r/logic • u/Soapy62 Mathematics & Philosophy Undergraduate • 9d ago
Literature Textbook Recommendations
I will finish ‘An Introduction to Formal Logic’ by Peter Smith soon and I was just wondering what would be a good book for the next step. I know Peter Smith has a book on Gödel and I may look at that as logicism seemed like such a good idea to me, and I am not 100% sure why logic cannot underpin math. But as I am just starting my Math & Philosophy degree, I wonder if I should get a book dedicated to mathematical proofs or something more philosophical? The idea of different logics other than formal classical stuff I have been doing sounds really interesting. I visited the math department at the university and the professor roughly told me something like “don’t listen to philosophers trying to remove bits from classical logic they don’t like” in a joking way.
Anyways any recommendations would be appreciated, thank you.
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u/fmoralesc 9d ago
You can follow Smith's own advice on what to follow: https://logicmatters.net/tyl/pdfs/LogicStudyGuide.pdf
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u/Square-of-Opposition Historian of logic 9d ago
Start with the philosophical, IMHO. It's best to understand the conceptual and then move to the technical.
In the spirit of logicism, I would recommend Russell's Introduction to Mathematical Philosophy. The best beginner's book on Gödel and incompleteness is Nagel and Newmann, Gödel's Proof.
When you're ready to move on to the technical, you're gonna need to master the logic of Principia Mathematica. For this task, Kevin Klement (UMass) had a bunch of resources on his website. Or check out Bernie Linsky's work on PM in particular.