What Hacker News says

neel_kOct 2018

The literature on this subject is both vast and populated by the work of the most eminent philosophers -- both continental and analytic -- of the last two hundred years.

Here are some books that I liked. However, there are three caveats. First, being a great philosopher does not mean that one is a great writer. Second, I don't agree with all of these philosophers (indeed, most of them don't agree with _themselves_, since they changed their minds over time). Finally, I myself am not a philosopher, so this list is necessarily somewhat idiosyncratic:

- Edmund Husserl's Philosophy of Arithmetic and Logical Investigations. In the first, he studies what we mean by numbers, and comes to (in my view) a very modern cognitive-scientific/computer-scientific view (ie, that we have direct access only to very small numbers and that our understanding of bigger numbers is symbolic). In the second, he turns around and rejects the idea that reductionism can turn logic into psychology, inventing phenomenology in the process and authoring the root source of modern continental philosophy.

- Alain Badiou's _Number and Numbers_. If you need a Maoist continental philosopher who would disdain the entire Internet Bayesian rationalist community for being a bunch of squishy relativists who don't genuinely believe in capital-T Truth or capital-R Reality, then have I got the man for you! (After all, one should believe in true things because they are true, not because it would let you win a bloody bet. You should believe in true things even if that would make you lose a bet.)

Badiou is a hard-core set-theoretic Platonist realist who passionately hates everything in logic that I love ("[...] if it is true that mathematics, the highest expression of pure thought, in the final analysis consists of nothing but syntactical apparatuses, grammars of signs, then a fortiori all thought falls under the constitutive rule of language"), and I love him for it.

- Ludwig Wittgenstein's _Tractatus Logico-Philosophicus_and Philosophical Investigations_. I find PI much more convincing than the Tractatus, but it's worth reading because it makes a strongly-argued case for logical realism. The big danger with Wittgenstein is that his epigrammatic style is infectious (he's the best writer on this list by a country mile).

- David Lewis's books _Convention_ and _Counterfactuals_. I read _Convention_ as formalizing Wittgenstein's idea of a language-game in terms of game theoretic ideas of equilibria (as well as less formal ideas like Schelling points). _Counterfactuals_ is good (despite Lewis's bonkers modal realism) because counterfactuals and causation are an important part of actual real-world-applicable logic (as opposed to formal logic).

- Michael Dummett's On the Logical Basis of Metaphysics. This is probably the book that has had the biggest impact on how I think about everything. His analysis of realism anti-realism is beautiful and subtle, and makes one of the best arguments for intuitionistic mathematics I have ever read.

thread

KrisAndrewMay 2014

I find the crossover between philosophy and mathematics/logic extremely interesting. I've read both of Wittgenstein's major works ("Tractatus Logico-Philosophicus" and "Philosophical Investigations") and found them very compelling. I tried to read Heidegger's "Being and Time", but it was beyond me at that point. I'll attempt it again next year maybe.

The essential point of the article is that systems without contradictions are not interesting. The contradictions create a point of discussion; a single, loose thread on the lapel of an otherwise perfectly tailored suit jacket. However, were you to don this suit and show up at a formal, elegant dinner party, everyone would see the flaw but no one would speak of it... at least not at the party. That would be gauche.

If you enjoyed the math, but not the Buddhism, you might enjoy "Philosophy of Arithmetic" by Husserl, or almost anything by Frege.

thread