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Single Idea 17885

[filed under theme 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic ]

Full Idea

Eventually Gödel ...expressed the hope that there might be a generalised completeness theorem according to which there are no absolutely undecidable sentences.

Gist of Idea

Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable

Source

report of Kurt Gödel (works [1930]) by Peter Koellner - On the Question of Absolute Undecidability Intro

Book Ref

-: 'Philosophia Mathematica' [-], p.2


A Reaction

This comes as a bit of a shock to those who associate him with the inherent undecidability of reality.

Related Idea

Idea 17883 Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner]


The 6 ideas from 'works'

For clear questions posed by reason, reason can also find clear answers [Gödel]
Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett]
Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel]
Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner]
Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner]
The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel]