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Are There Contingent, A Priori Truths?

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PAGE 1

1 ARE THERE CONTINGENT, A PRIORI TRUTHS? By DANIEL CARTER MCCAIN A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS UNIVERSITY OF FLORIDA 2006

PAGE 2

2 Copyright 2006 By Daniel Carter McCain

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3 ACKNOWLEDGMENTS I would like to thank my chair, Dr. Greg Ray, for the myriad observations he made on various drafts and for his tireless effort toward the completion of th is project. I would also like to thank my committee members, Dr. Kirk Ludwig and Dr. Michael Jubien, for their insightful comments and helpful suggestions at my defense. In addition, without the support of my fiance, Karen Garito, this project would not have co me to fruition. Finally, I could not imagine completing a task of this difficulty wit hout the help of my Lord Jesus Christ.

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4 TABLE OF CONTENTS ACKNOWLEDGMENTS...............................................................................................................3 ABSTRACT....................................................................................................................... ..............6 INTRODUCTION................................................................................................................... ........7 KRIPKEAN CANDIDATES.........................................................................................................10 Background..................................................................................................................... ......10 The “Standard Meter Bar” Example.....................................................................................10 Problems with the Kripkean Examples.................................................................................11 Conclusion..................................................................................................................... .......19 ACTUALIZED CANDIDATES....................................................................................................20 Background..................................................................................................................... ......20 Bostock’s Argument Against the “Actua l Inventor of the Zip” Example............................22 ‘All Actual Geniuses are Geniuses’......................................................................................27 Conclusion..................................................................................................................... .......29 PAST OBJECTIONS CONSIDERED IN LIGHT OF ‘ALL ACTUAL GENIUSES ARE GENIUSES’..........................................................................30 What Does it Mean for a Candidate to be “Philosophically Interesting”?...........................30 Donnellan’s Objections Revisited.........................................................................................31 Kitcher’s Objection Revisite d and Concluding Remarks.....................................................34 GETTING CLEAR ON ‘ALL ACTUAL GENISUES ARE GENISUES’...................................35 Clarification and Background...............................................................................................35 Analyzing ‘Actual’............................................................................................................. ...39 The Contingent A Priori and Knowledge of One’s Actuality..............................................42 Two-Dimensional Logic and the Contingent A Priori .........................................................44 Conclusion..................................................................................................................... .......49 A NON-INDEXICAL CA NDIDATE FOR THE CONTINGENT A PRIORI ............................................................................................................50 Introduction................................................................................................................... ........50 Williamson and Oppy’s Conversation..................................................................................50 Conclusion..................................................................................................................... .......56 CONCLUSION..................................................................................................................... .........57

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5 LIST OF REFERENCES............................................................................................................. ..60 BIOGRAPHICAL SKETCH.........................................................................................................61

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6 Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Arts ARE THERE CONTINGENT, A PRIORI TRUTHS? By Daniel Carter McCain December 2006 Chair: Greg Ray Major Department: Philosophy While most philosophers have thought that necessity and a priority are co-extensive, there have been some who have challenged this claim. I examine the claims of Kripke, Fitch, Bostock and Williamson to see whether the candidates they offer for the contingent a priori are viable. I conclude that, for vari ous reasons, each of them is not a true example of the contingent a priori However, I offer a candidate that avoids the pitfalls of these alleged examples: ‘All actual geniuses are geniuses’. I conclude the pa per by exploring and clarifying the semantic role of ‘actual’, in the process defending ‘All actu al geniuses are genius es’ as a contingent, a priori truth.

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7 INTRODUCTION From Immanuel Kant to philosophers of the present day, the possibi lity of a divergence between necessity and a priority has been denied. If Kant and those who agree with him are right, there can be no contingent, a priori propositions. Though the weight of tradition and the majority opinion of contemporary ph ilosophers fall in line with Kant there are dissenters. While the case for the necessary a posteriori and that for the contingent a priori are related, establishing one does not automatically establish the other. Therefore, I will focus on the case for the contingent a priori In this paper I will survey the literature on the contingent a priori in order to accomplish two things: 1) trace th e course the conversation has take n as different candidates for the contingent a priori have been refuted and new ones have de veloped, and 2) question whether it is plausible that a viable candidate will ever be offered. We will c onsider a few different types of candidates. The first sort of candidate considered will be the Kripkean examples. These depend on a linguistic stipulation that specifies the referent of a name in all possible worlds. It is argued by Kripke and others that proper name s have the same referent in all possible worlds. Thus, if one stipulates that the referent of a certain name is the individual or thing which satisfies a certain definite description, while it will be true a priori that the definite descri ption is true of and only of the referent of the name, it will be a contingent truth since the definite description might have been satisfied by someone else. We will next consider the sort of example that Fitch labels the “incorrigibility” type. There are, allegedly, contingent truths that one cannot believe falsely. These examples will depend on indexicality. For instance ‘I have a headache’ and ‘I exis t’ would arguably be in this

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8 group. It is then argued that if one cannot believe these truths fa lsely, then if one knows them to be true at all one knows them a priori We will next consider the sort of example that I’ll label the “actualized” type. These examples, like the Kripkean ones, depend on rigid designation to allow us to say things we can know a priori that are nonetheless false in some po ssible worlds. The difference is, while Kripkean proper names lack sense, actualized te rms do not. The “rigidification” is accomplished not by linguistic stipulation, but by the use of ‘actual’ and its va riants. For in stance, ‘actual receptionists’ has a discernable sense, but rigidl y designates all and only those things which are actually receptionists.1 Finally, we will examine a non-indexi cal candidate for the contingent a priori Examples of this sort could also be labe led the “self-satisfying” type. These examples are argued to be made true simply by believing them to be true. The trick is that they will be justified not by a deduction utilizing indexicality (one ’s knowledge of one’s existence or one’s belief states), but by an allegedly indexical-free, belief-forming mechanism. I will begin with the discussion f ound in Kripke’s Naming and Necessity which broke from traditional thought on the subject and offered the firs t candidate for the contingent a priori I will then examine Keith Donnellan’s response to Kripke in Donnellan’s paper “The Contingent A Priori And Rigid Designators”. In “A Priority and Necessity” Philip Kitcher argues that part of Donnellan’s analysis is ill-formed, but ag rees with his conclusion that there are no philosophically interesting versions of the contingent a priori I will also examine G.W. Fitch’s 1 There are two things that need to be said here. First, I am not claiming that the meaning of ‘actual’ is unambiguous. Rather, I will treat ‘actual’ in the same way it is treated in the papers I discuss (which will become clear later), so as to shed light on the conversation and see what merit it has. Second, I believe ‘actual’ is a rigidifier in the following sense: the phrase composed of ‘actual’ and the term it modifies refers to the same individual(s) no matter where the phrase occurs in a sentence (e.g. ‘Actual receptionists’ refers to the same individuals in ‘All actual receptionists have desks’ as it does in ‘Necessarily, a ll actual receptionists have desks’).

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9 argument against Kripke and his dismissal of a couple of other alleged contingent, a priori truths in “Are There Contingent A Priori Truths?” As these papers present certain problems fo r the Kripkean sort of candidates for the contingent a priori I will next consider can didates involving ‘actual’ and Bostock’s attempt to refute them in his paper “Necessary Truth and A Priori Truth”. Bostoc k’s comments here will lead me to suggest a different example from the one he considers, one that I believe meets his objections. I will also reconsider Donnellan and Kitcher’s objections in light of this new candidate, as well as the argum ent given by Albert Casullo. I will then investigate in what way the tw o-dimensional modal logic of Davies and Humberstone comes to bear on the ques tion of candidates of the contingent a priori that involve ‘actual’ and its variants. I will also examine Williamson’s attempt to offer an indexical-free, contingent, a priori truth and see whether Graham Oppy’s a ttempted rebuttal is effective. I will then conclude by recapping the status of the various candidates and summarizing what we have learned about the contingent a priori .

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10 KRIPKEAN CANDIDATES Background To properly understand Kripke’s al leged examples of contingent, a priori truths, we must remind ourselves of Kripke’s thesis that proper na mes are rigid designators. He writes, “Let’s call something a rigid designator if in every possible world it designates the same object, a nonrigid or accidental designator if that is not the case.”1 We already have the intuition, says Kripke, that when we talk about how a thing might have been we talk about a possible situation for that thing rather than talking about a di fferent thing that is very si milar to the original. Thus, our use of proper names should rigidly designate so that our talk of possible worlds captures our intuitions about counterfactuals. It is necessa ry that nine is greater than seven because both ‘nine’ and seven’ are rigid desi gnators that pick out the same object in every possible world. ‘The number of planets’, however, is a descri ption rather than a name. Thus, the phrase will designate whatever happens to be the number of planets in the world in question, not necessarily the number of planets in the actual world. Traditionall y, names have been considered abbreviated definite descriptions picking out whatever entity, if any, matches the description in the world in question. Kripke be lieves, however, that definite descriptions are used to fix reference of names, to make them rigid designat ors; names are not simply abbreviated definite descriptions. If they were we would be aski ng about some different, albeit very similar, individual from Alex when asking, “What if Alex had not been an engineer?” The “Standard Meter Bar” Example One of the interesting results Kripke believes this thesis provides (and one of the reasons it has been so hotly contested) is that it seems to allow us knowledge of contingent, a priori 1 In order to avoid trivial counter-examples, Kripke only requires that the rigid designators pick out the same object in the possible worlds in which the object exists.

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11 truths.2 One of Kripke’s examples of this goes as follows. Let us stipulate that ‘one meter’ refers to the length of S, where S is a certain stick or bar in Pa ris. Now consider the proposition ‘S is one meter long’. What are the epistemologi cal and metaphysical statuses of this proposition? Given that the definition of ‘one meter’ is “the length of S (a t the actual world),” the proposition seems to be straightforwardly a priori However, it is surely a contingent fact that S is the length it in fact is; we can easily imagine possible worlds in which S is longer or shorter than it actually is. Therefore, the proposition is on ly contingently true, though still a priori An important thing to examine is how the se ntence is being evaluated at merely possible worlds. Do we take what the sentence expresse s at the actual world and evaluate it at different possible worlds, or do we evaluate the sentence a ccording to what it expresses in each possible world? Kripke believes we must do the former because since names are defined not by synonym or abbreviated description but by fixing th e reference, the reference of the names at the actual world is what underlies our investig ations of modality. Thus, th e proposition is contingent, but will be a priori only in the actual world. In every me rely possible world the proposition would assert that a stick in the actual world is the same length as a stick in the merely possible one, something we cannot know a priori If, however, we choose to evaluate the proposition in the latter way, it will be necessary and a priori since in every possible world the proposition will be equivalent to something like ‘S (at this world) is the same length as S (at this world)’. Problems with the Kripkean Examples A worry that one might have with Kripke’s example is revealed by the discussion of modal analysis found above. There seems to be an odd sort of circularity between the definition of ‘one meter’ and the proposition in question. ‘One meter’ is defi ned as “the length of S,” but the proposition asserts that S is one meter long (i.e., that S is the length of S). While it does not 2 See pages 54-57 of Naming and Necessity for the discussion summarized here.

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12 seem problematic, the example seems somewhat c ontrived given that we do not normally assert propositions of this form, and the circularity coul d mask some semantic problem. It is unclear how strong this objection is, but fo r two reasons we shall not examin e it further. First, there are other, clearer objections we sha ll discuss that make this exampl e untenable. Second, Kripke has other examples of alleged contingent a priori truths that do not invol ve this same sort of oddness.3 Therefore, even if an “argument from oddness” can be made against the “Standard Meter Bar” example, it will not defeat Kripke’s ge neral assertion that his theory of proper names opens the possibility for contingent, a priori truths. In “The Contingent A Priori And Rigid Designators,” Keith Donnellan responds to Kripke’s theory of names and to the possibility of contingent a priori truths.4 He formulates one sort of “uneasiness” with Kripke’s examples, writing, “It might be put roughly as follows : If a truth is a contingent on e then it is made true, so to speak, by some actual state of affairs in the world that, at least in the sorts of examples we are interested in, exists independ ently of our language and our linguistic conventions.”5 It is difficult to see how definition by stipulat ion, on which Kripke’s examples depend, can give us epistemic access to non-linguistic states of affairs. The position Donnellan defends within this paper is that while we have no reason to de ny that definition by stip ulation is theoretically viable, such a procedure does not produce “interesting” contingent a priori truths. 3 ‘Neptune is the planet causing such and such discrepancies in the orbits of certain other planets’ is one example of an allegedly contingent a priori truth that does not involve such oddness. This example can be found on pg. 79 of Naming and Necessity It is similar to the “Standard Meter Bar” example in that it relies on stipulation. 4 Contemporary Perspectives in the Philosophy of Language eds. French, Uehling, and Wettstein. University of Minnesota Press, 1980 (pgs. 45-60) 5 ibid. (pg. 46)

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13 Donnellan begins by defending Kripke from Dummett’s attack on the idea that names can be introduced as rigid designators.6 He does so by making a di stinction between arguing for certain historic examples of names being introduced as rigid designators a nd arguing that it is in principle possible to introduce names in this way. He argues that it would be impossible, without an explicit stipulation, to tell if historic cases (such as Leve rrier’s ‘Neptune’) are actually examples of rigid designation. Donnellan be lieves, however, that the philosophical worries about the contingent a priori are equally strong even if introduc ing names as rigid designators is merely possible. As he sees no reason to deny the possibility, he next shows how such a procedure does not yield philosoph ically interesting, contingent, a priori truths.7 Donnellan argues that any examples of contingent a priori truths, if they are examples at all, that follow from the sti pulative introduction of a name as a rigid designator will not be worrisome (unlike Kripke’s alleged examples).8 He begins by noting the distinction between knowing that a sentence expresses a truth and kno wing the truth it expresses. For instance, I know that the sentence ‘Fhqwhgads ar e Fhqwhgads’ expresses a truth si nce a thing must be itself. If I do not know what Fhqwhgads are, however, I do not know the truth the sentence expresses. He then writes that we will re present the (Kripkean) stipulative introduction of a name with: (a) Provided that the exists, let “N is the ” express a contingent truth, where ‘the ’ is a definite description and ‘N’ is a name. Donnellan believes that using this locution help s bring certain relevant features to light (which we will see later). He also argues that while it may seem worrisome that we are stipulating that something is contin gently true, it is not suspect. So long as we pick a name that 6 ibid. (pgs. 47-50) 7 The idea that any examples of contingent a priori truths will be philosophically uninteresting is shared by many of those who disagree with Kripke (including Donnellan, Kitcher, and Bostock). I will explore later what ‘philosophically interesting’ may mean and whether the claim made by Donnellan and others is true. 8 ibid. (pgs. 51-8)

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14 is not already in use within the language, we are not attempting to make some non-linguistic state of affairs the case; rather we are simply creating a purely linguist ic state of affairs. Furthermore, Donnellan asserts that we do not come to have knowledge of any (non-linguistic) state of affairs by our act of stipulation. Donnellan has us consider Kripke’s “N eptune” example to illustrate his point.9 If the Neptunians knew of Leverrier’s st ipulation, would they be justif ied in saying he had discovered their planet as the cause of the perturbations? Could they, in th eir language and using their name for their planet, say he knew their planet was the cause of the perturbations? Donnellan takes the answers to these questions to be “No” and concludes that there is no knowledge of a nonlinguistic state of affairs given by the stipulation. Donnellan also turns our atten tion to the classic “Newman-1” example, which he takes to be analogous to the above example.10 He says that any knowledge resulting from the stipulation must be de re saying, “. . it would have to be knowledge about an individual in the sense that there is (or will be) an individual about whom we now know some thing and if that individual turns out to be John we now know something about John.”11 He says this is not simply because the proposi tions involve rigid designators; one could have de dicto knowledge as a result of rigid designation as well. What is required is that the rigid designators lack descriptive content in the propositi ons in question. It is his contention that this sort of stipulation fails to produce knowledge de re 9 See footnote 5 for the gist of the example. 10 ‘Newman-1 is the first child born in the 21st century,’ where ‘Newman-1’ is sti pulated to refer to the first child born in the 21st century. 11 ibid. (pg. 54)

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15 Having thus laid the foundation for his argument, Donnellan gives a rough characterization of two principl es that hold for a wide number of cases but fail for both the “Neptune” and “Newman-1” examples. One of these principles is as follows: “If an object is called by one name, say ‘N,’ by one group of people and by another name by a second group of people, say ‘M,’ and if, in the language of the first group ‘N is ’ expresses a bit of knowledge of theirs and if ‘is ’ is a translation of ‘is ’ into the language of the second group then if the re levant facts are known to the second group, they can say truly that the first group ‘knew that M is .”12 Obviously, the Neptunians cannot say that Leverrie r ‘knew that Enutpen is the planet causing such and such discrepancies in the orbits of certain other planets.’ Donnellan concludes that unless some other explanation ca n be given, Kripke’s examples fail to meet these criteria because they fail to produce knowledge of non-lingui stic matters (the second criterion is similar to the first, applying to temporal cases like Newman-1 rather than Neptune). So while Leverrier could have known (perhaps even a priori ) that the proposition expresses a truth he could not have known a priori the truth the proposition expresses. Donnellan notes that some might still wish to cl aim that these cases give examples of the contingent a priori that one has a priori knowledge of a linguistic fact that could have been otherwise. Donnellan concedes th at this could be true, but says that such examples are not philosophically interesting or worrisome, that they could be produced with names being stipulated rigid designators, and that trad itional definitions will yield similar results. One might object that Donnellan’s use of the two conditions is suspect for one reason or another. First, he readily admits that his c onditions allow certain counter-examples, one of 12 ibid. (pg. 55)

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16 which is Kripke’s “Hesperus/Phosphorus” example.13 If other of Kripke’s examples can be shown to have the same features that allo w general counter-examples to the conditions, Donnellan’s case would be much weaker. Second (and on a related note), Donnellan leaves open the possibility for some other explanation of why th e examples fail to meet the criteria. If such an explanation could be given, we would have less reason to deny the propositions in question could produce knowledge of non-linguistic matters. Philip Kitcher argues that we need no t agree with Donnellan that any knowledge produced by the stipulation must be de re .14 Consider the proposition ‘If Shorty exists then Shorty is a spy,’ where ‘Shorty’ refers to the shortest spy. The corresponding belief must be either de dicto or de re according to Donnellan (this is the alleged dilemma that Kitcher intends to deny). It cannot be de dicto because that would require that ‘Shorty’ have descriptive content, but the description was used merely to fix the reference. Therefore, it must be de re However, if the belief were de re I should be able to say, upon mee ting the shortest spy, “Ah, I knew ( a priori ) that you were the shortest spy.” I cannot do this, so my belief cannot be de re Therefore, I do not have a priori knowledge of the proposition expressed. Kitcher argues that contra ry to Donnellan’s argument, our belief in this case is de dicto Kitcher writes, “The fact that ‘the shortest spy’ was used to fix the reference of ‘Shorty’ does show that the name ‘Shorty’ does not have a particular descriptive content. However, to use that description to fix the reference of ‘Shorty’, I mu st intend to use ‘Shorty’ as an abbreviation for a closely related description: ‘Shorty’ must abbreviate ‘t he shortest actual spy’.”15 13 See footnote 22 of Donnellan’s paper. 14 Philip Kitcher, “A Prior ity and Necessity,” from Australasian Journal of Philosophy 58 (1980), pgs. 89-101 15 ibid. (pg. 91)

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17 Thus, my de dicto belief is ‘If there is a shor test actual spy then the shor test actual spy is a spy.’ Despite disagreeing with Donnellan’ s analysis, however, Kitcher agrees that while we might have knowledge of contingent a priori truths through stipulation, they should not cause any worry. In “Are There Contingent A Priori Truths,” G.W. Fitch considers and dismisses several alleged examples of the contingent a priori culminating in his dismissal of Kripke’s example.16 The candidates he considers prior to considering Kr ipke’s he calls the “incorrigibility” examples. The first he considers is offered by David Benfie ld: ‘I have a headache’ uttered by someone else at some specific time.17 This is certainly conti ngent, but it is clearly not a priori The proposition requires experiential ev idence to be justifiably believe d. Secondly, Fitch notes that examples of this sort purport special access to a priori knowledge; if Frank has a headache, he would be the only person in a position to know this a priori.18 Fitch argues that no human has special access to a priori knowledge (indeed, this would seem to show that the individual has some sort of individuating experiences he or sh e is drawing from), so examples of this sort cannot be contingent, a priori truths. Fitch next considers an example by Alvin Pl antinga. Consider ‘I know that 7+5=12’. While the contingency of this is clear, it’s a priority is much less so. One may be tempted to think that knowing the above tr uth requires knowing ‘I believe that 7+5=12’, and that this is certainly known a posteriori Plantinga argues that we cannot demand that to be a priori a truth must be known without the use of any experien ce, since certain experiences (namely those required to attain the concepts) are needed ev en to know ‘7+5=12’. 16 The Journal of Critical Analysis vol. 6, no. 4, Jan./Apr. 1977 17 Fitch, 119 18 ibid. (pg. 120)

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18 Fitch points out that the difference between th e two is that in the former experience acts as a justification for belief, while in the latter it does not.19 While experience is certainly necessary to know anything (even if only to acquire the concep ts involved), the hallmark of a priori knowledge is it either requires no justification or is justified purely on the basis of other a priori truths. Plantinga’s example satisfies neither of these. The third example considered by Fitch is ‘I exist,’ also given by Plantinga. Fitch replies that this too is justified on the basis of expe rience, albeit not any pa rticular experience. Furthermore, this is yet another ex ample that purports special access to a priori knowledge (only I can know a priori that I exist). For these reasons, this candidate for the contingent a priori must be dismissed as well. Fitch now moves on to Kripke’s ex ample, ‘Stick S is one meter long’.20 Fitch argues, very similar to Donnellan, that while those who de fine ‘meter’ as ‘the length of stick S’ know that ‘Stick S is one meter long’ expresses a truth, they do not know the truth it expresses.21 Because a priority must be maintained, the stipul ators must not have had any experience of S. Thus they are not acquainted with it, they do not know its length relative to other things, etc. Therefore, it is not clear, says Fitch, that they know what they’re saying when they utter ‘Stick S is one meter long’. He writes, “If we make the distinction between sentence s and propositions, then it seems clear that the fixers only know something about the la nguage they helped to form, not about the world the language is used to describe.” 19 ibid. (pg. 121) 20 ibid. (pg. 122) 21 ibid. (pg. 123)

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19 Thus, he dismisses Kripke’s alle ged example of the contingent a priori He closes his paper by remarking that while necessity and a priority ar e different conceptually (one is metaphysical while the other is epistemic), we have no reason as of yet to be lieve they are not co-extensive. Conclusion So, what can we conclude about the Kripkean candidates for the contingent a priori ? The worry about the “Standard Meter Bar” exampl e having an odd sort of circularity between the stipulation and the proposition in question doesn’t rule it out as a candidate. However, Donnellan’s worry is more problematic. While the problems with Donnellan’s argument that Kitcher and I point out s eem to be real problems for him, hi s conclusion that Kripke’s examples are not philosophically inte resting, a conclusion shared by Kitcher seems right.22 Fitch’s comments reveal the essential point in Donnella n’s paper without Donnellan’s unnecessary and problematic conditions and without insisting that the knowledge produced by Kripkean examples must be de re Fitch’s paper reveals the essential probl em with the Kripkean examples: linguistic stipulation alone cannot give us knowledge of a particular and, thus, cannot generate a priori knowledge of contingent states of affairs involvi ng that particular. It also notes in passing the failure of candidates of the incorrigibility type. 22 What this claim amounts to, and how it informs and directs the discussion on contingent, a priori truths, will be examined later.

