There's something about Gödel
Subtitle: the complete guide to the incompleteness theorem
By: Francesco Berto
Publisher: Wiley-Blackwell
Published: 2009
Place of publication: Malden, MA
Language: eng
Number of pages: 233
ISBN-13: 9781405197663; 9781405197670
Work titles: Tutti pazzi per Gödel!
Notes: Includes bibliographical references (p. [217]-224) and index.
Table of contents: title: The Gödelian symphony; title: Foundations and paradoxes; title: "This sentence is false"; title: The liar and Gödel; title: Language and metalanguage; title: The axiomatic method, or how to get the non-obvious out of the obvious; title: Peano's axioms; title: And the unsatisfied logicists, Frege and Russell; title: Bits of set theory; title: The abstraction principle; title: Bytes of set theory; title: Properties, relations, functions, that is, sets again; title: Calculating, computing, enumerating, that is, the notion of algorithm; title: Taking numbers as sets of sets; title: It's raining paradoxes; title: Cantor's diagonal argument; title: Self-reference and paradoxes; title: Hilbert; title: Strings of symbols; title: "In mathematics there is no ignorabimus"; title: Gödel on stage; title: Our first encounter with the incompleteness theorem; title: And some provisos; title: Gödelization, or say it with numbers!; title: TNT; title: The arithmetical axioms of TNT and the "standard model" N; title: The fundamental property of formal systems; title: The Gödel numbering; title: And the arithmetization of syntax; title: Bits of recursive arithmetic; title: Making algorithms precise; title: Bits of recursion theory; title: Church's thesis; title: The recursiveness of predicates, sets, properties, and relations; title: And how it is represented in typographical number theory; title: Introspection and representation; title: The representability of properties, relations, and functions; title: And the Gödelian loop; title: "I am not provable"; title: Proof pairs; title: The property of being a theorem of TNI (is not recursive!); title: Arithmetizing substitution; title: How can a TNT sentence refer to itself?; title: Fixed point; title: Consistency and omega-consistency; title: Proving G1; title: Rosser's proof; title: The unprovability of consistency and the "immediate consequences" of G1 and G2; title: G2; title: Technical interlude; title: "Immediate consequences" of G1 and G2; title: Undecidable1 and undecidable 2; title: Essential incompleteness, or the syndicate of mathematicians; title: Robinson arithmetic; title: How general are Gödel's results?; title: Bits of Turing machine; title: G1 and G2 in general; title: Unexpected fish in the formal net; title: Supernatural numbers; title: The culpability of the induction scheme; title: Bits of truth (not too much of it, though); title: The world after Gödel; title: Bourgeois mathematicians! : the postmodern interpretations; title: What is postmodernism?; title: From Gödel to Lenin; title: Is "biblical proof" decidable?; title: Speaking of the totality; title: Bourgeois teachers!; title: (Un)interesting bifurcations; title: A footnote to Plato; title: Explorers in the realm of numbers; title: The essence of a life; title: "The philosophical prejudices of our times"; title: From Gödel to Tarski; title: Human, too human; title: Mathematical faith; title: "I'm not crazy!"; title: Qualified doubts; title: From Gentzen to the Dialectica interpretation; title: Mathematicians are people of faith; title: Mind versus computer : Gödel and artificial intelligence; title: Is mind (just) a program?; title: "Seeing the truth" and "going outside the system"; title: The basic mistake; title: In the haze of the transfinite; title: "Know thyself" : Socrates and the inexhaustibility of mathematics; title: Gödel versus Wittgenstein and the paraconsistent interpretation; title: When geniuses meet; title: The implausible Wittgenstein; title: "There is no metamathematics"; title: Proof and prose; title: The single argument; title: But how can arithmetic be inconsistent?; title: The costs and benefits of making Wittgenstein plausible.