1/13/2008

Boghossian on ('metaphysical') analyticity

I've been thinking recently about an objection Paul Boghossian (and many others) make against the Tractarian/ Carnapian conception of an analytic truth, viz. a sentence that is true solely in virtue of the meaning of the sentence. (Boghossian calls this kind of analyticity 'metaphysical analyticity,' which I think is potentially misleading, given the staunch anti-metaphysical tastes of the logical empiricists. Oh well.)

Boghossian considers the notion of metaphysical analyticity untenable. Why? He asks a rhetorical question:
"Isn't it in general true---indeed, isn't it a truism---that for any statement S,

S is true iff for some p, S means that p and p?

How could the mere fact that S means that p make it the case that S is true?" (Boghossian 1996, "Analyticity Reconsidered," Nous [p.364]


Boghossian is not alone in this view: the basic idea can be found in Quine's "Carnap and Logical Truth," and is developed by Gilbert Harman, Elliott Sober, and Margolis & Laurence. How should we interpret this rhetorical question? Boghossian appears to be claiming that the truth of a sentence of the form 'S means that p' is never a sufficient condition for the the truth of a sentence of the form 'S is true'---that appears to be intended force of the rhetorical question in the quotation immediately above. And that is certainly one reasonable way of cashing out the notion of the truth of a sentence being `fixed exclusively by its meaning.'

If we do understand Boghossian's view in this way, then I think his claim is either misleading or incorrect. Consider a standard material biconditional of the form

(1) p iff q

If such a biconditional is true, we usually say that q is a necessary and sufficient condition for p. But as we teach undergraduates in Introduction to Logic classes, if this biconditional is true, then (within the classical propositional calculus) so is

(2) p iff [q and (r only if r)]

(Any other logical truth of the classical propositional calculus could be substituted for r only if r.) If we simply read off the surface structure of sentence-schema (2), one might think that q was no longer sufficient for the truth of p--because there appears to be a second condition that has to be met in order for p to be the case, namely that r only if r. Of course, strictly speaking, this is true: every sentence of the propositional calculus presupposes the truth of all the logical truths of the propositional calculus. However, it seems seriously misleading to me to say that the truth of q is not a sufficient condition for the truth of p in our original biconditional--for that is not the way we standardly understand sufficient conditions.

Hopefully the direct parallel with Boghossian's claim is clear. I certainly agree that his 'truism' quoted above is true. However, when a logical truth--which, as Carnap and Quine agree is a paradigmatic case of analytic truth (if there are any)--is substituted for p in his schema, then that instance of the truism will have (almost) exactly the form of the second biconditional (2). Then, in the usual sense of 'sufficient condition,' we will have a case in which (contra Boghossian) an instance of 'S means that p' is sufficient for 'S is true.' To say otherwise, we would have to give up either classical logic (specifically, the idea that (2) follows from (1)) or the usual understanding of sufficient conditions.

However, one could object that neither classical logic nor our standard view of sufficient conditions is sacrosanct. I think there are reasonable replies to these objections (telegraphically: for whatever non-classical logic you choose, you can substitute some other logical truth for 'r only if r' in (2) above, and the point carries); but I'll leave matters here since this post is too long already.

Comments and criticism from any angle are very welcome, but what I personally go back adn forth on with the above argument is whether it's a 'cheap point' or not... superficial logic-chopping, or genuine insight?

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