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The Limits of Abstraction
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
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. -
214 pages; ISBN 9780191567261
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