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20 ACTUALIZED CANDIDATES Background David Bostock puts forth yet a nother objection to the idea that there are contingent a priori truths in his paper “Necessary Truth and A Priori Truth.”1 He writes, “I believe that, in the end, Kripke’s two claims [that there are contingent a priori truths and that there are necessary a posteriori truths] must be admitted to be correct, but that does not have quite the significan ce that one is apt to suppose.”2 His conclusion is similar to that of Donnellan. Kri pke gets the results he cl aims but that they are ultimately not of much importance. However, Bostock reaches it for very different reasons. While Donnellan focuses on what sort of knowle dge is produced by alleged examples of the contingent a priori Bostock considers the question of rigi d designation from Kripke’s theory of proper names and argues that ri gid designation does not give us philosophically important examples of the contingent a priori Bostock begins by laying out some of the characteristics of the quantified, modal logic that underwrite Kripke’s notions of rigidity and necessity. The key notion is that of a possible world a counterfactual situation where every pro position has a determinate truth value. A possible or contingent proposition is one that is true in some possible world; a necessary proposition is one that is true in every possible world. Based on Kripke’s conception of names as ri gid designators Bostock introduces another “rigidified” part of speech. By specifying the extension of a pr edicate at every possible world one introduces a rigid predicate.3 To give an example that will arise later in Bostock’s argument, we could stipulate that the exte nsion of ‘cordate’ in all worlds is to be all and only those 1 Mind New Series, Vol. 97, No. 387 (Jul., 1988), pg. 343-379 2 ibid. (pg. 344) 3 ibid. (pg. 351)

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21 creatures that actually have hearts. In doi ng this Bostock separates the concern over the contingent a priori (and the necessary a posteriori ) from the viability of Kripke’s conception of naming. Rigidifying is a legitimate process ap art from the question of whether names (or predicates for that matter) are actually rigid and so the concerns over the purported material difference between necessity and a priority are valid ones. Note that Bostock once again takes the same line as Donnellan in ar guing that even if we do not in fact introduce terms as rigid designators or expressions, the worrie s over the material difference persist. Bostock says that we have a set of words in the English language – ‘actual’ and its variants that modify certain words or phr ases and make them “Kripkean” (or rigid).4 The function of these words is to anchor whatever th ey modify to the actual world even if we are considering counterfactual situati ons. For example, consider the proposition ‘All actual geniuses are geniuses’. If I ask whether this proposition is necessary, I am asking whether it is true in every possible world that every thing that is a genius in the actual worl d is a genius in that world. Within quantified modal logic an actuality operator, ‘ A ’, is used to accomplish what is accomplished by ‘actual’ and its variants in natural language.5 ‘ A ’ modifies a proposition, such that ‘ A ’ is to be interpreted as true at any world iff ‘ ’ is true at the actual world. ‘ A’ can also modify predicates; ‘ A Fx’ means ‘x is actually F’. As with other modal operators, when combined with other scoped operators the ‘ A ’ operator may take both wide-scope and narrowscope positions. 4 ibid. (pg. 355) 5 ibid. (pg. 356)

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22 Bostock’s Argument Against the “Act ual Inventor of the Zip” Example With the foundations thus laid, Bostoc k gives his argument that the use of ‘ A ’, while permitting a material difference between necessity and truth in every possible world, also gives us results that do not match with our intu itive notions of nece ssity and contingency. “Let ‘ p ’ be any plainly contingent proposition, that happens to be true as things are, but could easily have been otherwise. Then ‘ A p ’ will be true. But then it follows further that ‘ A p ’ will be true in all possible worlds, for it will be true in all worlds that it is true in this world that p If truth in all worlds suffices for necessity, we must then conclude that it is a necessary truth that A p But this is surely absur d. We cannot really turn a contingent proposition into a necessary one by a dding such qualifications as ‘actually’ or ‘in fact’ or ‘as things are’, and the correct conclusion to draw is evidently that the criterion of truth in all possible worlds is no longer an adequate criterion of necessity.”6 In order to remove the alleged counter-intui tive results of our working notion of modality (and thus of our modal system), Bostock suggest s a different way of ha ndling ‘actual’ and its variants. In what follows we will examine his system and his reasons for promoting it. This method will, according to Bostock, allow us to re present sentences containing ‘actually’ without giving counter intuitive results. He writes, “The general idea is to treat ‘actually’ not as a new moda l operator but as a device for indicating relative scope, so that the word no longer occurs explicitly in our formal language, where scope is shown diff erently, by order and bracketing.”7 6 ibid. (pg. 357-8) 7 ibid. (pg. 360)

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23 I will briefly explain the changes Bostock suggests and the advantages of making this revision. I will then question Bostock’s motivation for the change and some of the assertions he makes about the effects of the change. Bostock works with ‘It is possible that th e person who did actually invent the zip should not have done so’.8 The “old” formalization of this proposition would look something like the following: x ( A y(Fy y = x) ~Fx), where ‘F’ is ‘invented the zip’. Bostock, however, suggests the following “new” formalization: x ( y (Fy y = x) & ~Fx). In the second formalization, ‘ A ’ is no longer present. Rather, the expression modified by ‘ A ’ in the first formalization is taken outside of the scope of the other modal quantifier and ‘ A ’ is removed. Thus, the modality is now a de re modality with the fo rmalization read as, ‘Concerning the person who did inve nt the zip, it is possible that he should not have done so’. Bostock believes that there are several reas ons to accept this trea tment of ‘actually’.9 First, this method can handle all instances of ‘ actually’. Second, Bostock argues that it is more versatile than the previous system. He says that there are examples of propositions that the original treatment of ‘actual’ and its variants cannot formalize, such as ‘It is possible that all the actual dogs should have existed a nd some other dogs as well’. Finally, this method eliminates what Bostock takes to be counter-intuitive resu lts (e.g. “philosophically interesting” necessary a posteriori truths). He writes, “The consequences of this [change in our modal system] for the divergence between necessary truth and a priori truth are clear: there is now no divergence – or at least none that is due to th e word ‘actually’.” Before movi ng on to the possible problem with 8 ibid. This proposition underlies the potential candidate ‘ 9 ibid. (pg. 360-362)

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24 Bostock’s move, let us examine his claim that his treatment allows us to formalize propositions that cannot be formalized by the traditional treatment. Bostock uses the example mentioned above to illu strate this point. He says the point of the sentence is to assert that there is a worl d in which all actual dogs exist and other (i.e. nonactual) dogs exist. The problem, however, is th at we cannot refer to the possible world in question when we treat ‘actual’ as a quantifier itself, so we have no way of evaluating the proposition asserted. The example can be represented with the following: w x(x w & Dxw & y(Dyw* y w & y x)), where ‘w’ is a variable ranging over possible wo rlds, ‘x’ ranges over pos sible objects, ‘w*’ denotes the actual world and ‘Dxw’ means ‘x is a dog in w’. Bostock notes that we can use ‘ x(Dx &’ in place of ‘ w x(x w & Dxw &’. We may also replace ‘ y(Dyw* ’ with ‘ y( A Dy ’. This suggestion could be used to tr y to represent the proposition in our usual system of modal logic. However, on ce we do we are unable to translate ‘y w’ since doing so would require asserting that the dog s that actually exist also exist in the world we are discussing We cannot do this because we have dropped the ‘ w’, which we would have to refer back to in order to make the assertion. Bostock’s method, on the other hand, can treat this sentence and those like it with ease. Without removing ‘ A ’ we formalize ‘It is possible that all the actual dogs should have existed and some other dogs as well’ as: ( x(x y (y = x)) & x (Dx & y( A Dy y & y x)), where ‘ ’ is a rigid-predicate variable that ranges over the possible world discussed. Therefore, the above formalization can be roughl y translated as ‘There is some such that there is a possible world in which everything in is in that world and ever ything in that world is in

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25 Furthermore, in that world there is some x such that x is a dog and all of the actual dogs are in the possible world and are not identical with x’. Then, utilizing the unique role ‘ ’ plays in the language, Bostock can eliminate ‘ A ’ and translate the proposition with the following: a( x ( x a Dx) & ( x(x y (y = x)) & x (Dx & y(y a y b & y x)))). Bostock admits that this method is somewhat cumb ersome, but says that it allows us to translate these sorts of sentences without needing a furt her device. We can translate these sorts of sentences while still utilizing ‘ A ’, but it requires a further device, like the one by Peacoke that Bostock discusses briefly.10 So there is a trade-off between having si mpler expressions on the one hand and not having to introduce a further device into our form al language on the other. Which one we would deem the simpler revision would largely be a matte r of preference, so Bostock’s “argument from simplicity” does not tip the scales toward one or the other. We must, therefore, examine his motivation for suggesting the revision in the firs t place (i.e. that the traditional treatment of ‘actual’ and its variants leads to counter-intuitive results). Bostock’s argument that we need a different way of handli ng ‘actual’ and its variants seems plausible on the surface. Consider the foll owing proposition: ‘All philosophers are pale’. This proposition is both contingent (it is tr ue in some worlds and not in others) and a posteriori ; it poses no problems for the idea that necessity and a priority are materially equivalent. However, suppose the proposition above is actually true and consider the proposition ‘It is actually the case that all ’. It seems to me that Bostock believes we have the intuition that the modal status of this proposition s hould be the same as the first. Since in our current system of 10 ibid. (pg. 361)

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26 modal logic the second proposition comes out ne cessary, Bostock believes there must be a problem with some component(s) of our system. However, do we really have the intuition th at these propositions should have the same modal status? We certainly do have the intuiti on (and rightly so) that it is not essential to philosophers that they be pale. That is, we believe the proposition ‘All philosophers are necessarily pale’ is false, and hence also that ‘It is actually the case that all philosophers are necessarily pale’ is false. However, this is th e narrow-scope reading of the necessity operator; it is clear from Bostock’s talk of contingent propositions and ‘ A ’ being a propositional modifier that he has in mind de dicto necessity. So, what are our in tuitions about ‘Necessarily, it is actually the case th at all philosophe rs are pale’? I must confess that I do not have clear, pre-theoretic intuiti ons on the status of de dicto modal statements that include ‘ A ’; my intuitions on de re modal statements including ‘ A ’ are reasonably clear though. However, I think there are a few reasons to think that Bostock’s conclusions about our intuitions and what we s hould do with our formal notion of necessity are either questionable or mistaken. First, since th e traditional “truth in all possible worlds” notion of necessity works in so many cases, it would seem irresponsible to throw it out unless intuitions are reasonably clear and widely shared. Second, I think there is serious do ubt that intuitions on this matter are in fact clear and widely shared. The fact there is continued debate would seem to be evidence of this. Third, it is at least possible that Bostock’s intuitions about the modal status of ‘ A p ’ are, unbeknownst to him, intuitions about the de re necessity claims. At the end of his paper, Bostock defends wh at he believes is a true example of the contingent a priori (378). His example is ‘If there is exactly one object that falls under the predicate, then it is necessary th at there is no more than one’, wh ere the predicate in question is a

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27 rigidified predicate. Bostock notes that if the antecedent is false, the conditional turns out to be contingent. However, given the nature of ri gidified predicates, we are able to know the proposition is true a priori Therefore, we have a contingent, a priori truth based on a Kripkean language, though of a different sort than the ones Kripke mentions. Bostock’s example seems to avoid the worry with the Kripkean examples (i.e. that we cannot understand them a priori ). While rigidified predicates, like Kripkean proper names, lack sense, since the predicate is mentioned rather than used it does not seem to present a problem for the example; we can understand the propos ition. However, since we cannot know a priori which things fall under the predicate, and since the predicate does not have a sense, the proposition concerns only a linguistic state of affairs. As we shall see later when we discuss what it is for an example to be philosophically interesting, Bost ock’s example fails to be so. So, while the example seems to be an example of the contingent a priori it is not of the so rt that interests us. ‘All Actual Geniuses are Geniuses’ While Bostock focuses on the actuality opera tor as a propositional modifier, one could offer a candidate for the contingent a priori that uses ‘ A ’ as a predicate modi fier. So, even if Bostock is correct that the propositional modifier use of ‘ A ’ gives us counterintuitive results when considered in conjunction wi th the wide-scope r eading of one of the other modal operators, that may simply give us reason to limit where we place ‘ A ’ rather than reform our method for assessing necessity. I will conc lude my argument against Bostoc k’s position by showing that the narrow reading of the actuali ty operator (the one that gives us the contingent a priori) does not lead to counter-intuitive results, contingent a priori aside. Consider ‘All geniuses are geniuses ’. This propos ition is true and a priori Now consider ‘All actual geniuses are geniuses’. This also seems to be a priori but what is its modal

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28 status? Consider the individuals who are geniuses in the actual wo rld. Is it true that they are geniuses in all possible worlds? Certainly not, since Albert Eins tein might have been a man of average or below average intelligence, so ‘All ac tual geniuses are geni uses’ is a contingent proposition. According to Bostock, the function of ‘ A ’ in this position is to take the term it modifies out of the scope of the other modal operator, so ‘All actu al geniuses are geniuses’ could be translated: ( x)( A Gx Gx). The above formula comes out false using our traditio nal system of modal logic, having the same truth conditions implicit in the possible worlds expl anation above. Therefore, in this case there is no divergence between our intu itions and our system and, t hus, no need for a Bostockean revision.11 Bostock briefly addresses the possibi lity of rigidified predicates (351).12 As rigidified predicates are similar to ‘actua l geniuses’ in our example, we should look at his remarks. Though Bostock’s treatment of ‘ A ’ as a sentential modifier only includes the wide-scope reading, his treatment of ‘ A ’ as a predicate modifier allows hi m to handle narrow-scope uses of ‘ A ’ as well. Bostock says one can intr oduce rigidified predicates by s tipulating what the extension of the predicate is to be in every possible world. In our example, the term ‘actual geniuses’ is taken to refer to all and only those thi ngs which are geniuses in the actua l world. Thus, in all merely possible worlds, the extension of the predicate is determined by the things that happen to be geniuses in the actual world and which also exist in the world in question. 11 Bostock makes implicit use of the principal that a proposition, p, is necessary just in case ‘ p’ is true. 12 It is noteworthy that while Bostock brings up the possibility of rigidified predicates, he does not involve them in his argument, nor does he say that they give counter-intuitive results.

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29 Bostock explicates some of the features of th is sort of rigidity with an example (351-2). ‘Cordate’ is to refer to all and only those creatures which ha ve hearts in the actual world.13 ‘Renate’ is to refer to all and only those creatu res which have kidneys in the actual world. Now we have two rigidified predicates. Suppose (as is the case) that it is a contingent, a posteriori truth that all those things which have hearts also have kidneys. It is, therefore, a necessary, a posteriori truth that all cordates are re nates. It is a contingent, a priori truth that all cordates have hearts since in some possible worlds they will not. Bostock believes that these fail to produce examples of the contingent a priori as well since he believes that his arguments we discusse d earlier cover these cases as well. As I have responded to his earlier arguments alr eady, I shall not revisit them here. Conclusion I admit that I have not decisively refuted Bo stock’s argument. What I have done, at best, is question whether he is warranted in assumi ng the things he does and advocating a revised modal system. I have shown that it may be the case that Bostock’s criticisms of purported contingent, a priori truths involving wide-scope uses of ‘ A ’ are ill-founded, and that narrowscope uses of ‘ A ’ can be used to form truths, like ‘All act ual geniuses are geniuses’, that do not fall prey to Bostock’s objections. 13 Bostock also says that if something has a heart in the actual world and does not exist in some possible world, it is still a cordate in that world. This makes it such that something is n ecessarily a cordate if it is one at all.

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30 PAST OBJECTIONS CONSIDERED IN LI GHT OF ‘ALL ACTUAL GENIUSES ARE GENIUSES’ What Does it Mean for a Candidate to be “Philosophically Interesting”? While Bostock’s worries do not apply to our curre nt candidate, there is another possible problem with candidates for the contingent a priori that depend on ‘actual’ and its variants. The Kripkean examples were said to be “philosophically unint eresting”. Can the same be said for our current candidate? First, let us consider what a “philosophically interesting” contingent, a priori truth would be. Donnellan, Kitcher and Bostock all admit th at uninteresting examples of the contingent a priori can be generated. However, none of them explains clearly what would make a case philosophically interestin g or uninteresting. In reference to ‘Provided the exists, “t is the ” expresses a contingent tr uth’, Donnellan says, “. . I am not sure whether in the circumst ances what sentences of form (A) express are both contingent and a priori But if they are they are harm less varieties of the contingent a priori examples of which we could produce without recourse to stipulations introducing rigid designators.”1 What would these be and why are they uninteres ting? Shortly after th e above quote, Donnellan says that one might argue that sentences of form (A) are both contingent and a priori since they assert something true about language that might have been false. Donnellan’s paper also utilizes a distinction between linguistic states of affairs and non-linguistic ones, so perhaps the uninteresting examples of the contingent a priori are simply statements of a priori knowledge of a contingent, linguistic state of affairs. 1 Contemporary Perspectives in the Philosophy of Language (pg. 56)

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31 If this is what Donnellan, Kitcher and Bostock have in mi nd it is clear why they think such examples are uninteresting. For one, they ar e ubiquitous; most (if not all) of our linguistic stipulations might have been othe rwise. Second, the contingent, a priori truth wouldn’t be ‘S is one meter long’, for instance. Rather, it would be ‘’O ne meter’ refers to the length of S’. Or, to put it in a locution similar to Donne llan’s, ‘Provided there is someth ing which is one meter, “S is one meter long” expresses a contingent truth’. I say allegedly since one might contest the idea that our knowledge of the linguistic stipulations is a priori So, what would be a philosophically interesting c ontingent a priori truth? If what is said above is correct, we need a priori knowledge of a non-linguistic state of affairs. As I have shown, Bostock has not given us a decisive reason to reject ‘All act ual geniuses are geniuses’. This example (and those like it) do not depend on the Kripkean theory of naming and at least seem to make reference to a non-linguistic state of affairs. Therefore, ‘All actual geniuses are geniuses’ would seem to be philosophically interesting. Donnellan’s Objections Revisited It is notable that Kripke’s examples seemed to be about non-linguistic states of affairs until they were probed by Donnellan. Might the sa me thing happen to our current candidate? At the very least, we have a reas on to reevaluate Donnellan’s claim rather than simply taking it to have provided a refutation of all pos sible candidates for the contingent a priori The examples Donnellan considered in his pape r were all based on rigidified proper names or other sorts of linguistic stipulations. As a resu lt, the terms did not have a sens e that contributed to the truth conditions in any direct way; the sole function of the sense was to fix the reference. Because of this, Donnellan could argue that while we possibly know a priori that the sentence expresses a truth, we cannot know the referent of the rigidified term a priori and thus cannot know what

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32 truth the sentence expresses. Examples involving ‘actual’ and its varian ts do have sense that may do more than simply fix the reference. Th erefore, we must see wh ether they are different from the sort of examples Donnellan consid ers in a way that will allow us to know a priori the truth they express. To do this I will step through th e various parts of Donne llan’s argument with ‘All actual geniuses are geniuses ’ as the sentence in question. One reason Donnellan rejects Kripke’s examples is that they fail to meet two criteria Donnellan set up to test whether they assert any non-linguistic truth. However, there is a problem applying these criteria to our current can didate. The criteria are designed for examples involving proper names. Furthermore, the criter ia cannot be easily adapted to the candidate we’re considering since to do so w ould require treating ‘actual genius’ as if it didn’t have a sense. So, Donnellan’s criteria, whatever force they ma y have against the Kripkean examples, simply do not apply to ‘All actual geniuses are geniuses’. When Donnellan is concludi ng his argument he attempts to show where the line of reasoning from rigid designation to contingent a priori truths went wrong. In doing so he gives two possible things that can be know n as a result of a stipulation: (A) Provided the exists, “t is the ” expresses a contingent truth.2 (B) Provided the exists, t is the .3 If we were to adapt these to our current candidate, they would be: (A’) Provided the exists, “The actual is a ” expresses a contingent truth. (B’) Provided the exists, the actual is a 2 It is important to note that Donnellan does not commit himself to form (A) knowledge being a priori He merely says that if we have a priori knowledge, it is form (A) rather than form (B). It is highly questionable whether we even have form (A) knowledge a priori 3 ibid.

