Is Logic Objective?

logicWhen you are trying to build a case for something, you really ought to avoid premises that don’t hold up. For example, in Universally Preferable Behavior: a Rational Proof of Secular Ethics, Stefan Molyneux states:

The laws of logic are derived from the behavior of matter and energy, at least at the perceptual level.

So reasoning about things that can be perceived must be derived from their objective behavior. OK, I’ll buy that for a dollar. But then …

Perceptual reality is consistent and objective – and it is from this consistency and objectivity that we derive the laws of logic… Thus … we must measure the validity of a statement relative to objective reality – both empirically, and logically. Logic as a discipline arises only as a result of the consistency of reality.

Wait, what? OK, here’s a logical statement:

If A implies B and B implies C, then A implies C.

In notation:

(A ⇒ B ^ B ⇒ C) ⇒ (A ⇒ C)

This is a logical axiom (AKA true statement) whose existence has nothing whatsoever to do with perceptual reality. You can test assertions till the cows come home and never prove it. That’s why it’s an axiom. Every mathematical system has a root set of axioms that, if we are to work in that system, have to be taken on faith. For example, the identity axiom in mathematics (x = x, or every thing equals itself) is not provable; it’s just true.

Logic is objective, but it is not perceptually objective; it’s conceptually objective. Everyone implicitly understands the transitivity of implication (the first axiom above), because axioms are self evident, though there certainly are axioms that are less intuitively obvious. For example:

Kolmogorovs-third-axiom

But this means that the second part of the following definition of truth (from UPB) does not hold:

Truth is a measure of the correlation between the ideas in our minds and the consistency of rationality, which is directly derived from the consistent behaviour of matter and energy in the real world. (Rational consistency, or internal logic.)

It is a leap to say that consistent behavior in the real world directly implies consistent behavior in internal logic.

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About jimbelton

I'm a software developer, and a writer of both fiction and non-fiction, and I blog about movies, books, and philosophy. My interest in religious philosophy and the search for the truth inspires much of my writing.
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2 Responses to Is Logic Objective?

  1. keithnoback says:

    Nice. As you imply, no theory is, in itself, true, though there are truths about the theory. And so, there can be no theory of truth.

    • jimbelton says:

      You certainly must have axioms, which are unprovable. Assuming your axioms are all true, then anything you prove based on them will also be true. The truth of your axioms is verifiable, via the consistency of the theorems that you can prove via them. If commutativity (a + b = b + a) has not been contradicted by the entirety of mathematics, it’s a good bet that it’s true. It’s just not provable by mathematics. This might be worth a follow up post. Ethics are of course not logic, so trying to apply the same sort of rigor to them is difficult. Stefan does a good job, and I find no flaws in his ethics, but some of his arguments for them are in the nature of appeals to science, IMO.

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