Single Idea 13621

[catalogued under 5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions]

Full Idea

Like the Deduction Theorem, one form of Reductio ad Absurdum (If Γ,φ|-[absurdity] then Γ|-¬φ) 'discharges' an assumption. Assume φ and obtain a contradiction, then we know ¬&phi, without assuming φ.

Gist of Idea

The Deduction Theorem and Reductio can 'discharge' assumptions - they aren't needed for the new truth

Source

David Bostock (Intermediate Logic [1997], 5.7)

Book Reference

Bostock,David: 'Intermediate Logic' [OUP 1997], p.227


A Reaction

Thus proofs from assumption either arrive at conditional truths, or at truths that are true irrespective of what was initially assumed.