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Gödel Forever Through 90 Years of Foundational Claims Ken Williams
- Format:
- Book
- Author/Creator:
- Williams, Ken, Author.
- Language:
- English
- Subjects (All):
- Kurt Gödel.
- Mathematik.
- Mathematics.
- Logik.
- Logics.
- Local Subjects:
- Kurt Gödel.
- Mathematik.
- Mathematics.
- Logik.
- Logics.
- Physical Description:
- 1 online resource (147 pages)
- Edition:
- 1st ed.
- Place of Publication:
- Hannover ibidem 2023
- Biography/History:
- Dr. Ken Williams studied Physics in Birmingham, Alabama, of the 1980ies . Since 2018 he is an Instructor of Physics, Math & Statistics with CLAS of The University of California, Santa Barbara. Previously, Williams held a postdoctoral fellowship at CEBAF (now Jefferson Lab) and teaching posts at a number of Institutions. His research papers have been published by, among other outlets, Physical Review D and the Journal of Physics
- Dr. Ken Williams studied Physics in Birmingham, Alabama, of the 1980ies . Since 2018 he is an Instructor of Physics, Math & Statistics with CLAS of The University of California, Santa Barbara. Previously, Williams held a postdoctoral fellowship at CEBAF (now Jefferson Lab) and teaching posts at a number of Institutions. His research papers have been published by, among other outlets, Physical Review D and the Journal of Physics
- Summary:
- Gödel Forever takes a critical look at several foundation claims on Gödelian incompleteness that have appeared in the literature over the years, strictly adhering to mathematical details. Rephrasing the words from Torkel Franzén: Ken Williams presents a new book on Gödel’s incompleteness theorem for a general audience since no existing book both explains the theorem from a mathematical point of view and reflects his experiences over the years of reading and commenting on references to the incompleteness theorem on the Internet. The range of critical review on the one hand and its elementary, if detailed, derivation of Gödel’s Result (on which it is based) on the other makes Gödel Forever a must read for the serious study of the meaning and consequences of Gödel's Incompleteness.
- Contents:
- Intro
- Introduction
- I. Arithmetization of Metamathematics (PRR ⇒ P ⇔ meta-P′ ⇔ meta-P → Pfp ⇔ P)
- PM's Formal System P
- The PRR
- Definition PRR ⇒ P
- Building PRFs and PRRs
- Correspondence
- Capture
- Ancillary PRRs
- What does isVar(x) say?
- Syntax PRRs
- Diagonal Composition
- Fixed-Point
- Incompleteness
- Deduction PRRs
- II. Indirect Self-Reference
- What does g not say?
- III. An Odious Turn
- Königsberg, 1930
- Warsaw, 1935
- Ohio, 1998
- Lisbon &
- Pisa, 2014
- IV. Wittgenstein's Perspective
- Toronto, 1988
- Toronto, 1999
- Cambridge, 2011
- New Haven, 1958
- Gödel the Mathematician
- References.
- Notes:
- Includes bibliographical references.
- Other Format:
- Print version: Williams, Ken Gödel Forever
- ISBN:
- 3-8382-7786-4
- Publisher Number:
- 9783838277868
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