[ExI] Why do the language model and the vision model align?

[Ben Zaiboc]

On 17/02/2026 12:05, Jason Resch wrote:
>
>
> On Mon, Feb 16, 2026, 1:33 PM Ben Zaiboc via extropy-chat <extropy-chat at lists.extropy.org> wrote:
>
>     On 16/02/2026 16:34, Jason Resch wrote:
>
>     > To advocate a bit for Platonism, I am wondering how you would class the existence of mathematical truths and objects. For example, assuming we agree that zero has infinite factors, that pi has infinite digits, and that there are infinite primes, and assuming we agree that these infinite factors, infinite digits, and infinite primes do not all exist in the physical universe, then where do they exist? They can't exist in human minds (as our minds can't hold infinite things) and we already agreed they don't exist physically. So we require some third manner of existence for such things as these. For this, I think "Platonic existence" is the perfect substitute for when neither physical, nor mental realms will do.
>
>
>     These things come into existence when data-processing systems think about them.
>
>
> But where do they exist? Or to ask another way: in what *sense* do they exist?


They exist in the minds thinking about them. The sense in which they exist is the same sense in which any concepts exist, whether or not they have any counterparts in the world outside the mind thinking about them.
The difference between concepts such as 'Beauty' and 'Nineteen' is that one relates to human psychology, and the other relates to the properties of matter, but they are both only meaningful within the context of a mind.


>
>     I don't see that there's any need to posit that they exist independently of this.
>
>
> The problem come comes in when we say there aren't infinite primes, or that e^pi*i + 1 = 0. Our mathematics breaks if there is some largest prime or if pi's digits don't go on forever.
>
> But the infinite primes, and pi's infinite digits exist neither in our heads, nor in the physical universe. Yet they must exist in some sense or else we must abandon mathematics we know it.

The concepts do exist in our heads. The actual values don't exist at all, unless someone calculates them. Maths is an expression of the properties of the universe, a consequence of the particular laws this universe uses, or at least a consequence of the way we see them. We don't have to abandon maths just because it might not be 'true', or might not actually exist in some hypothetical mystical plane of existence. We use maths because it's useful, not because it's true, or actually exists.

>
> When Godel (through his theorems) realized that mathematical truths cannot be a human invention (since mathematical truth transcends any human created axiomatic system), he came to the conclusion that objects in mathematics must have some kind of objective or Platonic existence, as they could not be our own creations.

I don't claim to know what Godel actually thought, but I do think that the argument about whether maths is discovered or invented is a false dichotomy, rather like the nature/nurture one.

Of course maths is a human invention. And a discovery. We invented a method of discovering certain things about the world.
Or to put it another way, we found a way of working certain things out.

Do those certain things exist independently of being worked out? That's kind of a non-question. Does a falling tree make a noise if nobody hears it?

>
> For this reason, I think idealism, nominalism, etc. are inadequate when it comes to accounting for the existence of mathematical truth and objects.
>
>
>     Do the possible configurations of a Game of Life exist somewhere, independently of an actual instance of the Game of Life working through them?
>
>
>
>
> If you agree that "2 + 2 = 4" is true independent of you, me, or the first mathematician to scribe that pattern on a clay tablet, then from this fact alone it can be shown that there exist more complex equations (universal Diophantine equations) whose solutions represent the outputs of every computable function.

I don't know what that means.
But, no, I don't agree about "2 + 2 = 4". Without someone to interpret it, that's just some squiggles. Squiggles are neither true nor false.

When you do have someone to interpret it, though, it just means that if you have two things, then add another two things, you have two things and two things. More conveniently expressed as 'four things'. Asking if this is true independently of people, basically boils down to 'Do things spontaneously appear or disappear?'. We can probably devise ways to determine this, although it always takes at least one person to look at the results, so it's still an open question. On the whole, though, if we assume that they don't, things seem to work pretty well.

