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NECESSITY AND APRIORICITY
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
2007 Shawn Burtoft
TABLE OF CONTENTS
A B S T R A C T ........................................... ............................. 4
1 INTRODUCTION ............... ............................................................ .5
Prelim inaries ........... .......................................... ......................... .......... .......
N ecessity/Contingency ...................... ...... ...................... .. ...................
A priori/A posteriori ............. ....... .................................. .......... ........ .... ......... .. 6
The Traditional View ...................................................8
The Challenge to the Traditional V iew ............................................................. ...............10
T hesis and Strategy ...................................... ............................ .... ................ 11
2 ID EN TITY STA TE M E N T S........................................................................ .....................14
N atu ral K in d s ...............................................................................................17
3 'ACTUAL', 'ACTUALLY', 'DTHAT' .......................................................... ...............19
T h e A ctu a l F .................................................................................19
K plan' s 'Dthat' Operator ......... .. ................ .................. ..... ...... .. .. ............ 21
A ll A actual F s are F s ...........................................................................23
A ctu ally P ........................................................ ...................................2 4
4 STATEMENTS ABOUT ESSENTIAL PROPERTIES.............................. ...............27
5 R E F E R E N C E F IX IN G ..................................................................................................30
6 THE ROLE OF THE LINGUISTIC VEHICLE................................. ...................... 34
Sentences vs. Propositions ................................................... .............. .. ...... 37
Frege's Puzzle ................................................... 38
L IST O F R E F E R E N C E S .............................................................................. ...........................46
B IO G R A PH IC A L SK E T C H .............................................................................. .....................48
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
NECESSITY AND APRIORICITY
Chair: Kirk Ludwig
My aim in this thesis is to show 1) that the standard examples of aposteriori necessity and
a priori contingency are not counterexamples to the traditional view of the relation between
necessity and aprioricity, and 2) that such examples rest on a common confusion, viz., failing to
recognize the role the linguistic vehicle plays in the suggested epistemic status of such examples.
I begin by pointing out a puzzle that arises in all such cases: for each alleged counterexample, C,
the considerations which are taken to show that C is necessary/contingent entail that there are
two sentences which express the same proposition though when considered, as it were, under the
aspect of one sentence is said to be apriori and under the aspect of the other is said to be a
posteriori. This results in three inconsistent claims of this form: it is apriori that; it is not a
priori that q; that = that q. If all three claims are true, it follows that there is a proposition
which is apriori and not apriori. Thus, on pain of contradiction, one of the three claims must be
rejected. I will argue that, in each case, rejecting either of two of the three claims rules out the
example as a counterexample to the traditional view, while rejecting the third is untenable. If this
is right, then, in each case, we can show that we do not after all have a counterexample to the
In this thesis, I will be considering a range of alleged examples of aposteriori necessity
and apriori contingency. For my purposes, it will not be necessary to give analyses of necessity
and priority, but it will be useful to fix some ideas at the outset. The following remarks and
schemas are meant to explicate some intuitive notions and equivalences that are the background
of the subsequent discussion.
For reasons that will emerge later in the discussion, I will distinguish between attributing
modal and epistemic properties to sentences and propositions. Propositions will be thought of as
they traditionally have been, as reified sentence meanings, insofar as they contribute to
determining under what conditions a sentence is true or false. To say that two sentences sl and s2,
in some language L, express the same proposition is to say that sl and s2 are synonymous in L.
When si and s2 are sentences in distinct languages, L1 and L2, we can say that they express the
same proposition iff s in L1 and s2 in L2 are intertranslatable. For simplicity, I ignore context
sensitive sentences, such as those involving indexical terms and those whose truth-values vary
from use to use because of tense. One example we will look at contains an indexical term but it
should be clear from the discussion that nothing hinges ignoring its context sensitivity.
Everything I need to say could be reformulated to adjust for context sensitivity.
I will be assuming the equivalences expressed in the following schemas, where 'p' is a
schematic letter for propositions and 's' is used for names or descriptions of sentences.
* It is necessary thatp iff it is not possible that it is not the case that.
* It is contingent thatp iff it is the case thatp and it is not necessary that p.
* s is necessarily true (in L) iff it is not possible that s is not true (in L).
* s is contingently true (in L) iffs is true (in L) and s is not necessarily true (in L).
Occasionally, I will employ the terminology of possible worlds. While I do not take
possible worlds talk to be basic, it is a useful heuristic when evaluating some of the examples we
will consider. In those instances, the relation between necessity, possibility, and contingency will
be understood as follows:
* It is necessary thatp iff it is the case thatp in every possible world.
* It is possible thatp iff it is the case thatp in some possible world.
* It is contingent thatp iff it is the case thatp in the actual world and it is not the case that
in every possible world.
* s is necessarily true (in L) iffs is true (in L) in every possible world.
* s is possibly true (in L) iffs is true (in L) in some possible world.
* s is contingently true (in L) iffs is true (in L) in the actual world and s is not true (in L) in
every possible world.
To say that something is apriori is to say that it is knowable independently of experience,
and, intuitively, this is just to say that there is a way of knowing it, or coming to know it, which
does not require empirical investigation. The sorts of things which are generally said to fall under
this category include logical and mathematical truths, e.g., propositions expressed by sentences
of the form 'P or -P' and '((P -* Q) & P) -* Q)', 'a is a', or the propositions expressed by '2 +
2 = 4', '2 > 1', etc., or axioms of formal systems like geometry, e.g., that a line contains at least
two points, and certain propositions which appear to be true, in some sense, by definition, such
as the proposition that all bachelors are unmarried males. These are typical examples of
propositions which are said to be apriori. By contrast, that the Earth is the third planet from the
Sun, that lions are carnivores, that the capital of France is Paris, and that Thomas Jefferson wrote
the Declaration of Independence are taken to be truths which are not knowable independently of
experience, and, hence, examples of aposteriori truths.
It should be noted that being knowable apriori appears to be relative, in some cases, at
least, to particular subjects, that is, it seems that in some cases a proposition may be knowable
(not just known) a priori by some but not by others. Consider the proposition expressed by
'Samuel Clemens is Mark Twain'. This is one of the standard examples of an aposteriori
necessity. But what was the epistemic status of this for Mark Twain? It seems that he, at least,
knew it to be true apriori, i.e., without empirical investigation. But it seems that it is not the case
that it is even knowable a priori for everyone. This seems to be the way Kripke (1980, p. 56) is
thinking about the apriori in his discussion of his standard meter bar example in Naming and
Necessity, as in the following passage.
What then is the epistemological status of the statement 'Stick S is one meter long at tO',
for someone who has fixed the metric system by reference to stick S? It would seem he
knows it a priori. For if he used stick S to fix the reference of the term 'one meter', then as
a result of this kind of 'definition'... he knows automatically, without further investigation,
that S is one meter long.... So in this sense, there are contingent a priori truths.
It is clear in this case that Kripke is assuming that this is not so for someone who has not fixed
the metric system by reference to stick S. That is, for many others at least, that S is one meter
long, Kripke is assuming, will neither be known a priori nor be knowable a priori. This suggests
that we shouldn't think that there are a priori truths simpliciter-i.e., that an a priori truth is
simply one which is knowable apriori by someone. Instead, it would be better to think of the
properties being apriori and being aposteriori as fundamentally relational properties, i.e., as
relating propositions/sentences to particular subjects. We can represent this as follows, where we
let 'k' stand for some knower.
* It is a priori thatp for k iff that p is knowable for k independently of experience.
* It is a posteriori thatp for k iff it is knowable thatp for k and it is not a priori for k that p.
* s is true a priori (in L) for k iff it is knowable that s is true (in L) for k independently of
* s is true aposteriori (in L) for k iff it is knowable that s is true (in L) for k and s is not true
a priori (in L) for k.
The Traditional View
The distinction between the apriori and aposteriori was first drawn clearly in the Modern
period. Hume and Leibniz identified apriori propositions with necessary and analytic
propositions. Leibniz (1714, 33) called such propositions "truths of reasoning" and contrasted
them with "truths of fact."
