Single Idea 13614

[catalogued under 5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens]

Full Idea

The Rule of Detachment is a version of Modus Ponens, and says 'If |=φ and |=φ→ψ then |=ψ'. This has no assumptions. Modus Ponens is the more general rule that 'If Γ|=φ and Γ|=φ→ψ then Γ|=ψ'.

Clarification

'Γ' names a set of assumptions

Gist of Idea

MPP: 'If Γ|=φ and Γ|=φ→ψ then Γ|=ψ' (omit Γs for Detachment)

Source

David Bostock (Intermediate Logic [1997], 5.3)

Book Reference

Bostock,David: 'Intermediate Logic' [OUP 1997], p.202


A Reaction

Modus Ponens is actually designed for use in proof based on assumptions (which isn't always the case). In Detachment the formulae are just valid, without dependence on assumptions to support them.