. Let and be interpretations8 of (formal language) L and let be an individual constant; then is a variant of if and only if and are the same or differ only in what they assign to (This implies, be it noted, that if is a -variant of then and have the same domain.) 9) if 9 = ( ) 10, then is true under if and only if / is true under at least one variant of One thing to notice before we being to spell out our proposal for quantified de re modal statements, is that Mates gives the truth-unde r-an-interpretation c onditions for quantified sentences in terms of interpretation variants interpretations just the same as the original except in what they assign to a single constant term and the truth of sentences that are the result of substituting in that name, for which the interpre tation may vary, to the formula that is a proper suffix of the quantified sentence under consideration. We wish to set out absolute truth conditions for languages under an intended interpretation (rathe r than simply interpretations) that include the sentence operator necessa rily. Whereas Mates considered variants of a certain interpretation, we must cons ider (something analogous to) a variant of the language under our consideration. Having said so, let us present our proposal. Let L and L be languages of the sort whose semantic s we have considered in the preceding chapters (both languages include the sentential operator N which is represented in the quasi8 An interpretation in Mates use is a map from the languages constant terms to individuals in the domain and from the languages predicate terms to sets of individuals in the domain. 9 For can be substituted any sentence of L. 10 For can be substituted any formula of L.

PAGE 215

215 formal philosophers shorthand as ). Let the set of singular refe rring constant terms of each language be called respectively, and 3. L is a variant of L just in case and either = or = { } and and are exactly alike in every other respect. For (4.), let be a sentence variable for L and a formula variable. 4. If = ( ) 11, then is true in L if and only if / is true in at least one variant of L In particular if = ( x )N( F ( x )), then is true if and only if, N( F ( a)) is true in at least one a variant of L Also, if = ( x )(N( F ( x )) (another sentence of L ), then is true if and only if N( F ( x )) is true in every a-variant of L Now since we have explicated the conditi ons under which a sentence of the form N( ()) is true in L given the preceding we have the conditi ons under which sentences of the forms ( x )N( ( x )) and ( x )N( ( x )) are true in L Finally, we have semantics for each of the basic forms we sought: de dicto de re with singular terms in the scope of the modal operator and quantified sentences in which quantification is into the scope of a modal operator.12 11 In this case, has at most free. 12 There are (at least) two further complications for this a pproach. First, one may wonder whether (and how) on this approach we can endorse the sentence, every physical object is such that necessarily it has a spatio-temporal location. There is the obvious de dicto reading of this sentence: It is nece ssary that every physical object has a spatio-temporal location, and a less obvious de re reading: If x is a physical object, then necessarily x has a spation-temporal location. I am uncertain whether the de re reading makes a problem for the conventionalist analytic-deflationary approach because qualifiers ar e placed on the sort of individuals over which x can range outside the scope of the modal operator. The antecedent of the conditional, if x is a physical object delimits that over which x ranges it can range only over physical objects. So, even on the supposed de re reading, the claim still seems to be de dicto in that it is a claim about the relationship of the predicates is a physical object and has a spatio-temporal location. The second worry is over whether there are enough, but not too many, members of that are such that they bear e to certain predicates (call these category names for sh ort). If there are no such names, then there would be no true de re modal claims relative to that language. If every name is a category name, then every de re modal claim would be true. As this point, we should recall our purpose for the formal language we have developed in this work. We mean our formal language to model a natural language like English. Since the formal language is meant only to be a model for natural language, it follows that the members of which bear relation e to some pair of predicates

PAGE 216

216 We have cleared a bit of the path for a conve ntionalist modal semantic s; what remains to be seen is whether we can make our work fit in with that of the broader philosophy of language community. Specifically, we desire to see if we can situate our proposal for the semantics of the sentences involving the modal opera tor N into a general semanti cal theory, i.e. theory of meaning. Fitting Things into a General Semantical Theory First, we will provide a very brief review to give so m e context to our efforts to situate our specific work into the broader context of meaning theories. What We Have Done So Far We have developed a generalization of the approach of Carnap in Meaning and Necessity to modality an d meaning that made use of state-descriptions. Our admissible interpretations of sets of atomic sentences were to be such as to prov ide, when considered in a class, an extensional treatment of the intensions of predicate terms. Ou rs is an effort in the arena of semantics to provide a workable notion of anal yticity in terms of the framew ork we have developed as the generalization of Carnap. We have suggested a semantics for the object language operator N when it occurs in sentences of the form NS where for S is substituted a sentence that is de dicto (such as ( x )(P1( x ) P2( x )) or de re (such as P1( a ) for a a singular term). We have also proposed semantics for sentences of the forms ( x )N( ( x )) and ( x )(N ( x )) where x / a is a sentence. of the formal language should be analogs of those names which are what Ludwig (2007) calls category names. So we should construct a specific formal language of the sort whose generic form we have developed here which is such that it includes among analogs of all and only the names of the natural language we wish to model. In particular, those names of the natural language we take to be category names should be such that their formal language analogs bear the relation e to pairs of predicates. In short, the natural language we model, and the level of comfort speakers have with its expansion to include new category names, should dict ate what category names the formal language includes as analogs.

