## Tuesday, September 13, 2011

### Malezieu and infinite sets

A commenter wondered whether Malezieu's principle (that a number of things - say 20 - exist because the first exists, the second exists,  and so on) applies because there are a finite number of things, and a finite time is all we have to count anything.

I don't think so. First of all, the fact that the first thing exists, the second thing exists, etc., is independent of anyone counting the things.  You object that nominating one of the things as 'first' is arbitrary, and therefore involves human choice.  I reply: take any of the things you like.  Then the fact that this thing exists, and the fact that any other one of the things exist, and the fact that any other one apart from those two exists, etc., ensures that all of them exist, and this fact is independent of any human counting going on.

Moreover, Malezieu's principle, as applied to an infinite universe, is a logical one.  We start with the nominalist assumption that only individual things exist.  We then assume that there are two possible worlds in which every individual in one is identical with some individual in the other.  Malezieu's principle then tells us that any oset of individuals that exists in one world, also exists in the other.  This is a logical consequence of the fact that existence claims relate to individual existence only.