Response from Jasper Reid on March 23, 2007

Given that mathematics is a body of universal and necessary truths, how could science (or anything else for that matter) not coincide with it? If the physical world was to violate the principles of mathematics, now that would be weird.

Response from Mark Sprevak on March 29, 2007

There is another question that might be worrying you: Why does the language of physics turn out to be mathematical? Why does mathematics turn out to be our best way of describing the physical world? I don't think that anyone has a good answer to this question. There may be no good answer, since it might just be a brute contingent feature of our world. One could imagine a world in which events were so disorganised that there would be no useful regularities that could be captured in a perspicious mathematical formalism.

Interestingly, Putnam and Quine have used the claim that mathematical language is central to our physics as a roundabout argument for the existence of mathematical objects. One of the best reasons we have to believe in the existence of an object is if our best physical theories make ineliminable reference to them (e.g. electrons). If, as appears to be true, our best physical theories make ineliminable reference to mathematics, then by parity of reasoning, we should believe that those mathematical objects exist. This ingenious line of argument has stimulated a lot of dicussion. Have a look at http://plato.stanford.edu/entries/mathphil-indis/ if you are interested.