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Single Idea 14106

[filed under theme 5. Theory of Logic / B. Logical Consequence / 8. Material Implication ]

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

The 7 ideas with the same theme [truth of P implies the truth of 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]