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Full Idea
It would be a vicious circle to define material implication as meaning that if one proposition is true, then another is true, for 'if' and 'then' already involve implication.
Gist of Idea
It would be circular to use 'if' and 'then' to define material implication
Source
Bertrand Russell (The Principles of Mathematics [1903], §037)
Book Ref
Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.33
A Reaction
Hence the preference for defining it by the truth table, or as 'not-p or q'.
| 12196 | A valid hypothetical syllogism is 'that which does not begin with a truth and end with a falsehood' [Sext.Empiricus] |
| 14106 | Implication cannot be defined [Russell] |
| 14108 | It would be circular to use 'if' and 'then' to define material implication [Russell] |
| 9520 | The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon] |
| 6879 | 'Material implication' is defined as 'not(p and not-q)', but seems to imply a connection between p and q [Mautner] |
| 6878 | A person who 'infers' draws the conclusion, but a person who 'implies' leaves it to the audience [Mautner] |
| 10689 | A step is a 'material consequence' if we need contents as well as form [Beall/Restall] |