Single Idea 13353

[catalogued under 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL]

Full Idea

The Principle of Negation says that Γ,¬φ |= iff Γ |= φ. We also say that φ,¬φ |=, and hence by 'thinning on the right' that φ,¬φ |= ψ, which is 'ex falso quodlibet'.

Gist of Idea

'Negation' says that Γ,¬φ|= iff Γ|=φ

Source

David Bostock (Intermediate Logic [1997], 2.5.E)

Book Reference

Bostock,David: 'Intermediate Logic' [OUP 1997], p.33


A Reaction

That is, roughly, if the formula gives consistency, the negation gives contradiction. 'Ex falso' says that anything will follow from a contradiction.