Thursday, June 01, 2006

Proving Before Defining

We have all run across him before. He's the guy who says, in response to every argument for something's existence (let's call it "X"), "You have to define X first." And then the argument gets diverted into word-chopping discussions of how to define X, before we even know whether there exists any X worth defining.

Most people have difficulty dealing with this word-chopper, because his point seems initially plausible. I would suggest, however, that this plausibility is merely apparent. It is simply wrong. To argue for the existence of X you don't need a definition of X. What is more, it is irrational to make such a claim, because the reverse is true. We can only define a thing if we know what sort of arguments could be made for its existence (or nonexistence). Any other sort of definition is merely stipulative definition of the term -- and, since we can stipulate as we please, the only thing worth arguing over when it comes to stipulative definitions is whether they are unnecessarily misleading in the context. (Not, of course, that you need to define "X" first even verbally -- that can come after the argument for X's existence, because it isn't necessary for the argument itself.) The only time anyone defines before they prove is when it's important for a premise of the argument -- a premise, not the conclusion.

This point might might be made clearer by an example of good practice in this regard. When Suarez in his Metaphysical Disputations argues for the existence of substantial forms, he begins by arguing for their existence, and ends by defining them. And it is easy to see why. The existence of substantial forms is not obvious; it has to be proven. But what we can say substantial forms are will depend on the sort of arguments we can give for them. All we need to do this is to have a vague notion of the sort of thing you might apply the label 'substantial form', so that you can determine the right sort of premises. Then, when you have shown that something of (more or less) this sort exists, you can look at the reasons you gave in order to give a proper definition of 'substantial form'. Since you already have the arguments for its existence in hand, you can use these to define the term in a non-arbitrary way. If you do it any other way, you have to (with magical intuitions, apparently) hit on exactly the right definition from the get-go. (This is a reason why the word-chopper mentioned above is often someone arguing for the negative: if you convince people that they can't ever prove something's existence before they've defined it, you've made it very, very difficult for them to prove that anything exists. If their definition is a little off -- e.g., part of it is confusing things that shouldn't be confused, or they have made a mistake in the precise formulation -- then it could block all their attempts to argue for its existence, even if what they are trying to prove exists along with good arguments for its existence.)

Another example is arguments for the existence of God. Thomas Aquinas is often criticized for arguing for the existence of a certain sort of thing (e.g., a first cause), and saying, "And this all men call God." But Aquinas, as is often the case, has the right idea. From a philosophical perspective, what you need to examine when you're examining whether God exists, is whether we have any reason to think that anything that would more or less be the sort of thing we would call 'God' exists. Once this is in hand you can look at the details of what sort of thing, precisely, this divine thing is. This is exactly how Aquinas proceeds.

The point is general, and fits many different fields of thought. You don't define until you prove, because the proof is the only thing that keeps your definition rooted in reality. Rarely, if ever, is it rational to try to define X before having shown (or assumed) that X exists. (The only cases in which it would be are ontological arguments, and those would only be relevant if sound ontological arguments weren't question-begging, which they are.)

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