I know you don't debate this anymore, but I got this off of slashdot this morning and it says in a much more succinct fashion what I have been saying:
Math theorems don't necessarily have to apply to the physical universe. The axioms on which the theorems are built are explicitly part of the theorems, leading to a logically self-consistent system. That is, you define the particular 'universe' you want to study by setting down axioms, then you prove things which you know are true about that universe because you've derived them in a logical fashion from those axioms you've set down.
This includes "If A, then A" of course.
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