Book #33: Incompleteness: The Proof and Paradox of Kurt Gödel by Rebecca Goldstein



Gödel was the most brilliant mathematician of the 20th century, and Goldstein, a novelist and philosophy professor (according to one of her anecdotes, she's roughly a contemporary of Rorty's), finds a way to explain his incompleteness theorems in plain language, wrapped up inextricably with the story of Gödel's life. Gödel was a lonely man, at odds with almost everyone he met other than Einstein, and Goldstein provides a narrative that demonstrates clearly why Gödel felt like an exile all of his life, even in the occasionally loving arms of Princeton's Institute for Advanced Study.

It's in her description of his philosophy that Goldstein really shines. She places Gödel's incompleteness theorem, which I've seen used to both support and refute positivism (that's the notion that there's no objective reality unmeasured by humans), in its proper context, which is to refute positivism and uphold Gödel's Platonism. She also carefully shows why Gödel and Wittgenstein (arguably the greatest philosopher of the 20th century, and certainly in a class with few others) disliked each other and refused to engage each other's philosophies, despite the fact that she believes that the Tractatus-era Wittgenstein (that's the early Wittgenstein of the Tractatus Logico-Philosophicus, mind you, before he became interested in deconstructing language) and Gödel were more-or-less in agreement.

Heady stuff, and it's admirable that Goldstein made into such a light read. I'm certainly not a Platonist - in fact, I feel quite a bit of kinship for Rorty's anti-essentialism, which leans towards the positivists - but I also believe that it's a hubristic mistake to discount the ineffable (much like the Tractatus, which ends "Whereof we cannot speak, thereof we must remain silent."). Despite my own prejudices against Platonism, I found myself able to appreciate Gödel's elegant theorems as both mathematical and philosophical positions, and found a greater understanding of the logical-mathematical side of philosophy, which has always previously left me cold (and is one of the main reasons I've had trouble understanding Wittgenstein and Quine, despite my admiration for both). Anyway, Incompleteness is a great book for lovers of philosophy or math from the general public, but not the practitioners. Then again, it ain't for them; it's for the rest of us.