Truths of fact are contingent and their opposite is possible. When a truth is necessary, its
reason can be found by analysis, resolving it into more simple ideas and truths, until we
come to those which are primary. Primary principles cannot be proved, and indeed have no
need of proof; and these are identical propositions whose opposite involves an express
Hume (1698, p. 40) made a similar distinction between what he called "relations of ideas" and
"matters of fact."
All the objects of human reason or inquiry may naturally be divided into two kinds, to wit,
"Relations of Ideas," and "Matters of Fact." Of the first kind are the sciences of Geometry,
Algebra, and Arithmetic, and, in short, every affirmation which is either intuitively or
demonstratively certain. That the square of the hypotenuse is equal to the square of two
sides is a proposition which expresses a relation between these figures. That three times
five is equal to half of thirty expresses a relation between these numbers. Propositions of
this kind are discoverable by the mere operation of thought, without dependence on what is
anywhere existent in the universe.... Matters of fact, which are the second objects of
human reason, are not ascertained in the same manner, nor is our evidence of their truth,
however great, of a like nature with the foregoing. The contrary of every matter of fact is
still possible, because it can never imply a contradiction....
Kant departed from this picture in one important respect, in the Critique of Pure Reason,
suggesting that there are some apriori truths which are not analytic, i.e., not "truths of
reasoning" or about "relations among ideas." For instance, he held that certain truths of
arithmetic, while apriori, were .ynl/heii. One example Kant gives is the proposition that 7 + 5 is
12. Kant took analytic propositions to be those in which the concept of the predicate is contained
in the concept of the subject.1 He maintained that the proposition that 7 + 5 is 12 did not meet
1 While, strictly speaking, propositions don't contain subjects and predicates, the use of these grammatical
categories helps represent the intuitive structure of the proposition expressed by subject-predicate sentences.
this criterion because the concept of 12 is not obtained by merely considering the union of 5 and
7. Yet it is clearly apriori since we can know the proposition without appeal to experience. In
this sense, he believed that there were synthetic apriori truths.
However, while Kant (Ibid., p. 38) differed from Hume and Leibniz in this respect, he
followed them in identifying the apriori with the necessary:
Now, in the first place, if we have a proposition which contains the idea of necessity in its
very conception, it is a judgment apriori; if, moreover, it is not derived from any other
proposition, unless from one equally involving the idea of necessity, it is absolutely a
priori. Secondly, an empirical judgment never exhibits strict and absolute, but only
assumed and comparative universality (by induction); therefore, the most we can say is-
so far as we have hitherto observed-there is no exception to this or that rule. If, on the
other hand, a judgment carries with it strict and absolute universality, that is, admits of no
possible exception, it is not derived from experience, but is valid absolutely apriori.
This view was also widely held among the early analytic philosophers who, despite Kant's
challenge, largely also identified the apriori with the analytic and the necessary. Ayer (1952, p.
31), for instance, is very explicit about this in Language Truth and Logic, a classic statement of
the widely influential views of the Logical Positivists:
Like Hume, I divide all genuine propositions into two classes: those which, in his
terminology, concern "relations of ideas," and those which concern "matters of fact." The
former class comprises the a priori propositions of logic and pure mathematics, and these I
allow to be necessary only because they are analytic. That is, I maintain that the reason
these propositions cannot be confuted in experience is that they do not make any assertion
about the empirical world, but simply record our determination to use symbols in a certain
Wittgenstein (1922, 5.525) took a very similar line in the Tractatus Logico-Philosophicus,
which served as an inspiration for the Vienna Circle and the Logical Positivists. He held that a
priori/necessary truths were tautologies and contrasted these with what he called "propositions
The certainty, possibility, or impossibility of a situation is not expressed by a proposition,
but by an expression's being a tautology, a proposition with sense, or a contradiction.
Propositions with sense give us information about the world and are contingent. Tautologies (and
contradictions), by contrast, are only said to be meaningful in the sense that they provide us with
information about the use of symbols in our system.
And, while Russell (1931, p. 103) wasn't as explicit on this point, it appears that he had
similar considerations in mind when he argued, in The Problems ofPhilosophy, that "all apriori
knowledge deals exclusively with the relations of universals," and took the truths of logic to be
One feature common to all these suggestions, including Kant's, is the view that all apriori
propositions are necessary and, conversely, that all aposteriori propositions are contingent.2 I
will refer to this as the traditional view. It can be expressed in the claim that all instances of (T)
(T) It is necessary that *- it is apriori that.
Up until the last half of the Twentieth Century, this was the accepted view regarding the
relation between the apriori and the necessary.
The Challenge to the Traditional View
The traditional view came under attack starting with the work of Saul Kripke. In his book
Naming and Necessity, which began as a series of lectures at Princeton in 1970, Kripke presents
a number of apparent examples of aposteriori truths which are necessary and a priori truths
which are contingent. Since then the number and range of such examples has grown and it is now
generally held that the relation between necessity and priority is not nearly as close as the
traditional picture suggests. For example, Scott Soames (2003, p. 372) writes:
2 Kripke talks as though 'a priori' and 'necessary' were taken to be synonymous, but I haven't come across any
evidence to suggest that the relation was taken to be anything stronger than necessarily extensional equivalence.
From our perspective today, we can see that not all necessary truths are a priori, not all a priori
truths are necessary, and not all members of either class are transparently so.
In a similar vein, Paul Boghossian and Christopher Peacocke (2000, p. 31), write:
Being a priori is to be sharply distinguished from being necessary.... Examples, and
reflection on the nature of the properties, both show that there are a priori propositions
which are not necessary. Kripke and Kaplan supplied conclusive examples.... Conversely,
in the presence of examples of the necessary a posteriori, it is clear that a proposition's
being necessary does not ensure that it is a priori.
The following is a list of some of the putative examples of the necessary aposteriori and
* Hesperus is Phosphorus
* Water is H20
* Actually, Kripke is a philosopher
* If Earth exists, then Earth is a physical object
* All actual philosophers are philosophers
* If someone wrote the Declaration of Independence then the actual person who wrote the
Declaration of Independence wrote something.
* If someone wrote the Declaration of Independence then dthat(the person who wrote the
Declaration of Independence)3 wrote something.
* S is one meter long at t (for someone who fixes 'one meter' by reference to the length of S
I will take up each of these examples and why they are thought to have the modal and epistemic
status suggested in the body of this thesis.
Thesis and Strategy
My aim is to show, not only that the standard examples of a posteriori necessity and a
priori contingency aren't counterexamples to the traditional view, but also that they rest on a
3 The expression 'dthat(the F)' is a term introduced by David Kaplan (1978) which by stipulation refers directly, in
the sense of contributing only an object to the proposition expressed by a sentence containing it, namely, the object,
if any, which is the denotation of 'the F'. See Chapter 3 for discussion.
common confusion, that of failing to recognize the role the linguistic vehicle plays in the
suggested epistemic status of such examples. The strategy is as follows. I begin by pointing out a
puzzle that arises in all such cases: for each alleged counterexample, C, the considerations which
are taken to show that C is necessary/contingent entail that there are two sentences which express
the same proposition though when considered, as it were, under the aspect of one sentence is said
to be apriori and under the aspect of the other is said to be aposteriori. This results in three
inconsistent claims of the following form.
* It is a priori that.
* It is not a priori that q.
* Thatp = that q.
Claims (i)-(iii) imply that there is a proposition which is apriori and not apriori. Thus, on pain
of contradiction, one of the three claims must be rejected. I will argue that, in each case, rejecting
either of two of the three claims rules out the example as a counterexample to the traditional
view, while rejecting the third is untenable. If this is right, then, in each case, we can show that
we do not after all have a counterexample to the traditional view.
I will begin, in Chapter 2, by considering alleged cases of a posteriori identities, those
involving proper names as well as so-called theoretical identities involving natural kind terms. In
Chapter 3, I'll look at examples that arise from the use of 'actual' and 'actually' as well as
related cases involving Kaplan's thata' operator. Chapter 4 deals with examples that appeal to
essential properties. In Chapter 5, I will consider the sorts of cases that arise from stipulative
reference fixing, such as Kripke's example of the standard meter bar in Paris. In the final
chapter, Chapter 6, I'll lay out the argument sketched above in greater detail and then conclude
by noting some striking linguistic similarities that all such examples seem to share which
suggests an explanation to the initial puzzle: the modal status of each example is based on the
proposition expressed whereas the epistemic status is based, at least in part, on knowledge about
the terms used to express it.