PAGE 217

217 The semantics for these sentences are given in terms of analyticity fo r our notion of it as previously developed. Now, Ive presented these object language se ntences as involving the (object language) symbol N with the understanding that we interp ret N as the (natural language) modal sentence operator necessarily. The (formal) language und er consideration for which We are trying to provide semantics for N is supposed to be a much-simplified version of a natural language (which might be regimented with the use of paraphrase) like English. (We have been considering, at the most fundamental level, only atomic sentences those of the form n( 1, n ) and trying to carve out a cl ass of admissible interpretations with respect to those sentences.) The bulk of our effort has been devoted to pr oviding the semantics for N with the hope that in so doing, we would be able to clear a path for conventionalist modal semantics a project directed toward the (general) goal of understand ing necessity as analyticity and specifically giving the semantics for sentences in which occu rs N in terms of our characterization of analyticity. Our Broader Goals Our efforts have been narrowly focused: on m a king precise, more s ubstantive and robust a specific proposal for analyticity and giving the semantics for a specific modal operator of the object language N. Our project mi ght be viewed as important more generally if we could use what we have done here in the service of a genera l semantical theory. That is, if we could situate our work in the context of a br oad-ranging project in the philos ophy of language project which is itself aimed at explaining the meaning of arbitrary sentences of a la nguage under consideration, then the work of this dissertation seems rele vant to the larger ph ilosophical context and

PAGE 218

218 community. So we will now try to place our work in the context of a theory of meaning to make it of use to others involved in the la rger philosophy of language project. General Semantical Theories As we said earlier, a ge neral semantical theory aims to provide the meaning of any sentence of an object language under considerati on. There is, of course, a diversity of views on this subject the most fundamental differences among which lurk in what ontological status a semantical theorist takes meanings to have. Some hold that meanings of sentences are the propositions that are expressed by the sentences we understand, and so, as such, these meanings are necessary existents. Others hold that talk of a sentences meaning is analogous to talk of a boards length and so is only convenient shorthand for a relation with regard to a certain sort of similarity. If each of a pair of boards is of the same le ngth, we could say, in a sort of formal mode, that the relational predicate is as long as applies to the orde red pair consisting of those two boards. The relation expressed by th e predicate is as long as is, in fact, an equivalence relation on the set of boards because it is reflexive (one board is as long as itself), symmetric (if board A is as long as board B, then board B is as long as board A) and transitive (if A is as long as B, and B is as long as C, then A is as long as C). So as a convenience, we might speak of a boards length as shorthand for an indication of which is-as-long-as-equivalence class the board is a member of. A board has length 7 just in case it belongs to th e is-as-long-as-equivalence class of boards each of which is such that it is as long as a board which is shaped exactly like a tape measure extended to 7. Just as talk of having a certain length can be made sense of even if we do not think there are any such things as lengths, but rather only equivalence classes relative to the predicate is as long as, a semanticist of the second sort (o ne who does not automatically assume that a

PAGE 219

219 sentences meaning is itself something which is of a certain ontological cat egory) might hold that talk of meaning is analogous to talk of lengths. Specifically, such a semanticist might hold that to say that a sentence has a certain meaning is just to say that the sentence is the same in meaning or means the same as another sentence. In formal mode, we could say that the relation expressed by predicate means the same as or means that is an equivalence relation: the relation is reflexive because a sentence means the same as itself, that is, means the same as or means that holds of the ordered pair (where is a sentence variable), the relation is symmetric because if means the same as holds of then it holds of and the relation is transitive because if means the same as holds of and then means that same as holds of Now, if we could somehow generate theorems of a meaning theory of the form of (5): 5. means the same as holds of OL, ML (where OL represents an arbitrary sentence of the language unde r consideration the object language, and ML represents an arbitrary sentence of the language in which the theory is presented (the metalanguage which we assume th e theorist to understand), then we would have satisfied a semanticist of the latter sort, if we assume that the semanticist is interested primarily in a theory of meaning which allows one who understands the meaning theory and the language in which the meaning theory is given (the me talanguage) to understand sentences of the language of which the meaning theory is a m eaning theory (the object language). Our project is of course aimed at clearing a path for conventionalist m odal semantics; a major motivation for this project is the desire to unde rstand sentences with modal operators without the use of possible worlds, propositions qua abstracta essential properties or other explanatory devices which would themselves require a place in our ontology. It is in line with our aims to opt

PAGE 220

220 for the approach that would please the second sort of semantic theorist. We should, and do, choose to understand talk of meanings as shorthand for talk about sameness of meaning. Compositional meaning theories So the sort of se mantical theory in which talk of meanings is consider ed analogous to talk of lengths is that sort within which we will try to situate our work. Given what we have done so far, we should desire another feature of the genera l semantical framework in which wed like to place our work, namely compositionality We have tried to carve out a notion of the inte nsions (explained extensionally) of predicate terms and argued that we can place restrictions on the use of semantically primitive singular terms to make true de re modal sentences involving those te rms. The notion of analyticity we have developed is such that whether or not a sentence is analytic depends upon the constituent predicate and singular terms of that sentence. Since whether or not a sentence is analytic depends upon its constituent parts and their mode of semantic combination, we should want the meaning theory in which we try to fit our work to be similarly compositional. As Lepore and Ludwig state in their (2007), A compositional meaning theory for a language L is a formal theory that enables anyone who understands the language in which the th eory is stated to understand the primitive expressions of L and the complex expression of L on the basis of understanding the primitive ones. (p. 18) Since we have made use of the notion of concep tual ability to underwri te our explanation of intensions of predicate terms, it is only natural that we would wish our proposal for analyticity to be such that one who has conceptual mastery w ith regard to the predicates occurring in a sentence which is analytic can understand the sentence as analytic on the basis of understanding the predicate and singular terms of the sentence (the sentences primitive expressions) given that

