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There's something about Gödel : = t...

Berto, Francesco.

There's something about Gödel : = the complete guide to the incompleteness theorem /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	There's something about Gödel :/ Francesco Berto.
Reminder of title:	the complete guide to the incompleteness theorem /
Author:	Berto, Francesco.
Published:	Malden, MA :Wiley-Blackwell, : c2009.,
Description:	xx, 233 p. :ill. ; : 23 cm.;
Subject:	Problems, exercises, etc. - Training of - Great Britain -
ISBN:	9781405197663 (cloth)

There's something about Gödel : = the complete guide to the incompleteness theorem /
Berto, Francesco.

There's something about Gödel :the complete guide to the incompleteness theorem /Francesco Berto. - Malden, MA :Wiley-Blackwell,c2009. - xx, 233 p. :ill. ;23 cm.

Includes bibliographical references (p. [217]-224) and index.

The Gödelian symphony -- Foundations and paradoxes -- "This sentence is false" -- The liar and Gödel -- Language and metalanguage -- The axiomatic method, or how to get the non-obvious out of the obvious -- Peano's axioms -- And the unsatisfied logicists, Frege and Russell -- Bits of set theory -- The abstraction principle -- Bytes of set theory -- Properties, relations, functions, that is, sets again -- Calculating, computing, enumerating, that is, the notion of algorithm -- Taking numbers as sets of sets -- It's raining paradoxes -- Cantor's diagonal argument -- Self-reference and paradoxes -- Hilbert -- Strings of symbols -- "In mathematics there is no ignorabimus" -- Gödel on stage -- Our first encounter with the incompleteness theorem -- And some provisos -- Gödelization, or say it with numbers! -- TNT -- The arithmetical axioms of TNT and the "standard model" N -- The fundamental property of formal systems -- The Gödel numbering -- And the arithmetization of syntax -- Bits of recursive arithmetic -- Making algorithms precise -- Bits of recursion theory -- Church's thesis -- The recursiveness of predicates, sets, properties, and relations -- And how it is represented in typographical number theory -- Introspection and representation -- The representability of properties, relations, and functions -- And the Gödelian loop -- "I am not provable" -- Proof pairs -- The property of being a theorem of TNI (is not recursive!) -- Arithmetizing substitution -- How can a TNT sentence refer to itself? -- Fixed point -- Consistency and omega-consistency -- Proving G1 -- Rosser's proof -- The unprovability of consistency and the "immediate consequences" of G1 and G2 -- G2 -- Technical interlude -- "Immediate consequences" of G1 and G2 -- Undecidable1 and undecidable 2 -- Essential incompleteness, or the syndicate of mathematicians -- Robinson arithmetic -- How general are Gödel's results? -- Bits of Turing machine -- G1 and G2 in general -- Unexpected fish in the

ISBN: 9781405197663 (cloth)

LCCN: 2009020156Subjects--Personal Names:

643058

MezzacappaSubjects--Topical Terms:

554762

--Training of--Great Britain--Problems, exercises, etc.

LC Class. No.: QA9.54 / .B4713 2009

Dewey Class. No.: 511.3

There's something about Gödel : = the complete guide to the incompleteness theorem /
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505 0 # $a The Gödelian symphony -- Foundations and paradoxes -- "This sentence is false" -- The liar and Gödel -- Language and metalanguage -- The axiomatic method, or how to get the non-obvious out of the obvious -- Peano's axioms -- And the unsatisfied logicists, Frege and Russell -- Bits of set theory -- The abstraction principle -- Bytes of set theory -- Properties, relations, functions, that is, sets again -- Calculating, computing, enumerating, that is, the notion of algorithm -- Taking numbers as sets of sets -- It's raining paradoxes -- Cantor's diagonal argument -- Self-reference and paradoxes -- Hilbert -- Strings of symbols -- "In mathematics there is no ignorabimus" -- Gödel on stage -- Our first encounter with the incompleteness theorem -- And some provisos -- Gödelization, or say it with numbers! -- TNT -- The arithmetical axioms of TNT and the "standard model" N -- The fundamental property of formal systems -- The Gödel numbering -- And the arithmetization of syntax -- Bits of recursive arithmetic -- Making algorithms precise -- Bits of recursion theory -- Church's thesis -- The recursiveness of predicates, sets, properties, and relations -- And how it is represented in typographical number theory -- Introspection and representation -- The representability of properties, relations, and functions -- And the Gödelian loop -- "I am not provable" -- Proof pairs -- The property of being a theorem of TNI (is not recursive!) -- Arithmetizing substitution -- How can a TNT sentence refer to itself? -- Fixed point -- Consistency and omega-consistency -- Proving G1 -- Rosser's proof -- The unprovability of consistency and the "immediate consequences" of G1 and G2 -- G2 -- Technical interlude -- "Immediate consequences" of G1 and G2 -- Undecidable1 and undecidable 2 -- Essential incompleteness, or the syndicate of mathematicians -- Robinson arithmetic -- How general are Gödel's results? -- Bits of Turing machine -- G1 and G2 in general -- Unexpected fish in the
505 0 # $a formal net -- Supernatural numbers -- The culpability of the induction scheme -- Bits of truth (not too much of it, though) -- The world after Gödel -- Bourgeois mathematicians! : the postmodern interpretations -- What is postmodernism? -- From Gödel to Lenin -- Is "biblical proof" decidable? -- Speaking of the totality -- Bourgeois teachers! -- (Un)interesting bifurcations -- A footnote to Plato -- Explorers in the realm of numbers -- The essence of a life -- "The philosophical prejudices of our times" -- From Gödel to Tarski -- Human, too human -- Mathematical faith -- "I'm not crazy!" -- Qualified doubts -- >From Gentzen to the Dialectica interpretation -- Mathematicians are people of faith -- Mind versus computer : Gödel and artificial intelligence -- Is mind (just) a program? -- "Seeing the truth" and "going outside the system" -- The basic mistake -- In the haze of the transfinite -- "Know thyself" : Socrates and the inexhaustibility of mathematics -- Gödel versus Wittgenstein and the paraconsistent interpretation -- When geniuses meet -- The implausible Wittgenstein -- "There is no metamathematics" -- Proof and prose -- The single argument -- But how can arithmetic be inconsistent? -- The costs and benefits of making Wittgenstein plausible.
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