<p>At the foundation, some aspects of mathematics existed before anyone could define them in terms of axioms. The concept of numbers might have been an invention, but cardinality certainly existed. Suppose you have a molecule with six binding sites, and six ligands. Whether or not anyone knew it, you now have a one-to-one mapping between ligands and sites. From something as basic as this, we can extrapolate the tendencies of molecular self-assembly in crystals, which even now is a hot topic in physical chem. (Hehe, I guess I can’t talk about the axiom of choice, as I’m still puzzling over the proof to the Banach-Tarski paradox. Then again, I’m not a mathematician. Talk to me about chemistry.)</p>
<p>And then, of course, there is the group of people who believe that our simple logical system does not work everywhere in reality, but only works from our point of reference. I don’t know enough about the basis of this belief to say anything else about it. I also don’t see how Max Tegmark’s theory of an infinite multiverse is holding up, if he’s illustrating its existence simply by saying that it’s “very probable.” Soooo if anyone wants to direct some light into my hole here, I’d be grateful! :p</p>