Single Idea 17888

[catalogued under 5. Theory of Logic / K. Features of Logics / 5. Incompleteness]

Full Idea

My undecidable arithmetical sentence ...is not at all absolutely undecidable; rather, one can always pass to 'higher' systems in which the sentence in question is decidable.

Gist of Idea

The undecidable sentence can be decided at a 'higher' level in the system

Source

Kurt Gödel (On Formally Undecidable Propositions [1931]), quoted by Peter Koellner - On the Question of Absolute Undecidability 1.1

Book Reference

-: 'Philosophia Mathematica' [-], p.6


A Reaction

[a 1931 MS] He says the reals are 'higher' than the naturals, and the axioms of set theory are higher still. The addition of a truth predicate is part of what makes the sentence become decidable.