Name: Philosophies of mathematics
ISBN: 9780631195443

Philosophies of mathematics

"During the first few decades of the twentieth century, philosophers and mathematicians mounted a sustained effort to clarify the nature of mathematics. This led to considerable discord, even enmity, and yielded fascinating and fruitful work of both a mathematical and philosophical nature. It was one of the most exhilarating intellectual adventures of the century, pursued at an extraordinarily high level of acuity and imagination. Its legacy principally consists of three original and finely articulated programs that seek to view mathematics in the proper light: logicism, intuitionism, and finitism. Each is notable for its symbiotic melding together of philosophical vision and mathematical work: the philosophical ideas are given their substance by specific mathematical developments, which are in turn given their point by philosophical reflection." "This book provides an accessible, critical introduction to these three projects, as it describes and investigates both their philosophical and their mathematical components."--BOOK JACKET.

What Hacker News says

leto_iiFeb 2024

GEB is one of the books that as an adult I have learned to not care about anymore. I've unsuccessfully tried reading it a few times (once made it a couple of hundred pages in) and came to the (personal) conclusion that if I want an intellectual challenge I'll just directly do maths instead of reading a semi-literary essay about maths.

Just like (some of) Joyce's work, GEB seems to me a puzzle who's main prize is the satisfaction of having understood it - obfuscation and abstruseness for their own sake.

For actually understanding Godel's work I would recommend Gödel's Proof (Nagel, Newman, somewhat ironically, prefaced by Hofstadter) or Philosophies of Mathematics (George, Velleman).

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enasterosophesJun 2022

Douglas Hofstadter's work provides several examples.

* Gödel, Escher, Bach: an Eternal Golden Braid (GEB)

* Metamagical Themas

* I Am A Strange Loop (IAASL)

GEB and IAASL are thematically similar, and both are worth a read if you're interested in both Gödel's theorems (plus related work eg Church-Turing) and Hofstadter's philosophy of mind. GEB is a lot more creative and fun; IAASL does a better job of communicating the key technical ideas like incompleteness.

Metamagical Themas is a collection of shorter work, generally technical and fun.

Although Hofstadter was the first to come to my mind, these other authors/works also provide fun and/or excellent examples of technical writing:

* Neal Stephenson's "In the Beginning was the Command Line"

* Velleman's "How To Prove It" and "Philosophies of Mathematics"

* Mittelbach & Goosens "The LaTeX Companion"

* Waldrop's "The Dream Machine"

* Nielsen & Chuang's "Quantum Computation & Quantum Information"

* Lakatos's "Proof & Refutations"

* Chambers "What is this thing called science?"

* Doxiadis & Papadimitriou's "Logicomix".

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ionfishJun 2009