Full Idea
In order that it be valid to infer q from p, it is only necessary that p should be true and that the proposition 'not-p or q' should be true.
Gist of Idea
Inferring q from p only needs p to be true, and 'not-p or q' to be true
Source
Bertrand Russell (Introduction to Mathematical Philosophy [1919], XIV)
Book Reference
Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.153
A Reaction
Rumfitt points out that this approach to logical consequences is a denial of any modal aspect, such as 'logical necessity'. Russell observes that for a good inference you must know the disjunction as a whole. Could disjunction be modal?...