Thinking about Mathematics
by Stewart Shapiro · first published 2000
9mentions
5recommended by
8HN commenters
2017–2023first – last mentioned
63% recommend38% neutral
Why HN recommends it
Clear survey of the main schools in the philosophy of mathematics, including logicism, formalism, intuitionism and structuralism; recommended as a readable introduction for anyone curious about what mathematics is.
Summarised by Claude from recommending comments
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…can do it, you can do it". Jesus' Son by Denis Johnson: A nice if brutal read. It was my first foray in DJ. I felt Cormac McCarthyish vibes. Blood Meridian by Cormac McCarthy: A classic. The Judge. Thinking About Mathematics by Stuart Shapiro: Highly recommended for anyone interested in the philosophical questions of mathematics. Shapiro writes clearly, concisely, and in a manner that is easy to read. The Liars' Club by…
on “Ask HN: Books you read in 2018?” ↗…mathematics. People are going to disagree about that, just like they disagree about almost every other part of philosophy. But there are books which give you a survey of different views, such as Shapiro’s “Thinking about mathematics” — which surely will bring you to “I know a bit about the philosophy of mathematics”-level. During my time as a master student in mathematics we used to have a joint seminar with students from philosophy…
on “The Unreasonable Effectiveness of Mathematics in the Natural Sciences (1960)” ↗…mathematics: Platonism vs. Formalism Someone linked the BBC video, which is great, but there’s also a wonderful book that discusses this and many other facets of mathematical philosophy: https://www.amazon.com/Thinking-about-Mathematics-Philosophy... (Sorry for the link spew) I highly recommend that book to anyone remotely interested in the field.
on “How Space and Time Could Be a Quantum Error-Correcting Code” ↗…it's impact on social relationships? Or are people who let religion shape their social relationships as mad as I am? Or is the argument flawed? (edit: No, I can not answer these question). Shapiro's "Thinking about mathematics" springs to my mind, IIRC in the first chapter(s) he gives a nice overview about what philosophers thought about numbers, the realm of numbers and whether they "exist" or not. I think some of that could…
on “Kosher search engine powered by 4 car batteries on a passively cooled server” ↗There are those philosophers which are as concerned with logic as you'd expect from a pure mathematician ;-) If you're interested, Shapiro's "Thinking about Mathematics: The Philosophy of Mathematics" gives a nice introduction into that topic, discussing several schools of philosophy and their thinkers (without forcing the authors pov on the reader). We had a seminar…
on “Hegelian contradiction and the prime numbers (part 2)” ↗In a similar vein, I'm currently halfway through 'Thinking About Mathematics' by Stewart Shapiro. It's a great introduction to the various philosophies of mathematics: logicism, formalism, intuitionism, structuralism, basically all of the different sorts of philosophical positions…
on “My Favorite Books 2020” ↗There’s an entire chapter devoted to Plato in Stewart Shapiro’s Thinking About Mathematics, the first book the author recommends. I think it’s pretty reasonable to recommend people start with an accessible contemporary survey rather than diving directly into Plato’s dialogues or any other particular…
on “Philosophy of mathematics – a reading list (2020)” ↗Yes. The book Thinking about mathematics by Stewart Shapiro covers it in chapter 10 and calls it Structuralism. https://en.wikipedia.org/wiki/Structuralism_(philosophy_of_m...
on “What Is Math?” ↗…terminology. But everyone else just uses the second-order induction axiom when talking about arithmetic, without explicitly talking about first or second-order logic. Steven Shapiro made this point in his book "Thinking About Mathematics".
on “Goodsteins theorem” ↗