Re: Existence of reals and observation of them

On Dec 13, 12:40 pm, lwal...@xxxxxxxxx wrote:

Is it possible for someone to be an expert on set theory
and standard analysis -- i.e., they've aced every set
theory and real analysis in university, read every last
book on the planet about set theory and real analysis,
and even earned a Ph.D. from a prestigious university in
analysis -- and yet still believe that there can exist a
credible system of mathematics other than Z(F)(C) and
standard R (and closely related theories and sets)?

Of course it's possible. The literature on alternatives is brimming
with books and papers, written by people with degrees in mathematics.
And if there is not enough such literature, then there's nothing
stopping someone with rigorous alternatives to present them. But just
spouting a bunch of free floating crank baloney is not such an
alternative.

I must agree with HdB here. The proponents of classical
mathematics do tend to assume that anyone who learns about
it and fully understands it will accept it and not raise
questions about alternate theories and sets.

What a RIDICULOUS assertion! Even the literature in philosophy of
mathematics that is steeped in classical mathematics raises all kinds
of contentious questions about classical mathematics and about
alternatives to classical mathematics, and there is also a great
amount written that is not even premised or centered on classical
mathematics.

As well as, at a basic level, it's not even a question of "accepting",
but rather of understanding what a proof from axioms IS and the sense
in which a proof stands as a proof whether one "accepts" the axioms or
not. One doesn't have to accept or commit to any particular set of
axioms just to work with them. One might or might not think of working
with axioms that one does not commit to as true to be a rather vacant
exercise, but still such commitment is not necessary to work with the
axioms to see what can be proven from them.

MoeBlee


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