While I have never been really convinced about the argument for theoretical entities in physics I think the argument is even weaker for mathematical objects. At the very best I think one could use it to support the idea that ‘conditional’ mathematical…

]]>Peter – something like that is probably right. We have no terribly good justification for using real numbers instead of rationals, or at least computable reals, except that the theory of all reals is much simpler and more easily axiomatized (maybe?). And something like this does seem to be a reasonable scientific virtue. But you’re right, there is the other view that the mathematics is just an approximation to what’s out there. But as Resnik and some others point out, in order to say that this structure is an approximation, you have to say this structure exists. So we’re still postulating it, and postulating it directly in the structure of the world rather than as something that approximates that structure is a better argument for its existence (assuming that either argument works).

]]>More importantly, on the mathematical objects indispensable for theoretical physics, how could we know otherwise, since our only knowledge of theoretical physics comes to us through its mathematics. There is no non-mathematical theoretical physics.

]]>Your basic idea (viz., spacetime points “are somehow much more intrinsic to the physical system than real numbers seem to be”) strikes me as intuitively right. I am wondering about one thing though: when physicists and philosophers of physics talk about spacetime these days, they identify a spacetime with an ordered pair , where M is a manifold and g_ab a metric tensor on that manifold. But the standard definitions of a manifold appeal to the real numbers in the definiens. Do you think this creates a problem for your basic idea?

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