Consistent ultrafinitist logic — mentioned by miga

Mon, 17 Oct 2022 20:02:31 GMT

Trying to find a formal system that encodes unbounded infinitary mathematical objects including most of maths, but yet to require that all statements are decidable within a finite number of steps... Is it contradiction in the proof, or rather a contradiction in assumptions? More on logic that permits all that *Bounded* Turing Machine does: https://arxiv.org/abs/2106.13309

Paper and discussion history. A mention is not an endorsement.

Consistent ultrafinitist logic — mentioned by miga

Mon, 17 Oct 2022 19:59:12 GMT

The assumption of this theorem is that we may encode any problem that is unbounded and infinite. What if we limit ourselves to *bounded* and *computable* functions only? See draft presented at many top logic conferences yet: https://arxiv.org/abs/2106.13309 Since the observable universe is bounded, and we are most interested in computable, why not to focus on maths that is most relevant to our universe instead of infinitary alternate?

Paper and discussion history. A mention is not an endorsement.

Consistent ultrafinitist logic · HackerPapers discussions

Consistent ultrafinitist logic — mentioned by miga

Consistent ultrafinitist logic — mentioned by miga