Wittgenstein’s Annotations to Hardy’s Course of Pure Mathematics
An Investigation of Wittgenstein’s Non-Extensionalist Understanding of the Real Numbers
Buch in deiner Nähe kaufen
Beschreibung
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.
Examines the annotations that Ludwig Wittgenstein made to his copy of G.H. Hardy’s classic textbook, A Course of Pure Mathematics
Features images of the annotations
Explores Wittgenstein’s later philosophy of mathematics as applied to the real numbers
Examines the annotations that Ludwig Wittgenstein made to his copy of G.H. Hardy’s classic textbook, A Course of Pure Mathematics Features images of the annotations Explores Wittgenstein’s later philosophy of mathematics as applied to the real numbers
Autor*in
Juliet Floyd
Themen in »Wittgenstein’s Annotations to Hardy’s Course of Pure Mathematics«
Wittgenstein G.H. Hardy Dedekind Philosophy of Real Numbers Non-extensionalist View of Mathematics Cantor’s Diagonal Method Hilary Putnam’s Philosophy of Mathematics Dedekind Cuts Cantor’s Diagonal Argument
Stimmen zu »Wittgenstein’s Annotations to Hardy’s Course of Pure Mathematics«
“The book goes far beyond their edition, providing access to important topics in the philosophy of mathematics seen from the special Wittgensteinian perspective.” (Volker Peckhaus, zbMATH 1529.01002, 2024)
“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)
()