[ExI] Gemini on Mathematical Realism

[Ben Zaiboc]

On 08/10/2026 12:52, Jason Resch wrote:
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>     Ben Wrote:
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>     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. 
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> 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.

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?


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> 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).
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> 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.
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>     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.
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> 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.

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.

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>     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'.
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> 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).
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> 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.
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>     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'.
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> 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:
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> 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?
-- 
Ben