The Spectre of Logic

A famous example of a logical paradox is: “This is a lie.”
If that is a lie, then it is a lie that it is a lie, so it is not a lie.

But if it is not a lie, then what it says is false, so it is a lie.
Whereas, if it is not a lie, then it is not the case that it is a lie.

Contradiction! So, logic gives us paradoxes. Still, so what?
Would we expect highly evolved apes to be perfectly logical?

Many scientists, having taken logical looks at the evidence, while giving very low prior probabilities to the existence of a transcendent Creator (having read books by Richard Dawkins and Bertrand Russell), do think of themselves as highly evolved apes, in a purely material world that just happens to exist, so they might not be too surprised to see their natural logic being shown to be contradictory. Modern logic is, after all, much more "rigorous" than natural logic ("rigorous" in the sense of mathematical). But if their looks at the evidence were not very logical, then their lack of surprise might not be very logical. And what if there is a logical proof that there is a transcendent Creator? Of course, they would think that there is unlikely to be such a proof, because of those very low priors. But at the end of the day there is such a proof.

Perhaps you think that it would still not be irrational of them to refuse to countenance the possibility of a transcendent Creator, much as this would not be irrational:

I see a tree, so I know it is a tree. That is certainly rational. I cannot rule out its being an alien quasi-stick-insect of a very convincing kind empirically, of course (that is what “very convincing” means); but so what? I naturally assume that it is no such thing, and even now, after thinking of this particular possibility, I still have no idea how unlikely it really is, so I cannot do better than continue to make that assumption. Making that assumption may well make my knowledge that I am looking at a tree a sort of gamble, but such is knowledge.

What if you had evidence that that tree was an alien quasi-stick-insect, though? What if you showed me that evidence? Should I not take a logical look at it? Your discovery would be very important, if your evidence was good enough (extraordinary claims do stand in need of extraordinary evidence). What if I looked at your evidence and saw nothing wrong with it but also saw that given my assumption, it must be defective; would that be logical enough? I might think so, but then, the alien might bite my head off and you would have tried to warn me (in a very scientific way).

Suppose that you had a very good argument for something that I did not like, not at all, but suppose that I gave your argument the time of day. If I let the strength of my dislike trump the logic of your argument, would I seem logical? Suppose that I deduced from my dislike that you must have made a mistake; suppose I say that there is probably something wrong with your argument (to err is human), and that I have better things to think about. Is the latter logical enough, but not the former? Surely we owe it to ourselves to be properly logical.

Even if our logic was flawed, it would still be our logic. Assuming that it was not flawed would, even then, just be a very human error. And maybe our logic is flawless:

    “The assertion that you are now reading is not true.”
    Let us call that assertion “L”, so that     L is true if, and only if, L is not true
    or, if “is true” is a vague predicate,        L is true insofar as L is not true.
    From the latter, it follows that L is as true as not,
    which it can be, if “is true” is a vague predicate.

There is only a contradiction if “is true” is not a vague predicate. And while that might not be a proof by reductio ad absurdum that “is true” is a vague predicate, it is close to being such a proof and very far from being a reason to doubt logic.