The Spectre of Logic

A famous example of a logical paradox is “this is a lie”:
if that is a lie, if it is a lie that it is a lie, then it is not a lie.

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

Contradictions seem to arise when we think logically. Still,
would we expect highly evolved apes to be perfectly logical?

Dawkins and Russell made many young scientists give very low prior probabilities to the existence of a transcendent Creator. Such scientists think of themselves as logical, but they also 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 logic being contradictory.

Even though they think of themselves as logical, do they notice that if their atheism is logical, and logic is contradictory, then their atheism is contradictory? Do they notice that atheism is logically impossible?

Fortunately there is a logical proof that there is a transcendent Creator. That is fortunate because it means that scientists can be logical. Of course, atheists would think it unlikely that there is 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 not be irrational of them to refuse to countenance the possibility of a transcendent Creator, even though there is such a proof, 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.

But what if you had evidence that that tree was an alien quasi-stick-insect and 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, so we would only be making a very human error if we assumed that logic was flawless (and we could hardly avoid such errors by being more logical). But maybe our logic is not flawed:

    “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 far from being a reason to doubt logic.