Ask HN: Introductory reading on philosophy of mathematics/formal logic?
Hey all,
I'm an undergraduate studying mathematics and computer science, and I've recently taken an interest in formal logic and the philosophy of mathematics. Previous courses have exposed me to beautiful ideas like Russell's paradox, Gödel's incompleteness theorem, and the Curry-Howard-Lambek correspondance.
I'm currently slogging through the final chapters of Hofstader's Gödel, Escher, Bach. What are some good next choices if I am interestred in diving deeper into the philosophy of mathematics?
Thanks! There's the classic "Believing the Axioms" by Penelope Maddy [0] [1], the excellent study guide "Teach Yourself Logic" [2], plenty of great articles on the Stanford Encyclopedia of Philosophy (e.g. [3] or [4]), Dana Scott's "Lambda Calculus: Some Models, Some Philosophy" [5], and too many other interesting rabbit holes to count (i.e. resolution, unification, cut elimination, nonstandard models of arithmetic...) [0] https://www.cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms1.pdf
[1] https://www.cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms2.pdf
[2] https://www.logicmatters.net/tyl/
[3] https://plato.stanford.edu/entries/settheory-alternative/
[4] https://plato.stanford.edu/entries/platonism-mathematics/
[5] https://lawrencecpaulson.github.io/papers/Scott-Models.pdf I like Quine's Methods of Logic (Fourth Edition).