Mathematics

If a certain concept is seen as indefinable, such as the concept of infinity, how can it be said to exist?

Comments

I'm not going to comment on infinity, but on the general point. First of all, which existence is in question: a concept or a thing? If a thing, it would seem possible that there could be something that exists but that we cannot conceptualise. So here there would be no question of a definition, yet the thing exists. If a concept, well, one in fact argue that some concepts must be undefined, or else the chain of definitions would have to go on for ever. (Though circles might be another possibility.) But if it is OK, indeed obligatory, that some concepts are undefined, then maybe it is OK for a concept to be indefinable.

There is a great deal of philosophical excitement over the question of what it is to grasp a concept, but I think that it is widely agreed that definition is not the only way in.

Read another response by Peter Lipton

Read another response about Mathematics