> Among these computable functions, include every possible Game of Life state and it's full evolution.
>
> Now you ask, is such a game "actual"?
>
> Here we need to qualify what work the word "actual" is doing here. What makes one computation (among the infinity of computations performed by this universal Diophantine equation) actual and another not?
>
> After all, what we consider our *actual physical universe* could itself be just one of the many outputs resulting from all the computations performed by such a platonically existing universal Diophantine equation.
>
>
>     Does it make any sense to claim that the 49 trillionth digit of Pi exists, unless and until some system actually calculates it?
>
>
> I think it makes no sense to say "Pi doesn't have an Nth digit because no one has computed it yet."
>
> I believe each of Pi's digits exists, whether or not some primate writes it down in a chalk board and looks at it.
>
> You believe there are more than 52 Mersenne primes, don't you?

I have no beliefs concerning Mersenne primes, mainly because I don't understand what they are. I did look up the definition, but that didn't help.

I think that saying "Pi doesn't have an Nth digit because no one has computed it yet" is a different thing to saying "The Nth digit of Pi is implicit in the structure and properties of the universe, and will appear when it is needed, but not before".

Personally, I don't think it's useful to say that something which could exist, does exist. I don't think that someone in ancient mesopotamia who said "there are no buildings half-a-mile tall" could reasonably be said to have been wrong, despite the fact that, given the right circumstances, it's possible to create buildings half-a-mile tall.

>
>
>     You could say that things like this exist in the same sense that gods or Santa Claus 'exist': as concepts in minds ('meta-existence'?).
>
>
> The difference is there is objective truth and properties associated with these objects. Mathematical objects can be studied rationally and their properties agreed upon, even by cultures that never meet or interact. Aliens on other worlds would discover the same digits of Pi as we discover. That's the difference between mathematical objects and ideas like Santa.
>
>
>     The fact that any mind in any particular universe is going to come up with the same answers every time (at least for the maths examples) is not really significant, except to show that the physical rules of that universe are consistent.
>
>
> In my view what makes something objective is being amenable to be studied, investigated, and revealing properties that independent researchers can agree on.
>
> This is what makes physics an objective field, and it is what makes mathematics an objective field.
>
> Note that unlike in fiction, people aren't free to just "make up" a 53rd Mersenne prime and claim prize money -- they must discover *an actual* Mersenne prime, that is, they must *discover* a new number having all the properties of a Mersenne prime.
>
>
>     So I reckon that there is no need for 'Platonic existence', for things that don't actually exist in the physical realm, because they do exist in the mental realm, whenever they are needed. They appear there as a result of computation. Otherwise, they don't actually exist, or maybe you could say that they exist potentially, implicit in the laws of nature (or in the case of gods & Santa, implicit in human psychology).
>
>
> There are different forms of existence.
>
> There is existence defined by being mutually causally interactive (what we normally think of as physical existence, or existing within this universe). 
>
> But then there is also existence for things which are acausal. For example, two bubble universes in eternal inflation that will never interact, or two decohered branches in many worlds, or even just other universes with different laws, which we presume must exist to explain the fine tuning of the laws of our own universe. In what sense do these other universes exist?
>
> Are they still worth of the full "concrete physical existence" when we can't see them and can't interact with them? Or should their existence be demoted to inferred/abstract/theoretical?
>
> If the latter, isn't that the same sort of existence that mathematical object have? Other physical universes can be studied via simulation, we can analyze their properties, what structures exist as a result of their different laws, etc.
>
> The abstract sort of existence that other possible universes have seems to be, to be the same sort mathematical objects have.

Ok, we can agree on that.
It could be called 'imaginary, but with rules'. Which is a subclass of 'imaginary'.

So I'd propose a simple classification system:

A) Stuff that physically exists (ducks, people, sofas, stars, magnetic fields, etc.)

B) Things that are imaginary (exist as information patterns in minds: Santa, Jealousy, Immoveable objects, Other minds, etc.)
    B1)  Imaginary things that conform to specific rules (Maths, Cricket scores, Cutlery etiquette, etc.)


-- 
Ben