The Limits of Abstraction
Seiten
2008
Oxford University Press (Verlag)
978-0-19-953363-3 (ISBN)
Oxford University Press (Verlag)
978-0-19-953363-3 (ISBN)
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. The Limits of Abstraction breaks new ground both technically and philosophically.
What 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.
What 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.
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.
1. PHILOSOPHICAL INTRODUCTION; THE CONTEXT PRINCIPLE; THE ANALYSIS OF ACCEPTABILITY; THE GENERAL THEORY OF ABSTRACTION
| Erscheint lt. Verlag | 22.5.2008 |
|---|---|
| Verlagsort | Oxford |
| Sprache | englisch |
| Maße | 140 x 218 mm |
| Gewicht | 285 g |
| Themenwelt | Geisteswissenschaften ► Philosophie ► Geschichte der Philosophie |
| Geisteswissenschaften ► Philosophie ► Philosophie der Neuzeit | |
| Mathematik / Informatik ► Mathematik | |
| ISBN-10 | 0-19-953363-6 / 0199533636 |
| ISBN-13 | 978-0-19-953363-3 / 9780199533633 |
| Zustand | Neuware |
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