An edition of There's something about Gödel
(2009)
There's something about Gödel
the complete guide to the incompleteness theorem
by Francesco Berto
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There's something about Gödel: the complete guide to the incompleteness theorem
2009, Wiley-Blackwell
in English
1405197668 9781405197663
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Book Details
Table of 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.
Edition Notes
Includes bibliographical references (p. [217]-224) and index.
Classifications
The Physical Object
ID Numbers
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| December 20, 2023 | Edited by ImportBot | import existing book |
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