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Universitext

Self-Reference and Modal Logic

Authors: Smorynski, Craig

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About this book

It is Sunday, the 7th of September 1930. The place is Konigsberg and the occasion is a small conference on the foundations of mathematics. Arend Heyting, the foremost disciple of L. E. J. Brouwer, has spoken on intuitionism; Rudolf Carnap of the Vienna Circle has expounded on logicism; Johann (formerly Janos and in a few years to be Johnny) von Neumann has explained Hilbert's proof theory-- the so-called formalism; and Hans Hahn has just propounded his own empiricist views of mathematics. The floor is open for general discussion, in the midst of which Heyting announces his satisfaction with the meeting. For him, the relationship between formalism and intuitionism has been clarified: There need be no war between the intuitionist and the formalist. Once the formalist has successfully completed Hilbert's programme and shown "finitely" that the "idealised" mathematics objected to by Brouwer proves no new "meaningful" statements, even the intuitionist will fondly embrace the infinite. To this euphoric revelation, a shy young man cautions~ "According to the formalist conception one adjoins to the meaningful statements of mathematics transfinite (pseudo-')statements which in themselves have no meaning but only serve to make the system a well-rounded one just as in geometry one achieves a well­ rounded system by the introduction of points at infinity.

Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook 74,89 €
price for Spain (gross)
  • ISBN 978-1-4613-8601-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 93,59 €
price for Spain (gross)
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Bibliographic Information

Bibliographic Information
Book Title
Self-Reference and Modal Logic
Authors
Series Title
Universitext
Copyright
1985
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York Inc.
eBook ISBN
978-1-4613-8601-8
DOI
10.1007/978-1-4613-8601-8
Softcover ISBN
978-0-387-96209-2
Series ISSN
0172-5939
Edition Number
1
Number of Pages
333
Topics