[jimt]

Actually, though, you can prove a negative, at least in some cases. I once took a rather painful Abstract Linear Algebra class that ended up proving that there was nothing after an "octonion," (or was it nothing after a 16-space transformation? -- I forget now...)

Your math is way beyond mine - I stopped at linear algebra, after differential equations.

Within the contraints of mathematical logic, you could certainly prove a negative. For instance, that there are no whole numbers between 1 and 2. But that's a function of the definitions.

In the context of the current discussion, it's a lot tougher. If I postulate the existence of gnorixes, for example, who control the rate of corrosion on pennies, can you prove they don't exist?

I couldn't.

[r9etb]

For instance, that there are no whole numbers between 1 and 2. But that's a function of the definitions.

Good point. The question is, though: is there any way we humans can avoid having to rely on making definitions at some level?

I think the answer is probably "no." For example, if we conside Physics in conjunction with Godel's Incompleteness Theorem, then we are left with something similar to what Kant said, and we're left to rely on definitions.

(BTW, according to the link, Godel's theorem seems to be an example of a negative proof...)