Originally Posted by

**lpetrich**
Some philosophies of mathematics affect which kinds of proof are valid, and thus affect which mathematical results are valid.

...

When Georg Cantor published his theory of transfinite numbers, one of his colleagues, Leopold Kronecker, rather strongly opposed it on finitist grounds. That theory remained controversial until the early 20th cy.

I don't think this is any problem at all. Different mathematicians start with different assumptions, so it's only proper that they should end up with different conclusions.

Again, this just shows that either mathematics is an empiric science or it's not a science at all, but if you want to say it's not a science then nothing is. Your choice.

EB