PAGE 221

221 the meaning of a complex expression (a sent ence) is determined by the meanings of the constituent parts. Indeed, we have proposed semantics for the se ntence operator N whic h indicate that the operator makes a specific and pred ictable contribution to the semantics of the sentences in which it occurs. The semantics we have proposed are such that the semantical contribution of N are regular in all sentences in which the operator occurs, that is, the contri bution is systematic and the operators behavior should be able to be understood in a compositional fashion. A compositional meaning theory seems to be our most likely candidate. An interpretive truth theory used in the serv ice of a compositional meaning theory Finally, we have been doing work in formal semantics, specifically, model-theoretic semantics. We have developed semantics for th e sentence operator N. Our development of these semantics was guided by the desire for a theory which made available an obvious and workable epistemology for sentences in which the operator appeared. We want the general semantical framework within which we situate ou r project to be such th at it is a theory of understanding meaning. So we should be happy with theorems of the form of (6): 6. s means that p. Where for s is substituted a structur al description of an object language sentence and for p is substituted a metalanguage sentence. But how can we get here? All we have done so far is provided a formal semantics for atomic sentences and sentences of the form ( Q x )(N( ( x )), and formal semantics only provides recursive and m odel-theoretic rules for determining whether a sentence of the object language is true in that language (under the intended interpretation). We have provided only extensional truth-theoretic information in our i nvestigation. But Donald Davidson has suggested a way to use the merely ex tensional truth-theoretic tools we have been

PAGE 222

222 developing in the service of compositional meaning theory. The suggestion is to let theorems of a purely extensional sort do the work of a co mpositional meaning theory; specifically, that sentences of the following form could be the theorems of a meaning theory that makes statements about the truth theory. The predi cate is T will be e xplained in a moment. 7. s is T if and only if p. Lepore and Ludwig have (2007) explained and clarified the suggestion. They write: We have seen above that the real achieveme nt of a theory which assigns meanings to expressions comes to no more than that th ey match object language sentences with metalanguage sentences alike in meaning. Davi dsons suggestion was that this could be achieved without meanings by noticing that a truth theory which meets Tarskis Convention T achieves the same result. Tarskis Convention T requires that an adequate theory of truth for a formal language have as theorems all sentences of the form [(7)] above in which s is replaced by a structural descript ion of an object language sentence, a description of it as formed out of its prim itive meaningful components, and in which p is replaced by a metalanguage sentence that transl ates it. If we know that a sentence of the form [(7)] is one of these th eorems, then we can replace is T if and only if with means that to yield a true M -sentence. (p. 28) As I understand it, the operative notion in Tarskis convention T is that of translation : if sentence of the metalanguage is a tr anslation of object language then and have the same meaning and a structural description of could be substituted for s and could be substituted for p in (7). How do we guarantee that our truth theo ry for the object language satisfies Tarskis convention T that is, how do we guarantee that is a translation of ? To begin the answer, we note that each of the semantic primitives predic ate terms, singular terms and sentence operators in our case will be assigned axioms in the truth theory for the object language which provide an interpretation of these terms into the metalanguage which is truth preserving; this truthpreserving interpretation is a kind of translation from object language to metalanguage of semantic primitives. These assignments are expressed by base axioms in the truth theory. Since and are sentences, we need to use various recursive axioms of the truth theory, in

PAGE 223

223 addition to the base axioms, such that we proceed in stages to produce in the last stage a sentence of the form means that in the metalanguage that to th e left of means that is to be considered the LHS of the stage and the that to th e right is to be considered the RHS. (Of course, I simplify the process greatly for the purpose of this exposition. See Lepore and Ludwigs 2007 pp. 34-39 for details) This procession in stages w ill be such that it constitutes a canonical proof of this sentence where a canonical proof of a sentence which meets Tarskis condition T (or a Tsentence) is a finite sequence of sentences of the metalanguage which ends with the T-sentence in question, each of which is such that no semantic vocabulary is introduced on the RHS, and each member of which is either a base axiom of the truth theory or is such that it is derived from a previous sentence by one of a finite number of recursive axioms for the truth theory. An example helps clarify this. Let the object language under consideration be a tiny sublanguage of Serbo-Croatian (call it S-C): in it are only one proper name and one predicate term. De ko is the proper name of S-C, and the predicate term of S-C is je pokvaren. The predicate is satisfied by the same individuals which satisfy the (English) metalanguage predicate term is rotten. An object language reference axiom is given in (8). 8. R1. RefS-C(De ko) = De ko And an object language truth (truthS-C) axiom for an atomic formula (essentially the translation of the predicate je pokvaren to the metalanguage) is: 9. B1. For all names je pokvaren is trueS-C iff RefS-C( ) is rotten. If a sentence of the form (10) 10. s is trueS-C if and only if p. is such that it is derived from base axiom R1 a nd a single application of tr uth axiom B1, then this sentence meets Tarskis convention T Sentence p is a translation of s which is obtained by

PAGE 224

224 insuring that complex p has the same semantic structure that the complex s has and that the corresponding semantic primitives of p are translations of those of s Explicitly, 11. De ko je pokvaren is trueS-C if and only if De ko is rotten satisfies Tarskis convention T And so, since De ko je pokvaren has the same semantic structure as De ko is rotten and the corresponding parts make identical meaning contributions to that of each respective complex, we can say that the latter translates the former and can claim the following as a meaning theorem: 12. (M) De ko je pokvaren means that De ko is rotten. How What We Have Done Might Fit in Let us illustrate how our proposal m ight fit in with an interpretive truth theory with an example of such a theory for a generic formal language L of the sort we have developed the semantics for earlier. We will give the truthL axiom for the sentence operator N. Since we have given the semantics for quantifie d into sentences of the form ( Q x )(N( ( x )) in terms of the sentences of the form N( ( a)) and variations of L, we need c onsider only sentences of the latter form when providing our truthL axiom. 13. For a sentence S of the form ( a), N(S) is trueL iff it is analytic that p. Where we replace p with a metalanguage translation of S, just as is to be expected in the interpretive truth theory. So far, so good, but what ar e we to make of it is analytic that p? We want (13) to be a interpretive axiom, so the string that lies to the right of the biconditional iff must be used But we also would like to be able to understand the sentence to the right of the biconditional using the tools we have devel oped regarding the noti on of analyticity.

