Some of the logical empiricists defended the claim that the basic mathematical axioms are definitions and that the theorems of mathematics are consequently analytic. This position has subsequently fallen out of favor. Critics have alleged that the position was refuted by Gödel’s Incompleteness Theorems, that it is obscure what “analytic” and “definition” are supposed to mean, that there are no “analytic” truths, or that the axioms cannot be definitions. True by Definition revisits this debate. It introduces the distinction between analytic and synthetic truths and explains the controversy around the distinction in the philosophy of mathematics and beyond. The book also defends a radical new position. It is argued that, in certain contexts, the axioms of arithmetic have the status of definitions; however...
I don't want to spoil the suspense. I am of course immediately suspicious of the impulse to introduce the synthetic/analytic distinction.
The author is a guy I know; he and his wife are both quality philosophers. Some of you might be into a work of philosophy of math.
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