Wittgensteins Annotations to Hardys Course of Pure Mathematics

This monograph examines the private annotations that Ludwig Wittgenstein made to his copy of G.H. Hardys classic textbook, A Course of Pure Mathematics. Complete with actual images of the annotations, it gives readers a more complete picture of Wittgensteins 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 Hardys textbook. They then go on to outline Wittgensteins 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 Wittgensteins attitude toward functions and limits.