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Wittgenstein s Annotations to Hardy s Course of Pure Mathematics: An Investigation of Wittgenstein s Non-Extensionalist Understanding of the Real Numbers free ebook download

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Author(s):	Juliet Floyd

Date:	2020	Format:	pdf	Language:	English	ISBN/ASIN:	3030484807
Pages:	330	OCR:		Quality:		ISBN13:
Uploader:	eternal	Upload Date:	4/27/2024 5:32:37 AM

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3030484807 pdf
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 (annotations on pages 2-9 of the 1941 edition of Hardy's book), the law of excluded middle in mathematics and the notion of an “improper picture," the continuum of real numbers (annotations on pages 10-30), and Wittgenstein’s attitude toward functions and limits, which scrutinizes his annotations on pages 40-47 and 117-121 and examines their challenges and meaning in light of underlying manuscripts.
Overall, the authors show that Wittgenstein’s argumentation should not be taken to reject Dedekind cuts per se, but only a one-sided, reductive extensionalism that belies actual mathematical practice. They discuss and defend Wittgenstein’s version of non-extensionalism and, in two final essays, debate the nature and contemporary relevance of this view.

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Tags: Annotations Course Hardy Investigation Mathematics Non-Extensionalist Pure Understanding Wittgenstein Wittgenstein

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Wittgenstein s Annotations to Hardy s Course of Pure Mathematics: An Investigation of Wittgenstein s Non-Extensionalist Understanding of the Real Numbers free ebook download

Category: Mathematics

Description: Click to see full description

Category:
Mathematics