Upper level math feels a bit extra sometimes.

Me: Hey, what da ring doin'?

God or whatever: Oh, lattice stuff again. (And a dozen other things I won't make obvious.)

GoW: This is how your universe has to work by the way. You cannot avoid it.

Me: I just... thanks, I guess.

I guess it also comes down to the growing body of what is considered canonical mathematics.

People went from hating imaginary numbers, to hating sets, to hating the choice axiom, to hating automated reasoning, etc... its fickle

I do not like intellectual conformity ideas of some grand standard model.

Oh look at that. I am some sort of agnostic. lol

Show thread

These things are just preferences

Like I am short on a constructive proof of Cantor's theorem: card(A) < card(P(A)). But proving one does not exist is not very constructive itself. So I get into half buying a proof.

And infinite sets are usually an axiom. Infinity probably needs to be coded as either an inference or an axiom to exist in any system. But I buy into infinity being an actual property of the universe, because inductively there are many examples of infinite objects generating data.

Show thread

Well I am in a mathematically constructive mood today.

Ah well. I am a fan of Brouwer. Him being the father of modern topology, and his intuitive school of mathematical philosophy give me less headaches.

Adopting another philosophy of mathematics for a day is a way to get a person to look at proofs critically.

Also computable << representable. Models of computation can do both.

So saying math object is magic machines cannot know, because it is not computable, is not a complete argument.

Show thread

Reject law of excluded middle globally. Only accept LEM locally.

Show older
Mathstodon

The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!