Mathematics Without Numbers

Towards a Modal-Structural Interpretation

By: Geoffrey Hellman

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Paperback | 25 November 1993

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168 Pages

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21.59 x 13.97 x 0.99

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Hellman here presents a detailed interpretation of mathematics as the investigation of "structural possibilities," as opposed to absolute, Platonic objects. After treating the natural numbers and analysis, he extends the approach to set theory, where he demonstrates how to dispense with a fixed universe of sets. Finally, he addresses problems of application to the physical world.

Industry Reviews

`Without doubt this volume is a major contribution to recent philosophy of mathematics and should be read by anyone interested in this difficult but philosophically central field.' Peter Clark, Times Higher Education Supplement `Several important insights are woven together and brought to bear on the nature of mathematics in this signal contribution to the philosophy of the field.' Daniel H. Cohen, Mathematical Reviews `rich, subtle, and insightful' Stewart Shapiro, Nous 'This is an exciting and intriguing book, rich in ideas and not short on technical ingenuity, that will doubtless repay careful study. A short review leaves no scope for the detailed critical assessment it merits.' Bob Hale, University of St Andrews, The Philosophical Review, Vol. 101, No. 4 (October 1992) 'the amount of mathematics developed within Hellman's modal framework is impressive ... Hellman's approach makes use of categorical modal-existence postulates, thus achieving truth-determinateness in a way not available to the traditional postulationist.' A.D. Irvine, University of British Columbia, History & Philosophy of Logic '...concise mathematical monograph...' Contemporary Physics, Vol. 38 No. 4, 1997 `Concise mathematical monograph.' Contemporary Physics

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