There's Something About Gödel: The Complete Guide to the Incompleteness TheoremBerto’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.

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Sommario
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  
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 
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 nonstandard models notion of proof objects obtained omegaconsistent paraconsistent paradox Peano philosophical philosophy of mathematics Platonic postmodern precisely predicate PrfTNr principle procedure proposition provable prove recursion theory recursive functions relation Robinson Arithmetic Second Theorem semantic sense sequence of formulas set theory settheoretic 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