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Single Idea 10689

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

Full Idea

A logical step is a 'material consequence' and not a formal one, if we need the contents as well as the structure or form.

Gist of Idea

A step is a 'material consequence' if we need contents as well as form

Source

JC Beall / G Restall (Logical Consequence [2005], 2)

Book Ref

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.4


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

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]