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Friday, March 18, 2011

The Analytic/Synthetic Distinction

I've been discussing moral noncognitivism lately, and the topic turned to the question of whether or not mathematical truths are analytic. Analytic truth is truth by definition (or truth by virtue of meaning), whereas synthetic truth is truth in relation to what is the case. There's a lot of controversial history in philosophy over how to construe this distinciton, and whether or not we should even take the distinction seriously. Some say it is not a principled distinction at all. Much of the disagreement stems from different attitudes towards the very notions of meaning and truth.

I prefer a pragmatic view of the distinction, since I regard meaning and truth as matters of how sentences are used, and not as properties of sentences themselves. Thus, sentences are neither analytic nor synthetic, but they can be used to make analytic or synthetic assertions. One consequence of this view is that all sentences can be used to make both analytic and synthetic assertions.

The distinction is drawn thus: An assertion is analytic if it is properly taken as a definition or rule. An assertion is synthetic if it is taken as a statement about a possible state of affairs.

For example, take this common example of analytic truth: "All bachelors are unmarried." Since the term "bachelor" means "unmarried man," the definitions of the terms indicate that this sentence is analytic. We naturally suppose that the sentence itself is true by definition. Yet, the sentence doesn't say anything. Only people say things, and a person could use this sentence in both analytic and synthetic ways. If somebody is using it to state the rule that equates bachelorhood with being unmarried, then they are making an analytic assertion. If they are using the sentence to say something about what may or may not be the case, however, then they are making a synthetic assertion. For example, somebody could use it to assert that every living bachelor is unmarried. That is a statement about what is the case. If we then investigated whether or not every living bachelor was unmarried, we would be able to confirm or deny the truth of the claim.

Of course, since we regard it as a rule, we expect that we must find that every living bachelor is unmarried. How could we possibly find one that was unmarried? Yes, if we regard the sentence as a rule, then of course it is a rule. My point is that we don't have to regard it that way. The sentence itself does not force this reading. It's only a convention which defines the sentence as a rule. If we have a hard time understanding this, it's only because we are so accustomed to this convention.

I think anybody who takes the analytic/synthetic distinction seriously will agree that analytic truths are rules. What is true by definition is true as a rule. It should be agreed, then, that analytic statements are assertions of rules. They can be corroborated by appeal to some rule-defining authority, but not by appeal to what is the case--unless we have disagreement about what is an appropriate rule-defining authority. My view is unique only in claiming that what defines a rule as such is not a sentence, but a convention, and that sentences can be used in both conventional and unconventional ways. I don't think that's an unreasonable position to take in the philosophy of language.

It might be harder for some to accept in the philosophy of mathematics, but I think the same goes for mathematical truths, like "2 + 2 = 4." We can take such equations as analytic truths, in so far as we regard them as rules. But we don't have to regard them that way. We can also use "2+2=4" to express a synthetic truth: namely, that if you add two to two you will get four. This statement is about what will happen, and not about what is or is not a rule.

There is nothing about sentences or equations themselves which makes them rules. We only think of them as rules because we use them to state rules.