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What is the logic for logical reasoning? | Andrew Brown

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Some say our capacity for abstract thought is a cognitive trick, yet this argument undermines itself. Can we trust our reason?

One of the oddest things about evolution is the fact we know that it's true. Odder still is the fact that we think it's important. This knowledge is almost entirely useless for our survival, or at least it has been up until very recently, yet we care about it passionately.

Why on earth (where evolution rules) should abstract truth be so important to us? Why should it be even comprehensible? Why on earth would it be to the advantage of a creature to care about the truth in abstract, or to have a grasp of logic, or mathematics? All these capacities had clearly evolved in us long before they were useful. In fact, in the case of mathematics, and of logical reasoning, you can still find earlier and more primitive versions a very short distance under the rational surface of our minds.

We make most of our decisions "irrationally", as we do most of our thinking, based on biased, short-cut heuristics, something which is only surprising in the light of some contemporary myths about rationality. What's really surprising is that we understand that there are other ways to think, and that these other ways – let's group them for a moment under "logical reasoning" – seem, so far as we can tell, to be timeless and objective truths.

That 200 and 200 makes 400, and 200 times 200, 40,000 are simple statements of truth, independent of whether we would like them to be so or not. Similarly, the laws of logic are there, and work to lead us to correct conclusions, whether we like them or not.

They were all discovered, rather than invented. They are features of the universe, not social conventions like money. This also goes for the facts that scientific theories explain: the world could be mathematically described long before human beings existed, and longer still before Galileo, Kepler and Newton.

Some people, I know, deny this. They would argue that what seem like features of the universe are just helpful cognitive tricks that we have stumbled on and that we have been selected for those cognitive habits without reference to their wider truths. That's clearly how a lot of instincts work: fish, for example, are easily scared by things moving above them without necessarily having any concept of birds, or even people fishing. A footballer can kick a ball or an opponent without the intellectual equipment required of an artillery officer trying to make a shell land on target. But the kind of reasoning needed to reach logical or mathematical conclusions is different in kind from the implicit knowledge we draw on for most of our lives.

I was at a seminar in Oxford last week where these questions were discussed and the most interesting intervention was made by the philosopher Ralph Walker, who argued that the claim that logical consistency is merely a cognitive trick must ultimately be self-defeating, since you can't coherently make the argument that logic is only a cognitive trick without relying on logical arguments, which in turn robs your argument of all its force.

I find this entirely convincing, even if I am not sure of being able to defend it against a sufficiently ruthless attack from a trained philosopher. I could only really defend myself with xkcd.

There is an analogy here with sight. No one doubts that our eyesight has evolved, nor that it is species-specific. We see the world very differently from the ways in which colour-blind animals do, or insects with their compound eyes. Animals with binocular vision see the world differently from those that have eyes set to look out the side for predators. But none of this is an argument that the world we see does not exist. The cat sees a bird on my lawn entirely differently to how I do. The blackbird, in turn, sees the cat in a way I would not recognise, while the worm it's eating doesn't see any of us at all. But the worm, the cat, the bird and I all exist. Our visions of each other are imperfect but not delusional.

I think the same goes for our intuitions about logic, rationality, and arithmetic. The really interesting question is whether the same is true of our moral intuitions or discoveries. It's a central claim of orthodox Christian theology that we can reason our way to the truth in moral questions and this has largely been taken over by the atheists and utilitarians who dominate moral discussions today. I believe it myself. But can anyone actually prove it is so?


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