Re: The reality of sets, on a scale of 1 to 10

On 3/22/2025 9:36 PM, Ross Finlayson wrote:

On 03/22/2025 01:07 PM, Moebius wrote:

Nuff said (concerning the context). :-P

>
Does it live in
a mathematical platonist's real universe
of all the mathematical objects?
>
Or rather, mathematical platonism's?

⎛ Most writers on the subject seem to agree
⎜ that the typical working mathematician is
⎜ a Platonist on weekdays and
⎜ a formalist on Sundays.
⎝
  — Philip J. Davis.
The typical working mathematician
can change coats so easily,
formalist one day and Platonist the next,
because
that's a distinction which
doesn't make a difference to what.they.do.
One might feel that lack.of.distinction
is a problem in need of a solution,
or a beautiful truth, all we need to know.
Whatever one's attitude towards it,
it is what it is.
⎛ If you try to divine from my posts here
⎜ what my own views are concerning these issues,
⎜ you will be misled.
⎜ Here, I'm engaged in a search for common ground,
⎜ without which one can build no higher structure.
⎜ What that search looks like, apparently,
⎜ is strict formalism.
⎜
⎜ I approach mathematics from the physical sciences.
⎜ I agree with Eugene Wigner on the unreasonableness
⎜ of its effectiveness there.
⎜
⎜ What I tell myself, when I wonder about
⎜ the unreasonable effectiveness of mathematics
⎜ in the physical sciences,
⎜ is that mathematics provides shapes, Jello.molds
⎜ into which our physical experiences fit
⎜ or do not fit.
⎜
⎜ Those shapes into which our experiences fit
⎜ have theorems attached by imperishable bonds.
⎜ These are our physical predictions from theory.
⎜ The imperishability of the bonds is merely
⎜ mathematics being mathematics.
⎜ Mathematics doesn't do 'perishability'.
⎜
⎜ It seems unreasonable for us to have
⎜ what could be called 'knowledge' about
⎜ conditions billions of years earlier or later
⎜ or billions of light.years away.
⎜ I put that down to mathematical argument
⎜ which reaches far, far beyond
⎜ anything our intuition might have to say,
⎜ but, because it's mathematical,
⎜ we know is imperishably bonded to this shape
⎝ which fits our much less extensive experience.