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090518s2009 maua b 001 0 eng |
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|a 2009020156
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|a 9781405197663 (hardcover : alk. paper)
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|a 1405197668 (hardcover : alk. paper)
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|a 9781405197670 (pbk. : alk. paper)
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|a 1405197676 (pbk. : alk. paper)
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|a 2009020156
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|a (OCoLC)361965956
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|a DLC
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|a QA9.54
|b .B4713 2009
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| 082 |
0 |
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|a 511.3
|2 22
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| 100 |
1 |
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|a Berto, Francesco.
|0 http://id.loc.gov/authorities/names/no2004071131
|1 http://viaf.org/viaf/7638508
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| 240 |
1 |
0 |
|a Tutti pazzi per Gödel!.
|l English
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| 245 |
1 |
0 |
|a There's something about Gödel :
|b the complete guide to the incompleteness theorem /
|c Francesco Berto.
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| 260 |
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|a Malden, MA :
|b Wiley-Blackwell,
|c 2009.
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| 300 |
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|a xx, 233 p. :
|b ill. ;
|c 24 cm.
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| 336 |
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|a text
|b txt
|2 rdacontent
|0 http://id.loc.gov/vocabulary/contentTypes/txt
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| 337 |
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|a unmediated
|b n
|2 rdamedia
|0 http://id.loc.gov/vocabulary/mediaTypes/n
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| 338 |
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|a volume
|b nc
|2 rdacarrier
|0 http://id.loc.gov/vocabulary/carriers/nc
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| 504 |
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|a Includes bibliographical references and index.
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| 505 |
0 |
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|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.
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| 600 |
1 |
0 |
|a Gödel, Kurt.
|0 http://id.loc.gov/authorities/names/n79007770
|1 http://viaf.org/viaf/97851774
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| 650 |
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0 |
|a Incompleteness theorem.
|
| 650 |
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0 |
|a Gödel's theorem.
|0 http://id.loc.gov/authorities/subjects/sh85055601
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| 650 |
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0 |
|a Mathematics
|x Philosophy.
|0 http://id.loc.gov/authorities/subjects/sh85082153
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| 600 |
1 |
7 |
|a Gödel, Kurt.
|2 fast
|0 http://id.worldcat.org/fast/fst00030398
|0 http://id.worldcat.org/fast/30398
|1 http://viaf.org/viaf/97851774
|
| 650 |
|
7 |
|a Gödel's theorem.
|2 fast
|0 http://id.worldcat.org/fast/fst00949806
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| 650 |
|
7 |
|a Incompleteness theorems.
|2 fast
|0 http://id.worldcat.org/fast/fst00968811
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| 650 |
|
7 |
|a Mathematics
|x Philosophy.
|2 fast
|0 http://id.worldcat.org/fast/fst01012213
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|
|
|t Library of Congress classification
|a QA9.54 .B4713 2009
|l Eck
|c Eck-Eck
|i 5521884
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| 927 |
|
|
|t Library of Congress classification
|a QA9.54 .B4713 2009
|l Eck
|c Eck-Eck
|e BROW
|b 092681486
|i 8741943
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