Wednesday, February 3, 2010

Some More Stuff About The Analytic/Synthetic Distinction

[The last paragraph of the first--and thus far customer review of Graham Priest's new book made me smile. And, obviously, I'd love to write that book.]

OK, so analyticity...

One of the funny things about the philosophical debate about analyticity is that it's often framed as a debate about "the analytic/synthetic distinction." Now, philosophy is sometimes characterized as the art of making distinctions, and even if this over-states things, it's still undoubtedly true that distinction-making is a central activity of philosophers, and that sentences of the form "Philosopher X denies the Y-Z distinction" tend to sound a bit odd. Moreover, this formulation tends to tilt the playing field heavily in favor of those defending the X-Y distinction. After all, they win the argument as long as there's some difference between X's and Y's. Those criticizing the distinction have the daunting task of trying to argue against all claims that X's and Y's are in any way different.

(Some friends of mine have this very nerdy running joke about starting a bar called "The Two Dogmas Of Alcoholism." We'd serve a shot called "The Analytic" and a shot called "The Synthetic" and both of them would be Jose Cuervo. When patrons had one of each and then asked what the difference was, the bar-tenders would all be trained to respond with, "ex-actly!")

Moreover, in the case of the analytic/synthetic distinction, given standard ways of categorizing all true statements into one column or the other, it's surely not the case that there are no differences between the things in the column where we write down various things that can be accurately translated into logical tautologies ("All bachelors are married"), mathematical truths and so on and the column where we write down the rest of the true statements. For one thing, trivially, the things in Column A have the property of "being the sort of statements that philosophers tend to refer to as analytic" and those in Column B lack that property. Depending on exactly how one carves up the lists, there might be more substantive differences as well--for example, the statements in Column A (but not the statements in Column B) might be instances of general logical claims. Whether those distinctions exist, or whether it can be useful to be clear on them, surely isn't at issue when people argue about the analytic-synthetic distinction.

What's at issue instead seems to be whether the true statements that are instances of general logical or mathematic truths have any of the special features that have often been imputed to them by philosophers, features related to how they become true, what sort of epistemic access we have to their truth, or some combination of the two. (As such, I generally think it might be better if instead of presenting it as an argument about "the analytic/synthetic distinction," we talked about it as an argument about "analyticity.") A while back, I made some objections to the claim that there's a distinction between the way that analytic statements are made true and the way that synthetic statements are, but of course, even if one rejects that distinction, that still leaves the much larger issue of whether there's some sort of epistemic distinction.

While I reject both, I tend to think the case for an epistemic distinction is much harder to respond to than the case for a truth-making distinction. (One of the interesting things about the debate is that often times even people who are vocally loyal to analyticity in one of the standard senses often find the other senses a bit incomprehensible. For example, in the session on "New Waves In The Philosophy Of Mathematics" at the Eastern APA, Roy Cook, who's defends a neo-Fregean program in the philosophy of math, said that he "didn't even know what it would mean" to say that true mathematical and other 'analytic' statements are made true in some special way that's different from how ordinary statements are made true.) Really getting into that involves tackling the issue of whether the elements of our overall package of beliefs about the world are confirmed or disconfirmed individually or holistically, how we can tell and what's at stake in the argument about all of that, and I'm not particularly keen to get into that right now.

For the moment, instead, I want to talk about a strange sort of intermediate sense of analyticity people often seem to appeal to, where the distinction is framed in terms of belief-revision. In the case of synthetic claims, belief-revision is a matter of refutation, whereas in the case of analytic claims, it's a matter of a change in meaning....we're just deciding to use words in different ways. Hence, maybe, the Newtonian claim that time and space are absolute has been refuted, whereas when we switch from Euclidean to non-Euclidean contexts and thus change our minds about whether there can be more than one straight line between any two points, we're just using the words "point" and "line" in new ways.

Without getting too deeply into the specific examples, this picture raises a lot of strange questions. Start with a particularly basic question:

Is all of this supposed to be descriptive or normative?

If the idea is supposed to be that, as a matter of fact, when we change our minds about an analytic claim, we're just changing the meaning of the terms involved, that seems to suggest that it's impossible for us to have incorrect beliefs about analytic matters, which seems to be fantastically implausible. Of course we sometimes believe contradictions, ocassionally explicitly (especially if you're named "Graham Priest" or "J.C. Beall") but more often implicitly. It's plausible that everyone's overall belief set is internally inconsistent all the time--maybe being a rational person means trying to recognize and correct the inconsistencies as efficiently as possible, but that doesn't mean that they aren't there.

