True by Definition

In 1924, with great self-confidence, Hans Reichenbach wrote,

It has become customary to reduce a controversy about the logical status of mathematics to a controversy about the logical status of the axioms. Nowadays one can hardly speak of a controversy any longer. The problem of the axioms of mathematics was solved by the discovery that they are definitions, that is, arbitrary stipulations...

>True By Definition revisits this debate. Thomas Donaldson introduces the distinction between analytic and synthetic truths, and explains the controversy around this distinction. He defends a radical new position, developing an abductive, empirical case for the consistency of the basic axioms of arithmetic.

The result is a thoroughgoing form of empiricism about arithmetic, on which the basic principles of arithmetic are analytic yet a posteriori. True By Definition contributes to discussions of fundamentality and metaphysical grounding, suggesting that there is a parallelism between relations of analytic entailment among sentences and relations of metaphysical ground among facts.