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Single Idea 10620

[filed under theme 5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth ]

Full Idea

At that time (c.1930) a concept of objective mathematical truth as opposed to demonstrability was viewed with greatest suspicion and widely rejected as meaningless.

Gist of Idea

Originally truth was viewed with total suspicion, and only demonstrability was accepted

Source

Kurt Gödel (works [1930]), quoted by Peter Smith - Intro to Gödel's Theorems 28.2

Book Ref

Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.254


A Reaction

[quoted from a letter] This is the time of Ramsey's redundancy account, and before Tarski's famous paper of 1933. It is also the high point of Formalism, associated with Hilbert.


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]