Friday, August 04, 2017
Metamathematics
This is apparently a real thing!
Instead, metamathematics is a quest to be precise about what it is you already believe in, such that we can use ordinary mathematical reasoning about those principles to get to know interesting things about the limits of what one can hope to prove and how different choices of what to take on faith lead to different things you can prove. Or, in other words, the task is to use ordinary mathematical reasoning to build a mathematical model of ordinary mathematical reasoning itself, which we can use to study it.
