Mathematics and Theory of Knowledge

[Peter G.]

Main Question or Discussion Point

Hi,

As part of my Theory of Knowledge course I am studying the areas of knowledge, more specifically, Mathematics.

I am researching about the idea of absolute and relative truths. I am looking for the most basic, fundamental principle of mathematics, that is, maybe an "assumption(?)" that enables mathematics to function, analogous to the fact that 0! = 1. It is defined as so in order to make factorials work. With that idea I could then argue that, if that principle existed and was not absolute, hence, relative, Mathematics would exist and not exist at the same time, going against the Law of non-contradiction for example.

Is there such a principle?

Thanks,
Peter

 

[homeomorphic]

Maybe what you are looking for is the existence of the empty set.

It's all based on that, plus various choices of axioms, maybe most commonly, Zermelo-Fraenkel axioms:

http://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory

I'm not sure about the philosophical implications.

 

[Peter G.]

Cool, thanks for the response! I will look into that!