PAGE 225

225 Our suggestion is to assert that a necessary and sufficient condition on the truth of an utterance of it is analytic that p is that A (S) where is in the extension of predicate A iff for each \( ) = g that is, under each admissible interpretation is true. Problems for and Questions about the Approac h We Ha ve Tried to Clear the Path for There are myriad questions and perhaps a fe w outright problems fo r the approach to modal semantics we have outlined. We are windi ng things to a close here, our path-clearing work having been finished. The following are issu es of pressing importance but not issues that we have the capacity to develop in this work. Perhaps future research can be undertaken to address these concerns. We have given a semantical (truthconditional ) analysis, not a mea ninggiving analysis First off, we m ay have immediate doubts as to the plausibility of (13): does N (or necessarily in something closer to English) really mean it is analytic that? On our proposed treatment, the truth conditions of S are the same as the truth condi tions for it is analytic that p (where for p we substitute a metalanguage tr anslation of the sentence of L named by S, given our treatment of analytic), but do not we have a word that translates more precisely N, namely necessarily as used in English? In response to this, I can only say that if we have in fact provided a serviceable semantical, truth-conditional analysis of necessarily, then we must be satisfied with this much. To try to provide a meaning-giving analysis of necessarily which participated in the same sort of extensional flavor we have made use of throughout this document, would, I believe, be close to impossible, because the gap between analysandum (necessarily) and analysans (that which necessarily is analy zed into in a meaning-giving way) would be so narrow that any pr oposal would be unsatisfactory. To preserve the meaning of necessarily in the analysans of would be to preserve the i ntensional feel of the term. To do

PAGE 226

226 that would be to give up on a kind of extensiona lly flavored approach. Doing so would be at odds with the spirit of understanding modal sema ntics in a conventionalis t analytic-deflationary way. Is I am here now analytic in English? If so, is it necessarily the case that I am here now? The theory we have sketched in this and th e preceding chapters is not one which treats indexical terms such as I, here and now or demonstrative terms such as that. Luckily, the general semantical theory into which We are tryi ng to fit our project is such that it provides a treatment of context sensitive la nguages, and so provides for me aning contributions to come from the speaker of a particular sentence, its place and time of uttera nce and that which the speaker of sentence demonstrates (if anything) when he utters the sentence. Given the fact that (1) for the interpretive truth theory (as compos itional meaning theory) into which We are trying to fit the present work, the fundamental bearer of (sameness of) meaning is that of a sentence utterance, (2) that strictly speaking for every utte rance there must be an utterer and (3) the utterer of any sentence is where he is when he utters the sentence he utters; it seems that it is a matter of meaning alone that the sentence I am here now, is analytic in English. A nd if we restrict what an utterer may reasonably demonstrate during his utterance of a sentence (and appropriately restrict the size of the area which may be consid ered part of what the utterer means with an utterance of here), th en the sentences, That(as demonstrative) is here now, and That(as demonstrative) is close now, are both analytic Of course, it should be obvious that it is only a contingent matter of fact that the utterer is where he is when he says what he sa ys, and that the physical objects of the speakers immediate environment are in that location only as a matter of happenstance. In these particular cases, theres a gulf between that which is analyt ic and that which is necessary. So, an account of modality that treats utterances of sentences as the primary bears of meaning

PAGE 227

227 must offer some sort of explanation for this gulf. An explanation might begin with something like the following.13 There are contingent matters of fact about ut terances of sentences which do not themselves seem to contribute anything to the semantic va lue of those utterances: one must be speaking when one utters something, if one utters a sent ence, one must be speaking a language, one must utter a certain number of syllables, must utter a certain number of words, etc. As a matter of happenstance, it is the case that those contingent features of th e bearers of meaning make true certain expressions of those bearer s given that they are always e xpressed in a certain manner. We want our theory to analyze necessity in terms of intensions (as we have given an account for them) and meaning constitutive pa tterns of use, but we do not wa nt to consider as necessary those statements whose truth in guaranteed simp ly by the (contingent) manner in which they are expressed. The sentences I am here now, I am sp eaking now, That is here now, and That is close now, seem to true as a (c ontingent) matter of how they are expressed. Indeed, it is part of the meaning constitutive pattern of use of the words I, now, here, close and (for some sense of the demonstrative) tha t to indicate the speaker, rela tive positions in space and time which are near to the speaker when he speaks and objects which are demonstrated respectively, but only a contingent feature of those words an the concepts that they express that makes true the preceding sentences. We might leave it at that and claim that only sentences that are not true simply by contingent matter of fact about how they are ex pressed are candidates fo r analyticity, but this leaves us with the unsatisfactory result that we have the modally loaded term contingent used 13 Kirk Ludwig observes that there is a difference between true-at-all-indices and true-in-virtue-of-semantic-content. We wish to employ the latter to analyze necessity, but th ere are concerns with indexical and demonstrative terms that I try to say a few preliminary words about in what follows.

