tag:blogger.com,1999:blog-6074393351940930654.post7059710823255315378..comments2022-11-18T05:59:11.703-05:00Comments on Philosophy, Science, and Method: Ramsey (1929) on distinctions between logic, mathematics, and philosophyJeff Helznerhttp://www.blogger.com/profile/07320832538596709257noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-6074393351940930654.post-40368520137611180632008-06-21T11:28:00.000-04:002008-06-21T11:28:00.000-04:00Or, e.g., real numbers as Dedekind cuts. It’s suc...Or, e.g., real numbers as Dedekind cuts. <BR/><BR/>It’s such an odd thing to say because one of the lasting contributions of the logicists (of which Ramsey was one) is the definitions of mathematical concepts they provided (e.g., the Frege/Russell definition of natural number).<BR/><BR/>I don’t think Ramsey had a clear understanding in his own mind of what he himself meant by ‘tautologies’ and ‘identities’ in this sentence. For example, he describes the multiplicative axiom as a ‘tautology’ in The Foundations of Mathematics (Mellor, p. 221). Clearly it isn’t. And the statement that mathematics issues in identities presumably derives from the Tractatus. But Wittgenstein’s point there was that mathematical propositions are really pseudo-propositions. (“A proposition of mathematics does not express a thought,” Tractatus 6.21.) But I don’t think Ramsey really understood that point. He seemed to think that Wittgenstein was merely arguing that the identity symbol is dispensable (see, e.g., Mellor, p. 194-95).Stephen Fogdallhttps://www.blogger.com/profile/08858619245607909761noreply@blogger.com