Single Idea 19129

[catalogued under 3. Truth / G. Axiomatic Truth / 2. FS Truth Axioms]

Full Idea

It is a virtue of the Friedman-Sheard axiomatisation that it is thoroughly classical in its logic. Its drawback is that it is ω-inconsistent. That is, it proves &exists;xφ(x), but proves also φ(0), φ(1), φ(2),

Gist of Idea

The FS axioms use classical logical, but are not fully consistent

Source

Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 4.3)

Book Reference

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.10


A Reaction

It seems the theory is complete (and presumably sound), yet not fully consistent. FS also proves the finite levels of Tarski's hierarchy, but not the transfinite levels.