more from GE Hughes/M Cresswell

Single Idea 9543

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

Full Idea

An axiomatic system is most naturally consistent iff no thesis is the negation of another thesis. It can be shown that every axiom is valid, that the transformation rules are validity-preserving, and if a wff α is valid, then α is not valid.

Gist of Idea

The rules preserve validity from the axioms, so no thesis negates any other thesis

Source

GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1)

Book Reference

Hughes,G./Cresswell,M.: 'An Introduction to Modal Logic' [Methuen 1972], p.19


A Reaction

[The labels 'soundness' and 'consistency' seem interchangeable here, with the former nowadays preferred]