[ExI] Gemini on Mathematical Realism

[Jason Resch]

On Wed, Oct 7, 2026, 4:57 AM Ben Zaiboc via extropy-chat <
extropy-chat at lists.extropy.org> wrote:

> On 06/10/2026 22:32, Jason Resch wrote:
> > Godel used almost the same argument to reach the same conclusion:
> >
> > "[The existence of] absolutely undecidable mathematical propositions,
> seems to disprove the view that mathematics is only our own creation; for
> the creator necessarily knows all properties of his creatures, because they
> can’t have any others except those he has given to them.
>
>
> This is not true. A creation often has properties that its creator didn't
> explicitly give it, and has no prior knowledge of.
>
> John Conway didn't know all the properties of his Game of Life, that has
> become a famous example of not knowing what a system will do before it does
> it. Mandelbrot didn't know all the properties of fractals. Those are just
> two immediately obvious examples. There are many more.
>


But note the two examples you gave are mathematical objects--the very kind
that Godel would say were discovered rather than created.

Compare this against the properties a fiction author creates for the
characters in his book, all of which are assigned explicitly or implicitly
through the text put on paper. There is no more to those characters than
what the author happens to write down.

But this is never true for objects in math. The number 3 has more
properties than could ever be written down in any book, even if you used
all the atoms in the observable universe as pages.


> Given this, it would seem that Godel was wrong, and the existence of
> undecidable propositions does not disprove the view that maths is our
> creation.
>
> In fact, the Game of Life is a good illustration of the whole thing:
> Glider guns had to be discovered, they weren't known until someone chanced
> upon them, but neither did they exist prior to Conway creating the rules of
> the game. So there was no pre-existing 'platonic' glider gun, until someone
> set up the rules that brought it into existence.
>

Yes and note you used the word "discovered" which I think is the
appropriate word for finding things like glider guns or other possible
structures or properties in GoL.

GoL was defined (I won't use created or discovered here to not beg the
question) in 1970, but it wasn't until 1982 that it was proven that one
could build a Turing machine in the game of life. And it wasn't until 2018
that someone found  a way to build a universal Turing machine with a
working tape.

This possibility was always there in the basic rules. But none of this was
immediately known to Conway when he out the rules down on paper.

So as Godel asked: could such a thing like GoL be "only our own creation"
when it has so many rich properties beyond what Conway originally knew? And
if these later-discovered properties were not known by Conway, and
therefore not specified by him, then where do they come from? How can two
isolated observers both discover the same properties of GoL or the
Mabdlebrot set, unless there is some sort of objective truth exists
concerning these objects? If the properties are already there, waiting to
be found, then mathematical objects are not *only* our creations.

Jason
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