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33 The flaw in the reasoning, according to Donnellan, is that while rigid designation can give us form (A) knowledge, it cannot give us form (B) knowledge. (A) is knowledge of a purely linguistic state of affairs while (B ) is knowledge of a non-linguistic st ate of affairs. Do we have form (B) knowledge if we know that all actual geniuses are geniuses? It seems that we do have form (B) knowledge if we know that all actual geniuses are geniuses, however. This is revealed if we c onsider why Kripke’s examples give us form (A) knowledge but not (B) The way in which we ca n have form (A) knowledge without form (B) knowledge is if ‘t’ does not have a sense that cont ributes to the truth conditions. This allows us to know that a sentence expresse s a (contingent) truth without knowing the truth it expresses by simply stipulating that it expresses a truth.4 If ‘t’ lacks a relevant sense and we do not know its referent a priori we do not know the truth expressed. ‘Is an actual genius’ is not lacking in sense, however, so we do not have this problem. One might make the point, however, that to have form (B) knowledge one must know ( a priori ) the referent of ‘t’ in order to know that is true of him (i.e. one must have de re knowledge). It is clear that D onnellan thought this was the case.5 It is also clear that we do not have a priori knowledge about any particular entity if we know all actual geniuses are geniuses; we do not even know who the actual geniuses are. Does this show that we do not have form (B) knowledge in this case? Kitcher does not thi nk so. As has already been shown with the example of ‘Shorty is a spy’, one can have a bit of de dicto knowledge about a non-linguistic state of affairs. The mistake Donnellan made, according to Kitcher, is requiring particular descriptive content rather than simply descriptive content. While do not have any knowledge of descriptive content about 4 Though this is not the sort of stipulation Kripke had in mind, Donnellan cashes out Kripke’s examples in these terms. (pg. 52) 5 Pg. 58 and elsewhere

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34 the referent of ‘t’ ( de re ), we do have knowledge of some of the descriptive content of ‘t’ ( de dicto ). Therefore, we can have form (B) knowledge despite our lack of de re knowledge. Kitcher’s Objection Revisite d and Concluding Remarks An interesting question arises from this, however. Kitcher, despite disagreeing with Donnellan’s analysis, agrees with the conclusion that only uninteres ting contingent a priori truths can be generated. How can this be give n that it seems we can have contingent a priori knowledge of non-linguistic states of affair s rather than simply linguistic ones? Kitcher says several thin gs about Donnellan’s conclu sion and the possibility of interesting contingent a priori truths. He says that anyone can come to a priori knowledge of contingent truths, but doing so requires linguis tic acts that are “at odds with the standard functions of language.”6 Kitcher believes that even ex amples that have a non-linguistic component are uninteresting because they require odd linguistic stipula tions in order to express. Given that our current candidate does not seem to involve this sort of stipulation, we have avoided Kitcher’s worry. It would seem, therefore, that none of the objections to the contingent a priori considered up to this point have provided a refutation of our current candidate. D onnellan fails to account for the fact that one can have form (B) knowledge without having knowledge de re and while Kripke’s examples do not provide this sort of knowledge, ‘All actua l geniuses are geniuses’ does. 6 Kitcher, 100

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35 GETTING CLEAR ON ‘ALL ACTUAL GENIUSES ARE GENIUSES Clarification and Background Casullo begins his pape r, “Actuality and the A Priori ,” by summarizing and addressing an argument by Kitcher which, though not appearing explicitly in the paper we discussed earlier, underlies and supplements the argument discu ssed earlier. Casullo begins by giving the following condition, which Kitcher believes is a condition on a priori warrants: is an a priori warrant for X’s belief that p if and only if is a process such that, given any total sequence of experiences which would have enabled X to form the belief that p (a) some process of the same type as could produce in X a belief that p (b) if a process of the same type as were to produce in X a belief that p then that process would warrant X’s belief that p (c) if a process of the same type as were to produce in X a belief that p then p (390-391). Casullo asks what knowledge, if any, this c ondition gives us about our own actuality. To see whether the knowledge of our own actuality is a priori Casullo says we must ask questions about what our knowledge would have been had our experiences been different. This fact, in combination with Kitcher’s view th at ‘actual’ is an indexical, necessitates we determine whether it is possible to believe in world w the truth expre ssed by ‘I’m actual’ in w*. If it is, then belief in one’s actuality is not a priori Kitcher argues that since this result w ould be extremely odd, we must deny that ‘I’m actual’ expresses different belief s at different worlds. Kitcher does not give up his belief that ‘actual’ is an indexical, but says that for the purpose of de termining and applying a criterion of a priority, the difference between th e tokens of ‘I’m actual’ doesn’t matter. Casullo notes that the upshot of this view is that ‘I’m actual’ is true in any world in which I be lieve it, so condition (c)

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36 is satisfied, and thus the knowledge of one’s actuality appears to be a priori (392). He argues, however, that Kitcher’s last move is ad hoc Let’s adopt the following notation. ‘S’ refers to the speaker. ‘[P]( )’ means ‘the proposition expressed by sentence P in world ‘ [P]( )’ means ‘world makes true the proposition expressed by P in Finally, ‘ ’ designates the actual wo rld and ‘w’ some other world. Casullo begins with the following summation of Kitcher’s claims: (1) The belief that S expresses in by tokening ‘I’m actua l’ = the belief that S expresses in w by tokening ‘I’m actual’ (2) [‘I’m actual’]( ) [‘I’m actual’](w). These claims are tantamount to saying that while the different tokens of ‘I’m actual’ express different propositions, they express the same belief. Casullo sums up Kitcher’s defense of this claim with: (3) If the belief that S expresses in by tokening ‘I’m actual’ the belief that S expresses in w by tokening ‘I’m actual’, then the belief which S expresses at by tokening ‘I’m actual’ is false at w. Casullo supplements (3) with: (4) It is not the case that the belief which S expresses at by tokening ‘I’m actual’ is false at w. He agrees with Kitcher that (3) and (4) entail (1), but Casullo thinks (3) is problematic. Since all that is needed to justify (4) is the trivial fact th at one cannot be wrong about one’s actuality, Casullo grants (4) and focuses on the previous pr emise (393). To disprove (3), Casullo has us grant (contrary to Kitcher): (6) The belief that I express in by tokening ‘I’m actua l’ = [‘I’m actual’]( ) (7) The belief that I express in w by tokening ‘I’m actual’ = [‘I’m actual’](w).

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37 Conjoin these and we get: (8) ‘The belief that I express in by tokening ‘I’m actual’ the belief I express in w by tokening ‘I’m actual’. Notice that (8) satisfies the antece dent of (3), so it would seem reasonable to conclude that S’s belief that he exists in is false at w. This is an absurd conclusion, Casullo points out, since the belief is true both at and w. He briefly considers the counter-argument that individuals are world-bound, but dismisses it because it woul d only be found persuasive by those who accept counter-part theory. Casullo now argues that Kitcher’s account cont radicts the very things he hopes to derive from it, namely that knowledge of one’s actu ality explains how we can have knowledge of contingent, a priori truths of the kind propos ed by Kripke. Casullo has us consider the Shorty examples mentioned earlier in this paper (If Shorty exists, then Shorty is a spy). Kitcher argues that to use ‘the shortest spy’ to fix the referent of ‘Shorty’, ‘Shorty’ must be acting as an abbreviation of ‘the shortest actual spy’ (394). Therefore, ‘Shorty is a spy’ is best represented by something like the following: (12) If there is a shortest actual spy, then the shortest actual spy is a spy. To determine whether (12) is known a priori on Kitcher’s account, we must examine the proposition the sentence expresses in and in w. Casullo has us grant that Shorty is a tall basketball player in w, while Kareem is the shortest spy in w. Now, ‘If Shorty exists, Shorty is a spy’ is clearly a priori Kripke understands it as a de re belief, picking out Shorty in both and w. Thus, it is a contingent truth; at w, Shorty is a tall basketball player. Since Kitcher takes it to be de dicto ‘Shorty’ refers to Shorty in and Kareem in w; thus, it is a necessary truth. Kitcher’s account is not only flawed, it does not help clarify the Kripkean examples.

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38 Casullo concludes by investigating whether knowledge of one’s actu ality “stands in any significant epistemic relationship” to the Kripkean examples of the contingent a priori (399). Casullo has us consider [‘If there is a shortest actual spy, then the shorte st actual spy is a spy’]( ). He argues that this example by Kitcher is of the sa me sort as beliefs Kripke takes to be examples of the contingent a priori Kitcher does not say how this sort of example is related or similar to knowledge of one’s actuality. It cannot be the case that they ar e both examples of noninferential a priori knowledge since that would require Kitcher’s account to be correct and we have reason to doubt its viability. However, Kitcher argues, more convincingly, that beliefs of the sort above can be validly inferred from the necessary trut h ‘All A’s are A’s’ and the knowledge of one’s actuality. We can produce a slew of contingent, a priori truths of the type ‘All actual A’s are A’s’ in this same way.1 Casullo leads us through the chain of r easoning showing the conn ection between ‘All actual A’s are A’s’ and knowledge of our own actuality (400). He has us consider ‘Actual A’s are actual A’s,’ noting that it expresses a necess ary truth in any world in which it is uttered. Therefore, [‘Actual A’s are actual A’s’](w*) is true What do we need to move from this belief to [‘Actual A’s are A’s’](w*)? The move cannot be immediate since the belie f would not be true at all worlds; there must be, therefore, some mediate knowledge to ju stify the inference. Casullo remarks that we must know that, “the extension of ‘A’s’ includes the extension of ‘Actua l A’s’ in the world I inhabit.” It is true a priori that if this is the actual world, then the extensions of ‘A’s’ and ‘Actual A’s’ will be the same. Therefore, if I know I am actual (i.e. that I inhabit the actual world), I know the contingent, a priori truth [‘Actual A’ s are A’s’](w*). 1 Notice that this is exactly the sort of candidate that has seemed, thus far, to be a viable example of the contingent a priori

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39 Casullo points out, however, that while the argument in the previous paragraphs is sufficient, it is not necessary (401) If one takes an indexical view of actual,’ ‘actual’ refers to the world of utterance. Thus, th e inference is justified since we need only know that w* is the world of utterance. Casullo has thus shown that the contingent a priori is not inexorably linked to knowledge of one’s actuality. Casullo concludes that we still have reason to doubt Kripke’s claims about the contingent a priori Noting that his conclusion is similar to Donnellan’s, Casullo writes that we have not stated the content of the belief. He says that if we accept Kripke’s semantic story about proper names and definite descriptions, we may be able know a priori that some sentences express contingent truths, but we do not know the truths they express. As I have already responded to Donnellan along these lines, I sha ll not retrace my steps here. Analyzing ‘Actual’ While Casullo’s paper seems to reveal that knowledge of one’s actuali ty is not required for knowledge of contingent, a priori truths, it does not give us any new reason to doubt our current candidate. However, as Casullo notes, on e might object that ‘All actual geniuses are geniuses’ is unclear because the semantic role of ‘actual’ still has not been made explicit. Though Donnellan’s worries seem to not apply to examples involving ‘actual’, the surface grammar may obscure rather than clarify the meaning of the sentence. We must, therefore, analyze ‘All actual geniuses ar e geniuses’ in order to see whether it is an unproblematic candidate for the contingent a priori Let’s begin with the following analysis of ‘All actual geniuses are geniuses’: (x)((x is a genius & x is in ) (x is a genius)),

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40 where ‘ ’ refers to the actual wo rld. In this treatment, ‘ ’ is a name that ri gidly designates the actual world. This immediately re-opens the door to Donnellan’s objectio n. In order to know the truth expressed by ‘All actual geniuses ar e geniuses’ we must know that our world is ; we must know that ‘ ’ refers to Can we know this a priori (or even at all)? One way we can have knowledge is by desc ription. For instance, I know that Plato was the teacher of Aristotle and that the teacher of Aristotle was th e student of Socrates, so I know that Plato was the student of Socrates. Knowle dge by description is in some sense inferential knowledge. Can I know that this world is through an inference of descriptions? No, because any description we might offer would also be sati sfied by another world if someone at that world were to offer it. ‘This world’, ‘the speaker’s wo rld’, ‘the world that exis ts’, and other variants will hold true at every possible world, though they won’t express the same truth at each world. What we need is a way to “pick out” our world from among all the possible worlds. This will give us knowledge of a particular world, allowing us to know that ‘ ’ refers to by having knowledge of a particular that also satis fies the description ‘the actual world’. Another way we can have knowledge is by acq uaintance. For inst ance, I am acquainted with my best friend and know things about him as a result of that acquaintance (e.g. that he is married). Assuming we are acquainted with our world, there are two ways in which acquaintance puts us in a privilege d position to pick out “our world” : (1) we are acquainted with one and only one world – our world, (2) no one in another world is acquainted with our world. Thus, what we could not do with knowledge by description we can do with knowledge by acquaintance – know the pa rticular world to which we want to refer. So, is this world with which we are acquainted ? Is it the actual world? That depends, in part, on whether the following accurately an alyzes ‘All actual geniuses are geniuses’:

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41 (x)((x is a genius and x is in my world) (x is a genius)), where ‘my world’ is intended to ac t as an indexical, not as a desc ription. I believe there are two good reasons to think that this treatment of ‘act ual’ is accurate. First, when we say ‘actual world’ and ‘my world’ we certainly intend to re fer to the same world, so the two phrases are materially equivalent. Second, this analysis explains the reasons me ntioned earlier why we cannot have knowledge by descripti on in this case. ‘This world’ ‘the speaker’s world’, ‘the world that exists’, and other variants will act as indexicals, referring to the world in which they are uttered or considered. Thus, though they do no t refer to a particular world when taken as descriptions, as indexicals they will have th e correct meaning at whatever world they are evaluated while still referring (as considered at a particular world) to a particular world. In what follows I will give a possible acc ount of how knowledge by acquaintance can act as the basis for us knowing a priori that ‘ ’ refers to (i.e. that our world is the actual world). I will not insist that we are therefore acquainted w ith the actual world, but simply that we have the knowledge of the actual world that we need.2 I will begin by giving a series of conditional prem ises that will lead us to this conclusion. I will then provide support for the antecedent of the first premise and explanation for the premises which may be found less than obvious. Thus, I will have proved that we can know a priori that our world is the actual world, not simply that ‘Our world is th e actual world’ expresses a truth; this is equiva lent to knowing that ‘ ’ refers to (1) If I think, then I exist. (2) If I exist, then I am actual. (3) If I am actual, then the world of wh ich I am a part is the actual world. 2 It may, however, be the case that we are acquainted with our world.

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42 (4) As a world is a complete state of affairs, my knowledge of myself either constitutes complete knowledge of the world or partial knowledge of it. (5) Either way, I know that there is an actual world and that my world is that world. Perhaps (4) is in need of a brief explanati on. My knowledge of myself would constitute full knowledge of the world if solipsism is true and I have complete knowledge of myself ( a priori ). Otherwise, I have only partial knowledge ( a priori ) of my world. I will not bother to defend the claim that I know that I think. It is important, however, to distinguish just what is meant by ‘ a priori ’ since it has been used in different ways. I will not attempt to give a thorough account; I will simply give a rough definition that will capture what is traditionally meant by the term and make explicit the feature relevant to this case. Something can be known a priori iff it can be known without having any experience that is not essential to acquiring the concepts involved (i.e. being able to use the words competently). The motivation behind this definition is that if we deny the cogitator reference to any and all experiences, he will be unable to employ concepts since they require experience to acquire. We maintain a priority however, by limiting the experiences in volved to the minimum required to acquire the concepts. The Contingent A Priori and Knowledge of One’s Actuality It is important to notice that the link between the contingent a priori and knowledge of one’s actuality has once again been asserted, albeit in a way differe nt from Kitcher’s view. This link holds if the above defense is required, but I do not believe it is. First, one might object that while I have provided a seemingl y viable analysis of ‘is an actual genius’, one must be acquainted with the actual geniuses themselves if one is to even understand ‘All actual geniuses are geniuses’, let alone believe it. As D onnellan suggests, if I do not know who the actual

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43 geniuses are, how can I say of them that they are geniuses? I ma y know that ‘All actual geniuses are geniuses’ expresses a truth, but I don’t know the tr uth it expresses. It is similar to ‘Fhqwhgads are Fhqwhgads’. Thus, what is needed is acquaintance with actual geniuses, not the actual world. I think noting an important distinc tion between proper names and quantitative expressions reveals the disanalogy between the cu rrent candidate and past ones. Proper names are singular referring terms wh ile quantitative expressions (d efinite descriptions, general terms/expression, etc.) are deno ting expressions; this dis tinction is based on Russell’s observations. I will not go into the arguments fo r and against the distinction between referring and denoting, other than noting the supporting intuiti on that the connection between a proper name and its referent is more direct than is th e connection between a definite description and the thing it describes.3 A proper name just is a title or label for an individual thing, while a quantitative expression simply picks out the thin g which uniquely satisfies it. How does this distinction help us? Consider ‘Newman-1 is the first child born in the 21st century’. The best way to represent ‘Newman-1’ would be w ith a constant rather than a variable, a formalization of the proposition being: F(c), where ‘F’ means is the first child born in the 21st century and ‘c’ refers to Newman-1. Since the formalization requires a constant, know ledge of the proposition requires knowing that c is the first child born in the 21st century. It requires knowledge of Newman-1 than cannot be gained just by the stipulation that was its origin, or by description. It requires acquaintance. 3 As evidence, reflect on the difference between ‘The author of Huckleberry Finn is Mark Twain’ and ‘Samuel Clemens is Mark Twain’, or ‘Mark Twain is Mark Twain’.

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44 Now consider ‘All Martians are gree n’, which could be represented by: ( x)(Mx Gx). Here we have a universally-quantif ied variable rather th an a constant. Thus, we do not need to be acquainted with Martians to understand the pr oposition. We don’t even to know whether such beings exist to understand the proposition. So, while our previous candidates may have been problematic, we have no reason to think that of ‘All actual geniuses are geniuses’. Two-Dimensional Logic and the Contingent A Priori In the paper by Bostock discussed earlier, he mentions a paper by Martin Davies and Lloyd Humberstone in which a twodimensional modal logic is us ed to handle the modality of ‘actual’ and its variants. In wh at follows I want to look at th e system, partly to understand our current candidate better and partly to see whethe r their system attempts to undermine, in any way not yet accounted for, the viabil ity of ‘All actual geniuses are geniuses’ as an example of the contingent a priori In “Reference, Contingency, and the Two-Dimensional Fram ework,” Davies begins by characterizing what he calls ‘t he two-dimensional framework’.4 There are some sentences, like ‘It is possible that everything that is actually red should have been shiny,’ that resist formulation using traditional modal logic. The usual way of handling these sorts of se ntences is to introduce an actuality operator, ‘ A ’ (84). Davies writes, “In terms of possible-worlds model-theo retic semantics for the modal language, a sentence ‘ A s’ is true with respect to a possibl e world, w, just in case the embedded sentence s is true with respect to the model’s designated or ‘actual’ world, w*. One result of this, which was noted earl ier in this paper, is that if ‘ A s’ is true at all it is necessarily true. This seems hard to reconcile, ho wever, with the fact that what is actually the 4 Philosophical Studies, 118, 2004 (pgs. 83-131)

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45 case is (at least mostly) a contingent matter. This leads Davies (and Humberstone) to suggest two sorts of necessity to clar ify the difference, and an additional modal operator to help characterize the two types of necessity. Davies and Humberstone suggest ‘ F ’ a “fixedly”-operator (85). While ‘ A ’ increases our modal language’s abil ity to express sentences by allowing us to vary our world of evaluation, wj, ‘ F ’ allows us to vary what world pl ays the role of the actual world, wi. Davies writes, “A sentence ‘ s’ is true with respect to a world wj with world wi playing the role of the actual world just in case, for every world w, the embedded sentence is true with respect to world w, with wi still playing the ro le of the actual world. A sentence ‘ F s’ is true with respect to a world wj with worl d wi playing the role of the ac tual world just in case, for every world w, the embedded sentence s is tr ue with respect to wj, but now with w playing the role of the actual world” (85-86). How this operator gives us two different notions of necessity can be seen by considering ‘ F A x’. If s does not contain A ‘ F A x’ is equivalent to ‘ s’. If, however, x is of the form ‘ A s’, where s is some contingent truth, then a di fference is revealed. While ‘ x’ is true, ‘ F Ax ’ is false since it is equivalent to ‘ F A s’ and thus to ‘ s’. As a result we have tw o different sorts of necessity, allowing us to maintain the intuition behind the sema ntics of ‘actually’ and the intuition that it is a contingent truth that the world that is in fact the actual world is the actual world. Thus the two-dimensionality of this system of modal logic is revealed (87). Before ‘ F ’ the only world we needed to consider when evaluating a sentence was wj; the logic was, thus, one-dimensional. Now, however, we must also consider wi since it can vary; thus, our logic is two-dimensional. While Davies goes into more detail about this and addresses many related

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46 tangents, I shall not go into those considerations here. Rather, we shall conclude our look at his paper by examining his comments on the contingent a priori Before going into Davies’ comments we shall give Evans’ characterizations of superficial (corresponding to ‘ ’) deep (corresponding to ‘ F ’) necessity and contingency, which Davies summarizes and uses in his comments (93-94).5 Superficial continge ncy is a property of sentences, and depends on how the se ntence embeds under the scope of ‘ ’ or ‘ ’. Davies lists three ideas associated with supe rficial contingency to help us understand the notion: truth with respect to worlds, purely internal to semantic theo ry, and properties of modal sentences (95). On the other hand, three ideas associated with deep contingency are: truth in worlds (being made true), not purely internal to semantic theory, and modal properties of se ntences. Davies inserts the following quotation by Evans, “If a deeply contingent statement is true, ther e will exist some state of affairs of which we can say both that had it not existed the sent ence would not have been true, and that it might not have existed. The truth of the se ntence will thus depend upon some contingent feature of reality.” Superficial contingency and necessity are simply the negation of deep c ontingency and necessity. Davies spend some time exploring and defe nding the notion of ‘truth in a world’ and showing that his D-necessity and Evans’ deep necessity are one and the same even though the former is put in terms of a modal operator, ‘ F ’, and the latter is not. Ho wever, I wish to move on to Davies’ application of two-dimensional moda l logic to alleged cases of the contingent a priori Davies begins by expounding Evans’ notion of epistemic equivalence (99). Essentially, two statements are epistemically equivalent iff they have the same content and, if both are 5 Davies calls superficial necessity ‘H-necess ity’ and deep necessity ‘D-necessity’ since ‘ ’ is truth along the horizontal and ‘ F ’ is truth along the diagonal in a two-dimensional system.