PAGE 228

228 to mark of those candidates for analyticity and analyticity was to be that which analyzed the modal concept of necessity for us. I will make another suggestion which is po ssible because the account of intension and meaning constitutive patterns of use is an extensi onal one. The proposal is first to translate (in a completely truth-conditional way (that is to offer a sentence whose truth conditions are identical which has now context sensitive elements such as I, now, here, close or that) those sentences which look to be made true in virt ue of meaning because of contingent matters of fact about how they are expressed into sentences which are not ma de true in the same way, then to check to see if the translations are such th at they are true as a matter of intensions or meaning constitutive patterns of use. For example, I might translate the sentence, I am here now, as Jesse Butler is in the northeast corner of the third fl oor of Library West at 12:30 PM, March 24th, 2008. Since our semantic account was to be ex tensional, if one sentence is true as a matter of meaning alone, then so should the other be, but this is clearly not the case. Sentences such as Everything that is scarlet is red, or Aristotle is a person, are still an alytic in English if we follow this suggestion, because they do not c ontain any context sensitive elements to begin with. Our account treats N as a (generalized) prop erty of sen tences, rather than as a sentence operator per se Finally, we understand N as a pr operty to sentences, as its ca pacity as sentence operator is understood exclusively on the basis of whether certain sentences which are prefixed by N are true or untrue: even thou gh sentences of the form ( Q x)(N( x)) are given semantics, and so prima facie it seems that N is a sentence operator, such sentences are given semantic values by determining whether there are substitution inst ance of them of the a ppropriate sort. I am uncertain what the benefits and liabilities are fo r our approach given this result, although such a

PAGE 229

229 result sits well with a sententialist view in philosophy of language, like that put forward recently by James Higginbotham14, according to which the complement clauses following that refer to themselves. Conclusion Finally, we take a m oment to re flect on the goals of this proj ect, to what extent progress has been made toward those goals, and in what areas more effort should be put towards shoring up claims that have been made. Our approach has been to develop a system of modal semantics that takes inspiration from those developed in Meaning and Necessity We have tried to show that the challenges posed by circularity, the problem of de re modality and a uniform treatment of quantification can be met by the conventionalist an alytic-deflationary approach. Of course, our arguments are not conclusive and could be strengthened. In particular, more depth could be taken in the treatment of concepts, their relations and the parallel structures of inte nsions and concepts. Also, our treatment of the topological/linguistic use restri ctions we have placed on particular classes of singular terms according to which our account is to be able to endorse de re modal claims is only the basic outline of such restric tions. More tempting evidence for th is thesis would be an actual demonstration of such restrictions for actual cla sses of singular terms of a natural language we wish to model. Finally, our brief outline of th e use of model theoretic techniques in aid of a conventionalist modal semantics within the larg er project of providing a compositional meaning theory is just a sketch. Ideally, we could be ab le to seamlessly integrate these two complimentary projects. In the future, I hope to engage in research on these and related topics. 14 For all references to James Higginbotham see (Higginbotham, J., 2006).

PAGE 230

230 APPENDIX A OUR MODEL-THEORETIC RE WORKING AND GE NERALIZATION OF CHAPTER THREE AND SYSTEMS OF QU ANTIFIED MODAL LOGIC In this appendix, we provide a sketch along with a few details about how the class of admissible interpretations could be used to play a role functionally identical to that played by the class of possible world in a typical system of quantified modal logic. The plan is the following. First, outline, very briefly, the material used to give semantics for the sy stem of modal logic of Fitting & Mendelsohn. Second, show how a class of interpretations, underst ood as in the Chapter Three, can take the place of possible worlds in this semantics (provided that we can make sense of an analogue of the notion of an ac cessibility relation between possible worlds1). Third, notice that on the view that a class of interpretations can take the place of a class of possible worlds, we seem committed to the existence of just a single (analogue of a) model structure with which to give semantics for intensional operators. This single model structure creates tension because validity is usually defined in terms of a class of model structures (and a ll the models of each of those model structures). Finally, take comfort in the conclusions of the research of Hawthorne and Hanson which shows that an understanding of va lidity in terms of a class of model structures rather than a single model structure ( the class of possible worlds) is poorly motivated, and that the basic properties of completeness and comp actness can be demonstrated for systems of quantified modal logic whose semantics are given in terms of single model st ructure rather than a class of model structures. 1 Ironically, it seems that class-of-inter pretations analogue of the accessibility relation that holds between pairs of worlds may be more intuitive. As we w ill see soon, one interpretation might be accessible relative to another if the way of speaking on the first is acceptable given the second.

PAGE 231

231 Outline of the Traditional Formal Approach A typical ex ample of a traditional approach to semantics for quantified modal logic is that taken by Fitting & Mendelsohn. They outline a vers ion of a traditional (Kripkean) approach in which the domain of the model is constant. I will present their semantics very briefly as a point of comparison for the system that we have deve loped based on Carnaps work. They consider a augmented frame with constant domains essentia lly a class of possible wo rlds, an accessibility relation between those worlds, and a domain of discourse for the frame represented symbolically as G, R, D where G, R and D represented the class of worlds, the accessibility relation and the domain respectively (p. 95). If 1, 2 G, we say that 1 bears relation R to 2 ( 1R 2) iff 2 is accessible from 1. The members of D are thought of as residing in possible worlds like 1, 2, etc. So naturally, an interpretation I2 is a map from (1) ordered pairs of pred icate letters (like P ) and worlds to sets of ntuples the members of which are in D, so example, I( P 1) = {d1, d2, d3, d109, d233, d12} where P is a predicate letter, 1 G and each of d1, d2, d3, d109, d233, and d12 are in D and (2) singular terms and worlds to members of D. One can think of the interp retation of a predicate term are giving the extension of the predicate at a particular wo rld, and can think of the interp retation of a singular term as indicating which individual is pick ed out by that singular term (be it a constant term or the result of an iota operator). A constant domain model then M is the four-tuple G, R, D, I A varying domain model (which we might represent as G, R, D I ) is similar except that the domain of the model D is the union of each of the domains of the each member of G. Formally, if we call the domain of the world (that over which the unive rsal quantifier ranges) D, then the 2 This notion of interpretation is different from, but simila r to, the notion of interpretation we have developed in the first part of this paper.

