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 ,-]].
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4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
10688
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'Equivocation' is when terms do not mean the same thing in premises and conclusion
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5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
10690
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Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought
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5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10691
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Logical consequence needs either proofs, or absence of counterexamples
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5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10695
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Logical consequence is either necessary truth preservation, or preservation based on interpretation
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5. Theory of Logic / B. Logical Consequence / 8. Material Implication
10689
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A step is a 'material consequence' if we need contents as well as form
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10696
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A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10693
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Models are mathematical structures which interpret the non-logical primitives
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6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
10692
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Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite
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