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47 understood, one cannot believe one and disbelieve the other. One example of this which is important for our investigation is th e epistemic equivalence of ‘s’ and ‘ A s’. One result of this is that we are in a position to know ‘ A s s’ a priori Davies’ example is that if someone understand the notion of actuality, he is in a position to know a priori ‘if the earth moves, the Earth actually moves’. Davies notes several things about this example. First, s can only be known a posteriori so A s can likewise only be known a posteriori though ‘ A s s’ is known a priori Second, while ‘ ( A s)’ is true, ‘ F A ( A s)’ is false (100). ‘ A s’ is superficially necessary and deeply contingent. ‘ A s s’, however, has the opposite properties; it is superficially contingent and deeply necessary. Thus, our example, and those of the same form, seems to show a correlation between a priority and deep necessity, t hough nothing about two-dimensional modal logic per se demands this. Davies now gets to the heart of the matte r, investigating whether there are deeply contingent, a priori truths. He says there are two pr oblems: 1) there are some noteworthy counter-examples to the claim that a priority and deep necessity coincide, and 2) while intuitions seem not to favor the contingent a priori it is very difficult to form an argument from them. We will conclude our look at Davies’ paper by considering each of these in turn. Davies gives the example of the belief that one has hands (101). While it is certainly possible that I am simply a brain in a vat, I am entitled to ignore th is possibility so long as there is no evidence in support of it, and am justified in believing I have hands. Similarly, Davies notes that when doing a mathematical proof, one is entitled to ignore the possibility (so long as there is no supporting evid ence) that one is suffering from a massive memory loss and, thus, cannot be sure the proof is be ing done correctly. In these cas es, Davies alleges, one has a priori

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48 beliefs for which defeaters could ar ise (i.e. certain experi ences would reveal them to be false, or at least unjustified) (102). Thus, we have certain a priori beliefs about contingent states of affairs. For my part, I do not see how Davies’ examples can properly be considered a priori He says that I am entitled to believe these things so long as there is no cont radictory evidence, but how do I know a priori whether there is contradictory eviden ce or not? I need to know there is no contradictory evidence for my belief to be justified, but I can only know this a posteriori Furthermore, the belief that I have hands was formed a posteriori ; I had to see my, or perhaps someone else’s, hands. It seem s that if anything here is a priori it is the epistemic warrant ‘I am entitled to believe x so long as there is no evid ence to the contrary’, wh ere ‘x’ is a variable ranging over a certain type of belief. If this warrant, or something like it, is true at all it is necessarily true, so Davies does not bolster the case for the contingent a priori Davies gives the following reductio ad absurdum Suppose there is a truth, s, which is both able to be known a priori and deeply contingent. Now, s is true iff a certain state of affairs, S, obtains. However, S may or ma y not obtain; there is no guarant ee that it will obtain (i.e. it is not a deeply necessary truth). Davies says that this may appear to be a contradiction since s would as a guarantee of S, but says this is a confusion between the modal and the epistemic notion of ‘guarantee’.6 What is needed is a step showing th at if S is not modally guaranteed than it cannot be epistemically guaranteed (by s or any other proposition), but Davies notes how similar this is to the assertion that if something is a priori then it is deeply necessary – the very thing we wished to prove (103). 6 Though Davies does not say exactly what this amounts to, he says s acts as an epistemic guarantee for S, but S is not modally guaranteed.

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49 So in the end, while Davies admits that there are strong intuitions (at least for some) against the possibility of contingent, a priori truths, he has given us no reason to doubt the possibility, nor does he claim to. Note that while Bostock’s clai ms about the impossibility of (philosophically inte resting) contingent, a priori were much stronger than Davies, his use of twodimensional modal logic did not present any proble ms more substantial than those Davies raises. Conclusion Casullo’s paper helped us understand the pr oblems with the Kripkean examples and how our current candidate does not fall prey to those problems. It did, however, reveal the need for an analysis of our current candidate. We have seen that a viable analysis of ‘is an actual genius’ can be given that not only allays concerns about the meaning of ‘A ll actual geniuses are geniuses’, but also separates the question of the contingent a priori from questions about the knowledge of one’s actuality. The two-dimensiona l modal logic of Davies and Humberstone has helped us understand our current candidate by revealing how the rigid designation accomplished by ‘actual’ affects the modal status of the proposition. We can also conclude that we have seen no reason to doubt that ‘All actual geniuses are geniuses’ is both contingent and a priori and that (bar some refutation being give n) we should accept it as such.

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50 A NON-INDEXICAL CANDIDA TE FOR THE CONTINGENT A PRIORI Introduction It is interesting that all of the candidates considered thus far have relied on indexicality in some way. In some cases this is clear, and in others the indexicality would be revealed if we were to analyze the proposition in question. One might be tempted to think that the contingent a priori if there is any such thing, depended upon indexicality. Timothy Williamson, however, wishes to separate indexicality fr om questions about the contingent a priori by providing and defending an indexical-free, contingent, a priori truth. Williamson and Oppy’s Conversation Williamson begins by suggesting the following: (1) There is at least one believer.1 Williamson notes that ‘is’ must be read tenselessly if the proposition is to be indexical-free. It is clear, setting aside for the time being the worry that God is a necessarily ex isting believer, that (1) is contingent. However, does one know (1) a priori ? Williamson writes, “Now since it is impossibl e to believe (1) falsely, it seems that one can know (1) a priori ” (114). Does this condition ensure a priority ? At the end of his paper Williamson briefly discusses the problem of providing a formal definition of ‘ a priori’ that lines up with our understanding of how the term should be employe d. He provides a couple of examples, shows how they are problematic, an d concludes by saying th at while one might question whether his condition is ne cessary, it is certainly sufficient. While he does not say why, I believe it is because the nature of a posteriori truths would seem to re quire that it be possible that they be believed falsely. Thus, anything wh ich is impossible to believe falsely must be a priori I see no problem with this, and agree that Williamson’s condition is at least sufficient. 1 Analysis, 46.3, June 1986 (pgs. 113-117). The Contingent A Priori: Has It Anything To Do With Indexicals?

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51 But now the worry is that one cannot know (1 ) without the use of indexicals. While (1) does not contain them, it is arguable that one cannot know that (1) is true without knowing: (2) I am a believer. If this is true we are presented with a dilemma. We can either admit that indexicality is, even in this case, required for some thing to be a contingent, a priori truth, or we can say that (2), and thus (1) as well, is not a priori at all because it is based on introspection. Therefore, we either have yet another indexical-base d example of the contingent a priori or no example of it at all. Williamson responds by arguing that one can know (1) a priori without the use of (2). He begins by providing the followi ng method of forming beliefs: (M) Given a valid deduction from the premise th at someone believes that P to the conclusion that P, believe that P. The set of beliefs formed according to this pr inciple, or belief-forming mechanism, would include only true beliefs (tha t is, (M) is infallible). Since this fact can be known a priori it follows that any knowledge produced in accordance with (M) is itself known a priori so long as the “input” is knowable a priori If we replace P with (1), the deduction from, (3) ‘Someone believes that there is at least one believer’, to (1) is clearly valid (115). Looking at (M), we see that the deduction from (3) to (1) is the input. We can certainly know that the deduction is valid a priori so we have an a priori warrant for believing (1), a contingent truth. (M) can also be used to generate other indexical-free, contingent, a priori truths. For instance, ‘There is at least one thing which ex ists’ is certainly contingent, and by (M) we can know it a priori without reference to the ‘I exist’. Williamson concludes his argument by addressing the objection that God is a necessarily existing believer, thus making (1) necessary rather than contingent. We can modify (1), getting:

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52 (1’) There is at least one fallible believer. The deduction for (M) goes as follows. If someone be lieves that (1’), this be ing is either fallible or infallible. If fallible, then (1 ’) follows trivially. If infallible, then the being’s belief that (1’) must be true. So, we can know (1’) a priori, and it is certainly contingent since there are possible worlds in which God, an infallible believer, is the only believer that exists. In “Williamson and the Contingent A Priori ” Graham Oppy denies that Williamson has adequately supported his conclusion.2 Oppy begins by arguing that the way (M) is formed hides the fact that it actually c ontains an indexical (189 ). Rather than putting things in the imperative (i.e. ‘believe p’), Oppy suggest s two ways one could use (M). (M’) If from the fact that I believe that P it follows that P is true, then I shall have a true belief if I believe that P. (M”) If from the fact that someone believes th at P it follows that P is true, then anyone can form a true belief by believing that P. (M’) is clearly problematic because of the i ndexical. Oppy argues that because (M”) is universally quantified and (1 ) is existentially quantified, while we can know (M”) a priori it has not been shown that we can know (1) a priori Before continuing with Oppy’s pa per let’s look more closely at hi s claim. If things are as he says and one is trying to infer an existentia l from only a universal, th en his objection would be valid because of the lack of existential import. However, this is not the case. We are inferring (1) not from (M), but from ‘Someone believes that (1 )’, another existentially quantified statement. On the basis of this deduction the universally quantified ‘Anyone can form a true belief by believing that (1)’ is made by way of (M), but this suffers no problems with existential import. Oppy’s objection, therefore, is unsubstantiated. 2 Analysis, 47.3, October 1987 (pgs. 188-193)

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53 Oppy has misunderstood (M). (M’’) is inte nded to be a proposition in a deduction, while (M) is a belief-forming mechanism, not a proposition. Furthermore, it is (in some ways) similar to the reading that Oppy anticipates Williamson would use in replying to his objection (190). Oppy formulates this reading as: (APK) Bxp p Therefore, p. He notes that it is similar to modus ponens except that it is only trut h-preserving when used. He then argues that even on th is reading of (M) the inference to (1) is not justified. Oppy has us suppose that there is a computer that exists in a world in which there are no subjects (i.e. no one who has beliefs). If this computer operates in accordance with modus ponens it will produce only true results, but this is not so for APK. The machine will generate ‘There is at least one believer’, which is fals e. Therefore, any inference based on APK would not be valid. Oppy admits that this objection is somewh at questionable, but I believe that it is hopelessly flawed. Let’s remember that the purpose of (M) is to produce truths that are impossible to believe falsely. So, does the thought experiment above disprove Williamson’s claim? No. The computer does not have belief s at all, so it certainl y does not have any false beliefs. If it did have beliefs, then (1) would be true. Let us, therefore, move on to another objection Oppy lays out. Consider a subject with limited self-aware ness (i.e. who can competently use words like ‘believer’ without knowing that the terms apply to him) (192).3 Now, as far as he knows his world has no subjects. So, what will keep him from concluding, via APK, that some world other than his own, which happens to be subject-less, ha s at least one believer? Oppy believes that it is 3 This presumably helps to avoid sneaking in knowledge based on indexicals.

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54 a hidden indexical, linking the conclusion to the wo rld of utterance (i.e. th e actual world). After all, someone wishing to use APK can only use it validly in her world, though there is no explicit reference to her world or her as the believer which satisfies the condition. Oppy says that one might object that we “simpl y take it for granted” that we are talking about the world of utterance when there are no exp licit operators or indexical elements. He says, however, that this is irrelevant since it is a pr agmatic concern; logicall y, we must take such indexicality into account. Oppy suggests th e following representation of APK, and thus formalization of (M): Bxp p Therefore, p( ), where ( ) is an operator which fixes the world at whic h p, and thus the whole argument, is to be evaluated as the world of utterance. Th erefore, Oppy concludes, Williamson’s argument provides no reason to think that one can separate the contingent a priori from indexicality (193). In “The Contingent A Priori : A Reply”, Williamson responds to Oppy’s objection.4 Williamson argues that APK is not an accurate representation of (M), and that APK itself is problematic (219). Williamson wr ites, “[I]f p is false and be lieved by no one, APK will take you from the vacuously true supposition Bxp p to the false supposition p.” Williamson says that the following would be more similar to (M) and would also produce indexical-free examples of the contingent a priori : (MAPK) Given the belief that if someone be lieves that P then P, believe that P. He remarks that both (M) and (MAPK) should be understood, not as infe rence rules, but as “something like abstract mechanisms for generating beliefs.” 4 Analysis, 48.4, Oct. 1988 (pgs. 218-221)

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55 There are two problems with Williamson’s rema rks here. First, he is operating with a rather radical notion of the a priori. As Fitch points out, if our experience is used to justify our belief in the proposition, rather th an simply help us acquire the requisite concepts, then our knowledge should not be considered a priori Thus, knowledge produced by (M) and (MAPK) is not a priori .5 (MAPK) is suspect for an additional reason. The belief ‘If someone believes that P then P’ could be false. For instance, I co uld believe that if someon e believes that pigs can fly then pigs can fly. In this case, (MAPK) would generate the fa lse ‘Pigs can fly’. Thus both (M) and (MAPK) fail to be truth-preserving. One might also worry that the imperative mood of (M) and (MAPK) is masking some sort of indexicality (that is, that it is a trick fo r hiding the indexicality that would be clear if (M) or (MAPK) were put in propositional form as part of a deduction. Ho wever, since (M) and (MAPK) are belief-forming mechanisms rather than steps in deductions, Williamson’s examples do not make use of indexicals in the way Oppy be lieves it does. Therefore, while there may be reasons to be worried about Williamson’s account, they are by no means decisive rebuttals of it. Williamson notes that Oppy’s indexicalized APK suffers from the same problems as the version without indexicals and, as a result, fails to be truth pr eserving (220). If, however, one tries to show that (MAPK) fails to be truth-preserving in the case of the subject-less world this attempt will fail because the input, ‘If someone be lieves that in w there is at least one believer then in w there is at least one believer,’ is itself false. Williamson addresses a possible concern th at Oppy mentioned but did not dwell on. What of the objection that it is questionable wh ether someone who does not know that he is a believer understands ‘There is at least one believer’? Williamson writes, 5 It is possible that Williamson’s thoughts about the nature of the a priori stem from his Reliablist position. However, since the other authors we’ve discussed a ll seem to accept the more traditional notion of the a priori it is outside the scope of this paper to investigate the case for Williamson’s notion.

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56 “What should also be noted is that even if a negative answer we re correct, it would constitute no objection to my argum ent. For it would not show my a priori knowledge (with understanding) of the cont ingent truth that there is at least one believer to be indexical-dependent in any se nse not applicable to my a priori knowledge of the necessary truth that all believers are believers.” One could, of course, argue that we ca nnot know ‘All believers are believers’ a priori because of the sort of experience necessary to acquire the c oncept ‘a believer’, but this seems implausible, and would undermine many of the traditional examples of the a priori Conclusion While Oppy’s objections to Williamson’s examples are off the mark, there are reasons to doubt that his examples give us examples of the contingent a priori Both (M) and (MAPK) fail to be truth-preserving in worlds without subjects, albeit for differe nt reasons. Furthermore, we could at least question whether the examples are really indexical-free because of the imperative mood. It would seem, therefore, that Williamson doe s not give us a reason to believe that the contingent a priori can be separated from indexicality.

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57 CONCLUSION In what follows I want to briefly review each of the sort of candidates considered, summarizing why they are or are not true examples of the contingent a priori I will also point to the ways in which the failure of the earlier candidates shaped the formation of the later ones. The “incorrigibility” examples were dismisse d rather quickly by Fitch. The problem with this class of examples is that they do not qualify as a priori truths. They all depend on experience in order to provide justification for belief in the proposition in question. While even legitimate examples of the a priori depend on experience, it is to acquire the concepts involved rather than justify belief in the proposition. The Kripkean examples (the “Standard Meter Bar”, “Neptune”, etc.) fail to be examples of the contingent a priori The main problem with this sort of example, revealed by Donnellan and Fitch, is one of the results of the act of rigid de signation (that is, the stipulative introduction of the name involved). The name lacks sense, so it is impossible to know what the sentence means without having knowledge of a particular (the referent); thus, we cannot know the proposition a priori The upshot of this sort of candida te is if we could know the truth the proposition expresses, the rigid desi gnation allows us to say things about a particular that are true a priori in this world and false in some possible worlds. To avoid the problems with the Kripkean ex amples, some have suggested examples using ‘actual’ and its variants, which allow for rigid designation without robbing any of the terms of their sense. These examples hang on a distin ction between the world that determines the extension of the predicate or truth of the proposi tion and the world at which the proposition is to be evaluated. While Bostock tries to show that the utilization of this di stinction requires changes in our system of modal logic a nd a dissociation of the notion of ‘necessity’ from “truth in all

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58 possible worlds”, I show that his assertions are questionable at be st. In addition, whatever merit his observations have applies on ly to wide-scope uses of ‘ A ’, leading me to suggest a candidate that relies on a narrow-scope use of ‘ A ’: ‘All actual geniuses are geniuses’. I also dismiss Bostock’s ‘If there is exactly one object that falls under the predic ate, then it is necessary that there is no more than one’. To understand th e sentence one must understand the rigidified predicate in question. Howe ver, one cannot understand it a priori because, like the Kripkean examples, it lacks sense, and Donnellan and F itch show us it would take knowledge of the particulars involved, something we can only have a posteriori to understand the predicate. I then re-consider objections by Donnellan, Kitcher and Bostock, de monstrating that ‘All actual geniuses are geniuses’ can be known a priori and that knowledge of this truth produces more than just linguistic knowledge. In response to the object ion that perhaps the meaning of the sentence is still unclear, I provide a viable analysis that utilizes a distinction be tween knowledge by description and knowledge by acquaintance. Th is distinction helps re veal how the current candidate differs from the former ones. The pr evious candidates involved proper names. Since proper names are singular referring terms, more is required to have knowledge of the referent of a proper name than is required for a definite de scription, a denoting expression. This helped us see more clearly why the previous candidates failed where the current candidate succeeds. The paper by Davies, while not giving us a reason to doubt our current candidate, helped us under the trick being accomplished by ‘actual’ By allowing us to vary the world of evaluation, ‘actual’ and its vari ants increases the power of our modal system, allowing us to assert and evaluate things we could not before. It is the in creased power that allows for examples of the contingent a priori to be produced.

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59 Williamson, wanting to separate the question of the contingent a priori from indexicality, sought to offer an indexical-free, contingent, a priori truth. However, as we saw, his examples failed, strengthening the case that it is the special sort of indexicality of ‘actual’ that allows for examples of the contingent a priori .

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60 LIST OF REFERENCES Bostock, David. “Necessary Truth and A Priori Truth.” Mind New Series, Vol. 97, No. 387, Jul., 1988 (pp. 343-379) Davies, Martin. “Reference, Contingenc y, and the Two-Dimensional Framework.” Philosophical Studies 118, 2004 (pp. 83-131) Donnellan, Keith. “The Contingent A Priori and Rigid Designators.” Contemporary Perspectives in the Philosophy of Language eds. French, Uehling, and Wettstein. University of Minnesota Press, 1980 (pp. 45-60) Fitch, G.W. “Are There Con tingent A Priori Truths.” The Journal of Critical Analysis vol. 6, no. 4, Jan./Apr. 1977 (pp.119 123) Kitcher, Philip. “A Priori ty and Necessity,” from Australasian Journal of Philosophy 58, 1980 (pp. 89-101) Kripke, Saul. Naming and Necessity. Harvard University Press. 1980 Oppy, Graham.“Williamson and the Contingent A Priori. ” Analysis 47.3, Oct. 1987 (pp. 188-193) Williamson, Timothy. “The Contingent A Priori : A Reply.” Analysis 48.4, Oct. 1988 (pp. 218-221) Williamson, Timothy. “The Contingent A Priori : Has It Anything To Do With Indexicals?” Analysis 46.3, June 1986 (pp. 113-117).

