Monday, November 30, 2009

Why Truth-Functionality and the (Non-Epistemic) Analytic/Synthetic Distinction Make Strange Bedfellows

Discussions of "the" analytic/synthetic distinction tend to confuse things by using that definite article, but several distinct distinctions have been proposed using those terms. As far as I can tell, most of them are, in one form or another, epistemic distinctions--for example, we can be absolutely certain about analytic truths, whereas even the best-established synthetic truths are still known only in a fallible, probabilistic way (this is the sort of thing that seems to be built into standard Bayesian epistemology), or synthetic truths have to be discovered empirically while analytic truths are ones that we have epistemic access to merely by virtue of knowing the meanings of all of the terms involved (this seems to be about what Boghossian is getting at in his defense of the distinction), or analytic and synthetic statements are (rationally) revised away in different ways, such that synthetic claims can be empirically refuted, but belief-change about analytic matters has to be a change-of-meaning issue (this is the version of the distinction that Grice and Strawsson stamp their feet and insist on in what I can't help but think of as their very aptly-titled article "In Defense Of A Dogma"). Some of these epistemic formulations of the distinction are such that I think even the hard-core Quinean has relatively little quarrel with them, and others are, I think, deeply misguided and can lead to a dogmatic and undeserved sense of certainty about matters logical and mathematical. None of that, however, is anything that I'm going to get into right now.

What I'm interested on touching on instead is the more robust, more-than-just-epistemic sense of analyticity held by those who take the distinction to be about truth-making.* This is the strongest (but most famous) sense of the distinction, where synthetic statements are "made true by virtue of the way the world is," whereas analytic statements are "made true by virtue of the meanings of the terms involved." How to understand the second option is a complicated and confusing issue, and if my personal feeling is that the most sophisticated-sounding explications of it tend to devolve into hand-waving and places where "here a miracle occurs" is written on the conceptual chalkboard, I can happily accept for my present purposes that people who talk that way are talking sense, even if it is a deep and subtle sort of sense that I have troubling grasping.** At the moment, at any rate, I won't be arguing against the details of any such proposal for understanding the claimed truth-making distinction. My target here is much broader than that: I want to suggest a reason to be suspicious of the suggestion that there's any sort of truth-making distinction between "analytic" and "synthetic" truths, at least given a standard story about the truth-functional nature of logical connectives. If I'm not sure that it quite adds up to a full-fledged objection yet, I do think it at least strongly points the way to one.

Here it is.

Let P be a true statement--for the sake of convenience, let's use the old stock example "snow is white." In classical logic, (P v Q) follows from it, regardless of the content of Q. As long as we know that Q is some regular, meaningful, declarative sentence, the kind of thing that can be legitimately taken as the interpretation of a propositional variable, we know that the truth of P guarantees the truth of (P v Q), even though we don't know the specific content of Q, or even whether it is true or false.

Now, fiddle that picture just a little bit, to give us one new piece of information. We still know that P is "snow is white," and that that's true, and we're still in the dark about the specific content of Q, but now we also know that Q is false. At this point, we know not just that (P v Q) is true, but that it's true exclusively because P is true. Remember, whether or not there are any "analytic" statements, made true in a slightly mysterious secondary way, P is a completely banal "synthetic" statement, made true by the actual whiteness of the fluffy white stuff on the ground.

Now, you'd think that at this point in the argument, we know everything there is to know about how (P v Q) becomes true. Given that we know that it's false, we know that Q does no work in the process, and we know that P is "made true by the world" in the boringly normal fashion.

But wait. Let's consider two scenarios. For the sake of simplicity, in both options, Q is a (false) statement about snow.***

(1) Q is "snow is green."

(2) Q is "snow is not white." (Q=~P)

Now, in scenario (1), (P v Q) is a "synthetic" statement, made true by the world through the truth of its first disjunct. In scenario (2), however, (P v Q) is an "analytic" statement, made true in some other way.

So my almost-objection is this: there's something deeply counter-intuitive about the suggestion that, despite the fact that we knew that (P v Q) was true before we knew whether Q was even a true statement or a false one, despite the fact that we knew that Q wasn't going to be doing any work in making (P v Q) true before we even knew what it's specific content was, and despite the fact that P itself isn't made true in different ways in scenarios (1) and (2), (P v Q) arrives at truth in fundamentally different ways depending on the specific content of Q.

So the challenge I'd throw to defenders of a (more-than-just-epistemic) analytic/synthetic distinction is approximately this:

If one takes confirmation to work on a case-by-case, statement-by-statement basis, no one would argue with the claim that the story we should tell about how to confirm P is very different from the story we should tell about how to confirm (P v ~P). Whether or not we should take confirmation to work that way is a question for another time. Your claim about truth-making, however, seems to put you in a very strange and awkward position, and it looks like a position you have to good reason to put yourself in.

You admit that P is made true by the way snow is, and that ~P is made false by the same thing. Why not extend that analysis in a straightforward way, given the way that the truth or falsity of disjunctions and conjunctions works as a function of the truth or falsity of their components, to cover the way that (P v ~P) is made true and (P & ~P) is made false? Why, in other words, take anything but the way that snow is to do any work in the story we tell about how complex statements entirely about snow are, or are not, made true?

*I take it that some (but not all) formulations of the epistemic distinction are at least strongly suggested by the truth-making distinction, but again, that's a separate issue. And, of course, the epistemic distinctions can be quite independently motivated, and it's not uncommon to read defenses of (epistemic senses of) the analytic/synthetic distinction by theorists who profess to be unsure about how seriously to take talk of things being made true by virtue of anything but the objects referred to in the sentences being the way the sentence says they are.

**By way of at least gesturing at an example of the sort of thing I'm talking about, an expressivist version of the truth-making distinction holds that the way that analytic statements become true has something to do with the way they express the speaker's commitment to certain vaguely-defined linguistic norms or "rules of use" that have somehow made it into our language. I think that the evidence for the existence of such "rules" is non-existent and that demands for precise explanation of what these "rules" would or could even consist of tend to be met with vague and rather unhelpful analogies. To say that two people who set up a chess board and then move around the pieces in disallowed ways are "violating the rules of chess" is simply to say that their game is inconsistent with a bunch of actual written rules explicitly stipulated and agreed on by a bunch of human beings, and that as such what they're doing doesn't count as an instance of chess. To say that asserting a contradiction amounts to violating "rules of use" or whatever, on the other hand, is to say nothing that even could be remotely similar, both because languages arise not from explicit stipulation and agreement but in a sprawling, unplanned way, and because--assuming a logically orthodox picture of things--contradictions definitely count as instances of language. The classical assumption that contradictions are always false entails that they are meaningful, understandable bits of whatever language they are asserted in.

***We're talking about very, very closely related falsehoods at that, considering that the second statement is actually entailed by the first one, which should underline the strangeness lurking in all of this.

No comments: