more from E.J. Lemmon

### Single Idea 9536

#### [catalogued under 4. Formal Logic / B. Propositional Logic PL / 4. Soundness of PL]

Full Idea

If any application of the nine derivation rules of propositional logic is made on tautologous sequents, we have demonstrated that the result is always a tautologous sequent. Thus the system is consistent.

Gist of Idea

If any of the nine rules of propositional logic are applied to tautologies, the result is a tautology

Source

E.J. Lemmon (Beginning Logic [1965], 2.4)

Book Reference

Lemmon,E.J.: 'Beginning Logic' [Nelson 1979], p.80

A Reaction

The term 'sound' tends to be used now, rather than 'consistent'. See Lemmon for the proofs of each of the nine rules.