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61 BIOGRAPHICAL SKETCH Daniel Carter McCain was born on July 16, 1982 to Daniel Ross McCain and Doris Carter McCain. He was raised in Jacksonvi lle, Florida and gradua ted from Englewood High School in 2000. He also attained the rank of Eagle Scout in the Boy Scouts of America. Carter, as he prefers being called, attended the Universi ty of South Florida and then the University of North Florida, where he graduated cum laude with a B.A. in philosophy in 2004. After graduating from the University of Fl orida in 2006 with an M.A. in philosophy, he will marry Karen Garito and transition into professional ministry with the Graduate and Faculty Ministries branch of InterVarsity Christian Fellowship. His long-term goals are to attend Seminary, attain an M.Div., and to eventually serve in a pastoral role at a local church.


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ARE THERE CONTINGENT, A PRIORI TRUTHS?


By

DANIEL CARTER MCCAIN






















A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF ARTS
UNIVERSITY OF FLORIDA

2006


































Copyright 2006

By

Daniel Carter McCain









ACKNOWLEDGMENTS

I would like to thank my chair, Dr. Greg Ray, for the myriad observations he made on

various drafts and for his tireless effort toward the completion of this project. I would also like

to thank my committee members, Dr. Kirk Ludwig and Dr. Michael Jubien, for their insightful

comments and helpful suggestions at my defense. In addition, without the support of my fiancee,

Karen Garito, this project would not have come to fruition. Finally, I could not imagine

completing a task of this difficulty without the help of my Lord Jesus Christ.









TABLE OF CONTENTS

A CK N O W LED G M EN T S ...................................................... ........................................ 3

A B S T R A C T ........................................... ............................. 6

INTRODUCTION ....................... ........ .. .. .... ..... ...................

K R IPK E A N C A N D ID A TE S ............................................................................. ......................10

B ack g rou n d ............................ ........... ................................................................10
The "Standard M eter B ar" E xam ple ......................................................................... ... ... 10
Problem s w ith the K ripkean Exam ples............................................................ ... ............ 11
C o n clu sio n .........................................................................19

A C TU A L IZED CA N D ID A TE S.......................................................................... ....................20

B ack g rou n d ......................................................... ... ....... .......................... ............... 2 0
Bostock's Argument Against the "Actual Inventor of the Zip" Example ............................22
'A ll A actual G eniuses are G eniuses'. ........................................................... .....................27
C o n clu sio n .........................................................................2 9

PAST OBJECTIONS CONSIDERED IN LIGHT OF
'ALL ACTUAL GENIUSES ARE GENIUSES' ................. ............ ....................... 30

What Does it Mean for a Candidate to be "Philosophically Interesting"? ...........................30
D onnellan's O objections R evisited......... ............................................... ..... ............... 31
Kitcher's Objection Revisited and Concluding Remarks...............................................34

GETTING CLEAR ON 'ALL ACTUAL GENISUES ARE GENISUES' ...............................35

C clarification and B background ......... .. ............. ............................................................35
A analyzing 'A ctual'..................3........ ........................................... 39
The Contingent A Priori and Knowledge of One's Actuality ................ .......... ..........42
Two-Dimensional Logic and the Contingent A Priori ................................................44
C on clu sion .................................................................................4 9

A NON-INDEXICAL CANDIDATE FOR THE
C O N TIN G EN T A PR IO R I ........................................................................... ......................... 50

Introduction ............. .............. .. ......... .................................50
Williamson and Oppy's Conversation ............. .... ......... .......... ............... 50
C o n clu sio n .........................................................................5 6

C O N C L U SIO N ............................................................................................57




4









L IST O F R E F E R E N C E S ............................................................................... ...........................60

B IO G R A PH IC A L SK E T C H ............................................................................... .....................6 1









Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Arts

ARE THERE CONTINGENT, A PRIORI TRUTHS?

By

Daniel Carter McCain

December 2006

Chair: Greg Ray
Major Department: Philosophy

While most philosophers have thought that necessity and priority are co-extensive,

there have been some who have challenged this claim. I examine the claims of Kripke, Fitch,

Bostock and Williamson to see whether the candidates they offer for the contingent apriori are

viable. I conclude that, for various reasons, each of them is not a true example of the contingent

apriori. However, I offer a candidate that avoids the pitfalls of these alleged examples: 'All

actual geniuses are geniuses'. I conclude the paper by exploring and clarifying the semantic role

of 'actual', in the process defending 'All actual geniuses are geniuses' as a contingent, a priori

truth.









INTRODUCTION

From Immanuel Kant to philosophers of the present day, the possibility of a divergence

between necessity and priority has been denied. If Kant and those who agree with him are

right, there can be no contingent, apriori propositions. Though the weight of tradition and the

majority opinion of contemporary philosophers fall in line with Kant, there are dissenters. While

the case for the necessary aposteriori and that for the contingent apriori are related,

establishing one does not automatically establish the other. Therefore, I will focus on the case

for the contingent a priori.

In this paper I will survey the literature on the contingent apriori in order to accomplish

two things: 1) trace the course the conversation has taken as different candidates for the

contingent apriori have been refuted and new ones have developed, and 2) question whether it is

plausible that a viable candidate will ever be offered. We will consider a few different types of

candidates.

The first sort of candidate considered will be the Kripkean examples. These depend on a

linguistic stipulation that specifies the referent of a name in all possible worlds. It is argued by

Kripke and others that proper names have the same referent in all possible worlds. Thus, if one

stipulates that the referent of a certain name is the individual or thing which satisfies a certain

definite description, while it will be true apriori that the definite description is true of and only

of the referent of the name, it will be a contingent truth since the definite description might have

been satisfied by someone else.

We will next consider the sort of example that Fitch labels the incorrigibilityy" type.

There are, allegedly, contingent truths that one cannot believe falsely. These examples will

depend on indexicality. For instance, 'I have a headache' and 'I exist' would arguably be in this









group. It is then argued that if one cannot believe these truths falsely, then if one knows them to

be true at all one knows them apriori.

We will next consider the sort of example that I'll label the "actualized" type. These

examples, like the Kripkean ones, depend on rigid designation to allow us to say things we can

know apriori that are nonetheless false in some possible worlds. The difference is, while

Kripkean proper names lack sense, actualized terms do not. The "rigidification" is accomplished

not by linguistic stipulation, but by the use of 'actual' and its variants. For instance, 'actual

receptionists' has a discernable sense, but rigidly designates all and only those things which are

actually receptionists.1

Finally, we will examine a non-indexical candidate for the contingent apriori. Examples

of this sort could also be labeled the "self-satisfying" type. These examples are argued to be

made true simply by believing them to be true. The trick is that they will be justified not by a

deduction utilizing indexicality (one's knowledge of one's existence or one's belief states), but

by an allegedly indexical-free, belief-forming mechanism.

I will begin with the discussion found in Kripke's Naming and Necessity, which broke

from traditional thought on the subject and offered the first candidate for the contingent apriori.

I will then examine Keith Donnellan's response to Kripke in Donnellan's paper "The Contingent

A Priori And Rigid Designators". In "A Priority and Necessity" Philip Kitcher argues that part

of Donnellan's analysis is ill-formed, but agrees with his conclusion that there are no

philosophically interesting versions of the contingent apriori. I will also examine G.W. Fitch's



1 There are two things that need to be said here. First, I am not claiming that the meaning of 'actual' is unambiguous.
Rather, I will treat 'actual' in the same way it is treated in the papers I discuss (which will become clear later), so as
to shed light on the conversation and see what merit it has. Second, I believe 'actual' is a rigidifier in the following
sense: the phrase composed of 'actual' and the term it modifies refers to the same individuals) no matter where the
phrase occurs in a sentence (e.g. 'Actual receptionists' refers to the same individuals in 'All actual receptionists have
desks' as it does in 'Necessarily, all actual receptionists have desks').









argument against Kripke and his dismissal of a couple of other alleged contingent, apriori truths

in "Are There Contingent A Priori Truths?"

As these papers present certain problems for the Kripkean sort of candidates for the

contingent apriori, I will next consider candidates involving 'actual' and Bostock's attempt to

refute them in his paper "Necessary Truth and A Priori Truth". Bostock's comments here will

lead me to suggest a different example from the one he considers, one that I believe meets his

objections. I will also reconsider Donnellan and Kitcher's objections in light of this new

candidate, as well as the argument given by Albert Casullo.

I will then investigate in what way the two-dimensional modal logic of Davies and

Humberstone comes to bear on the question of candidates of the contingent apriori that involve

'actual' and its variants. I will also examine Williamson's attempt to offer an indexical-free,

contingent, apriori truth and see whether Graham Oppy's attempted rebuttal is effective. I will

then conclude by recapping the status of the various candidates and summarizing what we have

learned about the contingent apriori.









KRIPKEAN CANDIDATES

Background

To properly understand Kripke's alleged examples of contingent, apriori truths, we must

remind ourselves of Kripke's thesis that proper names are rigid designators. He writes, "Let's

call something a rigid designator if in every possible world it designates the same object, a

nonrigid or accidental designator if that is not the case."1 We already have the intuition, says

Kripke, that when we talk about how a thing might have been we talk about a possible situation

for that thing, rather than talking about a different thing that is very similar to the original. Thus,

our use of proper names should rigidly designate so that our talk of possible worlds captures our

intuitions about counterfactuals. It is necessary that nine is greater than seven because both

'nine' and seven' are rigid designators that pick out the same object in every possible world.

'The number of planets', however, is a description rather than a name. Thus, the phrase

will designate whatever happens to be the number of planets in the world in question, not

necessarily the number of planets in the actual world. Traditionally, names have been considered

abbreviated definite descriptions, picking out whatever entity, if any, matches the description in

the world in question. Kripke believes, however, that definite descriptions are used to fix

reference of names, to make them rigid designators; names are not simply abbreviated definite

descriptions. If they were we would be asking about some different, albeit very similar,

individual from Alex when asking, "What if Alex had not been an engineer?"

The "Standard Meter Bar" Example

One of the interesting results Kripke believes this thesis provides (and one of the reasons

it has been so hotly contested) is that it seems to allow us knowledge of contingent, apriori


1 In order to avoid trivial counter-examples, Kripke only requires that the rigid designators pick out the same object
in the possible worlds in which the object exists.









truths.2 One of Kripke's examples of this goes as follows. Let us stipulate that 'one meter'

refers to the length of S, where S is a certain stick or bar in Paris. Now consider the proposition

'S is one meter long'. What are the epistemological and metaphysical statuses of this proposition?

Given that the definition of 'one meter' is "the length of S (at the actual world)," the proposition

seems to be straightforwardly apriori. However, it is surely a contingent fact that S is the length

it in fact is; we can easily imagine possible worlds in which S is longer or shorter than it actually

is. Therefore, the proposition is only contingently true, though still apriori.

An important thing to examine is how the sentence is being evaluated at merely possible

worlds. Do we take what the sentence expresses at the actual world and evaluate it at different

possible worlds, or do we evaluate the sentence according to what it expresses in each possible

world? Kripke believes we must do the former because since names are defined not by synonym

or abbreviated description but by fixing the reference, the reference of the names at the actual

world is what underlies our investigations of modality. Thus, the proposition is contingent, but

will be apriori only in the actual world. In every merely possible world the proposition would

assert that a stick in the actual world is the same length as a stick in the merely possible one,

something we cannot know apriori. If, however, we choose to evaluate the proposition in the

latter way, it will be necessary and apriori since in every possible world the proposition will be

equivalent to something like 'S (at this world) is the same length as S (at this world)'.

Problems with the Kripkean Examples

A worry that one might have with Kripke's example is revealed by the discussion of

modal analysis found above. There seems to be an odd sort of circularity between the definition

of 'one meter' and the proposition in question. 'One meter' is defined as "the length of S," but

the proposition asserts that S is one meter long (i.e., that S is the length of S). While it does not

2 See pages 54-57 of Naming and Necessity for the discussion summarized here.









seem problematic, the example seems somewhat contrived given that we do not normally assert

propositions of this form, and the circularity could mask some semantic problem. It is unclear

how strong this objection is, but for two reasons we shall not examine it further. First, there are

other, clearer objections we shall discuss that make this example untenable. Second, Kripke has

other examples of alleged contingent apriori truths that do not involve this same sort of

oddness.3 Therefore, even if an "argument from oddness" can be made against the "Standard

Meter Bar" example, it will not defeat Kripke's general assertion that his theory of proper names

opens the possibility for contingent, apriori truths.

In "The Contingent A Priori And Rigid Designators," Keith Donnellan responds to

Kripke's theory of names and to the possibility of contingent a priori truths.4 He formulates one

sort of "uneasiness" with Kripke's examples, writing,

"It might be put roughly as follows: If a truth is a contingent one then it is made true, so

to speak, by some actual state of affairs in the world that, at least in the sorts of examples

we are interested in, exists independently of our language and our linguistic

conventions."5

It is difficult to see how definition by stipulation, on which Kripke's examples depend, can give

us epistemic access to non-linguistic states of affairs. The position Donnellan defends within

this paper is that while we have no reason to deny that definition by stipulation is theoretically

viable, such a procedure does not produce "interesting" contingent apriori truths.





3 'Neptune is the planet causing such and such discrepancies in the orbits of certain other planets' is one example of
an allegedly contingent a priori truth that does not involve such oddness. This example can be found on pg. 79 of
Naming and Necessity. It is similar to the "Standard Meter Bar' example in that it relies on stipulation.
4 Contemporary Perspectives in the Philosophy of Language, eds. French, Uehling, and Wettstein. University of
Minnesota Press, 1980 (pgs. 45-60)
5 ibid. (pg. 46)









Donnellan begins by defending Kripke from Dummett's attack on the idea that names can

be introduced as rigid designators.6 He does so by making a distinction between arguing for

certain historic examples of names being introduced as rigid designators and arguing that it is in

principle possible to introduce names in this way. He argues that it would be impossible, without

an explicit stipulation, to tell if historic cases (such as Leverrier's 'Neptune') are actually

examples of rigid designation. Donnellan believes, however, that the philosophical worries

about the contingent apriori are equally strong even if introducing names as rigid designators is

merely possible. As he sees no reason to deny the possibility, he next shows how such a

procedure does not yield philosophically interesting, contingent, apriori truths.7

Donnellan argues that any examples of contingent apriori truths, if they are examples at

all, that follow from the stipulative introduction of a name as a rigid designator will not be

worrisome (unlike Kripke's alleged examples).8 He begins by noting the distinction between

knowing that a sentence expresses a truth and knowing the truth it expresses. For instance, I

know that the sentence 'Fhqwhgads are Fhqwhgads' expresses a truth since a thing must be itself.

If I do not know what Fhqwhgads are, however, I do not know the truth the sentence expresses.

He then writes that we will represent the (Kripkean) stipulative introduction of a name with:

(a) Provided that the $ exists, let "N is the D" express a contingent truth,

where 'the V' is a definite description and 'N' is a name.

Donnellan believes that using this locution helps bring certain relevant features to light

(which we will see later). He also argues that while it may seem worrisome that we are

stipulating that something is contingently true, it is not suspect. So long as we pick a name that


6 ibid. (pgs. 47-50)
7 The idea that any examples of contingent a priori truths will be philosophically uninteresting is shared by many of
those who disagree with Kripke (including Donnellan, Kitcher, and Bostock). I will explore later what
'philosophically interesting' may mean and whether the claim made by Donnellan and others is true.
8 ibid. (pgs. 51-8)









is not already in use within the language, we are not attempting to make some non-linguistic

state of affairs the case; rather we are simply creating a purely linguistic state of affairs.

Furthermore, Donnellan asserts that we do not come to have knowledge of any (non-linguistic)

state of affairs by our act of stipulation.

Donnellan has us consider Kripke's "Neptune" example to illustrate his point.9 If the

Neptunians knew of Leverrier's stipulation, would they be justified in saying he had discovered

their planet as the cause of the perturbations? Could they, in their language and using their name

for their planet, say he knew their planet was the cause of the perturbations? Donnellan takes the

answers to these questions to be "No" and concludes that there is no knowledge of a non-

linguistic state of affairs given by the stipulation.

Donnellan also turns our attention to the classic "Newman-1" example, which he takes to

be analogous to the above example.10 He says that any knowledge resulting from the stipulation

must be de re, saying,

". .. it would have to be knowledge about an individual in the sense that there is (or will

be) an individual about whom we now know something and if that individual turns out to

be John we now know something about John."11

He says this is not simply because the propositions involve rigid designators; one could have de

dicto knowledge as a result of rigid designation as well. What is required is that the rigid

designators lack descriptive content in the propositions in question. It is his contention that this

sort of stipulation fails to produce knowledge de re.





9 See footnote 5 for the gist of the example.
10 'Newman-1 is the first child born in the 21st century,' where 'Newman-1' is stipulated to refer to the first child
born in the 21st century.
1 ibid. (pg. 54)









Having thus laid the foundation for his argument, Donnellan gives a rough

characterization of two principles that hold for a wide number of cases but fail for both the

"Neptune" and "Newman-l" examples. One of these principles is as follows:

"If an object is called by one name, say 'N,' by one group of people and by another name

by a second group of people, say 'M,' and if, in the language of the first group 'N is O'

expresses a bit of knowledge of theirs and if 'is u' is a translation of 'is O' into the

language of the second group then if the relevant facts are known to the second group,

they can say truly that the first group 'knew that M is D."12

Obviously, the Neptunians cannot say that Leverrier 'knew that Enutpen is the planet causing

such and such discrepancies in the orbits of certain other planets.' Donnellan concludes that

unless some other explanation can be given, Kripke's examples fail to meet these criteria

because they fail to produce knowledge of non-linguistic matters (the second criterion is similar

to the first, applying to temporal cases like Newman-1 rather than Neptune).

So while Leverrier could have known (perhaps even apriori) that the proposition

expresses a 1i nilh, he could not have known apriori the truth the proposition expresses.

Donnellan notes that some might still wish to claim that these cases give examples of the

contingent apriori, that one has apriori knowledge of a linguistic fact that could have been

otherwise. Donnellan concedes that this could be true, but says that such examples are not

philosophically interesting or worrisome, that they could be produced with names being

stipulated rigid designators, and that traditional definitions will yield similar results.

One might object that Donnellan's use of the two conditions is suspect for one reason or

another. First, he readily admits that his conditions allow certain counter-examples, one of


12 ibid. (pg. 55)









which is Kripke's "Hesperus/Phosphorus" example.13 If other of Kripke's examples can be

shown to have the same features that allow general counter-examples to the conditions,

Donnellan's case would be much weaker. Second (and on a related note), Donnellan leaves open

the possibility for some other explanation of why the examples fail to meet the criteria. If such

an explanation could be given, we would have less reason to deny the propositions in question

could produce knowledge of non-linguistic matters.

Philip Kitcher argues that we need not agree with Donnellan that any knowledge

produced by the stipulation must be de re.14 Consider the proposition 'If Shorty exists then

Shorty is a spy,' where 'Shorty' refers to the shortest spy. The corresponding belief must be

either de dicto or de re according to Donnellan (this is the alleged dilemma that Kitcher intends

to deny). It cannot be de dicto because that would require that 'Shorty' have descriptive content,

but the description was used merely to fix the reference. Therefore, it must be de re. However,

if the belief were de re I should be able to say, upon meeting the shortest spy, "Ah, I knew (a

priori) that you were the shortest spy." I cannot do this, so my belief cannot be de re. Therefore,

I do not have a priori knowledge of the proposition expressed.

Kitcher argues that contrary to Donnellan's argument, our belief in this case is de dicto.

Kitcher writes,

"The fact that 'the shortest spy' was used to fix the reference of 'Shorty' does show that

the name 'Shorty' does not have a particular descriptive content. However, to use that

description to fix the reference of 'Shorty', I must intend to use 'Shorty' as an abbreviation for a

closely related description: 'Shorty' must abbreviate 'the shortest actual spy'."15




13 See footnote 22 of Donnellan's paper.
14 Philip Kitcher, "A Priority and Necessity," fromAustralasian Journal oJ I 1,il.. -.1 l, 58 (1980), pgs. 89-101
15 ibid. (pg. 91)









Thus, my de dicto belief is 'If there is a shortest actual spy then the shortest actual spy is a spy.'

Despite disagreeing with Donnellan's analysis, however, Kitcher agrees that while we might

have knowledge of contingent apriori truths through stipulation, they should not cause any

worry.

In "Are There Contingent A Priori Truths," G.W. Fitch considers and dismisses several

alleged examples of the contingent apriori, culminating in his dismissal of Kripke's example.16

The candidates he considers prior to considering Kripke's he calls the incorrigibilityy" examples.

The first he considers is offered by David Benfield: 'I have a headache' uttered by someone else

at some specific time.17 This is certainly contingent, but it is clearly not apriori. The

proposition requires experiential evidence to be justifiably believed. Secondly, Fitch notes that

examples of this sort purport special access to apriori knowledge; if Frank has a headache, he

would be the only person in a position to know this apriori.18 Fitch argues that no human has

special access to apriori knowledge (indeed, this would seem to show that the individual has

some sort of individuating experiences he or she is drawing from), so examples of this sort

cannot be contingent, apriori truths.

Fitch next considers an example by Alvin Plantinga. Consider 'I know that 7+5=12'.

While the contingency of this is clear, it's a priority is much less so. One may be tempted to

think that knowing the above truth requires knowing 'I believe that 7+5=12', and that this is

certainly known aposteriori. Plantinga argues that we cannot demand that to be apriori a truth

must be known without the use of any experience, since certain experiences (namely those

required to attain the concepts) are needed even to know '7+5=12'.



16 The Journal of CriticalAnalysis vol. 6, no. 4, Jan./Apr. 1977
17 Fitch, 119
18 ibid. (pg. 120)









Fitch points out that the difference between the two is that in the former experience acts

as a justification for belief, while in the latter it does not.19 While experience is certainly

necessary to know anything (even if only to acquire the concepts involved), the hallmark of a

priori knowledge is it either requires no justification or is justified purely on the basis of other a

priori truths. Plantinga's example satisfies neither of these.

The third example considered by Fitch is 'I exist,' also given by Plantinga. Fitch replies

that this too is justified on the basis of experience, albeit not any particular experience.

Furthermore, this is yet another example that purports special access to apriori knowledge (only

I can know apriori that I exist). For these reasons, this candidate for the contingent apriori

must be dismissed as well.

Fitch now moves on to Kripke's example, 'Stick S is one meter long'.20 Fitch argues,

very similar to Donnellan, that while those who define 'meter' as 'the length of stick S' know

that 'Stick S is one meter long' expresses a truth, they do not know the truth it expresses.21

Because a priority must be maintained, the stipulators must not have had any experience of S.

Thus they are not acquainted with it, they do not know its length relative to other things, etc.

Therefore, it is not clear, says Fitch, that they know what they're saying when they utter 'Stick S

is one meter long'. He writes,

"If we make the distinction between sentences and propositions, then it seems clear that

the fixers only know something about the language they helped to form, not about the

world the language is used to describe."






19 ibid. (pg. 121)
20 ibid. (pg. 122)
21 ibid. (pg. 123)









Thus, he dismisses Kripke's alleged example of the contingent apriori. He closes his paper by

remarking that while necessity and a priority are different conceptually (one is metaphysical

while the other is epistemic), we have no reason as of yet to believe they are not co-extensive.

Conclusion

So, what can we conclude about the Kripkean candidates for the contingent apriori?

The worry about the "Standard Meter Bar" example having an odd sort of circularity between the

stipulation and the proposition in question doesn't rule it out as a candidate. However,

Donnellan's worry is more problematic. While the problems with Donnellan's argument that

Kitcher and I point out seem to be real problems for him, his conclusion that Kripke's examples

are not philosophically interesting, a conclusion shared by Kitcher seems right.22 Fitch's

comments reveal the essential point in Donnellan's paper without Donnellan's unnecessary and

problematic conditions and without insisting that the knowledge produced by Kripkean examples

must be de re. Fitch's paper reveals the essential problem with the Kripkean examples: linguistic

stipulation alone cannot give us knowledge of a particular and, thus, cannot generate apriori

knowledge of contingent states of affairs involving that particular. It also notes in passing the

failure of candidates of the incorrigibility type.
















22 What this claim amounts to, and how it informs and directs the discussion on contingent, a priori truths, will be
examined later.









ACTUALIZED CANDIDATES

Background

David Bostock puts forth yet another objection to the idea that there are contingent a

priori truths in his paper "Necessary Truth and A Priori Truth."1 He writes,

"I believe that, in the end, Kripke's two claims [that there are contingent apriori truths

and that there are necessary aposteriori truths] must be admitted to be correct, but that

does not have quite the significance that one is apt to suppose."2

His conclusion is similar to that of Donnellan. Kripke gets the results he claims but that they are

ultimately not of much importance. However, Bostock reaches it for very different reasons.

While Donnellan focuses on what sort of knowledge is produced by alleged examples of the

contingent apriori, Bostock considers the question of rigid designation from Kripke's theory of

proper names and argues that rigid designation does not give us philosophically important

examples of the contingent apriori.

Bostock begins by laying out some of the characteristics of the quantified, modal logic

that underwrite Kripke's notions of rigidity and necessity. The key notion is that of possible

world, a counterfactual situation where every proposition has a determinate truth value. A

possible or contingent proposition is one that is true in some possible world; a necessary

proposition is one that is true in every possible world.

Based on Kripke's conception of names as rigid designators Bostock introduces another

rigidifiedd" part of speech. By specifying the extension of a predicate at every possible world

one introduces a rigid predicate.3 To give an example that will arise later in Bostock's argument,

we could stipulate that the extension of 'cordate' in all worlds is to be all and only those

1 Mind, New Series, Vol. 97, No. 387 (Jul., 1988), pg. 343-379
2 ibid. (pg. 344)
3 ibid. (pg. 351)









creatures that actually have hearts. In doing this Bostock separates the concern over the

contingent apriori (and the necessary aposteriori) from the viability of Kripke's conception of

naming. Rigidifying is a legitimate process apart from the question of whether names (or

predicates for that matter) are actually rigid and so the concerns over the purported material

difference between necessity and priority are valid ones. Note that Bostock once again takes

the same line as Donnellan in arguing that even if we do not in fact introduce terms as rigid

designators or expressions, the worries over the material difference persist.

Bostock says that we have a set of words in the English language 'actual' and its

variants that modify certain words or phrases and make them "Kripkean" (or rigid).4 The

function of these words is to anchor whatever they modify to the actual world even if we are

considering counterfactual situations. For example, consider the proposition 'All actual geniuses

are geniuses'. If I ask whether this proposition is necessary, I am asking whether it is true in

every possible world that every thing that is a genius in the actual world is a genius in that world.

Within quantified modal logic an actuality operator, 'A', is used to accomplish what is

accomplished by 'actual' and its variants in natural language.5 'A' modifies a proposition, O,

such that 'A D' is to be interpreted as true at any world iff 'D' is true at the actual world. 'A'

can also modify predicates; 'A Fx' means 'x is actually F'. As with other modal operators, when

combined with other scoped operators the 'A' operator may take both wide-scope and narrow-

scope positions.


4 ibid. (pg. 355)
5 ibid. (pg. 356)









Bostock's Argument Against the "Actual Inventor of the Zip" Example

With the foundations thus laid, Bostock gives his argument that the use of 'A', while

permitting a material difference between necessity and truth in every possible world, also gives

us results that do not match with our intuitive notions of necessity and contingency.

"Let 'p' be any plainly contingent proposition, that happens to be true as things are, but

could easily have been otherwise. Then 'Ap' will be true. But then it follows further that

'Ap' will be true in all possible worlds, for it will be true in all worlds that it is true in

this world thatp. If truth in all worlds suffices for necessity, we must then conclude that

it is a necessary truth that Ap. But this is surely absurd. We cannot really turn a

contingent proposition into a necessary one by adding such qualifications as 'actually' or

'in fact' or 'as things are', and the correct conclusion to draw is evidently that the

criterion of truth in all possible worlds is no longer an adequate criterion of necessity."6

In order to remove the alleged counter-intuitive results of our working notion of modality

(and thus of our modal system), Bostock suggests a different way of handling 'actual' and its

variants. In what follows we will examine his system and his reasons for promoting it. This

method will, according to Bostock, allow us to represent sentences containing 'actually' without

giving counter intuitive results. He writes,

"The general idea is to treat 'actually' not as a new modal operator but as a device for

indicating relative scope, so that the word no longer occurs explicitly in our formal

language, where scope is shown differently, by order and bracketing."7


6 ibid. (pg. 357-8)
7 ibid. (pg. 360)









I will briefly explain the changes Bostock suggests and the advantages of making this revision. I

will then question Bostock's motivation for the change and some of the assertions he makes

about the effects of the change.

Bostock works with 'It is possible that the person who did actually invent the zip should

not have done so'.8 The "old" formalization of this proposition would look something like the

following:

0Ox (AVy(Fy y = x) -Fx), where 'F' is 'invented the zip'.

Bostock, however, suggests the following "new" formalization:

Ex (Vy (Fy y = x) & 0 -Fx).

In the second formalization, 'A' is no longer present. Rather, the expression modified by 'A' in

the first formalization is taken outside of the scope of the other modal quantifier and 'A' is

removed. Thus, the modality is now a de re modality with the formalization read as,

'Concerning the person who did invent the zip, it is possible that he should not have done so'.

Bostock believes that there are several reasons to accept this treatment of 'actually'.9

First, this method can handle all instances of 'actually'. Second, Bostock argues that it is more

versatile than the previous system. He says that there are examples of propositions that the

original treatment of 'actual' and its variants cannot formalize, such as 'It is possible that all the

actual dogs should have existed and some other dogs as well'. Finally, this method eliminates

what Bostock takes to be counter-intuitive results (e.g. "philosophically interesting" necessary a

posteriori truths). He writes, "The consequences of this [change in our modal system] for the

divergence between necessary truth and apriori truth are clear: there is now no divergence or

at least none that is due to the word 'actually'." Before moving on to the possible problem with


8 ibid. This proposition underlies the potential candidate '
9 ibid. (pg. 360-362)









Bostock's move, let us examine his claim that his treatment allows us to formalize propositions

that cannot be formalized by the traditional treatment.

Bostock uses the example mentioned above to illustrate this point. He says the point of

the sentence is to assert that there is a world in which all actual dogs exist and other (i.e. non-

actual) dogs exist. The problem, however, is that we cannot refer to the possible world in

question when we treat 'actual' as a quantifier itself, so we have no way of evaluating the

proposition asserted. The example can be represented with the following:

3wax(xsw & Dxw & Vy(Dyw* -- yew & yfx)),

where 'w' is a variable ranging over possible worlds, 'x' ranges over possible objects, 'w*'

denotes the actual world and 'Dxw' means 'x is a dog in w'. Bostock notes that we can use

'O3x(Dx &' in place of 'HwHx(xsw & Dxw &'. We may also replace 'Vy(Dyw* -*' with

' Vy(ADy -*'. This suggestion could be used to try to represent the proposition in our usual

system of modal logic. However, once we do we are unable to translate 'yew' since doing so

would require asserting that the dogs that actually exist also exist in the worldwe are discussing.

We cannot do this because we have dropped the '3w', which we would have to refer back to in

order to make the assertion.

Bostock's method, on the other hand, can treat this sentence and those like it with ease.

Without removing 'A' we formalize 'It is possible that all the actual dogs should have existed

and some other dogs as well' as:

[3O(Vx(xsp +-+ y (y = x)) & 3x (Dx & oVy(ADy -y ysp & y x)),

where '0' is a rigid-predicate variable that ranges over the possible world discussed. Therefore,

the above formalization can be roughly translated as 'There is some 0 such that there is a

possible world in which everything in 0 is in that world and everything in that world is in P.









Furthermore, in that world there is some x such that x is a dog and all of the actual dogs are in

the possible world and are not identical with x'. Then, utilizing the unique role '0' plays in the

language, Bostock can eliminate 'A' and translate the proposition with the following:

aa(Vx(xsa Dx) & 3PO(Vx(xsp Hy (y = x)) &

Ex (Dx & VDy(ysa -y yb & y x)))).

Bostock admits that this method is somewhat cumbersome, but says that it allows us to translate

these sorts of sentences without needing a further device. We can translate these sorts of

sentences while still utilizing 'A', but it requires a further device, like the one by Peacoke that

Bostock discusses briefly.10

So there is a trade-off between having simpler expressions on the one hand and not

having to introduce a further device into our formal language on the other. Which one we would

deem the simpler revision would largely be a matter of preference, so Bostock's "argument from

simplicity" does not tip the scales toward one or the other. We must, therefore, examine his

motivation for suggesting the revision in the first place (i.e. that the traditional treatment of

'actual' and its variants leads to counter-intuitive results).

Bostock's argument that we need a different way of handling 'actual' and its variants

seems plausible on the surface. Consider the following proposition: 'All philosophers are pale'.

This proposition is both contingent (it is true in some worlds and not in others) and aposteriori;

it poses no problems for the idea that necessity and priority are materially equivalent.

However, suppose the proposition above is actually true and consider the proposition 'It is

actually the case that all '. It seems to me that Bostock believes we have the intuition that the

modal status of this proposition should be the same as the first. Since in our current system of


10 ibid. (pg. 361)









modal logic the second proposition comes out necessary, Bostock believes there must be a

problem with some components) of our system.

However, do we really have the intuition that these propositions should have the same

modal status? We certainly do have the intuition (and rightly so) that it is not essential to

philosophers that they be pale. That is, we believe the proposition 'All philosophers are

necessarily pale' is false, and hence also that 'It is actually the case that all philosophers are

necessarily pale' is false. However, this is the narrow-scope reading of the necessity operator; it

is clear from Bostock's talk of contingent propositions and 'A' being a propositional modifier

that he has in mind de dicto necessity. So, what are our intuitions about 'Necessarily, it is

actually the case that all philosophers are pale'?

I must confess that I do not have clear, pre-theoretic intuitions on the status of de dicto

modal statements that include 'A'; my intuitions on de re modal statements including 'A' are

reasonably clear though. However, I think there are a few reasons to think that Bostock's

conclusions about our intuitions and what we should do with our formal notion of necessity are

either questionable or mistaken. First, since the traditional "truth in all possible worlds" notion

of necessity works in so many cases, it would seem irresponsible to throw it out unless intuitions

are reasonably clear and widely shared. Second, I think there is serious doubt that intuitions on

this matter are in fact clear and widely shared. The fact there is continued debate would seem to

be evidence of this. Third, it is at least possible that Bostock's intuitions about the modal status

of 'Ap' are, unbeknownst to him, intuitions about the de re necessity claims.

At the end of his paper, Bostock defends what he believes is a true example of the

contingent apriori (378). His example is 'If there is exactly one object that falls under the

predicate, then it is necessary that there is no more than one', where the predicate in question is a









rigidified predicate. Bostock notes that if the antecedent is false, the conditional turns out to be

contingent. However, given the nature of rigidified predicates, we are able to know the

proposition is true apriori. Therefore, we have a contingent, apriori truth based on a Kripkean

language, though of a different sort than the ones Kripke mentions.

Bostock's example seems to avoid the worry with the Kripkean examples (i.e. that we

cannot understand them apriori). While rigidified predicates, like Kripkean proper names, lack

sense, since the predicate is mentioned rather than used it does not seem to present a problem for

the example; we can understand the proposition. However, since we cannot know apriori which

things fall under the predicate, and since the predicate does not have a sense, the proposition

concerns only a linguistic state of affairs. As we shall see later when we discuss what it is for an

example to be philosophically interesting, Bostock's example fails to be so. So, while the

example seems to be an example of the contingent apriori, it is not of the sort that interests us.

'All Actual Geniuses are Geniuses'

While Bostock focuses on the actuality operator as a propositional modifier, one could

offer a candidate for the contingent apriori that uses 'A' as a predicate modifier. So, even if

Bostock is correct that the propositional modifier use of 'A' gives us counter-intuitive results

when considered in conjunction with the wide-scope reading of one of the other modal operators,

that may simply give us reason to limit where we place 'A' rather than reform our method for

assessing necessity. I will conclude my argument against Bostock's position by showing that the

narrow reading of the actuality operator (the one that gives us the contingent apriori) does not

lead to counter-intuitive results, contingent apriori aside.

Consider 'All geniuses are geniuses'. This proposition is true and apriori. Now

consider 'All actual geniuses are geniuses'. This also seems to be a priori, but what is its modal









status? Consider the individuals who are geniuses in the actual world. Is it true that they are

geniuses in all possible worlds? Certainly not, since Albert Einstein might have been a man of

average or below average intelligence, so 'All actual geniuses are geniuses' is a contingent

proposition. According to Bostock, the function of 'A' in this position is to take the term it

modifies out of the scope of the other modal operator, so 'All actual geniuses are geniuses' could

be translated:

(Vx)(AGx oGx).

The above formula comes out false using our traditional system of modal logic, having the same

truth conditions implicit in the possible worlds explanation above. Therefore, in this case there

is no divergence between our intuitions and our system and, thus, no need for a Bostockean

revision.11

Bostock briefly addresses the possibility of rigidified predicates (3 51).12 As rigidified

predicates are similar to 'actual geniuses' in our example, we should look at his remarks.

Though Bostock's treatment of 'A' as a sentential modifier only includes the wide-scope reading,

his treatment of 'A' as a predicate modifier allows him to handle narrow-scope uses of 'A' as

well. Bostock says one can introduce rigidified predicates by stipulating what the extension of

the predicate is to be in every possible world. In our example, the term 'actual geniuses' is taken

to refer to all and only those things which are geniuses in the actual world. Thus, in all merely

possible worlds, the extension of the predicate is determined by the things that happen to be

geniuses in the actual world and which also exist in the world in question.






11 Bostock makes implicit use of the principal that a proposition, p, is necessary just in case p' is true.
12 It is noteworthy that while Bostock brings up the possibility of rigidified predicates, he does not involve them in
his argument, nor does he say that they give counter-intuitive results.









Bostock explicates some of the features of this sort of rigidity with an example (351-2).

'Cordate' is to refer to all and only those creatures which have hearts in the actual world.13

'Renate' is to refer to all and only those creatures which have kidneys in the actual world. Now

we have two rigidified predicates. Suppose (as is the case) that it is a contingent, aposteriori

truth that all those things which have hearts also have kidneys. It is, therefore, a necessary, a

posteriori truth that all cordates are renates. It is a contingent, apriori truth that all cordates

have hearts since in some possible worlds they will not.

Bostock believes that these fail to produce examples of the contingent apriori as well

since he believes that his arguments we discussed earlier cover these cases as well. As I have

responded to his earlier arguments already, I shall not revisit them here.

Conclusion

I admit that I have not decisively refuted Bostock's argument. What I have done, at best,

is question whether he is warranted in assuming the things he does and advocating a revised

modal system. I have shown that it may be the case that Bostock's criticisms of purported

contingent, a priori truths involving wide-scope uses of 'A' are ill-founded, and that narrow-

scope uses of 'A' can be used to form truths, like 'All actual geniuses are geniuses', that do not

fall prey to Bostock's objections.













13 Bostock also says that if something has a heart in the actual world and does not exist in some possible world, it is
still a cordate in that world. This makes it such that something is necessarily a cordate if it is one at all.









PAST OBJECTIONS CONSIDERED IN LIGHT OF 'ALL ACTUAL GENIUSES ARE
GENIUSES'

What Does it Mean for a Candidate to be "Philosophically Interesting"?

While Bostock's worries do not apply to our current candidate, there is another possible problem

with candidates for the contingent apriori that depend on 'actual' and its variants. The Kripkean

examples were said to be "philosophically uninteresting". Can the same be said for our current

candidate?

First, let us consider what a "philosophically interesting" contingent, apriori truth would

be. Donnellan, Kitcher and Bostock all admit that uninteresting examples of the contingent a

priori can be generated. However, none of them explains clearly what would make a case

philosophically interesting or uninteresting. In reference to 'Provided the D exists, "t is the Q"

expresses a contingent truth', Donnellan says,

". .. I am not sure whether in the circumstances what sentences of form (A) express are

both contingent and apriori. But if they are they are harmless varieties of the contingent

a priori, examples of which we could produce without recourse to stipulations

introducing rigid designators."1

What would these be and why are they uninteresting? Shortly after the above quote, Donnellan

says that one might argue that sentences of form (A) are both contingent and a priori since they

assert something true about language that might have been false. Donnellan's paper also utilizes

a distinction between linguistic states of affairs and non-linguistic ones, so perhaps the

uninteresting examples of the contingent a priori are simply statements of a priori knowledge of

a contingent, linguistic state of affairs.




1 Contemporary Perspectives in the Philosophy of Language (pg. 56)









If this is what Donnellan, Kitcher and Bostock have in mind it is clear why they think

such examples are uninteresting. For one, they are ubiquitous; most (if not all) of our linguistic

stipulations might have been otherwise. Second, the contingent, apriori truth wouldn't be 'S is

one meter long', for instance. Rather, it would be "One meter' refers to the length of S'. Or, to

put it in a locution similar to Donnellan's, 'Provided there is something which is one meter, "S is

one meter long" expresses a contingent truth'. I say allegedly since one might contest the idea

that our knowledge of the linguistic stipulations is apriori.

So, what would be a philosophically interesting contingent a priori truth? If what is said

above is correct, we need apriori knowledge of a non-linguistic state of affairs. As I have

shown, Bostock has not given us a decisive reason to reject 'All actual geniuses are geniuses'.

This example (and those like it) do not depend on the Kripkean theory of naming and at least

seem to make reference to a non-linguistic state of affairs. Therefore, 'All actual geniuses are

geniuses' would seem to be philosophically interesting.

Donnellan's Objections Revisited

It is notable that Kripke's examples seemed to be about non-linguistic states of affairs

until they were probed by Donnellan. Might the same thing happen to our current candidate? At

the very least, we have a reason to reevaluate Donnellan's claim rather than simply taking it to

have provided a refutation of all possible candidates for the contingent apriori. The examples

Donnellan considered in his paper were all based on rigidified proper names or other sorts of

linguistic stipulations. As a result, the terms did not have a sense that contributed to the truth

conditions in any direct way; the sole function of the sense was to fix the reference. Because of

this, Donnellan could argue that while we possibly know apriori that the sentence expresses a

truth, we cannot know the referent of the rigidified term a priori and thus cannot know what









truth the sentence expresses. Examples involving 'actual' and its variants do have sense that

may do more than simply fix the reference. Therefore, we must see whether they are different

from the sort of examples Donnellan considers in a way that will allow us to know apriori the

truth they express. To do this, I will step through the various parts of Donnellan's argument with

'All actual geniuses are geniuses' as the sentence in question.

