MARC Record from Library of Congress

LEADER: 04375cam a2200325 a 4500
001 2009020156
003 DLC
005 20100526144722.0
008 090518s2009 maua b 001 0 eng
010 $a 2009020156
020 $a9781405197663 (hardcover : alk. paper)
020 $a1405197668 (hardcover : alk. paper)
020 $a9781405197670 (pbk. : alk. paper)
020 $a1405197676 (pbk. : alk. paper)
035 $a(OCoLC)ocn361965956
040 $aDLC$cDLC$dYDX$dBWX$dIUL$dDLC
041 1 $aeng$hita
050 00 $aQA9.54$b.B4713 2009
082 00 $a511.3$222
100 1 $aBerto, Francesco.
240 10 $aTutti pazzi per Gödel!$lEnglish
245 10 $aThere's something about Gödel :$bthe complete guide to the incompleteness theorem /$cFrancesco Berto.
260 $aMalden, MA :$bWiley-Blackwell,$c2009.
300 $axx, 233 p. :$bill. ;$c24 cm.
504 $aIncludes bibliographical references (p. [217]-224) and index.
505 0 $aThe 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.
650 0 $aIncompleteness theorems.
650 0 $aGödel's theorem.
650 0 $aMathematics$xPhilosophy.
600 10 $aGödel, Kurt.