A Structural Account of Mathematics
Clarendon, 2004 - 380 oldal
Charles Chihara's new book develops and defends a structural view of the nature of mathematics, and uses it to explain a number of striking features of mathematics that have puzzled philosophers for centuries. The view is used to show that, in order to understand how mathematical systems areapplied in science and everyday life, it is not necessary to assume that its theorems either presuppose mathematical objects or are even true.Chihara builds upon his previous work, in which he presented a new system of mathematics, the constructibility theory, which did not make reference to, or presuppose, mathematical objects. Now he develops the project further by analysing mathematical systems currently used by scientists to show howsuch systems are compatible with this nominalistic outlook. He advances several new ways of undermining the heavily discussed indispensability argument for the existence of mathematical objects made famous by Willard Quine and Hilary Putnam. And Chihara presents a rationale for the nominalisticoutlook that is quite different from those generally put forward, which he maintains have led to serious misunderstandings.A Structural Account of Mathematics will be required reading for anyone working in this field.
Mit mondanak mások - Írjon ismertetőt
Nem találtunk ismertetőket a szokott helyeken.
1 Five Puzzles in Search of an Explanation
2 Geometry and Mathematical Existence
3 The van Inwagen Puzzle
6 Minimal AntiNominalism
7 The Constructibility Theory
8 Constructible Structures
Más kiadások - Összes megtekintése
abstract account of mathematics analysis applications argued arithmetic assertions axioms believe cardinality Chapter characterization Chihara claim Colyvan conclusion confirmation constructibility quantifiers Constructibility Theory discussion domain ematical empirical evidence example existence of mathematical explain fact fictionalist Field first-order first-order logic Frege Fregean geometry Gödel Hellman Hilbert Hilbert's axioms identity indispensability argument infer justified logical Maddy math mathematical entities mathematical objects mathematical theory mathematicians mereology metalogical modal modal logic model theory natural number attribute nominalistic number theory ontological ontological commitments open-sentence ordered pair Peano arithmetic Penelope Maddy philosophers philosophy of mathematics physical objects physical world Platonic Platonists position possible to construct possible worlds postulates principle problem proof properties puzzle question Quine Quine's real numbers realist reasoning relation Resnik satisfies scientific theory scientists semantics sentences set theory set-theoretical Shapiro simple type theory sort space specific statements structuralist supposed theorems thesis things true truth type theory typosynthesis vector