One reason Donnellan rejects Kripke's examples is that they fail to meet two criteria

Donnellan set up to test whether they assert any non-linguistic truth. However, there is a

problem applying these criteria to our current candidate. The criteria are designed for examples

involving proper names. Furthermore, the criteria cannot be easily adapted to the candidate

we're considering since to do so would require treating 'actual genius' as if it didn't have a sense.

So, Donnellan's criteria, whatever force they may have against the Kripkean examples, simply

do not apply to 'All actual geniuses are geniuses'.

When Donnellan is concluding his argument he attempts to show where the line of

reasoning from rigid designation to contingent a priori truths went wrong. In doing so he gives

two possible things that can be known as a result of a stipulation:

(A)Provided the D exists, "t is the Q" expresses a contingent truth.2

(B) Provided the P exists, t is the Q.3

If we were to adapt these to our current candidate, they would be:

(A') Provided the P exists, "The actual P is a Q" expresses a contingent truth.

(B') Provided the P exists, the actual P is a Q.





2 It is important to note that Donnellan does not commit himself to form (A) knowledge being a priori. He merely
says that ifwe have a priori knowledge, it is form (A) rather than form (B). It is highly questionable whether we
even have form (A) knowledge a priori.
3 ibid.









The flaw in the reasoning, according to Donnellan, is that while rigid designation can give us

form (A) knowledge, it cannot give us form (B) knowledge. (A) is knowledge of a purely

linguistic state of affairs while (B) is knowledge of a non-linguistic state of affairs. Do we have

form (B) knowledge if we know that all actual geniuses are geniuses?

It seems that we do have form (B) knowledge if we know that all actual geniuses are

geniuses, however. This is revealed if we consider why Kripke's examples give us form (A)

knowledge but not (B) The way in which we can have form (A) knowledge without form (B)

knowledge is if 't' does not have a sense that contributes to the truth conditions. This allows us

to know that a sentence expresses a (contingent) truth without knowing the truth it expresses by

simply stipulating that it expresses a truth.4 If't' lacks a relevant sense and we do not know its

referent apriori, we do not know the truth expressed. 'Is an actual genius' is not lacking in

sense, however, so we do not have this problem.

One might make the point, however, that to have form (B) knowledge one must know (a

priori) the referent of 't' in order to know that D is true of him (i.e. one must have de re

knowledge). It is clear that Donnellan thought this was the case.5 It is also clear that we do not

have a priori knowledge about any particular entity if we know all actual geniuses are geniuses;

we do not even know who the actual geniuses are. Does this show that we do not have form (B)

knowledge in this case?

Kitcher does not think so. As has already been shown with the example of 'Shorty is a

spy', one can have a bit of de dicto knowledge about a non-linguistic state of affairs. The

mistake Donnellan made, according to Kitcher, is requiring particular descriptive content rather

than simply descriptive content. While do not have any knowledge of descriptive content about

4 Though this is not the sort of stipulation Kripke had in mind, Donnellan cashes out Kripke's examples in these
terms. (pg. 52)
5 Pg. 58 and elsewhere









the referent of 't' (de re), we do have knowledge of some of the descriptive content of 't' (de

dicto). Therefore, we can have form (B) knowledge despite our lack of de re knowledge.

Kitcher's Objection Revisited and Concluding Remarks

An interesting question arises from this, however. Kitcher, despite disagreeing with

Donnellan's analysis, agrees with the conclusion that only uninteresting contingent a priori truths

can be generated. How can this be given that it seems we can have contingent apriori

knowledge of non-linguistic states of affairs rather than simply linguistic ones?

Kitcher says several things about Donnellan's conclusion and the possibility of

interesting contingent a priori truths. He says that anyone can come to a priori knowledge of

contingent truths, but doing so requires linguistic acts that are "at odds with the standard

functions of language."6 Kitcher believes that even examples that have a non-linguistic

component are uninteresting because they require odd linguistic stipulations in order to express.

Given that our current candidate does not seem to involve this sort of stipulation, we have

avoided Kitcher's worry.

It would seem, therefore, that none of the objections to the contingent a priori considered

up to this point have provided a refutation of our current candidate. Donnellan fails to account

for the fact that one can have form (B) knowledge without having knowledge de re, and while

Kripke's examples do not provide this sort of knowledge, 'All actual geniuses are geniuses' does.


6 Kitcher, 100









GETTING CLEAR ON 'ALL ACTUAL GENIUSES ARE GENIUSES

Clarification and Background

Casullo begins his paper, "Actuality and the A Priori," by summarizing and addressing

an argument by Kitcher which, though not appearing explicitly in the paper we discussed earlier,

underlies and supplements the argument discussed earlier. Casullo begins by giving the

following condition, which Kitcher believes is a condition on apriori warrants:

a is an a priori warrant for X's belief thatp if and only if a is a process such that, given

any total sequence of experiences which would have enabled X to form the belief that,

(a) some process of the same type as a could produce in X a belief thatp, (b) if a process

of the same type as a were to produce in X a belief that p then that process would warrant

X's belief that p, (c) if a process of the same type as a were to produce in X a belief that p

thenp (390-391).

Casullo asks what knowledge, if any, this condition gives us about our own actuality. To

see whether the knowledge of our own actuality is apriori, Casullo says we must ask questions

about what our knowledge would have been had our experiences been different. This fact, in

combination with Kitcher's view that 'actual' is an indexical, necessitates we determine whether

it is possible to believe in world w the truth expressed by 'I'm actual' in w*. If it is, then belief

in one's actuality is not apriori.

Kitcher argues that since this result would be extremely odd, we must deny that 'I'm

actual' expresses different beliefs at different worlds. Kitcher does not give up his belief that

'actual' is an indexical, but says that for the purpose of determining and applying a criterion of a

priority, the difference between the tokens of 'I'm actual' doesn't matter. Casullo notes that the

upshot of this view is that 'I'm actual' is true in any world in which I believe it, so condition (c)









is satisfied, and thus the knowledge of one's actuality appears to be apriori (392). He argues,

however, that Kitcher's last move is ad hoc.

Let's adopt the following notation. 'S' refers to the speaker. '[P](a)' means 'the

proposition expressed by sentence P in world a. 'p,[P](a)' means 'world 1 makes true the

proposition expressed by P in a. Finally, 'a' designates the actual world and 'w' some other

world.

Casullo begins with the following summation of Kitcher's claims:

(1) The belief that S expresses in a by tokening 'I'm actual' = the belief that S expresses in w by
tokening 'I'm actual'

(2) ['I'm actual'](a) ['I'm actual'](w).

These claims are tantamount to saying that while the different tokens of 'I'm actual' express

different propositions, they express the same belief. Casullo sums up Kitcher's defense of this

claim with:

(3) If the belief that S expresses in a by tokening 'I'm actual' the belief that S expresses in w
by tokening 'I'm actual', then the belief which S expresses at a by tokening 'I'm actual' is
false at w.

Casullo supplements (3) with:

(4) It is not the case that the belief which S expresses at a by tokening 'I'm actual' is false at w.

He agrees with Kitcher that (3) and (4) entail (1), but Casullo thinks (3) is problematic. Since all

that is needed to justify (4) is the trivial fact that one cannot be wrong about one's actuality,

Casullo grants (4) and focuses on the previous premise (393). To disprove (3), Casullo has us

grant (contrary to Kitcher):

(6) The belief that I express in a by tokening 'I'm actual' = ['I'm actual'](a)

(7) The belief that I express in w by tokening 'I'm actual' = ['I'm actual'](w).









Conjoin these and we get:

(8) 'The belief that I express in a by tokening 'I'm actual' the belief I express in w by tokening
'I'm actual'.

Notice that (8) satisfies the antecedent of (3), so it would seem reasonable to conclude that S's

belief that he exists in a is false at w. This is an absurd conclusion, Casullo points out, since the

belief is true both at a and w. He briefly considers the counter-argument that individuals are

world-bound, but dismisses it because it would only be found persuasive by those who accept

counter-part theory.

Casullo now argues that Kitcher's account contradicts the very things he hopes to derive

from it, namely that knowledge of one's actuality explains how we can have knowledge of

contingent, apriori truths of the kind proposed by Kripke. Casullo has us consider the Shorty

examples mentioned earlier in this paper (If Shorty exists, then Shorty is a spy). Kitcher argues

that to use 'the shortest spy' to fix the referent of 'Shorty', 'Shorty' must be acting as an

abbreviation of 'the shortest actual spy' (394). Therefore, 'Shorty is a spy' is best represented by

something like the following:

(12) If there is a shortest actual spy, then the shortest actual spy is a spy.

To determine whether (12) is known a priori on Kitcher's account, we must examine the

proposition the sentence expresses in a and in w. Casullo has us grant that Shorty is a tall

basketball player in w, while Kareem is the shortest spy in w. Now, 'If Shorty exists, Shorty is a

spy' is clearly apriori. Kripke understands it as a de re belief, picking out Shorty in both a and

w. Thus, it is a contingent truth; at w, Shorty is a tall basketball player. Since Kitcher takes it to

be de dicto, 'Shorty' refers to Shorty in a and Kareem in w; thus, it is a necessary truth.

Kitcher's account is not only flawed, it does not help clarify the Kripkean examples.









Casullo concludes by investigating whether knowledge of one's actuality "stands in any

significant epistemic relationship" to the Kripkean examples of the contingent apriori (399).

Casullo has us consider ['If there is a shortest actual spy, then the shortest actual spy is a spy'](a).

He argues that this example by Kitcher is of the same sort as beliefs Kripke takes to be examples

of the contingent apriori. Kitcher does not say how this sort of example is related or similar to

knowledge of one's actuality. It cannot be the case that they are both examples of noninferential

a priori knowledge since that would require Kitcher's account to be correct and we have reason

to doubt its viability. However, Kitcher argues, more convincingly, that beliefs of the sort above

can be validly inferred from the necessary truth 'All A's are A's' and the knowledge of one's

actuality. We can produce a slew of contingent, a priori truths of the type 'All actual A's are

A's' in this same way.1

Casullo leads us through the chain of reasoning showing the connection between 'All

actual A's are A's' and knowledge of our own actuality (400). He has us consider 'Actual A's

are actual A's,' noting that it expresses a necessary truth in any world in which it is uttered.

Therefore, ['Actual A's are actual A's'](w*) is true. What do we need to move from this belief

to ['Actual A's are A's'](w*)?

The move cannot be immediate since the belief would not be true at all worlds; there

must be, therefore, some mediate knowledge to justify the inference. Casullo remarks that we

must know that, "the extension of 'A's' includes the extension of 'Actual A's' in the world I

inhabit." It is true apriori that if this is the actual world, then the extensions of 'A's' and

'Actual A's' will be the same. Therefore, if I know I am actual (i.e. that I inhabit the actual

world), I know the contingent, a priori truth ['Actual A's are A's'](w*).


1 Notice that this is exactly the sort of candidate that has seemed, thus far, to be a viable example of the contingent a
prior.









Casullo points out, however, that while the argument in the previous paragraphs is

sufficient, it is not necessary (401). If one takes an indexical view of actual,' 'actual' refers to

the world of utterance. Thus, the inference is justified since we need only know that w* is the

world of utterance. Casullo has thus shown that the contingent apriori is not inexorably linked

to knowledge of one's actuality.

Casullo concludes that we still have reason to doubt Kripke's claims about the contingent

apriori. Noting that his conclusion is similar to Donnellan's, Casullo writes that we have not

stated the content of the belief. He says that if we accept Kripke's semantic story about proper

names and definite descriptions, we may be able know apriori that some sentences express

contingent truths, but we do not know the truths they express. As I have already responded to

Donnellan along these lines, I shall not retrace my steps here.

Analyzing 'Actual'

While Casullo's paper seems to reveal that knowledge of one's actuality is not required

for knowledge of contingent, apriori truths, it does not give us any new reason to doubt our

current candidate. However, as Casullo notes, one might object that 'All actual geniuses are

geniuses' is unclear because the semantic role of 'actual' still has not been made explicit.

Though Donnellan's worries seem to not apply to examples involving 'actual', the surface

grammar may obscure rather than clarify the meaning of the sentence. We must, therefore,

analyze 'All actual geniuses are geniuses' in order to see whether it is an unproblematic

candidate for the contingent a priori.



Let's begin with the following analysis of 'All actual geniuses are geniuses':

(x)((x is a genius & x is in a) -* (x is a genius)),









where 'a' refers to the actual world. In this treatment, 'a' is a name that rigidly designates the

actual world. This immediately re-opens the door to Donnellan's objection. In order to know

the truth expressed by 'All actual geniuses are geniuses' we must know that our world is a; we

must know that 'a' refers to a. Can we know this apriori (or even at all)?

One way we can have knowledge is by description. For instance, I know that Plato was

the teacher of Aristotle and that the teacher of Aristotle was the student of Socrates, so I know

that Plato was the student of Socrates. Knowledge by description is in some sense inferential

knowledge. Can I know that this world is a through an inference of descriptions? No, because

any description we might offer would also be satisfied by another world if someone at that world

were to offer it. 'This world', 'the speaker's world', 'the world that exists', and other variants

will hold true at every possible world, though they won't express the same truth at each world.

What we need is a way to "pick out" our world from among all the possible worlds. This will

give us knowledge of a particular world, allowing us to know that 'a' refers to a by having

knowledge of a particular that also satisfies the description 'the actual world'.

Another way we can have knowledge is by acquaintance. For instance, I am acquainted

with my best friend and know things about him as a result of that acquaintance (e.g. that he is

married). Assuming we are acquainted with our world, there are two ways in which

acquaintance puts us in a privileged position to pick out "our world": (1) we are acquainted with

one and only one world our world, (2) no one in another world is acquainted with our world.

Thus, what we could not do with knowledge by description we can do with knowledge by

acquaintance know the particular world to which we want to refer.

So, is this world with which we are acquainted a? Is it the actual world? That depends,

in part, on whether the following accurately analyzes 'All actual geniuses are geniuses':









(x)((x is a genius and x is in my world) -* (x is a genius)),

where 'my world' is intended to act as an indexical, not as a description. I believe there are two

good reasons to think that this treatment of 'actual' is accurate. First, when we say 'actual

world' and 'my world' we certainly intend to refer to the same world, so the two phrases are

materially equivalent. Second, this analysis explains the reasons mentioned earlier why we

cannot have knowledge by description in this case. 'This world', 'the speaker's world', 'the

world that exists', and other variants will act as indexicals, referring to the world in which they

are uttered or considered. Thus, though they do not refer to a particular world when taken as

descriptions, as indexicals they will have the correct meaning at whatever world they are

evaluated while still referring (as considered at a particular world) to a particular world.

In what follows I will give a possible account of how knowledge by acquaintance can act

as the basis for us knowing apriori that 'a' refers to a (i.e. that our world is the actual world). I

will not insist that we are therefore acquainted with the actual world, but simply that we have the

knowledge of the actual world that we need.2

I will begin by giving a series of conditional premises that will lead us to this conclusion.

I will then provide support for the antecedent of the first premise and explanation for the

premises which may be found less than obvious. Thus, I will have proved that we can know a

priori that our world is the actual world, not simply that 'Our world is the actual world' expresses

a truth; this is equivalent to knowing that 'a' refers to a.

(1) If I think, then I exist.

(2) If I exist, then I am actual.

(3) If I am actual, then the world of which I am a part is the actual world.



2 It may, however, be the case that we are acquainted with our world.









(4) As a world is a complete state of affairs, my knowledge of myself either constitutes complete
knowledge of the world or partial knowledge of it.

(5) Either way, I know that there is an actual world and that my world is that world.

Perhaps (4) is in need of a brief explanation. My knowledge of myself would constitute

full knowledge of the world if solipsism is true and I have complete knowledge of myself (a

priori). Otherwise, I have only partial knowledge (apriori) of my world.

I will not bother to defend the claim that I know that I think. It is important, however, to

distinguish just what is meant by 'apriori' since it has been used in different ways. I will not

attempt to give a thorough account; I will simply give a rough definition that will capture what is

traditionally meant by the term and make explicit the feature relevant to this case.

Something can be known apriori iff it can be known without having any experience that

is not essential to acquiring the concepts involved (i.e. being able to use the words

competently).

The motivation behind this definition is that if we deny the cogitator reference to any and all

experiences, he will be unable to employ concepts since they require experience to acquire. We

maintain priority, however, by limiting the experiences involved to the minimum required to

acquire the concepts.

The Contingent A Priori and Knowledge of One's Actuality

It is important to notice that the link between the contingent apriori and knowledge of

one's actuality has once again been asserted, albeit in a way different from Kitcher's view. This

link holds if the above defense is required, but I do not believe it is. First, one might object that

while I have provided a seemingly viable analysis of 'is an actual genius', one must be

acquainted with the actual geniuses themselves if one is to even understand 'All actual geniuses

are geniuses', let alone believe it. As Donnellan suggests, if I do not know who the actual









geniuses are, how can I say of them that they are geniuses? I may know that 'All actual geniuses

are geniuses' expresses a truth, but I don't know the truth it expresses. It is similar to

'Fhqwhgads are Fhqwhgads'. Thus, what is needed is acquaintance with actual geniuses, not the

actual world.

I think noting an important distinction between proper names and quantitative

expressions reveals the disanalogy between the current candidate and past ones. Proper names

are singular referring terms while quantitative expressions (definite descriptions, general

terms/expression, etc.) are denoting expressions; this distinction is based on Russell's

observations. I will not go into the arguments for and against the distinction between referring

and denoting, other than noting the supporting intuition that the connection between a proper

name and its referent is more direct than is the connection between a definite description and the

thing it describes.3 A proper name just is a title or label for an individual thing, while a

quantitative expression simply picks out the thing which uniquely satisfies it. How does this

distinction help us?

Consider 'Newman-1 is the first child born in the 21st century'. The best way to

represent 'Newman-1' would be with a constant rather than a variable, a formalization of the

proposition being:

F(c),

where 'F' means is thefirst child born in the 21st century and 'c' refers to Newman-1. Since the

formalization requires a constant, knowledge of the proposition requires knowing that c is the

first child born in the 21st century. It requires knowledge of Newman-1 than cannot be gained

just by the stipulation that was its origin, or by description. It requires acquaintance.


3 As evidence, reflect on the difference between 'The author of Huckleberry Finn is Mark Twain' and 'Samuel
Clemens is Mark Twain', or 'Mark Twain is Mark Twain'.









Now consider 'All Martians are green', which could be represented by:

(Vx)(Mx -- Gx).

Here we have a universally-quantified variable rather than a constant. Thus, we do not need to

be acquainted with Martians to understand the proposition. We don't even to know whether such

beings exist to understand the proposition. So, while our previous candidates may have been

problematic, we have no reason to think that of 'All actual geniuses are geniuses'.

Two-Dimensional Logic and the Contingent A Priori

In the paper by Bostock discussed earlier, he mentions a paper by Martin Davies and

Lloyd Humberstone in which a two-dimensional modal logic is used to handle the modality of

'actual' and its variants. In what follows I want to look at the system, partly to understand our

current candidate better and partly to see whether their system attempts to undermine, in any way

not yet accounted for, the viability of 'All actual geniuses are geniuses' as an example of the

contingent a priori.

In "Reference, Contingency, and the Two-Dimensional Framework," Davies begins by

characterizing what he calls 'the two-dimensional framework'.4 There are some sentences, like

'It is possible that everything that is actually red should have been shiny,' that resist formulation

using traditional modal logic. The usual way of handling these sorts of sentences is to introduce

an actuality operator, 'A' (84). Davies writes,

"In terms of possible-worlds model-theoretic semantics for the modal language, a

sentence 'As' is true with respect to a possible world, w, just in case the embedded

sentence s is true with respect to the model's designated or 'actual' world, w*.

One result of this, which was noted earlier in this paper, is that if 'As' is true at all it is

necessarily true. This seems hard to reconcile, however, with the fact that what is actually the

4 Philosophical Studies, 118, 2004 (pgs. 83-131)









case is (at least mostly) a contingent matter. This leads Davies (and Humberstone) to suggest

two sorts of necessity to clarify the difference, and an additional modal operator to help

characterize the two types of necessity.

Davies and Humberstone suggest 'T', a "fixedly"-operator (85). While 'A' increases our

modal language's ability to express sentences by allowing us to vary our world of evaluation, wj,

'F' allows us to vary what world plays the role of the actual world, wi. Davies writes,

"A sentence 'os' is true with respect to a world wj with world wi playing the role of the

actual world just in case, for every world w, the embedded sentence is true with respect to

world w, with wi still playing the role of the actual world. A sentence 'Fs' is true with

respect to a world wj with world wi playing the role of the actual world just in case, for

every world w, the embedded sentence s is true with respect to wj, but now with w

playing the role of the actual world" (85-86).

How this operator gives us two different notions of necessity can be seen by considering TAx'.

If s does not contain A, Ax' is equivalent to 'os'. If, however, x is of the form 'As', where s is

some contingent truth, then a difference is revealed. While 'ox' is true, 'TAx' is false since it is

equivalent to As' and thus to 'os'. As a result we have two different sorts of necessity,

allowing us to maintain the intuition behind the semantics of 'actually' and the intuition that it is

a contingent truth that the world that is in fact the actual world is the actual world.

Thus the two-dimensionality of this system of modal logic is revealed (87). Before 'TF

the only world we needed to consider when evaluating a sentence was wj; the logic was, thus,

one-dimensional. Now, however, we must also consider wi since it can vary; thus, our logic is

two-dimensional. While Davies goes into more detail about this and addresses many related









tangents, I shall not go into those considerations here. Rather, we shall conclude our look at his

paper by examining his comments on the contingent a priori.

