Rebecca Goldstein, Incompleteness ***

Incompleteness is from the Great Discoveries series, in which a novelist undertakes to explain a great scientific discovery in literary terms without oversimplifying the technical details. In this case, Goldstein tackles Gödel's incompleteness theorems.

Very little of the book –– only about 20 pages –– actually attempts to explain the theorems. In fact, surprisingly little is about Gödel at all. Goldstein devotes significant time explaining the Vienna Circle, of which Gödel was a member despite apparently disagreeing with their very raison d'etre. As her chapter title puts it, Gödel was "A Platonist among the Positivists."

Goldstein's major thesis is that Gödel felt like an exile among his peers because (a) logical positivism came to dominate Anglo-European philosophy and (b) that dominant group managed to misinterpret his work so that it supported their point of view, which was anathema to him. She makes this case most effectively in the introduction while describing his unlikely friendship with Albert Einstein. In fact, I think you could get most of the value from this book by reading just the introduction.

Intellectually, the most interesting aspect of Incompleteness for me is its compelling argument for Platonism, for an objective realm of abstract things. "Einstein and Gödel's metaconvictions were addressed to the question of whether their respective fields are descriptions of an objective reality––existing independent of our thinking of it––or, rather, are subjective human projections, socially shared intellectual constructs." I personally believe this is a false dichotomy, that science is a subjectively projected organization that we use to understand an objective reality to which we have no access other than through our constructs (which I wouldn't characterize as "socially shared" or "intellectual").

I'm rating Incompleteness with one fewer stars than the first time I read it. During this reading, I felt indignant on Gödel's behalf about how much attention Goldstein paid to Wittgenstein and to formalism in mathematics. It short-changes the proofs themselves and limits Gödel's strange biography to a series of anecdotes in the epilogue.