Chapter 24 Lower-level logic

Please don’t read, this needs a lot of work.

One of the wonderful things about logic is that one can study it at many different levels. In the previous section, a \sayworking subset of logic which is kind of necessary (and remarkably, also sufficient) for all other mathematics was described. In this section, I write down many amazing things I have discovered on the internet, which allow us to develop logics (yes, logics in the plural) for various purposes.

At this point we are no longer entirely in the realm of mathematics proper - it really sits on the boundary between philosophy and mathematics. There are a few fundamental questions we are interested in the answer to,

  • what does it mean for something to be true?

  • when is something true?

  • how can we prove that something is true?

  • can we mechanise our intuitions about whether or not something is true (this is essentially equivalent to the question \saycan we codify mathematics on a computer, but not completely)