[ExI] Gemini on Mathematical Realism

[Jason Resch]

On Thu, Oct 8, 2026 at 2:40 PM Ben Zaiboc via extropy-chat <
extropy-chat at lists.extropy.org> wrote:

> On 08/10/2026 12:52, Jason Resch wrote:
> >
> >     Ben Wrote:
> >
> >     As I keep saying (and as I think that Gemini is saying, if I
> understand correctly), the properties come into being as a consequence of
> the system being created (and used.
> >
> >
> > I don't buy it. How can one finite act, by finite beings, in a finite
> universe, create infinite properties?
>
>
> Good question. I don't know the answer. I just know that, as far as we can
> tell, it happens.
>

Are you sure? How would things be any different if the truth already
existed before a human made any scratches on a chalk board?


>
> There's probably some mathematical theory that does explain it though.
> Maybe an LLM knows one, or can hallucinate one.
>
> Although.. Doesn't the invention of real numbers create this situation?
>

Even just the introduction of natural (whole) numbers, with addition and
multiplication, introduce infinite incomprehensible unprovable truths.


>
>
> >
> > As I see it, either finite acts only create finite things, and there
> aren't infinite primes or digits of Pi, or there are infinite primes and
> digits of Pi, and our finite acts can only finitely grope at them (but they
> can't create them).
> >
> > Gemini's hybrid view (which I think is best described as contingent
> platonism) seems to combine the least intuitive aspects of both platonism
> and constructivism. It has the infinitely incomprehensible objects of
> platonism, but it conditions their existence on finite and temporal human
> activity.
> >
> >     If Conway created GoL but nobody ever played it, I don't think it
> would really make sense to claim that glider guns existed. After all,
> nobody would have heard of them! The term, and the concept, would never
> exist). There may be an infinity of such properties, but before the system
> existed, they didn't exist either. And if nobody ever reveals them by
> playing the game or running the system, whatever it might be, then it
> probably makes sense to say that they still don't exist yet, even though
> the potential for them does.
> >
> >
> > What would you say if someone in another far away galaxy (outside our
> light cone) discovered them, would they exist? If you say it would not
> exist in that case, the must the question of existence be answered
> separately for every observer? If you meet a guy on the street who's never
> heard of Conway or his GoL, does it not exist for him?
>
>
> I think we're starting to get into "what is the meaning of the word
> 'exist'?" territory here.
>

Yes, that is the main topic of this thread as far as I am concerned (what
does the existence of mathematical truth depend on). There were usually 2
primary answers to this, Gemini introduces a third:

1. Platonism: Nothing
2. Formalism: It doesn't exist beyond human activity manipulating symbols
in an axiomatic system.
3. Gemini: It exists infinitely the moment a first human writes down some
axioms.


>
> I will say, though, that if someone outside our light cone did discover
> something, /we would never know about it/. I don't know about anyone else,
> but I think that this is a significant fact.


> Obviously if someone has no knowledge of a thing, and that thing has no
> impact on him, then it doesn't exist for him. I know that the [unknowable
> thing with no impact on my life] doesn't exist for me. Whether it's
> theoretically possible or not makes no difference to that.
>

Isn't existence objective though? Do you accept stars could exist beyond
our cosmological horizon, stars you will never know about. If so then
existence is a relation that's independent of what any particular subject
knows or has access to.


>
> >
> >
> >     Otherwise, you end up saying that an infinity of things that we have
> absolutely no knowledge of, can't even imagine, and will never ever see,
> definitely 'exist'.
> >
> >
> > That is a view I have learned to make peace with. Setting aside the
> hundreds of billions of galaxies and the 10^22 other star systems in the
> observable universe, there are at least 10^120 bubble universes with
> different vacuum energies, and at least 10^500 possible string theory
> universes. There are also very many integers and digits of Pi and primes we
> will never see (most of them in fact).
> >
> > This is what it means to be finite beings with finite brains in a finite
> observable universe which sits in a plausibly infinite space, in a
> plausibly infinite multiverse, which may fall out of an infinite Ruliad or
> the set of all mathematical objects or all possible computations.
> >
> >     I can't see such a viewpoint being any use at all, and of course you
> can never know if it's true. It becomes something like another kind of
> 'halting problem'.
> >
> >
> > It is easy to think that such an ontology has no consequences, but quite
> surprisingly, that is a false assumption. If all computations exist, then
> there are testable consequences that follow. I documented 98 examples of
> these consequences from a survey of the literature here:
> >
> > https://zenodo.org/records/19474213
>
>
> None of that makes any sense to me, but then hypothetical and unknowable
> universes and other imaginary things aren't really my field. It might as
> well be theology as far as I'm concerned. Even the first idea: "If all
> computations exist" sounds like nonsense to me. Does it include 1+1=5?
>
> All I can say (or rather ask) is, are there any /real-world/ consequences,
> that are testable? You are claiming that this viewpoint actually does have
> some use. What is it? How does it help anybody live a better life, or make
> better decisions, etc?
>

I fed the paper into NotebookLM and had it answer your questions, you can
also ask any follow up questions you might have. I also asked Google to
create a slide deck and a simulated conversational deep-dive between two
AIs discussing the paper. You can access it here:
https://notebook.google.com/notebook/b0bd5a63-1029-4724-a80d-c624d6a86261

Jason
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