[xamuel]

When philosophers study mankind's knowledge, it's more typical to study the things mankind would ideally know at the end of all time assuming mankind could continue forever.

(Formally: the knowledge predicate is usually assumed to satisfy modus ponens: if mankind knows "A implies B" and mankind knows "A", then mankind knows "B")

Under this abstraction, if mankind knows the axioms of logic and Peano arithmetic, then mankind [ideally eventually] knows the primality of all primes.

Contrast: Which Turing machines will mankind [ideally eventually] know are never-halting? This is a much harder question and the answer is probably not "all never-halting Turing machines"

[schoen]

It's a little funny that mankind gets to use a full-fledged infinite-tape Turing machine in order to compute arbitrarily large computations, since no such machine would fit in our universe.

https://en.wikipedia.org/wiki/Limits_of_computation

https://en.wikipedia.org/wiki/Transcomputational_problem

[fooker]

The description of a Turing machine that can do arbitrarily large computations can be finite. See: Kolmogorov complexity.

[schoen]

Sure, but it feels a little funny in one way to say that people "know" all of its output, although I'd agree that for other purposes being able to write a program to generate something is a relatively good description of what it means to understand it.

[JackFr]

> then mankind [ideally eventually] knows the primality of all primes

We already know the primality of all primes. They're prime. All numbers though . . .