28 September 2006

It's turtles all the way down

I haven't yet grasped the relationship between proof and truth. And the ground is sufficiently tricky that I have a hard time trusting anything I read. I got something from the local public library called Fundamentals of Mathematics, which has an introductory chapter on model theory—but they go around proving things about models and logic using ordinary mathematical reasoning. This is like writing a Python compiler in Python: one feels that some bootstrapping must be involved somewhere. It's probably in a later chapter, but in the meantime my brain involuntarily rejects everything the book claims. Unproductive.

No comments: