4

After reading What is "ultrafinitism" and why do people believe it?, I became interested in ultrafinitism and am looking for books or references that I can read to learn more about it. Any recommendations? I am particularly intrigued by the existence of self-verifying theories.

qbt937
  • 296
  • 1
    Edward Nelson was a well-known ultrafinitist. Some of his papers are on ultrafinitism, and his book "Predicative Arithmetic" is heavily influenced by ultrafinitist concerns. None of his books are "Ultrafinitism: The Book" though. I don't recall him discussing self-verifying theories but I certainly haven't read everything he's written. Still, I don't think self-verifying theories had anything to do with his stance on ultrafinitism. – Derek Elkins left SE Dec 19 '17 at 00:11
  • It makes no sense to deny the existence of , lets say, Graham's number, just because it is too large to graps its magnitude. Sorry, but I do not consider ultrafinitism to be valid. – Peter Jun 08 '18 at 09:21
  • 1
    @Peter Interpreted in that way, I agree that ultrafinitism doesn't make all that much sense. However, I am more interested in computational interpretations of logic (https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence). Ultrafinitism requires all functions to be computationally efficient, which is something that makes sense to study (complexity theory). There may also be ways to encode statements about Graham's number indirectly (I don't know), just like intuitionistic logic can use double negation to talk about classical logic. – qbt937 Jun 12 '18 at 04:17

0 Answers0