>>12889279Logic by Nicholas jj Smith is okay
Mathematical proofs do well like Hammack's book of proof. As long as you see how it can be used in a debate or just reading you'll get a lot out of it. Equivalent relationships are a good way to justify whether something is equal to another or is an asymmetric relationship. It really tidies up any informal debate either for you to know what to ask or what's important or, if they're really passionate, just to be able to ask questions they can generally fill in that format. The wiki has a few stages of them.
For inference rules those are good but to know which inference rules are most important you have to study metaphysics but that'll make your convos a bit abstract but the reward is having good solutions instead of simply being very communicable.
Going down from proofs you could learn some set theory. It's not particularly necessary to accept set theory but if you're a foundationalist it's a really good framework to work from.
After that I found some of my latest insights from linear algebra which helped my structure. Getting into physics afterwards makes your proofs beefier because you can derive physical things which can serve as an analogy or as a way-up or way-down point if you're a foundationalist.
Just make sure you have a good foundation (or question, or use you want out of it) when you go in that you can always reference back to. The more universal it is the better but any foundation works if it's more communicable.
Also obligatory methylphenidate helped me get a lot of good studying down and I'm obsessed with studying now.