Kripke (1980) argued famously that certain identity statements of the form 'a is b', where 'a'
and 'b' are proper names, such as (1) and (2), if true, are necessarily true and true aposteriori.
(1) Hesperus is Phosphorus
(2) Butch Cassidy is Robert LeRoy Parker
They are said to be necessarily true because it is assumed that, for any x and y, ifx = y then
necessarily x = y. Call this the identity thesis (I).
(I) (x)(y)(x = y Ox = y)
According to Kripke, (I) is a thesis about objects:
It was clear from (x)O(x = x) and Leibniz's law that identity is an internal relation: (x)(y)(x
= y -* x = y). (What pairs (x, y) could be counterexamples? Not pairs of distinct objects,
for then the antecedent is false; nor any pair of an object and itself, for then the consequent
Cases like (1) and (2) are said to be examples of the latter, for the pair (Hesperus, Phosphorus) is
a pair of an object and itself, and the same goes for the pair (Robert LeRoy Parker, Butch
Cassidy).5 It follows, then, in conjunction with (I), that (1) and (2) express necessary truths.
On the other hand, such examples are said to be aposteriori because knowledge of them is
not a matter of reasoning alone, but requires some empirical work. As Frege pointed out, it was
considered a great astronomical discovery that Hesperus is Phosphorus. And it apparently came
as a surprise to many that Butch Cassidy was Robert LeRoy Parker because, according to wanted
posters, he was someone else.6
4 Ibid. (p. 3).
5 am assuming here that proper names refer directly; later in this chapter, I will consider the implications of a
Fregean view of proper names in such contexts.
6 According to wanted posters, Butch Cassidy was George Parker.
However, it is difficult to see why such examples are said to be aposteriori given the
argument that they are necessary. For example, if, as suggested, (1) is true because of (I) then it
is true because the pair (Hesperus, Phosphorus) is the same pair as (Hesperus, Hesperus)-
likewise, if (2) is true because of (I), it is true because the pair (Robert LeRoy Parker, Butch
Cassidy) is the same pair as (Butch Cassidy, Butch Cassidy). If this is right, then presumably (1)
and (lb) express the same proposition.
(lb) Hesperus is Hesperus
So there is a puzzle here: the reasons for thinking that (1) is necessarily true require that it
express the same proposition as (lb) yet the former is said to express an aposteriori truth
whereas the latter is generally thought to expresses an apriori truth. How do we account for
this? It seems to me that there are two possibilities, but neither accommodates the view that
examples like (1) and (2) are cases of aposteriori necessity.
One explanation is the Fregean line that the difference between sentences of the form 'a
is b' and 'a is a' is due to some difference in cognitive content. For example, 'Hesperus is
Phosphorus' may be held to express an aposteriori truth because there are distinct senses7
associated with 'Hesperus' and 'Phosphorus', which go into the propositions expressed by the
sentence, and it takes some empirical investigation to see that they pick out the same object. But,
while this view captures the intuition that the proposition expressed is aposteriori, it seems in
conflict with the reasons for supposing it is necessary. For example, if an accurate account of
what (1) expresses is something like (Ic),
(Ic) The first star visible in the evening is the first star visible in the morning
7 Here 'sense' can be taken as a general placeholder for any of the usual candidates: definite descriptions, modes of
presentation, primary intensions, etc.
then (1) is contingent (if true) because the descriptions 'the first star visible in the evening' and
'the first star visible in the morning' are not necessarily coextensive.
A rigidified description account would avoid this difficulty. This sort of account would
invoke modifiers that in effect turn definite descriptions into expressions which designate the
same object in every possible world. A common way of doing this is by prefixing the nominal of
a definite description with the term 'actual'. For example, the description 'the actual first star
visible in the evening' is said to pick out the same object in every possible world. If this is right,
then (Id) expresses a necessary truth.
(Id) The actual first star visible in the evening is the actual first star visible in the morning.
However, there are problems with this response on behalf of someone who holds that (1)
expresses an aposteriori and necessary proposition. For one thing, those who accept that such
examples are necessary and aposteriori tend to reject description theories of proper names. This
was part of the motivation, in fact, for seeing sentences such as (1) as expressing necessary truths
in the first place. So it is unlikely they would be willing to endorse such an account. For another
thing, in Naming and Necessity, Kripke made a convincing case against description theories in
general. Perhaps the most obvious problem is that proper names don't appear to be semantically
equivalent to definite descriptions. For instance, it's not required for competency in the name
'Aristotle' that one associate any definite description, rigid or not, with Aristotle (e.g., suppose
it's suggested that 'Aristotle' is equivalent to the description 'the (actual) man who taught
Alexander the Great'; one could fail to know that Aristotle taught Alexander the Great, yet be
able to use and understand sentences containing the name 'Aristotle'). In the next chapter, I will
argue that a further problem for the rigidified description account is that the use of 'actual', and
other such rigidifiers, give rise to the very same puzzle that arises in the case of proper names.
The other option is to say that what is a posteriori is that the terms flanking the identity
sign corefer-thus, the idea is that (1) is a posteriori because it is about, in part, the terms
included in it. One problem with this line is that it forces us to give up the intuitive view that
identity claims are about the referents of the contained terms. And, again, examples like (1) and
(2) are supposed to be necessary because of (I), which is a metaphysical thesis, not a linguistic
thesis. As Kripke ibidd. pp. 107-108) points out, "If you say for every x and y, ifx = y then
necessarily x = y, or something like that-no names occur in that statement at all, nor is anything
said about names." So, while the metalinguistic suggestion accounts for the intuition that such
examples are a posteriori, it is at odds with the reasons given for thinking that they're necessary.
If these statements were even in part about the names, why should they be necessary? It is surely
a contingent matter whether two names corefer.8
Similar considerations raise difficulties for the view that theoretical identity claims
involving natural kind terms are necessary aposteriori. If we assume, with Kripke and Putnam,
that the quantifiers in the identity thesis range over natural kinds as well as particulars, then the
suggestion that theoretical identity claims like (3) and (4) are examples of aposteriori necessity
results in the same puzzle.9
(3) Water is H20
(4) Gold is AU
8 This worry is insurmountable when we turn to true identity statements made using demonstratives such as 'this is
that'. Clearly those very uses of the demonstratives might have picked out things different from the ones they picked
out. So even if some story could be told about proper names, it would not be general enough to handle the problem.
9 I will not have anything to say in this thesis about the status of these examples if natural kinds terms are taken not
to be analogous to names. Thus, my conclusion here is conditional on the assumption that natural kinds terms
function like names of properties.
If (3) and (4) are said to be necessarily true because they are instances of (I) then they are
necessarily true in virtue of expressing the same propositions as (3b) and (4b), respectively.
(3b) Water is water
(4b) Gold is gold
Yet (3) and (4) are alleged to express aposteriori truths whereas (3b) and (4b) are true apriori.
The same solutions we considered in the case of proper names are available here, with the
same consequences. Either what is motivating the view that theoretical identities are aposteriori
is the thought that there are distinct senses associated with the natural kind terms flanking the
identity sign, or it is the thought that it is not apriori that such terms pick out the same natural
kinds. But, by parity of reasoning, neither solution appears to be compatible with the claims that
such examples are necessarily true.
In this chapter, I have been concerned with pointing out that there is a genuine puzzle that
arises in the cases of identity statements which are said to be a posteriori and necessary. The
puzzle is that given the reasons for thinking that such examples are counterexamples to the
traditional view leads to the view that there are two sentences which express the same
proposition though looking at it the one way and the other lead to different judgments as to
whether the proposition is a priori or a posteriori. In the following chapters, I aim to show that all
the alleged putative counterexamples give rise to the same puzzle.
