1
فلسفه::
نحوی
Thus, from the Tractatus to at least 1944, Wittgenstein maintains that "mathematical propositions" are not real propositions and that "mathematical truth" is essentially non-referential and purely syntactical in nature.
The demarcation between contingent propositions, which can be used to correctly or incorrectly represent parts of the world, and mathematical propositions, which can be decided in a purely formal, syntactical manner, is maintained by Wittgenstein until his death in 1951 (Zettel �701, 1947; PI II, 2001 Ed.
Finally, critics argue that the problem with #4 is that there is no evidence for the claim that the relevant operation is logical in Wittgenstein's or Russell's or Frege's sense of the term-it seems a purely formal, syntactical operation (Rodych 1995).
Though mathematics and mathematical activity are purely formal and syntactical, in the Tractatus Wittgenstein tacitly distinguishes between purely formal games with signs, which have no application in contingent propositions, and mathematical propositions, which are used to make inferences from contingent proposition(s) to contingent proposition(s).
#1; PR �159) by inventing purely formal mathematical calculi, with 'stipulated' axioms (PR �202), syntactical rules of transformation, and decision procedures that enable us to invent "mathematical truth" and "mathematical falsity" by algorithmically deciding so-called mathematical 'propositions' (PR ��122, 162).
واژگان شبکه مترجمین ایران