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Episteme

Philosophy of Mathematics Today

Editors: Agazzi, Evandro, Darvas, György (Eds.)

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About this book

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.

Table of contents (21 chapters)

Table of contents (21 chapters)

Buy this book

eBook $89.00
price for USA in USD
  • ISBN 978-94-011-5690-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
Softcover $119.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Philosophy of Mathematics Today
Editors
  • Evandro Agazzi
  • György Darvas
Series Title
Episteme
Series Volume
22
Copyright
1997
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-011-5690-5
DOI
10.1007/978-94-011-5690-5
Hardcover ISBN
978-0-7923-4343-1
Softcover ISBN
978-94-010-6400-2
Edition Number
1
Number of Pages
XXIX, 361
Topics

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