But wait. If the two-tiered picture of belief revision supposed to be normative--that is to say, it's about how people *should* revise their beliefs--does that mean that, when you realize that you're wrong about an analytic matter (given how you're using the terms, you have some beliefs that jointly yield a contradiction), you shouldn't revise your beliefs to correct the inconsistency? Because, if you should, then your change-of-belief on the analytic matter is *not* a matter of deciding to use your terms in a new way, it's a matter of using them in the old way and substantively changing your mind. If someone used the word "bachelor" in the standard way, and believed that some bachelors were married, then when the inconsistency was pointed out to them, *shouldn't* they (while continuing to use the word "bachelor" to refer to unmarried males) move to reject their old belief that some bachelors were married? And wouldn't this be a matter of their old belief being refuted rather than them now making a decision to use the words in a new way?

It could be objected that, realistically, no one would hold this strange belief about bachelors, but:

(1) Let's not be too quick about that. In In Contradiction, Graham Priest argues for legal true contradictions. Given strangely-worded marriage laws, and the belief that legal dialetheias are possible, one could in fact see how a dialetheist could convince themselves that there are some married bachelors--men who both are and are not married under the inconsistency-generating law.

(2) Abstract from the example. After all, once you understand that "bachelor" means "unmarried" male, the logical inference from "John is a bachelor" to "John is unmarried" is an extremely simple and intuitive, since all it involves is a single instance of conjunction-elimination. However, lots of "analytic" truths can only be discovered as a result of much more complicated and less intuitively obvious chains of inference. For example, if you go with Frege (and against Kant) in thinking of mathematical truths as being "analytic," it's very obviously possible for people who understand the meanings of all the terms involved in a mathematical sentence to fail to grasp its truth.

Often times, in Intro classes, I'll spend a while explaining what "set" is, what it means for two sets to "have the same cardinality" and so on and no one will be lost. Then I'll show them that (and why), for example, the set of all whole numbers has the same cardinality as the set of all even numbers, and again, no one will be lost. Then I'll ask them if they think that all transfinite sets will have the same cardinality, and they'll either be unsure or raise their hands to say yes, absolutely, that should be true. Then I'll show them Cantor's diagonal proof that not all transfinite sets have the same cardinality, and, despite the fact that the proof is delightfully simple and straight-forward, some of them won't get it, or in fact will resist the counter-intuitive conclusion, despite having seen all the steps in the proof, and try to poke holes in it. So, we have a putatively "analytic" matter (do all transfintie sets have the same cardinality?) about which, even when they understand all the terms perfectly, many people will come to the wrong conclusion.

Are the students who get it and thus change their minds about whether all transfinite sets have the same cardinality somehow being irrational? If not, then not only is the claim that belief revision is a matter of change-of-meaning in analytic cases unworkable as a universal descriptive claim, it looks equally problematic as a normative claim.

Now, someone could say at this juncture of the argument that the claim isn't that revising away beliefs about analytic matters is (or even should be) a matter of change-of-meaning rather than refutation. Rather, perhaps, the claim could be that revising away analytic *truths* should be a matter of change of meaning rather than refutation--i.e. if you start with a *true* statement about analytic issues and you want to end up with another *true* statement, that seems to contradict it (e.g. you go from "there is always one and only one straight line between two points" to "there are infinitely many straight lines between two points"), then the belief-change must have been merely a matter of using the terms in a different way. Put that way, whatever you think about the specific examples (Putnam has a good discussion about the geometry case in "Is Logic Empirical?" that makes clear that this particular example isn't as straightforward as it seems), it's hard to argue. The only kind of "belief revision" that gets you from a true statement to another true statement that employs the same terms and seems to contradict the first one is a change of meaning.

But, wait, this is just as true if we're talking about "synthetic" claims! If I stop believing that it was raining at 3:01 on January 3rd in South Miami and I start believing that it wasn't raining then, and both statements are true, and there are no true contradictions, I must have started using the word "rains" in a different way, so that the light drizzle on January 3rd counted under the first definition and didn't count under the second one.

So, given that, what's the difference?

Or am I just missing something fundamental about what people are getting at when they claim that there's a distinction in terms of modes of belief revision?

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