Sunday, February 08, 2009

Modal-Analytic Truths

I think I agree with much of what Williamson says in this chapter. It seems clear, for example, that no metaphysical conception of analyticity will vindicate the idea that analytic truths are insubstantial. There are, however, a couple of small points that Williamson makes that I disagree with.

Williamson claims that this sentence:

S1: It is raining iff it is actually raining.

expresses a modal-analytic truth. I disagree.

A modal-analytic sentence is a sentence the meaning of which is sufficient for truth. A meaning is sufficent for truth "just in case necessarily, in any context any sentence with that meaning is true." In what follows, I will assume that the meanings of sentences are propositions. Hence, it will be ligitimate to say that a proposition is sufficient for truth. With this definition in mind, we can easily show that S1 is not a modal-analytic truth.

To see that S1 does not express a modal-analytic truth, first consider the following sentence:

S2: It is raining iff it is raining in actuality.

If we take 'actuality' as an indexical that picks out the world of whatever context it is expressed in, then this sentence, just like S1, will express a true proposition in any context. Whatever proposition it expresses will be contingent. And, most importantly, whatever proposition it expresses will fail to be sufficient for truth. To see that this latter claim is true, let 'Alpha' name whatever world happens to be the actual world. Now, it is clear that the proposition expressed by S2 in a context that has alpha as its world will be the same as the proposition expressed by the following sentence:

S3: It is raining iff it is raining in Alpha.

Let's call the proposition expressed by S2 and S3 in such a context, say our context, 'P'. Since 'Alpha' is a name, rather than an indexical, then in any context, S3 will express P. Consider a context C that is such that alpha is not the world of C. Suppose that in the world of C it is not raining whereas in the alpha it is raining. Then, the proposition expressed by S3 in C will be false. That is, P will be false in C. But, that means that the sentence S3 will be false in C. So, possibly, in some context, a sentence that has P as its meaning is false. So, P is not sufficeint for truth. But, P was the meaning of S2 in our context. So, the meaning of S2 (in our context) is not suffient for truth. So, S2 is not modal-analytic

I say that the same kind of argument will show that the meaning of S1 is not sufficient for truth. That is, S1 is not modal-analytic. All we need is a non-indexical adverb that happens to have the same meaning as 'actually' in our context. Let's introduce the adverb 'alpha-ly' to be just such an adverb. Now, we can run an argument perfectly parallel to the one introduced above. The conclusion of that argument is that the meaning of S1 is not sufficient for truth and hence S1 is not modal analytic.

I think a general lesson can be learned from this exercise. Namely that sentence is modal-analytic only if its meaning is necessary. If the meaning of a sentence is contingent, then we can always come up with a way of expressing that meaning using non-indexical terms. Whatever sentence we come up with will express the contingent proposition in a context where that proposition is false. Hence, the proposition will not be suffient for truth. Hence, any sentence that expresses that proposition will fail to be modal-analytic. So, contrary to what Williamson says, the notion of modal-analyticity does not violate the Kripke contstraint on analytic truths. That is, if analytic truths are modal-analytic, then analytic truths are necessary, just as Kripke claims.


Blogger avwake said...

Hey Joshua,

In the account of Modal-Analyticity, I think we're supposed to take the meaning of a sentence to be its character (see, for instance, footnote 10, pg. 59).

If that's right, then things work out (I think) in the way that Williamson claims they do.

S1 will be modal-analytic because its character, C, is such that, for any context, c, C(c) = some true proposition.

This also explains, I guess, why he says that not all sentences which express, in a context, a necessary truth are modal-analytic. Taken with respect to a context, c, with me as the agent 'I am not Tony Blair' expresses a necessary truth. But, it is not modal-analytic because its character doesn't deliver a true proposition in every context.

10:38 AM  
Blogger Joshua said...


Yes, you are right. My post is all false.


5:35 PM  

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