I take the view that physical existence is in some sense a 'part' of
mathematics. However physical properties by themselves aren't
mathematical properties. Which properties do we call 'physical'?
There appear to be three main classes of properties that we interpret
as 'physical': *spatial* properties, *topological* (or containment)
properties, and *functional* properties.
Perhaps one should say that physical properties are 'partial'
mathematics. Let me try to clarify what I mean by analogy - take the
prime factorization of a non-prime number. The primes are in some
sense 'components' (or building blocks) of the non-primes. By analogy
with this, one could say that physical properties are *metaphysical
components* of mathematical entities. Physical properties by
themselves are not mathematical properties, but in combination with
other (non-physical) metaphysical entities, you build mathematical
entities. Or another analogy might be that physical properties are in
some sense 'the metaphysical square root' of mathematics.
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