Before going into Davies' comments we shall give Evans' characterizations of superficial

(corresponding to 'o') deep (corresponding to '~F) necessity and contingency, which Davies

summarizes and uses in his comments (93-94).5 Superficial contingency is a property of

sentences, and depends on how the sentence embeds under the scope of 'o' or '0'. Davies lists

three ideas associated with superficial contingency to help us understand the notion: truth with

respect to worlds, purely internal to semantic theory, and properties of modal sentences (95). On

the other hand, three ideas associated with deep contingency are: truth in worlds (being made

true), not purely internal to semantic theory, and modal properties of sentences. Davies inserts

the following quotation by Evans,

"If a deeply contingent statement is true, there will exist some state of affairs of which we

can say both that had it not existed the sentence would not have been true, and that it

might not have existed. The truth of the sentence will thus depend upon some contingent

feature of reality."

Superficial contingency and necessity are simply the negation of deep contingency and necessity.

Davies spend some time exploring and defending the notion of 'truth in a world' and

showing that his D-necessity and Evans' deep necessity are one and the same even though the

former is put in terms of a modal operator, T, and the latter is not. However, I wish to move on

to Davies' application of two-dimensional modal logic to alleged cases of the contingent a priori.

Davies begins by expounding Evans' notion of epistemic equivalence (99). Essentially,

two statements are epistemically equivalent iff they have the same content and, if both are


5 Davies calls superficial necessity 'H-necessity' and deep necessity 'D-necessity' since 'V' is truth along the
horizontal and 'F' is truth along the diagonal in a two-dimensional system.









understood, one cannot believe one and disbelieve the other. One example of this which is

important for our investigation is the epistemic equivalence of 's' and 'As'. One result of this is

that we are in a position to know 'As -* s' apriori. Davies' example is that if someone

understand the notion of actuality, he is in a position to know apriori 'if the earth moves, the

Earth actually moves'.

Davies notes several things about this example. First, s can only be known aposteriori,

so As can likewise only be known aposteriori, though 'As <- s' is known apriori. Second,

while 'o(As)' is true, 'FA(As)' is false (100). 'As' is superficially necessary and deeply

contingent. 'As -* s', however, has the opposite properties; it is superficially contingent and

deeply necessary. Thus, our example, and those of the same form, seems to show a correlation

between a priority and deep necessity, though nothing about two-dimensional modal logicper se

demands this.

Davies now gets to the heart of the matter, investigating whether there are deeply

contingent, apriori truths. He says there are two problems: 1) there are some noteworthy

counter-examples to the claim that a priority and deep necessity coincide, and 2) while intuitions

seem not to favor the contingent apriori, it is very difficult to form an argument from them. We

will conclude our look at Davies' paper by considering each of these in turn.

Davies gives the example of the belief that one has hands (101). While it is certainly

possible that I am simply a brain in a vat, I am entitled to ignore this possibility so long as there

is no evidence in support of it, and am justified in believing I have hands. Similarly, Davies

notes that when doing a mathematical proof, one is entitled to ignore the possibility (so long as

there is no supporting evidence) that one is suffering from a massive memory loss and, thus,

cannot be sure the proof is being done correctly. In these cases, Davies alleges, one has apriori









beliefs for which defeaters could arise (i.e. certain experiences would reveal them to be false, or

at least unjustified) (102). Thus, we have certain a priori beliefs about contingent states of

affairs.

For my part, I do not see how Davies' examples can properly be considered apriori. He

says that I am entitled to believe these things so long as there is no contradictory evidence, but

how do I know apriori whether there is contradictory evidence or not? I need to know there is

no contradictory evidence for my belief to be justified, but I can only know this aposteriori.

Furthermore, the belief that I have hands was formed aposteriori; I had to see my, or perhaps

someone else's, hands. It seems that if anything here is apriori it is the epistemic warrant 'I am

entitled to believe x so long as there is no evidence to the contrary', where 'x' is a variable

ranging over a certain type of belief. If this warrant, or something like it, is true at all it is

necessarily true, so Davies does not bolster the case for the contingent apriori.

Davies gives the following reduction adabsurdum. Suppose there is a truth, s, which is

both able to be known apriori and deeply contingent. Now, s is true iff a certain state of affairs,

S, obtains. However, S may or may not obtain; there is no guarantee that it will obtain (i.e. it is

not a deeply necessary truth). Davies says that this may appear to be a contradiction since s

would as a guarantee of S, but says this is a confusion between the modal and the epistemic

notion of 'guarantee'.6 What is needed is a step showing that if S is not modally guaranteed than

it cannot be epistemically guaranteed (by s or any other proposition), but Davies notes how

similar this is to the assertion that if something is apriori, then it is deeply necessary the very

thing we wished to prove (103).




6 Though Davies does not say exactly what this amounts to, he says s acts as an epistemic guarantee for S, but S is
not modally guaranteed.









So in the end, while Davies admits that there are strong intuitions (at least for some)

against the possibility of contingent, apriori truths, he has given us no reason to doubt the

possibility, nor does he claim to. Note that while Bostock's claims about the impossibility of

(philosophically interesting) contingent, apriori were much stronger than Davies, his use of two-

dimensional modal logic did not present any problems more substantial than those Davies raises.

Conclusion

Casullo's paper helped us understand the problems with the Kripkean examples and how

our current candidate does not fall prey to those problems. It did, however, reveal the need for

an analysis of our current candidate. We have seen that a viable analysis of 'is an actual genius'

can be given that not only allays concerns about the meaning of 'All actual geniuses are

geniuses', but also separates the question of the contingent apriori from questions about the

knowledge of one's actuality. The two-dimensional modal logic of Davies and Humberstone has

helped us understand our current candidate by revealing how the rigid designation accomplished

by 'actual' affects the modal status of the proposition. We can also conclude that we have seen

no reason to doubt that 'All actual geniuses are geniuses' is both contingent and apriori, and that

(bar some refutation being given) we should accept it as such.









A NON-INDEXICAL CANDIDATE FOR THE CONTINGENT A PRIOR

Introduction

It is interesting that all of the candidates considered thus far have relied on indexicality in

some way. In some cases this is clear, and in others the indexicality would be revealed if we

were to analyze the proposition in question. One might be tempted to think that the contingent a

priori, if there is any such thing, depended upon indexicality. Timothy Williamson, however,

wishes to separate indexicality from questions about the contingent a priori by providing and

defending an indexical-free, contingent, apriori truth.

Williamson and Oppy's Conversation

Williamson begins by suggesting the following:

(1) There is at least one believer.1

Williamson notes that 'is' must be read tenselessly if the proposition is to be indexical-free. It is

clear, setting aside for the time being the worry that God is a necessarily existing believer, that (1)

is contingent. However, does one know (1) apriori?

Williamson writes, "Now since it is impossible to believe (1) falsely, it seems that one

can know (1) a priori" (114). Does this condition ensure a priority? At the end of his paper

Williamson briefly discusses the problem of providing a formal definition of 'a priori'that lines

up with our understanding of how the term should be employed. He provides a couple of

examples, shows how they are problematic, and concludes by saying that while one might

question whether his condition is necessary, it is certainly sufficient. While he does not say why,

I believe it is because the nature of a posteriori truths would seem to require that it be possible

that they be believed falsely. Thus, anything which is impossible to believe falsely must be a

priori. I see no problem with this, and agree that Williamson's condition is at least sufficient.

1 Analysis, 46.3, June 1986 (pgs. 113-117). The C. ',i,,A,. rA Priori: HasIt, i, lr,,l. To Do With Indexicals?









But now the worry is that one cannot know (1) without the use of indexicals. While (1)

does not contain them, it is arguable that one cannot know that (1) is true without knowing:

(2) I am a believer.

If this is true we are presented with a dilemma. We can either admit that indexicality is, even in

this case, required for something to be a contingent, a priori truth, or we can say that (2), and

thus (1) as well, is not a priori at all because it is based on introspection. Therefore, we either

have yet another indexical-based example of the contingent apriori, or no example of it at all.

Williamson responds by arguing that one can know (1) a priori without the use of (2).

He begins by providing the following method of forming beliefs:

(M) Given a valid deduction from the premise that someone believes that P to the conclusion
that P, believe that P.

The set of beliefs formed according to this principle, or belief-forming mechanism, would

include only true beliefs (that is, (M) is infallible). Since this fact can be known a priori it

follows that any knowledge produced in accordance with (M) is itself known apriori so long as

the "input" is knowable apriori. If we replace P with (1), the deduction from,

(3) 'Someone believes that there is at least one believer',

to (1) is clearly valid (115). Looking at (M), we see that the deduction from (3) to (1) is the

input. We can certainly know that the deduction is valid apriori, so we have an apriori warrant

for believing (1), a contingent truth.

(M) can also be used to generate other indexical-free, contingent, a priori truths. For

instance, 'There is at least one thing which exists' is certainly contingent, and by (M) we can

know it apriori without reference to the 'I exist'.

Williamson concludes his argument by addressing the objection that God is a necessarily

existing believer, thus making (1) necessary rather than contingent. We can modify (1), getting:









(1') There is at least one fallible believer.

The deduction for (M) goes as follows. If someone believes that (1'), this being is either fallible

or infallible. If fallible, then (1') follows trivially. If infallible, then the being's belief that (1')

must be true. So, we can know (1') a priori, and it is certainly contingent since there are possible

worlds in which God, an infallible believer, is the only believer that exists.

In "Williamson and the Contingent A Priori" Graham Oppy denies that Williamson has

adequately supported his conclusion.2 Oppy begins by arguing that the way (M) is formed hides

the fact that it actually contains an indexical (189). Rather than putting things in the imperative

(i.e. 'believe p'), Oppy suggests two ways one could use (M).

(M') If from the fact that I believe that P it follows that P is true, then I shall have a true
belief if I believe that P.

(M") If from the fact that someone believes that P it follows that P is true, then anyone can
form a true belief by believing that P.

(M') is clearly problematic because of the indexical. Oppy argues that because (M") is

universally quantified and (1) is existentially quantified, while we can know (M") apriori, it has

not been shown that we can know (1) apriori.

Before continuing with Oppy's paper let's look more closely at his claim. If things are as

he says and one is trying to infer an existential from only a universal, then his objection would be

valid because of the lack of existential import. However, this is not the case. We are inferring (1)

not from (M), but from 'Someone believes that (1)', another existentially quantified statement.

On the basis of this deduction the universally quantified 'Anyone can form a true belief by

believing that (1)' is made by way of (M), but this suffers no problems with existential import.

Oppy's objection, therefore, is unsubstantiated.



2 Analysis, 47.3, October 1987 (pgs. 188-193)









Oppy has misunderstood (M). (M") is intended to be a proposition in a deduction, while

(M) is a belief-forming mechanism, not a proposition. Furthermore, it is (in some ways) similar

to the reading that Oppy anticipates Williamson would use in replying to his objection (190).

Oppy formulates this reading as:

(APK) Bxp -p p

Therefore, p.

He notes that it is similar to modusponens except that it is only truth-preserving when used. He

then argues that even on this reading of (M) the inference to (1) is not justified.

Oppy has us suppose that there is a computer that exists in a world in which there are no

subjects (i.e. no one who has beliefs). If this computer operates in accordance with modus

ponens it will produce only true results, but this is not so for APK. The machine will generate

'There is at least one believer', which is false. Therefore, any inference based on APK would

not be valid.

Oppy admits that this objection is somewhat questionable, but I believe that it is

hopelessly flawed. Let's remember that the purpose of (M) is to produce truths that are

impossible to believe falsely. So, does the thought experiment above disprove Williamson's

claim? No. The computer does not have beliefs at all, so it certainly does not have any false

beliefs. If it did have beliefs, then (1) would be true. Let us, therefore, move on to another

objection Oppy lays out.

Consider a subject with limited self-awareness (i.e. who can competently use words like

'believer' without knowing that the terms apply to him) (192).3 Now, as far as he knows his

world has no subjects. So, what will keep him from concluding, via APK, that some world other

than his own, which happens to be subject-less, has at least one believer? Oppy believes that it is

3 This presumably helps to avoid sneaking in knowledge based on indexicals.









a hidden indexical, linking the conclusion to the world of utterance (i.e. the actual world). After

all, someone wishing to use APK can only use it validly in her world, though there is no explicit

reference to her world or her as the believer which satisfies the condition.

Oppy says that one might object that we "simply take it for granted" that we are talking

about the world of utterance when there are no explicit operators or indexical elements. He says,

however, that this is irrelevant since it is a pragmatic concern; logically, we must take such

indexicality into account. Oppy suggests the following representation of APK, and thus

formalization of (M):

Bxp p

Therefore, p(a),

where (0) is an operator which fixes the world at which p, and thus the whole argument, is to be

evaluated as the world of utterance. Therefore, Oppy concludes, Williamson's argument

provides no reason to think that one can separate the contingent apriori from indexicality (193).

In "The Contingent A Priori: A Reply", Williamson responds to Oppy's objection.4

Williamson argues that APK is not an accurate representation of (M), and that APK itself is

problematic (219). Williamson writes, "[I]f p is false and believed by no one, APK will take you

from the vacuously true supposition Bxp -* p to the false supposition p." Williamson says that

the following would be more similar to (M) and would also produce indexical-free examples of

the contingent a priori:

(MAPK) Given the belief that if someone believes that P then P, believe that P.

He remarks that both (M) and (MAPK) should be understood, not as inference rules, but as

"something like abstract mechanisms for generating beliefs."



4 Analysis, 48.4, Oct. 1988 (pgs. 218-221)









There are two problems with Williamson's remarks here. First, he is operating with a

rather radical notion of the a priori. As Fitch points out, if our experience is used to justify our

belief in the proposition, rather than simply help us acquire the requisite concepts, then our

knowledge should not be considered a priori. Thus, knowledge produced by (M) and (MAPK)

is not a priori.5 (MAPK) is suspect for an additional reason. The belief 'If someone believes

that P then P' could be false. For instance, I could believe that if someone believes that pigs can

fly then pigs can fly. In this case, (MAPK) would generate the false 'Pigs can fly'. Thus both

(M) and (MAPK) fail to be truth-preserving.

One might also worry that the imperative mood of (M) and (MAPK) is masking some

sort of indexicality (that is, that it is a trick for hiding the indexicality that would be clear if (M)

or (MAPK) were put in propositional form as part of a deduction. However, since (M) and

(MAPK) are belief-forming mechanisms rather than steps in deductions, Williamson's examples

do not make use of indexicals in the way Oppy believes it does. Therefore, while there may be

reasons to be worried about Williamson's account, they are by no means decisive rebuttals of it.

Williamson notes that Oppy's indexicalized APK suffers from the same problems as the

version without indexicals and, as a result, fails to be truth preserving (220). If, however, one

tries to show that (MAPK) fails to be truth-preserving in the case of the subject-less world this

attempt will fail because the input, 'If someone believes that in w there is at least one believer

then in w there is at least one believer,' is itself false.

Williamson addresses a possible concern that Oppy mentioned but did not dwell on.

What of the objection that it is questionable whether someone who does not know that he is a

believer understands 'There is at least one believer'? Williamson writes,

5 It is possible that Williamson's thoughts about the nature of the a priori stem from his Reliablist position.
However, since the other authors we've discussed all seem to accept the more traditional notion of the a priori, it is
outside the scope of this paper to investigate the case for Williamson's notion.









"What should also be noted is that even if a negative answer were correct, it would

constitute no objection to my argument. For it would not show my a priori knowledge

(with understanding) of the contingent truth that there is at least one believer to be

indexical-dependent in any sense not applicable to my a priori knowledge of the

necessary truth that all believers are believers."

One could, of course, argue that we cannot know 'All believers are believers' apriori because of

the sort of experience necessary to acquire the concept 'a believer', but this seems implausible,

and would undermine many of the traditional examples of the a priori.

Conclusion

While Oppy's objections to Williamson's examples are off the mark, there are reasons to

doubt that his examples give us examples of the contingent apriori. Both (M) and (MAPK) fail

to be truth-preserving in worlds without subjects, albeit for different reasons. Furthermore, we

could at least question whether the examples are really indexical-free because of the imperative

mood. It would seem, therefore, that Williamson does not give us a reason to believe that the

contingent apriori can be separated from indexicality.









CONCLUSION

In what follows I want to briefly review each of the sort of candidates considered,

summarizing why they are or are not true examples of the contingent apriori. I will also point to

the ways in which the failure of the earlier candidates shaped the formation of the later ones.

The incorrigibilityy" examples were dismissed rather quickly by Fitch. The problem with

this class of examples is that they do not qualify as apriori truths. They all depend on

experience in order to provide justification for belief in the proposition in question. While even

legitimate examples of the a priori depend on experience, it is to acquire the concepts involved

rather than justify belief in the proposition.

The Kripkean examples (the "Standard Meter Bar", "Neptune", etc.) fail to be examples

of the contingent apriori. The main problem with this sort of example, revealed by Donnellan

and Fitch, is one of the results of the act of rigid designation (that is, the stipulative introduction

of the name involved). The name lacks sense, so it is impossible to know what the sentence

means without having knowledge of a particular (the referent); thus, we cannot know the

proposition a priori. The upshot of this sort of candidate is if we could know the truth the

proposition expresses, the rigid designation allows us to say things about a particular that are true

apriori in this world and false in some possible worlds.

To avoid the problems with the Kripkean examples, some have suggested examples using

'actual' and its variants, which allow for rigid designation without robbing any of the terms of

their sense. These examples hang on a distinction between the world that determines the

extension of the predicate or truth of the proposition and the world at which the proposition is to

be evaluated. While Bostock tries to show that the utilization of this distinction requires changes

in our system of modal logic and a dissociation of the notion of 'necessity' from "truth in all









possible worlds", I show that his assertions are questionable at best. In addition, whatever merit

his observations have applies only to wide-scope uses of 'A', leading me to suggest a candidate

that relies on a narrow-scope use of 'A': 'All actual geniuses are geniuses'. I also dismiss

Bostock's 'If there is exactly one object that falls under the predicate, then it is necessary that

there is no more than one'. To understand the sentence one must understand the rigidified

predicate in question. However, one cannot understand it apriori because, like the Kripkean

examples, it lacks sense, and Donnellan and Fitch show us it would take knowledge of the

particulars involved, something we can only have aposteriori, to understand the predicate.

I then re-consider objections by Donnellan, Kitcher and Bostock, demonstrating that 'All

actual geniuses are geniuses' can be known apriori and that knowledge of this truth produces

more than just linguistic knowledge. In response to the objection that perhaps the meaning of the

sentence is still unclear, I provide a viable analysis that utilizes a distinction between knowledge

by description and knowledge by acquaintance. This distinction helps reveal how the current

candidate differs from the former ones. The previous candidates involved proper names. Since

proper names are singular referring terms, more is required to have knowledge of the referent of

a proper name than is required for a definite description, a denoting expression. This helped us

see more clearly why the previous candidates failed where the current candidate succeeds.

The paper by Davies, while not giving us a reason to doubt our current candidate, helped

us under the trick being accomplished by 'actual'. By allowing us to vary the world of

evaluation, 'actual' and its variants increases the power of our modal system, allowing us to

assert and evaluate things we could not before. It is the increased power that allows for

examples of the contingent apriori to be produced.









Williamson, wanting to separate the question of the contingent a priori from indexicality,

sought to offer an indexical-free, contingent, apriori truth. However, as we saw, his examples

failed, strengthening the case that it is the special sort of indexicality of 'actual' that allows for

examples of the contingent apriori.









LIST OF REFERENCES

Bostock, David. "Necessary Truth and A Priori Truth." Mind, New Series, Vol. 97, No. 387, Jul.,
1988 (pp. 343-379)

Davies, Martin. "Reference, Contingency, and the Two-Dimensional Framework." Philosophical
Studies, 118, 2004 (pp. 83-131)

Donnellan, Keith. "The Contingent A Priori and Rigid Designators." Contemporary Perspectives
in the Philosophy of Language, eds. French, Uehling, and Wettstein. University of
Minnesota Press, 1980 (pp. 45-60)

Fitch, G.W. "Are There Contingent A Priori Truths." The Journal of CriticalAnalysis vol. 6,
no. 4, Jan./Apr. 1977 (pp.119 123)

Kitcher, Philip. "A Priority and Necessity," from Australasian Journal ofPhilosophy, 58, 1980
(pp. 89-101)

Kripke, Saul. Naming and Necessity. Harvard University Press. 1980

Oppy, Graham."Williamson and the Contingent A Priori."Analysis, 47.3, Oct. 1987
(pp. 188-193)

Williamson, Timothy. "The Contingent A Priori: A Reply."Analysis, 48.4, Oct. 1988
(pp. 218-221)

Williamson, Timothy. "The Contingent A Priori: Has It Anything To Do With Indexicals?"
Analysis, 46.3, June 1986 (pp. 113-117).









BIOGRAPHICAL SKETCH

Daniel Carter McCain was born on July 16, 1982 to Daniel Ross McCain and Doris

Carter McCain. He was raised in Jacksonville, Florida and graduated from Englewood High

School in 2000. He also attained the rank of Eagle Scout in the Boy Scouts of America. Carter,

as he prefers being called, attended the University of South Florida and then the University of

North Florida, where he graduated cum laude with a B.A. in philosophy in 2004.

After graduating from the University of Florida in 2006 with an M.A. in philosophy, he

will marry Karen Garito and transition into professional ministry with the Graduate and Faculty

Ministries branch of InterVarsity Christian Fellowship. His long-term goals are to attend

Seminary, attain an M.Div., and to eventually serve in a pastoral role at a local church.