A Structural Account of Mathematics
By (author) Charles S. Chihara
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Structural Account of Mathematics by Charles S. Chihara
Book DescriptionCharles 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 are applied 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 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 nominalistic 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.
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Book DetailsISBN: 9780199228072
(233mm x 155mm x 21mm)
Imprint: Clarendon Press
Publisher: Oxford University Press
Publish Date: 17-May-2007
Country of Publication: United Kingdom
Books By Author Charles S. Chihara
Structural Account of Mathematics, Hardback (November 2003)
This work 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.
Worlds of Possibility, Paperback (October 2001)
A critical exposition of modal realism, the philosophical doctrine that there exists many possible worlds of which the actual world is just one. It argues for modality without worlds and offers an account of the role of interpretations or structures of the formal languages of logic.
Constructibility and Mathematical Existence, Paperback (June 1991)» View all books by Charles S. Chihara
Concerned with the problem of existence in mathematics, this volume develops a mathematical system in which there are no existence assertions but only assertions of constructibility. It explores the philosophical implications of such an approach in the writings of Field, Burgess, Maddy and Kitcher.
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