Ideas from 'Logical Consequence' by JC Beall / G Restall [2005], by Theme Structure
[found in 'Stanford Online Encyclopaedia of Philosophy' (ed/tr Stanford University) [plato.stanford.edu ,]].
green numbers give full details 
back to texts

expand these ideas
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
10688

'Equivocation' is when terms do not mean the same thing in premises and conclusion

5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
10690

Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought

5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10691

Logical consequence needs either proofs, or absence of counterexamples

5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence =
10695

Logical consequence is either necessary truth preservation, or preservation based on interpretation

5. Theory of Logic / B. Logical Consequence / 8. Material Implication
10689

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

5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10696

A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises

5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10693

Models are mathematical structures which interpret the nonlogical primitives

6. Mathematics / A. Nature of Mathematics / 6. Proof in Mathematics
10692

Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite
