There's Something About Gödel: The Complete Guide to the Incompleteness Theorem

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John Wiley & Sons, 13 set 2011 - 256 pagine
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Berto's highly readable and lucid guide introduces students and the interested reader to Gödel's celebrated Incompleteness Theorem, and discusses some of the most famous - and infamous - claims arising from Gödel's arguments.

  • Offers a clear understanding of this difficult subject by presenting each of the key steps of the Theorem in separate chapters
  • Discusses interpretations of the Theorem made by celebrated contemporary thinkers
  • Sheds light on the wider extra-mathematical and philosophical implications of Gödel's theories
  • Written in an accessible, non-technical style
 

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Pagine selezionate

Sommario

Foundations and Paradoxes 1 This sentence is false 2 The Liar and Gcidel
2
Language and metalanguage
6
The axiomatic method or how to get the non obvious out of the obvious
6
Peanos axioms 6 and the unsatisfied Iogicists Frege and Russell
6
Bits of set theory
7
The Abstraction Principle
8
Bytes of set theory
9
Properties relations functions that is sets again
10
Cantors diagonal argument
Selfreference and paradoxes
Hilbert
Strings of symbols
in mathematics there is no ignorabimus 3 Godel on stage
Our first encounter with the Incompleteness
Mathematical Faith
Mind versus Computer Godel

Calculating computing enumerating that is
11
notion of algorithm
Taking numbers as sets of sets
Its raining paradoxes
GcJdeI versus Wittgenstein and
Epilogue
Copyright

Altre edizioni - Visualizza tutto

There's Something About Gdel: The Complete Guide to the Incompleteness Theorem
Francesco Berto
Anteprima non disponibile - 2009
There's Something About Gdel: The Complete Guide to the Incompleteness Theorem
Francesco Berto
Anteprima non disponibile - 2009
There's Something About Gödel: The Complete Guide to the Incompleteness Theorem
Francesco Berto
Anteprima non disponibile - 2009
Visualizza tutto »

Parole e frasi comuni

algorithm argument arithmetical truths axiomatic axioms of TNT basic belongs calculus called Cantor’s chapter Church’s Thesis claim consistency proof contradiction corresponding defined definition equivalent exists expressions fact false finitary formal language formal system Franzén Frege Gbdel Gédel given formula Godel number Godel sentence Godel’s Theorem Godelian Gottlob Frege Hilbert’s incompleteness inconsistent infinite instance interpretation intuitive issue Juliette Binoche Liar Liar paradox lncompleteness Theorem logicians mathematicians means metalanguage metamathematical metaphysical mind natural numbers negation non-standard models notion of proof objects obtained omega-consistent paraconsistent paradox Peano philosophical philosophy of mathematics Platonic postmodern precisely predicate PrfTN-r principle procedure proposition provable prove recursion theory recursive functions relation Robinson Arithmetic Second Theorem semantic sense sequence of formulas set theory set-theoretic skeptical specific strings of symbols syntactic syntax talk theorem of TNT things TNT formula TNT is consistent TNT1 true Turing machine Typographical Number Theory undecidable unprovable Wittgenstein

Informazioni sull'autore (2011)

Francesco Berto teaches logic, ontology, and philosophy of mathematics at the universities of Aberdeen in Scotland, and Venice and Milan-San Raffaele in Italy. He holds a Chaire d'Excellence fellowship at CNRS in Paris, where he has taught ontology at the École Normale Supérieure, and he is a visiting professor at the Institut Wiener Kreis of the University of Vienna. He has written papers for American Philosophical Quarterly, Dialectica, The Philosophical Quarterly, the Australasian Journal of Philosophy, the European Journal of Philosophy, Philosophia Mathematica, Logique et Analyse, and Metaphysica, and runs the entries “Dialetheism” and “Impossible Worlds” in the Stanford Encyclopedia of Philosophy. His book How to Sell a Contradiction has won the 2007 Castiglioncello prize for the best philosophical book by a young philosopher.

Informazioni bibliografiche

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TitoloThere's Something About Gödel: The Complete Guide to the Incompleteness Theorem
AutoreFrancesco Berto
EditoreJohn Wiley & Sons, 2011
ISBN1444357611, 9781444357615
Lunghezza256 pagine
  
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