Re: The reality of sets, on a scale of 1 to 10 (theory of theories)

On 3/23/2025 11:23 AM, Ross Finlayson wrote:

On 03/23/2025 10:33 AM, Jim Burns wrote:

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

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

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Nuff said (concerning the context). :-P

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

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⎛ 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.
>
>
>

 Oh, what about a mathematical universe hypothesis?

It might have something to do with fractals... Perhaps, well, sometimes I think we (our universe) might be contained within a black hole residing inside our parent universe. Two massive black holes might of merged in our parent, there merger was "fertile", and created us, perhaps?. Our universe. This is just thinking out loud here for fun. Whatever! ;^)

 Combining a strong mathematical platonism with
a strong mathematical universe hypothesis and
a strong logicist positivism, is there "A Theory",
at all?
 The Theory?