Single Idea 13350

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

Full Idea

The Principle of Assumptions says that any formula entails itself, i.e. φ |= φ. The principle depends just upon the fact that no interpretation assigns both T and F to the same formula.

Gist of Idea

'Assumptions' says that a formula entails itself (φ|=φ)

Source

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

Book Reference

Bostock,David: 'Intermediate Logic' [OUP 1997], p.30


A Reaction

Thus one can introduce φ |= φ into any proof, and then use it to build more complex sequents needed to attain a particular target formula. Bostock's principle is more general than anything in Lemmon.