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Single Idea 11069

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

Full Idea

Gödel's Second Incompleteness Theorem says that true unprovable sentences are clearly semantic consequences of the axioms in the sense that they are necessarily true if the axioms are true. So semantic consequence outruns provability.

Gist of Idea

Gödel's Second says that semantic consequence outruns provability

Source

report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Robert Hanna - Rationality and Logic 5.3

Book Ref

Hanna,Robert: 'Rationality and Logic' [MIT 2006], p.134