Stats for nerds
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2015–2018years
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Mentions per year
What Hacker News says
- 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.
- I read Badiou's Number and Numbers. The first half was a good introduction to the history of attempts to axiomatize various kinds of numbers. The second half was a so-so introduction to surreal numbers. The book seems like some notes that Badiou wrote for himself while studying mathematics. Not really sure where any of the reviewers and blurb-givers got the idea that the book had anything to do with philosophy or capitalism or politics.
- > The people who do are continental philosophers who tend to get laughed out of the room
And for good reason. For example, philosophers (Zizek included) raved about Badiou's Number and Numbers. It is a nice history of the approaches to formalizing the concept of number, but there is no philosophy there. As soon as Badiou or Derrida or any other continental philosophers try to do anything else with mathematics it just becomes a grossly inappropriate and confusing analogy.
