more from Kurt Gödel

Single Idea 19123

[catalogued under 5. Theory of Logic / K. Features of Logics / 3. Soundness]

Full Idea

Gödel showed PA cannot be proved consistent from with PA. But 'reflection principles' can be added, which are axioms partially expressing the soundness of PA, by asserting what is provable. A Global Reflection Principle asserts full soundness.

Gist of Idea

If soundness can't be proved internally, 'reflection principles' can be added to assert soundness

Source

report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Halbach,V/Leigh,G.E. - Axiomatic Theories of Truth (2013 ver) 1.2

Book Reference

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.3


A Reaction

The authors point out that this needs a truth predicate within the language, so disquotational truth won't do, and there is a motivation for an axiomatic theory of truth.

Related Idea

Idea 19124 A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness [Halbach/Leigh]