PAGE 232

232 varying domain D = { D | G}. Finally a valuation v is an assignment of free variables to values in the domain (either D or D ), so we have: 1. If R is an n-place relation symbol, M ||v R( x1,, xn) iff v (x1), v (x2), v (xn) I (R, ). 2. M, ||v ~X iff it is not the case that M, ||v X 3. M, ||v X & Y iff M, ||v X and M, ||v Y 4. M, ||v X iff for every G, if R then M, ||v X 5. M, ||v X iff for some G, R and M, ||v X 6. M, ||v ( x ) iff for every x -variant w of v in M, M, ||w 7. M, ||v ( x ) iff for some x -variant w of v in M, M, ||w 8. M, ||v ( t ) iff M, ||w where w is the x -variant of v such that w ( x ) = (v I)( t ). (Where we associate with each term t a value in denoted by ( v I)(t ) in the following way. If x is a free variable, (v I)(x ) = v ( x ). If c is an individual constant (v I)(c, ) = I(c, ). If f in an n-place function symbol, then ( v I)( t )(f( t1, tn), ) = I(f, )((v I)(t1, ),, (vI)( tn, )). If M, ||vx for exactly one x-variant v of v then ( x )( x ) designates at with respect to v and ( v I)(( x )( x ))) = v ( x ). How Our Model-Theoretic Reworking Can Support the Traditional Approach Now for eve ry G, let \ be our interpretation proxy for The interpretation proxy is a map from expressions to elements of th e (varying or constant) domain which imitates the traditional interpretation I. So first we stipulate th at for any individual d in such that for some individual constant expression I( ) = d, then \( ) = d. Second, we need the notion of a relation R that holds between interpretation proxies that imitates the relation R that holds between worlds. Specifically, let \ R \ iff R Given all this we have (where the sequence v is just as before):

PAGE 233

233 1a. If R is an n-place relation symbol, \ ||v R( x1,, xn) iff v ( x1), v ( x2), v ( xn) \(R).3 2a. \ ||v ~X iff it is not the case that \ ||v X 3a. \ ||v X & Y iff \ ||v X and \ ||v Y 4a. \ ||v NX iff for every G, if \ R \ then \ ||v X 5a. \ ||v ~N~X iff for some G, \ R \ and \ ||v X 6a. \ ||v ( x ) iff for every x -variant w of v \ ||w 7a. \ ||v ( x ) iff for some x -variant w of v \ ||w 4 8a. \ ||v ( t ) iff \ ||w where w is the x -variant of v such that w ( x ) = (v \)(t ). (Where we associate with each term t a value in the range of \, denoted by ( v \)( t ) in the following way. If x is a free variable, ( v \)(t ) = v ( x ). If c is an individual constant ( v \)(c) = ( \)(c). If f in an n-place function symbol, then ( v \)(f( t1, tn)) = \(f)((v \)(t1),, (v \)(tn))5. If \ ||vx for exactly one x -variant v of v then ( x )( x ) designates on \, with respect to v and ( v \)(( x )( x ))) = v ( x ). (A simpler way might be to say ( v \)(( x )( x ))) = ( \)(( x )( x ))) if the interpretation \ is defined over formulas formed with the iota-operator. If the preceding is correct, then, on the f ace of things, the set of interpretations { \}G, the modal operator N and the relation R that holds between certain pairs of these relations can provide the usual semantics for the formal language with the inte nsional operators and 3 Specifically, If R is an n-place relation symbol, and a0, an are individual constants, \ || (R(a0, an)) iff \(a0), \(a1), \(an) \(R). 4 We might be able to give the semantics for 7a. by using a Matesian-style semantics in which no reference was made sequences but only to the truth of sentences which were the result of various individual constants substituted for variables in the formula The Matesian-style 7a (call it a ) might go: \ || ( x) iff for some interpretation \ which is exactly like \ except possibly with regards to what it assigns to the individual constant \ || x/ 5 We havent developed interpretations to include functions like f in their domain, but this could be done easily and straightforwardly in set theoretic fashion similar to how interpretations were defined for n-place predicate terms.

