Wittgenstein's Annotations to Hardy's Course of Pure Mathematics

An Investigation of Wittgenstein's Non-Extensionalist Understanding of the Real Numbers

By: Juliet Floyd, Felix MÃ¼hlhÃ¶lzer

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Paperback | 1 September 2021

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344 Pages

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23.39 x 15.6 x 1.83

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$216.36

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This monograph examines the private annotations that Ludwig Wittgenstein made to his copy of G.H. Hardy's classic textbook, A Course of Pure Mathematics. Complete with actual images of the annotations, it gives readers a more complete picture of Wittgenstein's remarks on irrational numbers, which have only been published in an excerpted form and, as a result, have often been unjustly criticized.

The authors first establish the context behind the annotations and discuss the historical role of Hardy's textbook. They then go on to outline Wittgenstein's non-extensionalist point of view on real numbers, assessing his manuscripts and published remarks and discussing attitudes in play in the philosophy of mathematics since Dedekind. Next, coverage focuses on the annotations themselves. The discussion encompasses irrational numbers, the law of excluded middle in mathematics and the notion of an "improper picture," the continuum of real numbers, and Wittgenstein's attitude toward functions and limits.

Industry Reviews

"There are some books that one learns from them what one expected or hoped to learn; but then there are books that go well beyond the brief laid out in their titles, and the book ... is one such. Called Wittgenstein's Annotations to Hardy's Course of Pure Mathematics, the book is actually an extensive and deeply informed examination of Wittgenstein's philosophy of mathematics in all of its aspects ... ." (Juliette Kennedy, Philosophia Mathematica, Vol. 30 (2), 2022)

"The book is very rich in information for the Wittgenstein scholar as well as for students of Wittgenstein's commentaries on the development of mathematics." (Michael Otte, Mathematical Reviews, May, 2022)

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