Monday, January 22, 2007

The Scientific Method

I've held up the scientific method of acquiring knowledge as a standard to which I hold religious claims of truth. It behooves me then to describe what the scientific method actually is, and take the opportunity to explain why scientists use that method instead of another.

The scientific method does the jobs we expect a knowledge-creating system to do: It creates agreement between people, and it generates accurate predictions of future experience. I'm firm about the creating agreement criterion, but I'm open-minded about the "predicting the future" part. If you have a method of generating agreement, I really want some pragmatic reason why I should buy in to that method. Religion has a poor track record on both these criteria.

The scientific method starts off by admitting as evidence only facts, those statements that everyone can verify by direct observation. You can see what the clock, the ruler, the voltmeter, the gas chromatograph reads. Although as Quine notes, the meaning of statements about evidence rests on the whole edifice of language, but one's assent or dissent to such statements is a result only of observation. You might have to know the whole English language to understand the statement, "The cat is on the mat," but you have to actually look at the cat to agree or disagree with it.

As it happens, amazingly enough, huge numbers of people just all agree (or all disagree) with a mind-bogglingly enormous number of these sorts of statements. There's no complicated rational analysis involved, people don't have to think it through, they just look and see. I point to the tree and say, "Hey, that's a tree," and everyone around me (who speaks English) says, "Yup, that is, indeed, a tree." (Out of personal vanity, I'll refrain from reproducing their further comments on the subtly and perspicacity of such observations.)

Simply because everyone agrees (save a few benighted souls whom we simply arbitrarily exclude from the conversation), we label these statements "true" (or "false" if everyone disagrees). "True" is just a word; if we define "true" to mean (among other things) the same for everyone, then any statement to which everyone does in fact offer the same assent is therefore "true".

I'm not making any grandiose metaphysical claims here. I'm just creating an arbitrary label which I can apply to a category of my own experience. The only metaphysical claim I'm making now is that I'm interested in what I see people agree on.

This is only the first piece of the puzzle; all we've done so far is create a list of facts.

The second piece of the puzzle is the ancient Greeks' invention (discovery?) of deductive logic. They found that there was a pattern in our intuitive understanding of the facts we observe. If we use deductive logic from true premises, we always end up with true conclusions. And if we end up with a false conclusion, we can always trace that falsity back to the premises and never to deductive logic itself.

The Greeks were so enamored with deductive logic that they more-or-less discarded perceptual facts as hopelessly unreliable and admitted only deductive logic itself as a way to knowledge. This reliance was apparently gloriously vindicated by Euclid's geometry, which seemed to yield real knowledge about the world using only pure deductive logic.

But there was a fly in the ointment. To use deductive logic, you have to start with some premises, premises which themselves are not deduced from anything. At first, nobody cared all that much: All of Euclid's premises seemed blindingly obvious and beyond the range of serious doubt. All of them, that is, except one: the parallel postulate. This postulate just didn't seem quite as intuitively "truthy" as the rest. All attempts to deduce the proposition as a theorem simply failed, some more spectacularly than the rest. Nor could one just do away with it: Almost all of the theorems of Euclidian geometry which actually seem to talk about real world rely on this postulate.

Then Lobachevsky, Bolyai and Riemann blew the doors off the whole idea with their invention (discovery?) of Non-Euclidean Geometry. Suddenly there was mass epistemic confusion: Was it really true that the sum of the interior angles of a triangle was exactly 180 degrees? Euclid says yes, Lobachevsky and Riemann say either less or more. All of them appear to be equally rigorous in their deductions; the only difference is in that pesky non-truthy parallel postulate.

Deductive logic also faced difficulty on another front. Even the ancient Greeks noted that you could create apparently well-formed, intuitively meaningful statements in ordinary natural language that were self-contradictory from the standpoint of deductive logic. Epimenides the Cretan said, "All Cretans are liars." Is this statement true? If so, Epimenides is lying and the statement is false. Is it false? If so, Epimenides is telling the truth, which contradicts the assertion that he's a liar.

Again, logicians and mathematicians tried to mightily to wriggle out of these sorts of paradoxes. The most heroic effort was Whitehead and Russell's seminal work Principia Mathematica, which built an "elaborate system of types" to avoid paradoxes like Epimenides'. Heroic as it was, Gödel upset the applecart by proving that any logical method as powerful as Principia (powerful enough, that is, to describe ordinary arithmetic) was necessarily incomplete.

Deductive logic, while obviously a powerful tool, cannot stand on its own. On the one hand, it proves "too much": The angles of a triangle add up to exactly 180 degrees, they add up to less than 180 degrees, they add up to more than 180 degrees. On the other hand, it proves too little: You can't use any set of postulates to prove that those same postulates are consistent and complete. (You can prove the consistency and completeness of some set of postulates by using different postulates, but the same problem remains for the new postulates).

That's enough for today. In my next post, I'll talk about the failure of the Logical Positivists' Empiricism and the triumph of Popper's Falsificationism.

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