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?


Gilbert Wesley Purdy said...

I'm pleased to find an apparently meaningful blog engaged in using logic calculus. First, though, might I suggest that you delete the two previous non-comments? They seem ominous. They could be interesting puzzles, yes, but also could be a virus laden trap. If I'm out of the loop on this one let me know.

It is difficult to be sure of Boghossian's point without more context. Is it clear that he is not saying: S iff (p only if p)? That to say the sentence is true that means p and p is true? This would then be quite different from your "p iff [q and (r only if r)]".

Anonymous said...

Well, surely one could say that
whatever is true is true by definition; is true by virtue of
the description of whatever is the case fitting the definition of such a case. The description of an action fitting the definition or category of an act of robbery for instance.
Makes me think that the difference between description and definition is not so substantial--perhaps just a matter of a definition being a more general description which casts a wider phenomenal net.
I could turn a description into a definition by saying that such and such description defines a such and such unique category. Seems that any description could describe a category. Hitting a small ball into a hole with a long handled club I might categorize as the action of blumphing---golf being a subcategory of blumphing.

Greg Frost-Arnold said...

Hi anonymous --

Interesting ideas... I think I would part ways with you at the very start: I do not believe that "whatever is true is true by definition." E.g. "Greg is 5 feet, 11 inches tall" does not seem to be true by definition according to any reasonable definition of the terms in that sentence. (I realize 'reasonable' is a fudge word, but separating good/ acceptable definitions from crummy ones is a very difficult and vexed matter.)

Anonymous said...

You could say that a general height is defined as that number obtained by measuring with a tape measure from the ground up or some such other conventional method. And that a 5' 11" height is defined as a measurement conforming to the above wherein the number obtained is 5'11".
And if the number was not 5'11" or did not conform to the above definition of height---then it is by definition not a height of 5'11".
I agree that definition is a can of worms and what fits within any definition may vary among folk--
For instance, one may say any log flattened on top fits the definition of a chair--fits in the chair category-- but another may exclude such a log from the category of chair.
So, if two folks differ as to what is allowed under a definition or description ---do they or do they not subscribe to the same definition?
And more broadly how does one define same and different?