Re: Relative Cardinality

Proginoskes wrote:
> Mathematics was designed to work outside of the physical universe.

You will have a tough time arguing this with WM as he is convinced that
ideas may be disconnected from the physical universe, but he has some
notion that mathematics exists in some real sense in our physical
reality. Of course he's the one that is the final arbiter as to what
"exists" and what doesn't "exist," and he is the final arbiter of
mathematical definitions such as what a "number" or "infinite" is
because he can obviously see what exists and what doesn't. So any
proofs to him are just "in principle" proofs and to WM this does not
apply to "mathematics." He is further convinced that all those who are
opposed to him are "set theorists" (and to WM, set theory is purely the
study of transfinite numbers) and not "real mathematicians." There
isn't even one actual set theorist or logician at UCSD, but I bet I
would have trouble finding a person even among the undergraduates here
who doesn't believe that "square root of 2 is a number."

Further WM has as much trouble distinguishing "in principle" and "in
practice" as he has with "for all" and "there exists."

Jiri

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