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How Mathematicians Think

ISBN: 9780691127385

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Interesting, but... by scottb :: NR7

The author has some interesting ideas, but he keeps missing some of the critical points, and there are some places where his exposition just runs off into cluelessness. Here's an example (pp. 293-294):

In Chapter 3, I discussed the irreducible ambiguity that characterizes the concept of infinity by considering the concept of the "ineffable". By definition, the "ineffable" is "that which cannot be put into words". Unfortunately (or is it fortunately?) "ineffable" is a word. Thus when we use the word "ineffable" we are articulating that which cannot, by definition, be articulated.

Sorry, but no. It may well be that infinity has aspects that are ineffable - however, the ineffability of infinity is not ineffable. This is a simple logical error - it's mistaking the signifier for the signified.

The author does this sort of thing in a lot of places, which has the tendency to obscure the deeper ideas he's trying to convey - some of which really do live out in the frontiers of the ineffable.

Some of the material on which he touches is also covered in Graham Priest's Beyond the Limits of Thought. Priest's book is a bit harder reading, but he captures the ideas much more firmly.

Posted 09 November 2007, Hide, Reply