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010 a| 2009020156;

020 a| 9781405197663 (hardcover : alk. paper);

020 a| 1405197668 (hardcover : alk. paper);

020 a| 9781405197670 (pbk. : alk. paper);

020 a| 1405197676 (pbk. : alk. paper);

035 a| (WaSeSS)ssj0000506364;

041 1 a| engh| ita;

049 a| EREEa| NEHH;

050 00 a| QA9.54b| .B4713 2009;

082 00 a| 511.32| 22;

100 1 a| Berto, Francesco.?| UNAUTHORIZED;

240 10 a| Tutti pazzi per Gödel!l| English?| UNAUTHORIZED;

245 10 a| There's something about Gödelh| [electronic resource] :b| the complete guide to the incompleteness theorem /c| Francesco Berto.;

260 a| Malden, MA :b| Wiley-Blackwell,;

300 a| xx, 233 p. :b| ill. ;c| 24 cm.;

504 a| Includes bibliographical references (p. [217]-224) and index.;

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 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.;

506 a| Available only to authorized users.;

538 a| Mode of access: World Wide Web;

600 10 a| Gödel, Kurt.=| ^A45470;

650 0 a| Incompleteness theorems.=| ^A396327;

650 0 a| Gödel's theorem.=| ^A207978;

650 0 a| Mathematicsx| Philosophy.=| ^A14926;

655 0 a| Electronic books.=| ^A491897;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=7104594;

947 a| (OCoLC)ocn361965956;

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999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 5927699-3001l| MNETm| JMUSICr| Ys| Yt| MNESSBKu| 10/14/2022x| EBOOKz| JERESOURCE;

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

Author/creator	Berto, Francesco
Format	Electronic
Publication Info	Malden, MA : Wiley-Blackwell,
Description	xx, 233 p. : ill. ; 24 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Gödel, Kurt. Incompleteness theorems. Gödel's theorem. Mathematics--Philosophy.

Uniform title	Tutti pazzi per Gödel! English
Contents	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 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.
Bibliography note	Includes bibliographical references (p. [217]-224) and index.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2009020156
ISBN	9781405197663 (hardcover : alk. paper)
ISBN	1405197668 (hardcover : alk. paper)
ISBN	9781405197670 (pbk. : alk. paper)
ISBN	1405197676 (pbk. : alk. paper)

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

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