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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 8 ideas from 'Logical Consequence'

'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall]
Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall]
Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall]
A step is a 'material consequence' if we need contents as well as form [Beall/Restall]
Models are mathematical structures which interpret the non-logical primitives [Beall/Restall]
Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall]
Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall]
A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall]