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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.
| 8072 | Sentences of apparent identical form can have different contextual meanings [Devlin] |
| 8073 | How do we parse 'time flies like an arrow' and 'fruit flies like an apple'? [Devlin] |
| 8082 | Where a conditional is purely formal, an implication implies a link between premise and conclusion [Devlin] |
| 8076 | The distinction between sentences and abstract propositions is crucial in logic [Devlin] |
| 8075 | Space and time are atomic in the arrow, and divisible in the tortoise [Devlin] |
| 8081 | 'No councillors are bankers' and 'All bankers are athletes' implies 'Some athletes are not councillors' [Devlin] |
| 8085 | Modern propositional inference replaces Aristotle's 19 syllogisms with modus ponens [Devlin] |
| 8086 | Predicate logic retains the axioms of propositional logic [Devlin] |
| 8087 | Golden ages: 1900-1960 for pure logic, and 1950-1985 for applied logic [Devlin] |
| 8088 | People still say the Hopi have no time concepts, despite Whorf's later denial [Devlin] |
| 8091 | Situation theory is logic that takes account of context [Devlin] |
| 8089 | Montague's intensional logic incorporated the notion of meaning [Devlin] |
| 8092 | Logic was merely a branch of rhetoric until the scientific 17th century [Devlin] |