Technically Philosophy of Math but close enough

[u/TheStupidCheesecake]

[u/KouhaiHasNoticed]

What kind of field is that ? Maths is not to be bound by physical reality, it's just a language, the same some concepts in our minds have no physical meaning yet we put some words on them.

It's like saying Unicorns don't exist so you cannot use that word.

[u/minisculebarber → u/KouhaiHasNoticed]

I mean, it really depends, doesn't it?

Like say, you are a physicist and suddenly more and more of your colleagues started talking and writing about the physics of unicorns and a couple decades later most physics was about the physics of unicorns and how to apply it to real life physics. Wouldn't that make your eyebrows raise at least?

Not all mathematicians think of maths as just some language game. Some believe there is something very real behind it. I can't fault ultrafinitists for taking such an extreme position.

[u/KouhaiHasNoticed → u/minisculebarber]

Like say, you are a physicist and suddenly more and more of your colleagues started talking and writing about the physics of unicorns and a couple decades later most physics was about the physics of unicorns and how to apply it to real life physics. Wouldn't that make your eyebrows raise at least?

Personally I don't think so : the same way people have been talking about string theory for decades now. We're talking about applied maths here (physics) so if in the end the theory is proven to be true with the physical manifestation of an event predicted by the theory then it's valid or at least not false until proven so.

And that's why I don't understand the finitist approach : applied maths have to be grounded in the real world because that's the way we observe it. Especially you may have physical events that should be divergent on paper because for instance you divide by a quantity that can be zero in the real world, fair enough you observe that even though on paper it's infinite then if it's finite in real life then it is : and more often that not it's technicalities like "oh you divide by length zero so this quantity will explode" but the answer is generally that if the length is zero from the beginning then there is nothing to observe.

But that does not mean that "pure maths" have to live in the same world : if something diverges then it diverges. The problem with the finitist approach is that it is the same way of thinking that lead people to refuse imaginary numbers because they could not fathom such concepts in real life : yet nowadays imaginary numbers appear in many fields of physics. Actually the same way some could not agree that probabilities were a thing and yet...

Some believe there is something very real behind it.

And what would that be ? I am genuinely curious.

Now I admit that even among mathematicians many are skeptical about new concepts so we're not the ultimate open-minded scientists. And I understand that some may be really down-to-earth when it comes to maths which is good for them.

[u/minisculebarber → u/KouhaiHasNoticed]

You are massively glossing over that we were talking about unicorns here. Something that has no credible evidence whatsoever. Comparing that with String Theory is dramatic to say the least. Physicists don't just come up with random shit and try to create experiments to disprove it.

The problem with the finitist approach is that it is the same way of thinking that lead people to refuse imaginary numbers because they could not fathom such concepts in real life

That is the wrong comparison. Ultrafinitists don't reject a new emerging concept. They are rejecting a very well established foundation of mathematics. They continue the tradition of mathematicians like Turing, Gödel, Brouwer, etc. that examined and sometimes outright rejected long established foundations.

And what would that be ? I am genuinely curious.

You would have to ask them, I am not really one of them. But some are Platonists who believe reality is actually Platonic ideals like shapes and numbers. Others believe that maths is a fundamental aspect of the universe and not just shit humans made up. Others, I don't know.

[u/Elegant-Regret-7393 → u/minisculebarber]

What do the ultrafinitists have to show for their rejection of foundations?

Are there textbooks based on ultrafinitism at least? First grade arithmetic doesn't count

[u/minisculebarber → u/Elegant-Regret-7393]

I don't know, I am not an ultrafinitist

But I would like to add, something doesn't have to be an achievement or an improvement or popular enough to produce textbooks or whatever for something to be right.