more from this thinker | more from this text
Full Idea
A definition of implication is quite impossible.
Gist of Idea
Implication cannot be defined
Source
Bertrand Russell (The Principles of Mathematics [1903], §016)
Book Ref
Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.14
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] |