Wednesday, 2 October 2013

Mathematical Platonism Is True Because it is Useful

I have briefly discussed mathematical Platonism in previous articles. This post is going to contain my current thoughts about it.

Mathematical Platonism is distinct from classic Platonism (so nothing about ideal forms, for instance) and holds that three propositions are true.

1. Mathematical objects exist.
2. Mathematical objects are independent of human beings.
3. Mathematical objects are abstract

Or, in condensed form, mathematical objects exist abstractly and independently of human beings. All possible mathematical objects exist, have always existed and will always exist, even if no mathematician ever ponders them.

In this post, I will argue that while there is no fact of the matter regarding whether mathematical objects exist, it is sensible and useful to treat them as if they do, and that this is enough to justify mathematical Platonism.