'ACTUAL', 'ACTUALLY', THATA'
The Actual F
It is worth noting at the outset of this chapter that some philosophers hold that 'actual' and
'actually' do not make any difference to the modal status of propositions expressed by sentences
containing them. 10 If this view is correct, then none of the examples we will consider in this
chapter present problems for the traditional view. The purpose of this chapter is to show that,
even if 'actual' and 'actually' do affect the modal status of sentences/propositions they are
involved with in the way often assumed, the standard examples involving them can be shown to
result in the same puzzle that arises in regards to proper names and natural kind terms.
In certain contexts, the use of 'actual' and 'actually' is said to result in cases of aposteriori
necessity and apriori contingency. Consider an example offered by Soames (2005, p. 31):
(5) If someone wrote the Declaration of Independence then the actual person who wrote the
Declaration of Independence wrote something.
Contrast (5) with (5*)
(5*) If someone wrote the Declaration of Independence then the person who wrote the
Declaration of Independence wrote something.
This is (presumably) necessarily true, whereas (5) is said to be contingent. The reason is that the
description in (5*), viz., 'the person who wrote the Declaration of Independence' is non-rigid,
i.e., it does not designate the same individual in every possible world, whereas the description in
(5), viz., 'the actual person who wrote the Declaration of Independence' is said to be a rigid
designator, i.e., to pick out the same individual in every possible world. If this is right then
evidently the term 'actual' is playing a part in individuating the proposition expressed by (5). If
the proposition expressed by the sentence is what is evaluated at different possible worlds (which
10 Michael Jubien, for example.
is the assumption we are operating under, as our question is whether there are propositions which
are apriori but contingent), then what 'actual' appears to do in such contexts is modify the
predicates within its scope in such a way as to have us only consider their (actual) extensions and
disregard their intensions.11 In this sense, 'the actual F' functions in a way similar to Kaplan's
(1978) thata' operator: expressions of the form [dthat(the F)]12 work like directly referring
terms in that nothing more is contributed to the meaning of the sentence than the unique object
denoted by [(the F)], even though there is a term appearing in it which has an intension, and our
grasping its intension is relevant to our understanding what it picks out. In 'the actual F', 'actual
F' functions to introduce just the actual extension of 'F' into the propositions, and then the
denotation of 'the actual F' is just the unique thing, if any, in the extension of 'F'. The
proposition expressed is individuated with respect not to the intension of 'F' but with respect to
Now, the consequent of (5) is said to be contingently true because the actual denotation of
'the person who wrote the Declaration of Independence' might not have written anything.
However, if this is what the consequent of (5) says, then prefixing the nominal of any
contingently true description of Thomas Jefferson with 'actual' and plugging it in the consequent
should get the same result. Consider (6).
(6) If someone wrote the Declaration of Independence then the actual third president of the US
If 'actual' works as suggested, i.e., by narrowing our focus to just the actual extension of the
predicate in its scope, then (5) and (6) express the same proposition; the consequent in each case
1For a more detailed account of the semantics of 'actual' and 'actually' in modal contexts see Kirk Ludwig's "A
Conservative Modal Semantics with Applications to de re Necessities and Arguments for Coincident Entities."
12 I will be using the left '[' and right ']' square brackets for Quinean corer quotes.
is about the same person, as the same extension is introduced into the proposition. But while (5)
and (6) are contingent for the same reason, i.e., because it is not necessary that the denotation of
those descriptions wrote something, (6) it seems isn't true apriori.
Once again, we see the same kind of puzzle. Given the suggested counterexample, we are
led to the view that there are two sentences which express the same proposition though seen in
relation to one it appears a priori and in relation to the other a posteriori.
Kaplan's 'Dthat' Operator
As I mentioned, when 'actual' is added to the nominal of a definite description, it functions
in a way similar to Kaplan's thata' operator. Again, expressions of the form [dthat(the F)] work
like directly referring terms in that nothing more is contributed by it to the proposition expressed
by a sentence containing it than the unique object denoted by [(the F)]. We can express its
function in a reference clause in which the description is deployed in the antecedent of a
conditional to constrain the value of a variable, and the referent is given as the value of a
For any x, for any nominal N, the denotation of [(the N)] is x -* the referent of [dthat(the
N)] is x.
Designators of the form [the actual F] and [dthat(the F)] are said to be rigid designators-like
(directly referring) proper names, they pick out the same object in all possible worlds in which
they have referents.
It should be evident at this point why rigidified descriptions do not avoid the initial
problem involving proper names and natural kind terms. Recall that in 2 the question was
raised as to how distinct identity sentences could be said to express the same proposition yet
differ with regard to being apriori/a posteriori. For example, how can it be that (1), repeated
(1) Hesperus is Phosphorus
is true aposteriori and (lb), repeated here,
(lb) Hesperus is Hesperus
is true apriori if the sentences 'Hesperus is Phosphorus' and 'Hesperus is Hesperus' express the
same proposition? One explanation was that (1) is true aposteriori because there are distinct
senses/descriptions/intensions associated with the names 'Hesperus' and 'Phosphorus' and it
takes some empirical work to see that they track the same object. The problem with this account
was that it seemed to render (1) contingent. For if a correct account of what (1) expresses comes
to something like
The first star visible in the evening is the first star visible in the morning then it would not
be necessarily true, because the descriptions flanking the identity sign (even fixing their
meanings) do not necessarily denote the same objects. But now consider (8) and (9) as possible
accounts of the proposition expressed by (1).
(8) The actual first star visible in the evening is the actual first star visible in the morning.
(9) Dthat(the first star visible in the evening) is dthat(the first star visible in the morning).
Would such rigidified descriptive accounts of (1) accommodate the view that it is necessary a
posteriori that Hesperus is Phosphorus? No, because the same puzzle arises with respect to these
examples. Take (8). If (8) is necessarily true, it is so because it says that a particular object bears
the identity relation to itself. And this is a fact independent of how the object is picked out. Thus,
if (8) is necessarily true, it expresses the same proposition as (10).
(10) The actual first star visible in the evening is the actual first star visible in the evening.
But (10) is presumably apriori, not aposteriori, so this line leads to the same problem we began
with: two sentences express the same proposition though in relation to one of them we want to
say the proposition is aposteriori and in relation to the other that it is a priori.
Likewise, if (9) is necessarily true, then it expresses the same proposition as (11).
(11) Dthat(the first star visible in the evening) is dthat(the first star visible in the
But whereas (9) would have to be true aposteriori to account for the initial puzzle, there doesn't
seem to be any reason to suppose that (11) is true aposteriori.
Thus, appealing to rigidified descriptive accounts of proper names to address the initial
problem doesn't work. Evidently, then, the correct explanation of why examples like (1)-(4) are
said to be a posteriori must appeal to the alternative suggestion that knowledge about the
linguistic vehicle is playing a role in such cases. We will examine this suggestion in greater
detail in the final chapter.
All Actual Fs are Fs
There are also examples where the use of 'actual' is said to result in contingent apriori
truths. Compare (12) and (13).
(12) All philosophers are philosophers.
(13) All actual philosophers are philosophers.
(12) appears to be necessarily true and apriori; however, (13) is supposedly contingent and true
apriori. The idea here is usually brought out by appeal to possible worlds. For example, (13) is
analyzed as (13b), where '@' represents the actual world:
(13b) (x)(x is a philosopher in @ -* x is a philosopher)
This is contingent because there are possible worlds where it is false. Thus, 'actual' appears to do
the same work here as above: it narrows our focus to the actual extension of the predicate in its
scope. For instance, (13) says of a some particular individuals-those people who happen to be
philosophers-that they are philosophers, and this is a contingent truth since it is not necessarily
the case that all (or some) of those individuals are philosophers. But notice that the same
problem arises here: if this is what (13) says then it is difficult to see why it is thought to be true
apriori, because it is not an apriori truth that those individuals who happen to be philosophers
are philosophers. Take a similar case.
(14) All actual Brooklyn residents are Brooklyn residents.
If 'actual' works as suggested, then here 'actual' is modifying 'Brooklyn residents' in such a way
as to have us only consider its actual extension, i.e., those individuals who happen to be residents
of Brooklyn, and it isn't necessarily the case that those individuals are Brooklyn residents.
However, it isn't apriori, either, that those people are Brooklyn residents. Consider (15).
(15) All actual Kings County residents are Brooklyn residents.
If (14) is said to be contingent because it is about the actual extension of 'Brooklyn residents'
then (14) and (15) express the same proposition (the actual residents of Brooklyn and the actual
residents of Kings County are the same). But (15) it seems isn't true apriori (many Brooklyn
residents don't know (15) is true). So it appears we have another case where two sentences
express the same proposition, though considered in relation to one we want to treat it as apriori,
while considered in relation to the other we want to take it to be aposteriori.
Another formula for generating putative examples of necessary aposteriori truths is
'Actually, P', where 'P' is replaced by a sentence expressing a contingent truth, for example,
(16) Actually, Ted Kennedy is a Massachusetts senator.
In such cases, 'actually' is said to function as a modal operator, and, since all (true) modal
sentences are necessarily true, instances like (16) are said to express necessary truths. As with
the previous example, the idea here is usually expressed in terms of possible worlds; (16), for
example, is analyzed as (16b),
(16b) Ted Kennedy is a Massachusetts senator in @.
which, if true, is true in every possible world. Evidently, on this suggestion, 'actually' does the
same work as 'actual': in effect, it narrows our focus to just the actual extension of the predicate,
disregarding its intension. For instance, suppose we introduce the term 'menator' as follows with
the understanding that its meaning is exhausted by its extension.
(x)(x is a menator iffx is John Kerry or x is Ted Kennedy)
Using this term gets us the same result-(17) expresses the same proposition as (16).
(17) Ted Kennedy is a menator.
However, (17) is presumably true apriori for us since it is true by stipulation that 'menator' is
true of Ted Kennedy or John Kerry; anyone familiar with the procedure for introducing the term
'menator' knows that (17) is true apriori.
Another way of achieving this effect, of a sentence that expresses the same proposition as
(16) but in relation to which we want to say, in contrast to (16), that what is expressed is
knowable apriori, is by introducing a special form of predicate which makes the extension of
the predicate explicit and is understood to contribute only the extension that it makes explicit.
We introduce the predicate form, [ext(al, a2, a3, ...,)], which functions as follows, letting 'ai',
'I2', 'a3', ... range over proper names.
For any ai, (2, s3, ..., and any xi, x2, x3, ..., if Ref(al) = xi, Ref(a2) = X2, Ref(a3) = x3, ...
then [ext(al, a2, 3, ...,)] is true ofx <- x = xl or x = x2 or x = x3 or....
Here we take this to be giving extensionally the satisfaction conditions for the predicate form.
Now, given the way [ext(al, a2, a3, ...,)] works, (18) expresses the same proposition as (16).
(18) Ted Kennedy is an ext(Ted Kennedy, John Kerry).
This is perhaps a better example for our purposes than (17) because it makes explicit in a way
available to anyone who understands the sentence the information about (17) that is available
only to the ones privy to the introduction of the term. We can as it were read off from (18) that
the proposition it expresses is true: one who understands how [ext(al, a2, a3, ...,)] works can
look at (18) and know it to be true apriori, even without knowing the referent of 'Ted Kennedy'.
So, again, we have a systematic way of going from a class of sentences which are supposed to
provide examples of necessary aposteriori sentences to sentences expressing the same
proposition which seem to be knowable apriori.
I have argued that the view that the examples in this chapter have the modal status they are
said to suggests that 'actual' and 'actually' behave in such a way as to restrict our attention to
just the extensions of the predicates in their scope. If this is right, then the reasons given for
supposing that such examples are necessary/contingent leads to the same puzzle as with identity
statements-namely, that there are two sentences which express the same proposition yet which
in relation to one seems apriori and in relation to the other aposteriori.
STATEMENTS ABOUT ESSENTIAL PROPERTIES
Consider sentences of the form 'if a exists then Fa', where 'F' is thought to express an
essential property of a, and a property that cannot be known apriori to be instantiated by a, for
(19) If Earth exists then Earth is a physical object.
This appears to be necessarily true and true aposteriori. The view that it is necessarily true rests
on the claim that
For any x, if x is a physical object, then necessarily if x exists, x is a physical object.and
the fact that Earth is physical object. It appears to be aposteriori because we cannot know a
priori that Earth is a physical object, because this requires knowing among other things that it
exists, and we cannot know that it exists apriori.
It seems to me there is an intuitively compelling way of seeing that something is going on
here which is very similar to what is going on in the alleged cases of aposteriori identity. Let's
assume, as suggested, that (19) is not true apriori. Now, imagine that elsewhere in the galaxy
there is a planet (call it Planet-X) much like Earth. For the sake of simplicity, assume that people
there speak a language similar to English in that it shares the same grammar and most of the
same terms, and all the non-referring terms have the same intensions.13 However, due to certain
physical limitations, the astronomers on Planet-X cannot observe Earth with their instruments
(perhaps other celestial objects are always aligned in such a way as to block direct observation).
Nonetheless, their observations of the behavior of other celestial bodies in our solar system lead
them to posit a planet with roughly Earth's physical properties and orbit. Further, suppose that
13 It can be thought of analogous to Twin English in Putnam's Twin Earth thought experiments.
they give the planet a name, say, 'Shmearth'. Intuitively, in this scenario (19) and (20) express
the same proposition.
(20) If Shmearth exists then Shmearth is a physical object.14
In this case, the referent of 'Earth' is the referent of 'Shmearth'-we can imagine the denizens of
Planet-X eventually developing the technology to observe Earth directly (or even travel to Earth)
at which time they would conclude that Shmearth exists. And this in conjunction with certain
linguistic knowledge, specifically, the knowledge that Earthlings use the name 'Earth' to refer to
what they call 'Shmearth' would put them in a position to see that 'Earth' and 'Shmearth'
corefer. The crucial point is that, due to the manner in which 'Shmearth' is introduced, the
astronomers on Planet-X know (20) to be true without further investigation; in positing Shmearth
to account for the behavior of other physical objects, they, in effect, stipulate that, if Shmearth
exists, Shmearth is a physical object. For the Planet-X astronomers, (20) is apriori.
Thus, if (19) is aposteriori, as suggested, then, once again, we have a case where two
sentences express the same proposition which in relation to one appears to differ in regards to its
status as apriori in relation to the other.
Another example of this sort involves complex demonstratives. Take (23).
(23) This table is made of wood.
It is often assumed that anything that is made of wood is essentially made of wood. 15 Thus, if the
demonstrative phrase 'this table' in (23) picks out an object which is made of wood, then (23) is
14 Similarly, if, like Le Verrier, another astronomer had hypothesized the existence of a planet to explain the
observed perturbations in Mercury's orbit but called it by another name, say, 'Shmulcan' then (21) and (22) could
have been said to express the same proposition:
(21) If Vulcan exists then Vulcan is a physical object.
(22) If Shmulcan exists then Shmulcan is a physical object.
15 This is questionable. We can imagine, over time, the table going through a process of petrifaction and turning to
stone (thanks to Kirk Ludwig for this example). A better example may be 'this table was originally made of wood'.
necessarily true.16 On the other hand, (23) appears to be aposteriori because it would require
some examination of the table to see that it is made of wood. But consider (24).
(24) This wood table is made of wood.
Assuming that the demonstratives 'this table' in (23) and 'this wood table' in (24) function as
directly referring terms, 17 (23) and (24) express the same proposition but, unlike (23), (24)
appears to be a priori.
Thus, these examples that appeal to essential properties give rise to the same puzzle we
have been noting all along: we can find different sentences which express the same proposition
but our intuitions about the a prioricity of the proposition differ in relation to the different
16 There is an existential concern in such cases-e.g., it isn't necessary that the table exists. For the purposes of this
paper, I will assume that this can be avoided by conditionalizing the examples-e.g.: if this table exists then it is
made of wood.
17 Complex demonstratives are often treated as directly referring terms. On this view, the nominal in the complex
demonstrative doesn't contribute to the truth conditions of the sentence in which it occurs. Kaplan (1978), McGinn
(1981), Peacocke (1981), and Davies (1982), e.g., each take this line. In contrast, Richard (1993) and Lepore and
Ludwig (2000) argue that the nominal contributes to the truth conditions of the sentence. On the latter view (23) and
(24) do not express the same proposition. Even if this is right, there could be terms that function in the way Kaplan
et. al. think actual complex demonstratives function, so the point can still be made.
