Re: because g⤨(g⁻¹(x))= g(y) [1/2] Re: how

On 5/3/2024 3:42 PM, Ross Finlayson wrote:

On 05/03/2024 07:06 AM, Tom Bola wrote:

Am 03.05.2024 15:41:24 WM drivels:

Le 02/05/2024 à 01:32, Tom Bola a écrit :

I think that WM has a very fixed idea of the
"world of math" which is fixed by nature and
not a creation of culture in the mind of men

I can imagine WM saying that, or thinking that, but,
when I emulate a curious four.year.old, and ask
"Why? Why? Why?",
his explanations stop at what he allegedly perceives.
What I see is a foundation which is
the one.man.culture of WM.
Very fixed, yes.
Fixed by nature?
Fixed by some larger.than.one culture?
Given what I see, WM's actions contradict that.

I don't know whether actual infinity is true.

>
Being true IN MIND is
all the Mathematicians want and need.

>
That there is a "theory of truth" has two schools:
"idealists" are "platonists" who
agree mathematics is discovered,
"nominalists" are "figurists" who
each say mathematics is invented.

Mathematicians might not be the best sources of
information about what it is mathematicians do.
I am thinking of novelists talking about
their characters --
inventions, if anything is an invention --
talking as though the novelists struggle with them
to get the plots to go where they want.
Which sounds like discovery.
We could perhaps imagine Platonic Realms of
St. Mary Mead or Trantor in which
these characters "really" exist, and in which
the authors are merely explorers.
Perhaps mathematicians, like authors, are inventing
but, because of the way human minds work,
they find it convenient or productive or whatever
to think of what they do as exploring.