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5. Theory of Logic / B. Logical Consequence / 7. Strict Implication

[it can never be that P is true and Q is false]

5 ideas
Russell's implication means that random sentences imply one another [Lewis,CI]
Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine]
Where a conditional is purely formal, an implication implies a link between premise and conclusion [Devlin]
Strict implication says false propositions imply everything, and everything implies true propositions [Mautner]
Necessary implication is called 'strict implication'; if successful, it is called 'entailment' [Girle]