Chihara - Structural Account of Mathematics (Oxford, 2004).pdf - Algebra & Trigonometry - Kuya

A Structural Account of Mathematics

Charles Chihara develops and defends a structural view of the nature of

mathematics, and uses it to explain a number of striking features of mathe-

matics that have puzzled philosophers for centuries. The view is used to show

that, in order to understand how mathematical systems are applied in science

and everyday life, it is not necessary to assume that its theorems either pre-

suppose 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 how

such 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 W. V.

Quine and Hilary Putnam. And Chihara presents a rationale for the nomi-

nalistic outlook 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.

Charles S. Chihara is Emeritus Professor of Philosophy at the University of

California, Berkeley.

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A Structural Account of

Mathematics

CHARLES S. CHIHARA

CLARENDON PRESS -OXFORD

OXFORD

UNIVERSITY PRESS

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First published 2004

First published in paperback 2007

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13579 10 8642

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