In Naming and Necessity, Kripke suggests that (25), where 'S' is a name for the standard
meter bar in Paris, is a contingent a priori truth, at least for the person who fixes the unit of one
meter in relation to S at t.
(25) S is one meter long at time t18
It is said to be contingent because it is not necessarily the case that S is one meter long at t. It is
supposed to be true apriori for the person who fixes the standard because one who fixes 'one
meter' by reference to S knows that whatever length S is a t that length will be one meter long.
(More specifically, the reference fixing definition for 'one meter' is something like: x is one
meter long iffx has the same length that S has at t. And it is apriori that S has the same length at
t that S has at t.)
There is a puzzle about this case, though. For it seems that the person who fixes 'one
meter' in this way, though he is said to know that (25) is true apriori, doesn't know what length
'one meter' picks out apriori, and thus arguably doesn't know what proposition is expressed by
(25). It is part of the story that, for all the fixer knows apriori, the length of S may vary, due to
certain physical conditions at any given time. But suppose the length of S doesn't actually vary
between the time he decides to fix 'one meter' by reference to the length of S at t and the time t;
in other words at any time prior to t, t-E, the length of S is identical to the length of S at t. Now,
even if the fixer knows the length of S at t-E (say he has measured it using imperial units) he is
not in a position to assert 'S at t-E is one meter' even though it is the same length as S at t, which
18 There is an existential worry about this example and others like it. Presumably, S could be destroyed prior to t, in
which case (25) isn't knowable a priori because it isn't a priori that S exists at t. This can be finessed by
conditionalizing the example by prefixing it with 'if S exists at t'. For simplicity, I am presenting the example in its
he supposedly knows a priori. This suggests that he does not know what length 'one meter'
picks out, for otherwise he could know that S at t-E is one meter because he knows its length.
An analogous case may make this clearer. Suppose the owner of a paint store decides to
develop a new color of paint to sell, which he stipulates will be called 'color X'. He assigns the
task of coming up with the new color to his assistant who will carry out the task by mixing a
number of existing paints in the back room. We can assume that the owner of the store has full
confidence in his assistant's judgment, so that whatever color the assistant decides upon will be
sold as the new color of paint, and, hence, will be the color X. By the end of the day, say, time t,
there will be several pails of the new paint on display in the front of the store. Now, what is the
epistemological status of (26) for the owner of the store in this scenario?
(26) The paint on display in the front of the store at t is color X paint.19
It seems he knows it apriori because it seems that one who fixes the reference of 'color X' in
this way knows, without doing any empirical work, that whatever color the new line of paint on
display is, at t, it is the color X. However, what is puzzling about this case is that the owner
clearly does not know apriori what property is picked out by 'color X'. For instance, suppose,
after the assistant comes up with the new color, he presents the owner with a number of different
colored swatches, among them one that the assistant decided is the new color, color X. Would
the owner be able to pick out-prior to being told by the assistant-which swatch is the color X?
Presumably not. For all he knows any one of the swatches, or none of them, is the color X. So
there is a puzzle here about what exactly the paint store owner is supposed to know apriori-
there is a sense in which he actually doesn't know the proposition expressed by (26) apriori,
because he does not grasp the proposition expressed; the idea is that, in order to grasp the
19 There is an existential worry here as well, but we can conditionalize on the existence of the paint the employee has
mixed and put on display in the front of the store to eliminate this problem, so I will proceed without the elaboration.
proposition, he must grasp the meaning of the predicate 'is color X'-in this case, it doesn't
appear that the shop owner grasps the meaning of 'is color X', and, thus, it doesn't seem correct
to say that he knows what proposition is expressed by (26). A more plausible suggestion, I think,
for what the owner knows in this case is that the color of the paint on display at t-whatever
color it happens to be-will be designated by the term 'color X'. Similarly, in the case of one
who fixes 'one meter' by reference to S, it seems more accurate to say that what he knows is not
(25), but rather that the length S at t-whatever length that happens to be-will be designated by
the term 'one meter'. Thus, it appears that his knowledge is after all metalinguistic, knowledge
that a sentence expresses a proposition that is true, and not knowledge of the proposition the
sentence expresses. The metalinguistic knowledge he has isn't something he requires empirical
knowledge to support because he is the person who introduces the term in a way that guarantees
the truth of the sentence. So all he has to know (existential worries aside) is that he has done so.
If this is right, it clearly shows that these cases are not cases of contingent apriori knowledge of
Apart from this, another problem with the 'one meter' case is that it gives rise to the same
puzzle we've been considering. Let us assume, with Kripke, that (25) is apriori for the person
fixing the reference of 'one meter' in this way. It also appears to be contingent. For instance,
suppose that, at t, S is 39.37 inches long (the equivalent of one meter in inches). This would
clearly be a contingent truth since S might have been shorter or longer than 39.37 inches at t.
However, notice that this consideration presupposes that (25), in this scenario, expresses the
same proposition as (27).
(27) S is 39.37 inches long at time t.
But, while (27) is clearly contingent, it cannot be said to be apriori for the person fixing 'one
meter' in this scenario, since for all he knows, prior to measuring S, it may be longer or shorter
than 39.37 inches at time t. So, once again, we have a case where two sentences express the same
proposition though the proposition seems to differ in its aprioricity relative to the different
sentences that express it. We'll return to this case in the following chapter.
THE ROLE OF THE LINGUISTIC VEHICLE
Up until this point, I have been concerned with pointing out a puzzle that arises in regards
to the putative examples of aposteriori necessity and apriori contingency: for each example, the
considerations which are taken to show that the example is necessary/contingent provide the
resources to show that there are two sentences which express the same proposition though the
proposition taken in relation to the different sentences seems to differ intuitively in its a
prioricity. The upshot is that each case leads to three inconsistent claims of the following form.
(i) It is a priori that.
(ii) It is not a priori that q.
(iii) That p = that q.
(i)-(iii) imply that there is a proposition which is apriori and not apriori (even in cases in which
we relativize aprioricity to an individual). Thus, on pain of contradiction, one of the three claims
must be rejected. In this chapter, I will argue that, in each case, rejecting either of two of the
three claims rules out the example as a counterexample to the traditional view, while rejecting
the third is untenable.
I initially stated the traditional view in terms of propositions: any instance of (T) is true.
(T) It is necessary that p it is apriori that p.
But we have seen that there are difficulties with the suggestion that the putative examples of a
posteriori necessity and apriori contingency are counterexamples to the traditional view.
Consider claims (a) and (b).
(a) It is a priori that Hesperus is Hesperus.
(b) It is not apriori that Hesperus is Phosphorus.
Intuitively, (a) is about a certain proposition: the proposition that Hesperus is Phosphorus, and
(b) is about a certain proposition: the proposition that Hesperus is Hesperus. But this leads to
problems when we consider the question whether (a) and (b) are about the same proposition. If
they are then we have a contradiction: (a) and (b) say that the same proposition is both apriori
and not apriori. Thus, on pain of contradiction, one of the following three claims must be false.
(a) It is a priori that Hesperus is Hesperus.
(b) It is not apriori that Hesperus is Phosphorus.
(c) That Hesperus is Hesperus is the same proposition as that Hesperus is Phosphorus.
If we reject (b) or (c) then
(1) Hesperus is Phosphorus
is not, as suggested, a case of a posteriori necessity. As we saw in 1, the reason for holding that
Hesperus is Phosphorus is necessary is that it is the same proposition as that Hesperus is
Hesperus. For suppose it is not. In that case, the pair (Hesperus, Phosphorus) are distinct objects
and hence it is not the case that Hesperus is Phosphorus and hence not necessary that Hesperus is
Phosphorus. In other words, the basis for thinking that (1) is necessary entails that (c) is true.
Thus, unless there is some other reason to think (1) is necessary, there is no basis for rejecting (c)
and it is difficult to see what other grounds one might have for holding that (1) is necessary.
