The Limits of Abstraction
By (author) Kit Fine
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Limits of Abstraction by Kit Fine
Book DescriptionWhat is abstraction? To what extent can it account for the existence and identity of abstract objects? And to what extent can it be used as a foundation for mathematics? Kit Fine provides rigorous and systematic answers to these questions along the lines proposed by Frege, in a book concerned both with the technical development of the subject and with its philosophical underpinnings. Fine proposes an account of what it is for a principle of abstraction to be acceptable, and these acceptable principles are exactly characterized. A formal theory of abstraction is developed and shown to be capable of providing a foundation for both arithmetic and analysis. Fine argues that the usual attempts to see principles of abstraction as forms of stipulative definition have been largely unsuccessful but there may be other, more promising, ways of vindicating the various forms of contextual definition. The Limits of Abstraction breaks new ground both technically and philosophically, and will be essential reading for all who work on the philosophy of mathematics.
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Book DetailsISBN: 9780199533633
(218mm x 140mm x 13mm)
Imprint: Oxford University Press
Publisher: Oxford University Press
Publish Date: 22-May-2008
Country of Publication: United Kingdom
Books By Author Kit Fine
Semantic Relationism, Paperback (July 2009)
Kit Fine argues for a fundamentally new approach to the study of representation in language and thought. His key idea is that there may be representational relationships between expressions or elements of thought that are not grounded in the intrinsic representational features of the expressions or elements themselves.
Modality and Tense, Hardback (July 2005)
Drawing together a series of essays on possibility, necessity, and tense, this book covers areas, such as: the possible-worlds analysis of counterfactuals; the compatibility of special relativity with presentism; and the nature of first-personal experience. It also argues for the existence of distinctive forms of natural and normative necessity.
Limits of Abstraction, Hardback (August 2002)» View all books by Kit Fine
Kit Fine develops a Fregean theory of abstraction, and suggests that it may yield a new philosophical foundation for mathematics, one that can account for both our reference to various mathematical objects and our knowledge of various mathematical truths.
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Author Biography - Kit Fine
Kit Fine is Silver Professor of Philosophy at New York University, specializing in Metaphysics, Logic, and Philosophy of Language. He has held fellowships from the Guggenheim Foundation and the American Council of Learned Societies and is a former editor of the Journal of Symbolic Logic. He is the author (with A. N. Prior) of Worlds, Times and Selves (Duckworth, 1977) and Reasoning with Arbitrary Objects (Blackwell, 1985) and has written papers in ancient philosophy, linguistics, computer science, and economic theory.
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