johncarlosbaez, 3 months ago

Today I got some questions about logic, like:

what do provability, decidability, consistency, and completeness mean?
how do we work with equality in set theory?

I don't know articles that explain topics like this to non-mathematicians, clearly and crisply, without becoming overlong or heavy with notation. Do you?

I looked around and found this "Introduction to First-Order Logic":

https://builds.openlogicproject.org/content/first-order-logic/introduction/introduction.pdf

but the very first sentence is

"You are probably familiar with first-order logic from your first introduction to formal logic."

which is basically a way of saying "fuck you - if you don't know this stuff already I won't explain it to you".

As a student I liked Boolos and Jeffrey's book "Computability and Logic":

http://alcom.ee.ntu.edu.tw/system/privatezone/uploads/Logic/20090928151927_George_S._Boolos,_John_P._Burgess,_Richard_C.

but that's more like a course than what I'm thinking of here: a collection of essays that explain different topics in plain English.

I also liked Hofstadter's "Gödel, Escher, Bach", but that's a massive quirky elaborate tale, not a simple clear explanation.

Wikipedia articles are packed with information but they aren't self-contained, clearly written essays. Articles in the Stanford Encyclopedia of Philosophy are better in some ways, but they often "show off" by including more advanced material.

Sigh....