On the other hand, if(b) is rejected then (1) is not aposteriori. So rejecting (b) or (c) is
tantamount to rejecting that (1) is both necessary and aposteriori.
That leaves (a). However, 'Hesperus is Hesperus' is an instance of the logical truth '(x)(x =
x)', which is a typical example of an apriori truth-such examples are generally cited in
contrast to the alleged cases of aposteriori identity. Rejecting (a) does not strike me as a
plausible choice because it threatens to undermine the apriori/aposteriori distinction altogether;
if propositions expressed by sentences of the form 'a = a' are not true apriori it is difficult to see
how a case could be made for anything being true apriori.2
20 Or at least, as I noted in 1, note 15, propositions expressed by sentences of the form: if a exists, then a = a.
Similar considerations present a problem for alleged cases of a priori contingency. Take
(d) It is apriori that all actual Brooklyn residents are Brooklyn residents.
(e) It is not a priori that all actual Kings County residents are Brooklyn residents.
(f) That all actual Brooklyn residents are Brooklyn residents is the same proposition as
the proposition that all actual Kings County residents are Brooklyn residents.
Consider (14) again.
(14) All actual Brooklyn residents are Brooklyn residents.
If(d) is false then (14) is not true apriori. On the other hand, if(f) is false then (14) is not
contingent for the reasons it is said to be. Again, that all actual Brooklyn residents are Brooklyn
residents is said to be contingent because it isn't necessary that the actual residents of Brooklyn,
i.e., those individuals who happen to be residents of Brooklyn, are Brooklyn residents (in
possible worlds talk: it isn't the case that the residents of Brooklyn in the actual world are
Brooklyn residents in every possible world). Such instances of the form 'all actual Fs are Fs' are
contrasted with things of the form 'all Fs are Fs' which are said to be necessary (e.g., omitting
'actual' in (14) results in a necessarily true sentence). Evidently, then, what 'actual' does is have
us consider (i.e., inject into the proposition only) the actual extension of the predicate in its
scope, ignoring its intension. We can see why such cases are usually presented in terms of
possible worlds, because this in effect gets the same result; when we are asked to consider the Fs
in the actual world we consider just those objects which happen to be Fs and evaluate claims
containing 'actual Fs' accordingly. But then any predicate which is true of those objects when
prefixed with 'actual' should get this result. For example, the objects picked out by 'actual Kings
County residents' are the very same objects picked out by 'actual Brooklyn residents'. Thus (14)
and (15) say the same thing about the same individuals.
(15) All actual Kings County residents are Brooklyn residents.
And this is just to say that (14) and (15) express the same proposition. If not, then (f) is false. But
then it is not clear why one would think (14) is contingently true, since it was said to be
contingent for the same reason that (15) is: because it is not necessary that the individuals picked
out by 'actual Brooklyn residents'/'actual Kings County residents' are Brooklyn residents. In
other words, if (14) is contingent for the reasons suggested, then (f) is true. Thus, if it is not the
case that (f) is true, then (14) is not contingent for the reasons given (and, again, it is difficult to
see what other reasons one might have for holding that (14) is contingent).
The other option is to reject (e). But it is not at all clear what would justify this; I do not
know the majority of Kings County residents, so it is difficult to see how I could be said to know
a priori that they are residents of Brooklyn (or residents of Kings County for that matter).
Thus, the most plausible candidates for rejection require giving up the view that (14) is a
counterexample to the traditional view.
Sentences vs. Propositions
The preceding arguments assume that being apriori and being aposteriori are
fundamentally properties of propositions. On this view, sentences (relative to a language) are
true apriori only in a derivative sense-they're true apriori in virtue of expressing propositions
which are apriori. But suppose this is incorrect. Suppose instead that sentences are the rightful
bearers of aprioricity. Does this go any way towards saving the view that there are genuine
examples of aposteriori necessity and apriori contingency? It does insofar as it avoids the
consequence that there are propositions which are both apriori and not apriori. However, it is
not clear how to explicate this suggestion in a way that would avoid the initial puzzle. What
would it mean to say that being apriori is fundamentally a property of sentences? The idea
would have to be spelled out presumably in terms of knowing a sentence to be true (or false) in
virtue of its semantic and syntactic properties, for example:
(S) A sentence s is true apriori (in L) iff s is knowably true (in L) in virtue of the meaning
of its contained terms and their arrangement.
But now the puzzle we began with can be recast in terms of synonymy. Consider claims (g)-(i).
(g) 'Hesperus is Hesperus' is true a priori.
(h) 'Hesperus is Phosphorus' is not true a priori.
(i) 'Hesperus is Hesperus' and 'Hesperus is Phosphorus' are synonymous.
According to (S), a sentence is true apriori iff it is knowably true in virtue of its form and
content. But if (i) is true, which, as shown, is required for the argument for the claim that
'Hesperus is Phosphorus' is necessarily true,21 then 'Hesperus is Phosphorus' and 'Hesperus is
Hesperus' do not differ in content (and they don't differ with respect to their syntactic form). So
while this line avoids explicit contradiction it does not go any way towards accounting for the
initial puzzle as to how two sentences which say the same thing can differ with respect to being a
The puzzle that arises in these cases, it seems to me, is just a variant of Frege's. Frege
(1892, p. 199) was concerned with the apparent difference in cognitive significance between
identity sentences which express the same proposition:
"a = a" and "a = b" are sentences of obviously different cognitive significance: "a = a" is
valid a priori and according to Kant is to be called analytic, whereas sentences of the form
"a = b" often contain very valuable extensions of our knowledge and cannot always be
justified in an a priori manner.
This is a puzzle about proper names. What the putative examples ofaposteriori necessity and a
priori contingency seem to show is that, in addition to names, the same puzzle can arise with
21 In conjunction with schema (SP) from the preliminary section.
22 Another problem with this line is that it comes close to accounting for a prioricity in terms of analyticity, but
many of the same alleged counterexamples are said to show that analyticity and a prioricity are to be sharply
* If someone wrote the Declaration of Independence then the actual person who wrote the
Declaration of Independence wrote something.
* If someone wrote the Declaration of Independence then the actual third president of the US
* This table is made of wood.
* This wood table is made of wood.
* All actual Brooklyn residents are Brooklyn residents.
* All actual Kings County residents are Brooklyn residents.
In each case, we have two sentences which apparently differ in cognitive value: one appears to
be informative whereas the other appears to be trivial. (The analog to the distinction between
being informative and trivial, for present purposes, is the a posteriorila priori distinction.)
Frege considered two solutions to the puzzle, a metalinguistic solution, which he rejected,
and his own solution which involved distinguishing between the referent of a term and its sense.
The metalinguistic solution would interpret 'Hesperus is Phosphorus' as something like
"Hesperus' refers to the same object as 'Phosphorus'.' The problem with this line, according to
Frege (1892), is that 'Hesperus is Phosphorus' doesn't appear to be about terms but rather about
objects-as he points out, the truths expressed by such examples are often considered great
discoveries about the world. His own solution was to explain the nontrivial (aposteriori) aspect
of such examples by positing distinct senses associated with the names flanking the identity sign;
for example, while the referent of 'Hesperus' and 'Phosphorus' may be one and the same,
'Hesperus is Phosphorus' may be informative (aposteriori) because it is possible to associate
distinct senses with those names and not be in an epistemic position to see that they track the
same object-for instance, if one thinks of Hesperus as the first visible star in the night sky and
Phosphorus as the first visible star in the morning sky then, on this account, it doesn't follow that
he knows apriori that 'Hesperus is Phosphorus' is true.
As we have seen, neither solution is compatible with the view that the examples considered
in this paper are genuine cases ofaposteriori necessity and apriori contingency. Earlier, we
noted that Frege's solution does not work because it either changes the modal status of the
example, making it compatible with (T), or it leads to the same puzzle in a new form ( 1-2).
The metalinguistic solution, on the other hand, is problematic for the reason Frege pointed out:
on the face of it, such examples do not appear to be about expressions. Moreover, the reasons
given for the suggested modal status of each example rule out the metalinguistic solution:
'Hesperus is Phosphorus', for example, is said to express a necessary truth because it is an
instance of the identity thesis which, as Kripke explicitly points out, is not a linguistic thesis; 'all
actual philosophers are philosophers' is said to be contingent because it is about individuals who
happen to be philosophers; 'S is one meter at t' is said to be contingent because it is about an
object which happens to be one meter long at t, and so on.
