[books] GEORGE LAKOFF & RAFAEL NUNEZ - Where Mathematics Comes From

I wrote about my initial reaction to this book here. In the end I had trouble separating the book's weaknesses as a book from the arguments it puts forward; I've had to remind myself that, as unsatisfying as it was to finish, I wouldn't have felt good assuming it never went anywhere if I put it down early.

According to my notes, the first time Lakoff and Nunez identify an actual person who holds the beliefs they attack is on page 251, more than halfway through the book. That person? Bishop George Berkeley, writing in 1734. I seem to have jotted some obscenities in the margin of my notebook at that point. They do get around to targetting more recent thinkers, though nobody later than the early 20th century. (Bertrand Russell is "pathological".)

I'm still willing to admit that there could be an insight beyond my comprehension here, but as far as I can tell, L&N's grand epistemological program consists of changing "this is a true abstract statement about thing X" to "this metaphor preserves inferences about thing X". At one point, by way of explaining why math appears to be such a good fit for the physical world, they say that "regularities" exist independent of humans. If regularities objectively exist in a way that the concepts we use to abstractly describe them do not, then we are using a sense of the word "exist" for which the book's thesis is trivially true. As the book winds down, much is made of the fact that nobody has ever seen a pile of e objects or walked i miles along a path, points I didn't need 400 pages of build-up to accept.

This is not, by the way, a fair representation of what the book focuses on. The bulk of it has to do with a particular conception of infinity that L&N say underlies most of mathematics. What they say hangs together, but they never present any results from cognitive science to show that it's true, which means that, again, they do something they complain about others doing: justifying an idea by showing that you can construct other things from it which, however, are conceptually prior.

Oh well, whatever, never mind.