Help understanding Gödel's theorems?

Question

What are the prerequisites to even begin to understand Gödel's theorems? I'm reading Hofstadter's book but would like a more fundamental approach to understanding these theorems. I have no knowledge in formal logic.

Answer 1

You have come to the right place (the (book-recommendation) tag)! There is a book on sale at Google Play called An Introduction to Gödel's Theorems. It discusses the basic arithmetic parts of his theorems, and explains it to where you may be able to understand his theorems. You can also buy Gödel's Theorem: An Incomplete Guide to its Use and Abuse. It talks about his incompleteness theorem and other mathematical things related to Gödel's theorem. But, it isn't complete (hence the title), but I'm sure it will help you. There's lots more out there, but here are two that I suggest you read.

Answer 2

It stands to reason the best approach would be to understand proofs. An excellent and often recommended book is "How to Prove It" by Daniel J. Velleman, which also contains a primer on sentential logic.

If you can formally prove (convince yourself of the truth of) the theorems yourself then you will certainly come to understand them. If you only seek explanations of just those theorems then you may miss knowledge that could only come about by you yourself following the proofs.

Lastly, the ability to read and write proofs is fundamental to mathematics. These would be essential skills to truly investigate the deepest understanding possible of not only his theorems, but all others.