Normative Is Not Descriptive

Posted by Ryft

Aug 20

The following is an exchange between myself and an atheist—we shall call him Steve—over the nature of the laws of logic, also known as Aristotle’s classic laws of thought. Another individual (our own Emil) was trying to refute Steve’s belief, that the law of non-contradiction could be easily falsified, by explaining to him that one cannot refute the laws of logic without using them, which only further confirms them. So Steve tried to illustrate how one can refute the laws of logic without presupposing them:

The law of non-contradiction says that something cannot be both true and false at the same time, so the way to falsify this would be to find something that could be both true and false at the same time.

Well, if you are going to attempt falsifying the law of non-contradiction, it would better serve your effort if you addressed what the law actually states. For any reader who did not immediately notice the error in his statement of the law, let me illustrate (using his language): "something cannot be both true and false at the same time and in the same respect"—the latter part being fundamentally important because something can be true in one respect and simultaneously false in a different respect.

But then he did admit,

The law of non-contradiction is descriptive, not prescriptive.

And this could be why Steve thinks the law is falsifiable, his statement here being clearly false. Observe the very language used to express the proposition: "something cannot be both true and false at the same time and in the same respect." That is not a descriptive statement. Descriptives are expressed by "is/is not" statements. Prescriptives or normatives are expressed by "can/cannot" statements. The former relates to what we know through experience (a posteriori), and the latter to what we know independent of experience (a priori).

Update: 21 August 2009

The second law of thermodynamics is descriptive and can be written, "Heat generally cannot flow spontaneously from a material at lower temperature to a material at higher temperature."

I am ignoring the significant problem that plagues such a statement (trying to derive a prescriptive from a descriptive on a basis other than sheer fiat) for it is irrelevant at any rate to the point I had made—viz. that the law of non-contradiction is an a priori normative statement. It categorically is not a descriptive statement, for nothing a posteriori produces it. I offered him a challenge, to describe an a posteriori (empirical) test of the law of non-contradiction. Just by trying to conceive of such a test, it will soon become evident that this prescriptive cannot be written as a descriptive. We shall see how he responds.

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http://www.dampes8n.com DampeS8N

It only seems irrational to try to test the Law of Non-Contradiction because it is so completely tested. Like testing to prove that gravity exists on Earth: you drop something.

Many scientific tests rely on predictable results. This law makes predictions. If there is a true-and-false question posed, it can’t be both true and false from the same respect.

So it can easily be tested, through a host of various mechanics—including a simple one, centered on the obvious locus of computer software. Either a bit is on, or it is off. Check a billion of them to see if even one is both. And if it is, the Law of Non-Contradiction is false. Otherwise, it continues to provide valid predictive results.

Newtonian gravity was in that camp, until a man named Einstein came by with a theory that explained things more accurately and in greater depth.

Who knows, perhaps quantum computing or memristors provide an avenue to defying and thus disproving the law. Or perhaps they don’t deal in Boolean logic at all.
http://www.aristophrenium.com Ryft

Thank you for answering the challenge, Will. And, by the way, I find it very refreshing to see someone with a mutual passion for intellectual exercise. (And thanks for the props on the new blog template. I like it too.)

Your answer, however, actually does not test the law of non-contradiction, so my point stands unrefuted. As you noted, we can test and observe that the bit is on, or that it is not. But notice the wording: is and is not. Descriptive, not prescriptive. And that is all we can test: what will or will not be the case (prediction to test) and what is or is not the case (observation of test). But there is no empirical test for what can or cannot be the case; that is apodeictic, not assertoric.

The law of non-contradiction is something we know independent of experience (a priori), the sort of thing brought to experience, not derived from experience (a posteriori). It is the very definition of the terms involved.

P.S. Quantum computing holds the potential you mentioned only under a Copenhagen epistemological interpretation of quantum mechanics. I think the Bohm ontological interpretation (which Einstein presciently favoured) holds more predictive value. The Bohm interpretation demonstrates that some features of the Copenhagen interpretation are not essential to quantum mechanics, but rather are just features of the interpretation; e.g., wave collapse, entanglement, the non-existence of particles while not being observed. The two interpretations are theoretically equivalent; i.e., they give the same theoretical predictions and are equally confirmed by the experimental results. (So stick that in your pipe and smoke it, von Neumann.)