Kripke on the contingent a priori

Jeff Speaks

April 5, 2005

1 Kripke’s case for the contingent a priori
 1.1 The separation of the modalities (33-39)
 1.2 The example of the standard meter (54-56)
 1.3 An extension of Kripke’s point: indexicals
2 Two challenges to Kripke’s account
 2.1 The definition of ‘a priori’
 2.2 Is every contingent fact knowable a priori?

1 Kripke’s case for the contingent a priori

1.1 The separation of the modalities (33-39)

We have seen that earlier authors like Ayer and Quine tend to run the categories of necessary truth and a priori knowable truth together. Kripke thinks that this is a mistake:

“Philosophers have talked ...[about] various categories of truth, which are sometimes called ‘a priori’, ‘analytic,’ ‘necessary’ ...these terms are often used as if whether there are things answering to these concepts is an interesting question, but we might as well regard them all as meaning the same thing. ...

...First the notion of a prioricity is a concept of epistemology. I guess the traditional characterization from Kant goes something like: a priori truths are those which can be known independently of any experience. ...

...The second concept which is in question is that of necessity. ...what I am concerned with here is a notion which is not a notion of epistemology but of metaphysics ...We ask whether something might have been true, or might have been false. Well, if something is false, it’s obviously not necessarily true. If it is true, might it have been otherwise? Is it possible that, in this respect, the world should have been different than the way that it is? ...This in and of itself has nothing to do with anyone’s knowledge of anything. It’s certainly a philosophical thesis, and not a matter of obvious definitional equivalence, either that everything a priori is necessary or that everything necessary is a priori. any rate they are dealing with two different domains, two different areas, the epistemological and the metaphysical.” (33-35)

Kripke’s point here is that the identification of the necessary with the a priori is a substantive one, and does not follow trivially from what we mean when we say ‘necessary’ or ‘a priori.’

From the fact that these two categories are conceptually distinct, it does not follow that they are extensionally distinct; it does not follow, that is, that that there are any examples of truths which are necessary but not knowable a priori, or a priori but not necessary. The next step in Kripke’s separation of the modalities is to show that the two categories do not even coincide: there are contingent a priori truths as well as necessary a posteriori ones. Today we will be talking about Kripke’s case for the existence of contingent a priori truths.

1.2 The example of the standard meter (54-56)

The main example of the contingent a priori Kripke is discusses is the example of the standard meter. Kripke imagines using the length of a certain stick -- ‘Stick S’ -- to fix the reference of the expression ‘one meter.’ He then asks us to consider the status of the proposition expressed by the sentence

The length of stick S at time t0 is one meter.

He first argues that this proposition expresses a contingent rather than a necessary truth:

“...there is an intuitive difference between the phrase ‘one meter’ and the phrase ‘the length of S at t0’. The first phrase is meant to designate rigidly a certain length in all possible worlds, which in the actual world happens to be the length of the stick S at t0. On the other hand, ‘the length of S at t0’ does not designate anything rigidly. In some counterfactual situations the stick might have been longer and in some shorter, if various stresses and strains had been applied to it. So we can say of this stick, the same way as we would of any other of the same substance and length, that if heat of a given quantity had been applied to it, it would have expanded to such and such a length. ...So [the fact that we have used stick S to fix the reference of ‘one meter’] does not make it a necessary truth that S is one meter long at t0. The reason is that one designator (‘one meter’) is rigid and the other designator (‘the length of S at t0’) is not.” (56-57)

The basic idea here is that this claim is contingent for just the same reason that any sentence of the form

The F is n.

where ‘the F’ is a non-rigid designator and ‘n’ is a rigid designator, is contingent. If one expression is a rigid designator and the other is not, then there is some object o such that in some world one of the expressions refers to it and the other does not. But then the sentence will be false with respect to that possible world, and hence not necessary.

But is the proposition expressed by this sentence contingent? Kripke argues that it is:

“What, then, is the epistemological status of the statement ‘Stick S is one meter long at t0’, for someone who has fixed the meter system by reference to stick S? It would seem that 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.” (56)

Kripke’s idea here seems to be that, though t may not be a priori for later users, this claim is at least a priori knowable for the parties to the initial stipulation which fixes the reference of ‘one meter.’ The intuitive idea is that if we have stipulated that ‘one meter’ is to stand for that length, whatever it is, which is the current length of stick S, then we can know, just by knowing this stipulation, that stick S is one meter long. But this is surely enough to make the knowledge in question a priori.

The way in which any reference-fixing definition can, seemingly, generate an instance of a priori knowledge.

1.3 An extension of Kripke’s point: indexicals

Work by a number of people after the publication of Naming and Necessity extended the category of the contingent a priori beyond the cases which fit Kripke’s description, to a number of cases involving indexicals, or expressions whose content, on a given occasion of use, depends systematically upon features of the context in which it is uttered. Indexicals include ‘I’, ‘here’, ‘now’, ‘actually’, ‘you’.

Just as in Kripke’s example the expression ‘one meter’ is associated with a description, so each of these indexicals is associated with a description:



the speaker of the context


the place of the context


the time of the context


the world of the context


the audience of the context

In Kripke’s example, ‘one meter’ did not mean the same thing as the descriptions associated with it; this description was, as he says, used to fix the reference of ‘one meter’, and not to give its meaning. The same is true of the above indexicals; they do not mean the same thing as their associated descriptions. Consider the following pairs of sentences:


If Saul Kripke had taught this class, then the speaker of the context, right now, would have been Saul Kripke.

If Saul Kripke had taught this class, then I, right now, would have been Saul Kripke.

If I decided to have class outside, I would have made the lawn be the place of the context.

If I decided to have class outside, I would have made the lawn be here.

Nonetheless, the relations between these indexicals and their associated descriptions is not quite the same as the relation between Kripke’s term ‘one meter’ and its associated description. In Kripke’s case, the description has a one-off use; it is used to introduce the expression, but then the expression can go on to be mastered by other speakers without their knowing anything about the description. This is not true of indexicals; the description fixes the reference on every occasion of use and, plausibly, understanding indexicals requires having some grasp of their associated description.

Cases of sentences involving indexicals which, on a given occasion of use, might express propositions which seem to be knowable a priori:

I am the speaker of the context.

I am here now.

Grass is green if and only if actually, grass is green.

Each of these also, relative to our imagined contexts of utterance, expresses a contingent truth. So each seems to be an example of the contingent a priori.

2 Two challenges to Kripke’s account

2.1 The definition of ‘a priori’

Suppose that everything in Kripke’s description of the case goes as he says, and that the speaker comes to know the proposition that the length of stick S is one meter on the basis of only that experience required for him to understand the proposition. Is this enough for it to count as a priori?

Examples which seem to indicate that it is not; uses of demonstratives.

2.2 Is every contingent fact knowable a priori?

One challenge to Kripke’s claim that the proposition that stick S is one meter long is a priori is that the line of reasoning given in defense of that claim seems, given a few further assumptions, to lead to the absurd conclusion that virtually any agent could know almost any contingent fact a priori.

Let ‘the F’ be any description which uniquely designates some object or magnitude. Then if we allow speakers to, solely on the basis of understanding the description, introduce a name which refers to the referent of the description, speakers could come to know a priori of the referent of that description that it is F. Example: knowing a priori how tall the tallest person in the world is.

Does this objection apply to the examples involving indexicals above?

(For more on these two objections to Kripke, see the chapter entitled “The contingent a priori” in Soames, Philosophical Analysis in the Twentieth Century, v. 2.)