ISBN: 9780197846872 - true by definition (4 resultados)

Hardcover. Condición: new. Hardcover. 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.With just as muchself-assurance, A.J. Ayer claimed that the truths of pure mathematics are " in the sense that each follows " Despite the bravado of its earlyadherents, this position has subsequently fallen out of favor. Critics have alleged that the position was refuted by Goedel's Incompleteness Theorems, that it is obscure what " and " are supposed to mean, that there are no " truths, or that the axioms cannot be definitions.True By Definition revisits this debate. Thomas Donaldson introduces the distinction between analytic andsynthetic 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 ofempiricism 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. True By Definition introduces the voluminous and confusing literature on the analytic/synthetic distinction. The volume presents the author's original research on the distinction, dealing with some of the central questions of epistemology, metaphysics, and the philosophy of mathematics. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.…

Condición: New.

Hardcover. Condición: Brand New. 304 pages. 6.55x1.16x9.30 inches. In Stock.

Buch. Condición: Neu. Neuware - 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.With just as much self-assurance, A.J. Ayer claimed that the truths of pure mathematics are 'analytic' in the sense that each follows 'simply from the definitions of the terms contained in it.' Despite the bravado of its early adherents, 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. 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.…