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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
Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead]
     Full Idea: Russell call 'if...then' implication, when the material conditional is a much better account; C.I.Lewis (in founding modern modal logic) preserved Russell's confusion by creating 'strict implication', and called that implication.
     From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Willard Quine - Reply to Professor Marcus p.177
     A reaction: [A compession of Quine's paragraph]. All of this assumes that logicians can give an accurate account of what if...then means, when ordinary usage is broad and vague. Strict implication seems to drain all the normal meaning out of 'if...then'.
Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead]
     Full Idea: In Mr Russell's idea of implication, if twenty random sentences from a newspaper were put in a hat, and two of them drawn at random, one will certainly imply the other, and it is an even bet the implication will be mutual.
     From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by C.I. Lewis - A Pragmatic Conception of the A Priori p.366
     A reaction: This sort of lament leads modern logicians to suggest 'relevance' as an important criterion. It certainly seems odd that so-called 'classical logic' should contain a principle so at variance with everyday reasoning.
Where a conditional is purely formal, an implication implies a link between premise and conclusion [Devlin]
     Full Idea: Implication involves some form of link or causality between the antecedent and the consequent of an if-then; normally it says that the conclusion is a consequence of the premise (where conditionals are just defined by 'true' and 'false').
     From: Keith Devlin (Goodbye Descartes [1997], Ch. 2)
     A reaction: This distinction is a key one when discussing 'If-then' sentences. Some are merely formal conditionals, but others make real claims about where you can get to from where you are.
Strict implication says false propositions imply everything, and everything implies true propositions [Mautner]
     Full Idea: Strict implication [not(p and not-q)] carries the paradoxes that a false proposition (p) implies any proposition (q), and a true proposition (q) is materially implied by any proposition (p).
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.270)
     A reaction: This seems to show that we have two drastically different notions of implication; one (the logician's) is boring and is defined by a truth table; the other (the ordinary interesting one) says if you have one truth you can deduce a second.
Necessary implication is called 'strict implication'; if successful, it is called 'entailment' [Girle]
     Full Idea: Necessary implication is often called 'strict implication'. The sort of strict implication found in valid arguments, where the conjunction of the premises necessarily implies the conclusion, is often called 'entailment'.
     From: Rod Girle (Modal Logics and Philosophy [2000], 1.2)
     A reaction: These are basic concept for all logic.