Philosophy of Mathematics Today

Nonfiction, Science & Nature, Mathematics, Logic, Religion & Spirituality, Philosophy
Cover of the book Philosophy of Mathematics Today by , Springer Netherlands
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: ISBN: 9789401156905
Publisher: Springer Netherlands Publication: December 6, 2012
Imprint: Springer Language: English
Author:
ISBN: 9789401156905
Publisher: Springer Netherlands
Publication: December 6, 2012
Imprint: Springer
Language: English

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. Weingartner's 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 Popper's 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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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. Weingartner's 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 Popper's 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.

More books from Springer Netherlands

Cover of the book Climate Change and United States Forests by
Cover of the book An Introduction to Neural Network Methods for Differential Equations by
Cover of the book Crime Modeling and Mapping Using Geospatial Technologies by
Cover of the book Marxism and the Question of the Asiatic Mode of Production by
Cover of the book Principle-Based Parsing by
Cover of the book Queen Elizabeth and the Revolt of the Netherlands by
Cover of the book The Edges of Augustanism by
Cover of the book Durability of Composites in a Marine Environment by
Cover of the book CADCAM: Training and Education through the ’80s by
Cover of the book The Communist Millennium by
Cover of the book The Impact of ICT on Quality of Working Life by
Cover of the book Background and Future Prospects in Life Cycle Assessment by
Cover of the book Current Status of Clinical Cardiology 1990 by
Cover of the book Micromechanics Modelling of Ductile Fracture by
Cover of the book Philosophy and Ideology by
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy