Topics Mathematics

Question In my class we had a discussion about the logic behind mathematics today. Unfortunately we didn't manage to come up with a solution to the question about which the discussion was. The question was: From the beginning of human kind we always used a logical counting pattern (today expressed as 1,2,3); do you believe that if at the beginning of human kind our logical thinking had lacked the idea of counting, maths would have turned out to be something completely different or would it even exist?

Accepted:
June 14, 2007

Comments

You are asking what we call a counterfactual question. Some such questions present little difficulty. For example, if your parents had never met, you would not be here asking hard questions.

Your counterfactual question is much harder, because you are asking us to imagine something that is quite remote from the world we know. You are asking what human beings and human life would be like if we lacked the idea of counting. Given the kind of intelligence we have, it's a foregone conclusion that we would count, I think. So you are really not asking about human beings, but about some less-endowed or differently-endowed beings (perhaps some distant pre-human ancestors) who are otherwise similar to us.

There isn't just one such species we might imagine (or discover). And the answer to your question could then be different for different non-counting but otherwise human-like species. I would doubt, though, that beings whose mental faculties do not lead them to count would do much else that we would call mathematics (geometry, for instance). But perhaps I am just lacking imagination here about alternate ways of life.

If you are interested in thinking more about our peculiar way of doing mathematics, I would recommend a look at Ludwig Wittgenstein's Remarks on the Foundations of Mathematics. It was not published in his lifetime, so is not a systematic book organized by its author himself. But it contains a lot of wonderful questions and insights.