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5. Theory of Logic / B. Logical Consequence / 8. Material Implication

[truth of P implies the truth of Q]

7 ideas
A valid hypothetical syllogism is 'that which does not begin with a truth and end with a falsehood' [Sext.Empiricus]
Implication cannot be defined [Russell]
It would be circular to use 'if' and 'then' to define material implication [Russell]
The paradoxes of material implication are P |- Q → P, and P |- P → Q [Lemmon]
'Material implication' is defined as 'not(p and not-q)', but seems to imply a connection between p and q [Mautner]
A person who 'infers' draws the conclusion, but a person who 'implies' leaves it to the audience [Mautner]
A step is a 'material consequence' if we need contents as well as form [Beall/Restall]