However, while the modal status of such examples does not appear to be language
dependent, the epistemic status does; the examples seem to be examples of the contingent a
priori or necessary aposteriori as the result of failing to separate what is known about the
proposition from what is known about the sentence expressing it, i.e., about its the linguistic
vehicle. The considerations which are supposed to show that a given example is
necessary/contingent entail that there are (at least) two sentences which express the same
proposition yet in relation to each of which the proposition appears to differ with respect to a
prioricity. If two sentences express the same proposition, then any difference in what we can
know when we are thinking of a proposition in relation to one or the other must rest on
something made available or not by the sentences themselves. Thus, if it is true that each
example has the modal status it is said to have, then the linguistic vehicle appears to be playing a
role in the suggestion that such examples are a priori/a posteriori. Consider again some of the
examples of the a priori and aposteriori that we discussed.
(1) Hesperus is Phosphorus (aposteriori)
(lb) Hesperus is Hesperus (apriori)
(2) water is H20 (aposteriori)
(2b) Water is water (apriori)
(3) All actual Brooklyn residents are Brooklyn residents (apriori)
(3b) All actual Kings County residents are Brooklyn residents (aposteriori)
(4) If someone wrote the Declaration of Independence then the actual person who wrote the
Declaration of Independence wrote something (a priori)
(4b) If someone wrote the Declaration of Independence then the actual person who was the
third president of the US wrote something (aposteriori)
(5) Actually, John Kerry is a Massachusetts senator (aposteriori)
(5b) John Kerry is an ext(John Kerry, Ted Kennedy) (apriori)
There is a theme here: each example that is said to be aposteriori contains distinct expressions
on either side of the copula (or in the case of (4b) contains distinct terms in the antecedent and
consequent), whereas each example which is said to be apriori contains identical expressions on
either side of the copula (or, in (4) contains identical terms in the antecedent and consequent).
This is the only linguistic difference between each pair. Thus, if, as suggested, each pair
expresses the same proposition, then it appears to be this linguistic fact that is motivating the
epistemic attributions in the alleged cases of aposteriori necessity and a priori contingency.
Two cases we looked at appear to be exceptions to this:
(19) If Earth exists then Earth is a physical object (aposteriori)
(25) S is on meter long at time t (apriori)
However, notice that in both of these examples what is apriori/aposteriori is relative to a
certain individual or group of individuals. (25), for instance, is supposed to be apriori for the
person who fixes 'one meter' by reference to S at t. Presumably, (25) is not apriori for anyone
else (unless he or she is privy to the decision to fix 'one meter' in this way). But what is it that
precludes others from knowing (25) to be true apriori? It can't simply be that they don't know
what 'one meter' means, because, assuming that the meaning of 'one meter' is the length
designated by that expression, the person who fixes 'one meter' in this way does not know what
the term 'one meter' means either, prior to t-recall that it is part of the story that the length of S
may vary prior to t and, for all this person knows, the length designated by 'one meter' may be
longer or shorter than the length of S at some time t-E, even if he knows the length of S at that
time. Suppose someone else decided, independently, to create a system of measurement, say the
"shmetric system," and fixed 'one shmeter' by reference to the length of some other object, S2 at
t. In such a case, following Kripke's line of reasoning, (25*) is apriori for this person.
(25*) S2 is one shmeter at t.
But now suppose that the lengths of S and S2 are identical at t. In this scenario, 'one meter' and
'one shmeter' designate the same length, but the metric user is not in a position to know apriori
that (25*) is true, nor is the shmetric user in a position to know apriori that (25) is true. One way
to account for this would be to say that (28) is not true apriori for either person.
(28) One meter is one shmeter
But, by hypothesis, (28) expresses the same proposition as (29) and (30), which are (presumably)
true a prior.
(29) One meter is one meter
(30) One shmeter is one shmeter
23 At the very least, (29) is true a priori for the metric user and (30) is a priori for the shmetric user.
So it appears the linguistic vehicle is playing a role in this case as well. And notice that (28)-(30)
exhibit the same characteristics as the earlier examples: (29) and (30), which are true apriori,
contain identical terms flanking the copula whereas (28), which is said to be true aposteriori
contains distinct terms flanking the copula.
The same can be seen in the case of (19).
(19) If Earth exists, then Earth is a physical object.
Recall the Planet-X thought experiment. In that scenario 'Earth' and 'Shmearth' refer to the
same object, yet, whereas (19) is supposedly true aposteriori, (20) is true a priori (for the
denizens of Planet-X).
(20) If Shmearth exists, then Shmearth is a physical object.
One way to explain this would be to say that the people on Planet-X don't know that (31) is true
(31) Shmearth is Earth
But, by hypothesis, (31) expresses the same proposition as (32), which is true apriori (at least
for those people on Planet-X).24
(32) Shmearth is Shmearth
So it seems the linguistic vehicle is playing a role in this case too. And, again, we see the same
characteristic: the apriori example, (32), contains identical terms, whereas the aposteriori
example, (31), contains distinct terms.
All this strongly suggests that the putative examples of the necessary aposteriori and
contingent apriori are the result of failing to recognize the role the linguistic vehicle plays in the
suggested epistemic status of such examples. If this is right then we have a solution to the initial
24 And, again, barring the existential worry.
puzzle as to how two sentences can express the same proposition/be synonymous yet differ as to
being apriori/a posteriori: the epistemic status of such examples is not wholly based on
knowledge of the proposition expressed/the meaning of the sentence, but rather it includes some
metalinguistic knowledge (or lack thereof) regarding the contained terms. The way one comes to
know the proposition expressed by such sentences is mediated by the linguistic vehicle. Take an
(1) Hesperus is Phosphorus
(lb) Hesperus is Hesperus
We can know that the proposition expressed by (lb) is true because the sentence expressing it is
logically true. But logical truth is a property of sentences and is recognized by attention to
sentence form. So knowledge that the proposition is true rests not just on grasping the
proposition but also on knowledge about the linguistic vehicle used to express it. (1) expresses
the same proposition and we grasp it as well, but the aid that the linguistic vehicle in (lb) gives
to knowing it is true is missing here. So what we know in the case of(lb) is essentially in part
linguistic. Hence, there is no knowledge of the truth of the proposition directly in these cases.
In this paper, I have been concerned with pointing out a problem that is common to the
putative examples of the necessary aposteriori and contingent a priori. I began by noting a
puzzle that arises in each case: the considerations which are taken as evidence that the example is
necessary/contingent leads to the view that there are two sentences which express the same
proposition which differs as to being apriori/aposteriori when considered as expressed by one
and the other. On the assumption that propositions are the bearers of aprioricity, which is
implicit in the traditional view, this leads to contradiction: there is a proposition, p, such that it is
apriori thatp and it is not apriori thatp. I argued that the best way to avoid this is by denying
that such examples are counterexamples to the traditional view. Finally, I noted a characteristic
exhibited by all such examples which suggests an explanation for the initial puzzle: the modal
status of each example is based on the proposition expressed whereas the epistemic status is not;
instead, it appears that the linguistic vehicle is playing a role in the view that such examples are a
priori/a posteriori. Thus, in these cases, there is no one thing that has both the alleged epistemic
and modal statuses which are to provide a counterexample to the traditional alignment of a
prioricity and necessity
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Shawn Burtoft was born on July 9, 1973 in Sarasota, Florida. He relocated to Marion,
Virginia, at age 12 and graduated from Marion Senior High School in 1991. He earned his B.S.
in philosophy from East Tennessee State University in 2006.
After earning his B.S. degree, Shawn entered the graduate program in philosophy at the
University of Florida, focusing primarily on issues in philosophy of language and metaphysics.
He is currently employed by the History of Science Society.
Upon completion of his M.A., Shawn will enter the Ph.D. program at UF. Upon
completion of his Ph.D., he will seek to establish an academic career in philosophy.