PAGE 234

234 The Approach of Hanson and Hawthorne in Validity a nd Intensional Languages Pleasing technical results (such as completeness) have been provided for some intensional languages by using Kripkean possible world sema ntics. One difference in the traditional, Kripkean approach is that semantics for these in tensional languages is gi ven in terms of a class of model structures and all the models for each of these model structures. In the approach that Carnap begins and that we ha ve developed (albeit in a somewhat different manner than has Carnap) in this paper, one inte rpretation proxy is to st and for a single model. (As we have just seen this does not change typical semantics for such languages at all.) Bu t on this suggestion for the formal semantics of intensi onal languages, there is only a single class of interpretation proxies, and so semantically accounting for prop erties of sentences ( like validity) cannot be exactly analogous to the traditional, Kripkean ac count. This situation may seem unsettling at first, especially because a completeness result fo r an intensional semantic system like those in Meaning and Necessity would allow us to pay less attenti on to an axiomatic (or natural) treatment of the deductio n procedure for such systems. If we cannot recycle Kripkes work on the semantics for quantified modal logic systems, then if wanted to make legitimate (in a technical sense) the systems we have develope d from Carnap and take for granted the truth preserving character of the semantic symbols we have make use of (namely || and ), we would be forced to develop a formal treatment of a axiomatic deduction sy stem for these systems and then find a proof of completeness for this system. Fortunately, we do not have to break all this new ground because the technical results of Hanson and Hawthorne show that semantics can be provided for intensiona l languages in such a way that only a single model structur e is used, that this semantics is intuitively just as appealing as was Kripkes original, and that similar formal results are available given this semantics and a

PAGE 235

235 usual axiomatic development of a deduction system for these intensional languages. In short, with a single model structure, th ey show that for any sentences and | ( is derivable from ) iff |= ( semantically entails ). We finally see that Ca rnap was correct in paying little attention to deduc tion method of his semantical systems in The Relationship between R and R Very briefly, we conclude with a comment on R the relation that held between any two interpretations \ 1 and \ 2 just in case that for the state-descriptions they represent respectively 1 R 2. In the development of our notion of intens ion (A Set of Interp retations Can Provide Intension), we stipulate that each interpretation of a particular class6 is used to define intension as a map between expressions and in dividuals or sets. If the interp retations are to be proxies for state-descriptions (as we have argued they should be), then, since the interpretations essentially describe correct semantic use in actual and coun terfactual situations, if We are to hold on the idea that intension is a (partial) model for how we use words to mean things, any interpretation must be accessible from any other. These interpre tations taken together are to circumscribe our use; ones mastery of the language means that on e has access to each of these interpretations. I believe we can take this observation as evidence that for any two members \ and \ of the class of admissible interpretations \ R\. This implies that the class of state-descriptions or possible worlds that the interpretations serve as proxies for is such that the worlds are fully connected by the accessibility re lation. This commitment may be support for or evidence against this account we have presented in this a ppendix and in Chapter Two and Chapter Three. 6 We canvassed ways in which this class was to be restrict ed in a subsequent section by developing the idea of an admissible interpretation.

PAGE 236

236 APPENDIX B A PROPERLY SEMANTICAL DIFFICULTY FOR METAPHYSICAL REALIST REDUCTIVE ACC OUNTS THAT IS AVOI DED BY THE ANALYTIC-DEFLATIONARY METHOD In spite of the difficulty of Chapter Five, we see that the approach We are trying to clear a path for has an obvious advantage over realist ap proaches to modal semantics. Another worry for approaches like Lewis and Ar mstrongs has to do with whethe r these sort of metaphysical approaches to understanding modality are at bottom helpful in terms of modal semantics One may have the hunch that meaning (or intension) and modality are closely related because for one to know the meaning of a term is to know in wh ich circumstances it is appropriate to use the term; and knowing what circumstances are the appr opriate ones for the terms use does not just involve whatever circumstances tu rn out to be to the actual ones If I know the meaning of the predicate is a mountain, then I know when to ca ll a particular landmass a mountain in actual or counterfactual circumstances. In other words, in any possible world in which I were confronted with a mountain, if I were competent with the predicate is a mount ain I would call the particular mountain a mountain. If we assume that objects (po ssible worlds) of a certain class serve as the truth-makers for our modal stat ements, then we must assume that we can unproblematically use our words to describe the c onstituents of those objects (worlds) and their arrangements, the predicates that hold of thos e constituents and the relations that hold among them. Indeed, it seems that we must assume that the class of objects is not to be used to provide us any information about intensions; if it were, th en it does not seem like we d have the right sort of truth-makers in these objects. For example, on a Lewisian approach, we assess the claim It is possible that there is a mountain 15 miles tall, by determining if there is a mountain of such height on any planet in a possi ble world accessible from the actual world. To do this we must

PAGE 237

237 know exactly what is to fall under the predicate is a mountain in arbitrary possible worlds, else we cannot determine whether there is such a mo untain on a planet in su ch a possible world. In short, possible worlds cannot tell us about semantic s (specifically intensions) as well as modality if an account of modality is to be explanatorily prior to an effort to an exp lication of intensions. One may hold that metaphysical concerns ove r modality should be considered primary and our talking about them secondary, but if one is in the business of holding (o r trying to develop) a compositional theory of meaning, then holding this primacy of metaphysics view with respect to modality does seem to cause tension. For if meaning is to understood in terms of truth conditions spelled out by truth-makers in term s of possible worlds, then how are the worlds themselves supposed to indicate the compositiona l feature of language? There may be recourse to spelling out the intensions or meanings of terms needed to do a compositional semantics in terms of possible worlds, but then it seems We are back to either Shalkowskis first objection or (if we choose Armstrongs approach) a puzzle ov er what the connection between a primitive state of affairs like Fa and the semantics for our predicate term F and singular term a. Either the semantics fo r the predicate term F mirrors the modal behavior of the F of the state of affairs or it does not. If it does not, our intuitions about our modal claims are mysterious, if it does, it seems We are stuc k with Shalkowskis first objection again: the account cannot be reductive if We are to have proper epistemic access to modal facts. Why not just go with the dispositional / linguistic / analytic-deflationary approach? The preceding is only a rough sketch of the dialectic and while it still needs developm ent, but I think we can see that semantics and modality are closely related.

