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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').
Gist of Idea
Where a conditional is purely formal, an implication implies a link between premise and conclusion
Source
Keith Devlin (Goodbye Descartes [1997], Ch. 2)
Book Ref
Devlin,Keith: 'Goodbye Descartes: the end of logic' [Wiley 1997], p.48
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.
| 8204 | Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead] |
| 9359 | Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead] |
| 8082 | Where a conditional is purely formal, an implication implies a link between premise and conclusion [Devlin] |
| 6880 | Strict implication says false propositions imply everything, and everything implies true propositions [Mautner] |
| 7789 | Necessary implication is called 'strict implication'; if successful, it is called 'entailment' [Girle] |