more from Volker Halbach

Single Idea 15653

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Number / g. Incompleteness of Arithmetic]

Full Idea

Peano Arithmetic cannot derive its own consistency from within itself. But it can be strengthened by adding this consistency statement or by stronger axioms (particularly ones partially expressing soundness). These are known as Reflexion Principles.

Gist of Idea

We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness

Source

Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.2)

Book Reference

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