Single Idea 13542

[catalogued under 5. Theory of Logic / K. Features of Logics / 2. Consistency]

Full Idea

Any system of proof S is said to be 'absolutely consistent' iff it is not the case that for every formula we have |-(S)φ.

Gist of Idea

A proof-system is 'absolutely consistent' iff we don't have |-(S)φ for every formula

Source

David Bostock (Intermediate Logic [1997], 4.5)

Book Reference

Bostock,David: 'Intermediate Logic' [OUP 1997], p.167


A Reaction

Bostock notes that a sound system will be both 'negation-consistent' (Idea 13541) and absolutely consistent. 'Tonk' systems can be shown to be unsound because the two come apart.

Related Idea

Idea 13541 For 'negation-consistent', there is never |-(S)φ and |-(S)¬φ [Bostock]