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 non-logical primitives

6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics

10692

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