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By J.R. Lucas

The Conceptual Roots of Mathematics is a finished learn of the basis of arithmetic. J.R. Lucas, some of the most unique Oxford students, covers an unlimited volume of floor within the philosophy of arithmetic, exhibiting us that it truly is truly on the middle of the learn of epistemology and metaphysics.

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Many modern philosophers make that assumption, and much philosophy of mathematics is massaged so as to conform to a prevailing materialism. It is an important question, and one to which the philosophy of mathematics is relevant, but it is not the concern of this book, which is concerned only with mathematics, and how it should be correctly understood. I have apologies to make. I idiosyncratically abandon the standard usage, and describe terms such as ‘all’, ‘some’ and ‘none’ as “quotifiers”. , to which a numerical answer can be given only with considerable artifice, ultimately depending on the logic of transitive relations, the topic of Chapter Nine.

In the middle of the twentieth century, philosophers aired their inability to see how we could know anything about the past, but it did not lead historians to go out of business; nor did the inability to solve the problem of “other minds” lead to actual autism. The contemporary inability to see how mathematical knowledge is possible should be seen in context of the mid-century inability to have knowledge of the past, or to see how one person could know whether another person had feelings. It is a difficulty to which anyone studying the philosophy of mathematics should address himself, but not a doubt that should debar him from adopting that account which seems to do most justice to the phenomena.

E. Moore’s Philosophical Papers and soon after published Ludwig Wittgenstein’s Tractatus Logico-Philosophicus. Ayer, Bernard Williams and Ted Honderich. Now jointly edited by Tim Crane and Jonathan Wolff, the ILP will continue to publish works at the forefront of philosophical research. Lucas First published 2000 by Routledge 11 New Fetter Lane, London EC4P 4EE Simultaneously published in the USA and Canada by Routledge 29 West 35th Street, New York, NY 10001 Routledge is an imprint of the Taylor & Francis Group This edition published in the Taylor & Francis e-Library, 2002.

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