PAGE 238

238 LIST OF REFERENCES Armstrong, D. M. (1997). A World of States of Affairs Cambridge: Cambridge University Press. Carnap, R. (1947). Meaning and Necessity (2nd ed.). Chicago: Univer sity of Chicago Press. Chalmers, D. (2006). Two-Dimensional Semantics. In Lepore, E. & Smith, B. (Eds.), The Oxford Handbook of Philosophy of Language (pp. 574 605). New York: Oxford University Press. Church, A. (1951). The Need for Abstra ct Entities in Semantic Analysis. Proceedings of the American Academy of Arts and Letters 80, 100-112. Davidson, D. (1963). Method of Extension and Intension. In Schlipp, P.A. (Ed.), The Philosophy of Rudolf Carnap (pp. 311). La Salle, Ill: Open Court. Fine, K. (2005). The Problem of De Re Modality. In Kit Fine, Modality and Tense: Philosophical Papers (pp. 40-104). Oxford: Clarendon Press. Fitting, M. & Mendelsohn, R. L. (1998). First Order Modal Logic Dordrecht, Netherlands: Kluwer Academic. Hanson, W. H. & Hawthorne, J. (1985). Validity in Intensional Languages: A New Approach. Notre Dame Journal of Formal Logic 26, 9 35. Higginbotham, J. (2006). Sententialism: The Th esis That Complement Clauses Refer to Themselves. Nous Supplement: Philosophical Issues 16, 101 119. Jubien, M. (2007). Analyzing Modality. In Zimmerman, D. (Ed.), Oxford Studies in Metaphysics v. 3 (pp. 99 139). New York: Ox ford University Press. Kaplan, D. (1998). Opacity. In Hahn, L. E. & Schlipp, P.A. (Eds.), The Philosophy of W.V. Quine (2nd expanded ed., pp. 229 294). La Salle, Ill: Open Court. Kaplan, D. (1968). Quantifying in. Synthese 20, 178 214. Koslicki, K. (1999). The Sema ntics of Mass Predicates. Nos 33, 46 91. Kripke, S. (1972/1980). Naming and Necessity Cambridge, MA: Harvard University Press. Lepore, E. & Ludwig, K. (2005). Donald Davidson: Truth, Meaning, Language, and Reality New York: Oxford University Press. Lepore, E. & Ludwig, K. (2007). Donald Davidsons Truth Theoretic Semantics. New York: Oxford University Press. Lewis, D. (1986). On the Plurality of Worlds Oxford: Basil Blackwell.

PAGE 239

239 Ludwig, K. (2003). The Mind-Body Problem: An Over view. In Stitch, S. & Warfield, T. (Eds.) The Blackwell Guide to the Philosophy of Mind (pp. 1-45). Malden, MA: Blackwell. Ludwig, K. (2007). De Re Necessities. Ludwig, K., & Ray, G. (1998). Semantics for Opaque Contexts. Philosophical Perspectives 12, 141-166. Mates, B. (1972). Elementary Logic (2nd ed.). Oxford: Oxford University Press. Myhill, J. (1963). An Alternative to the Method of Extension and Intension. In Schlipp, P.A. (Ed.), The Philosophy of Rudolf Carnap (pp. 299-311). La Salle, Ill: Open Court. Peacocke, C. (1992). A Study of Concepts Cambridge, MA: MIT Press. Putnam, H. (1975). The Meaning of Meaning. In Hilary Putnam, Mind, Language and Reality: Philosophical Papers v. 2 (pp. 215-271). Cambridge: Cambridge University Press. Putnam, H. (1980). Models and Reality. Journal of Symbolic Logic 45, 464-482. Quine, W. V. (1960). Word and Object Cambridge, MA: MIT Press. Quine, W. V. (1976). Three Grades of Modal Involvement. In W.V. Quine, Ways of Paradox (pp. 158-176). Cambridge: Harvard University Press. Ray, G. (1996). Ontology-Free Modal Semantics. Journal of Philosophical Logic 25, 333-361. Salmon, N. U. (1981) Reference and Essence Princeton: Princeton University Press. Searle, J. (1975). The Logical st atus of fictional discourse. New Literary History 6, 319-332. Shalkowski, S. (1994). The Ontological Ground of Alethic Modality. The Philosophical Review 103, 669-688. Sidelle, A. (1989). Necessity, Essence and Individuation: A Defense of Conventionalism .Ithaca: Cornell University Press. Sidelle, A. (2007). Conventionalism a nd the Contingency of Convention. Sider, T. (2003). Reductive Theories of M odality. In Loux, M. & Zimmerman, D.W. (Eds.) Oxford Handbook of Metaphysics (pp. 180-208). Oxford: Oxford University Press. Thomasson, A. L. (2005). Modal Conceptualism: A Clarification and Defense. Williamson, T. (2005). Armchair Philosophy, Me taphysical Modality and Counterfactual Thinking. Proceedings of the Aristotelian Society 105, 1-23. Wittgenstein, L. (1961). Tractatus Logico-Philosophicus London: Routledge & Kegan Paul.

PAGE 240

240 BIOGRAPHICAL SKETCH Jesse Butler graduated in 1995 from Brown Univ ersity with an A.B. in mathematics, in 2001 from The University of Tennessee, Knoxville with an M.S. in computer science, in 2005 with an M.A. in philosophy and in 2009 with a PhD in Philosophy both from The University of Florida.