Description: Philosophy of Mathematics Today, Paperback by Agazzi, E. (EDT); Darvas, György (EDT), ISBN 9401064008, ISBN-13 9789401064002, Brand New, Free shipping in the US Mathematics is often considered as a body of knowledge that is essen tially independent of linguistic formulations, in the sense that, once the content of this knowledge has been grasped, there remains only the problem of professional ability, that of clearly formulating and correctly proving it. However, the question is not so simple, and P. Weingartners paper (Language and Coding-Dependency of Results in Logic and Mathe matics) deals with some results in logic and mathematics which reveal that certain notions are in general not invariant with respect to different choices of language and of coding processes. Five example are given: 1) The validity of axioms and rules of classical propositional logic depend on the interpretation of sentential variables; 2) The language dependency of verisimilitude; 3) The proof of the weak and strong anti inductivist theorems in Poppers theory of inductive support is not invariant with respect to limitative criteria put on classical logic; 4) The language-dependency of the concept of provability; 5) The language dependency of the existence of ungrounded and paradoxical sentences (in the sense of Kripke). The requirements of logical rigour and consistency are not the only criteria for the acceptance and appreciation of mathematical proposi tions and theories.
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Book Title: Philosophy of Mathematics Today
Number of Pages: Xxix, 361 Pages
Publication Name: Philosophy of Mathematics Today
Language: English
Publisher: Springer Netherlands
Subject: Philosophy & Social Aspects, History & Philosophy, Logic
Publication Year: 2012
Type: Textbook
Item Weight: 22.3 Oz
Author: György Darvas
Item Length: 9.4 in
Subject Area: Mathematics, Philosophy, Science
Item Width: 6.3 in
Series: Episteme Ser.
Format: Trade Paperback
