MARC Record from Library of Congress

LEADER: 04173nam a22003018a 4500
001 2009020156
003 DLC
005 20090527143742.0
008 090518s2009 mau b 001 0 eng
010 $a 2009020156
020 $a9781405197663 (hardcover : alk. paper)
020 $a9781405197670 (pbk. : alk. paper)
040 $aDLC$cDLC
041 1 $aeng$hita
050 00 $aQA9.54$bB4713 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.
263 $a0911
300 $ap. cm.
504 $aIncludes bibliographical references 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 -- 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 theorem.
650 0 $aGödel's theorem.
650 0 $aMathematics$xPhilosophy.
600 10 $aGödel, Kurt.