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Ideas of JC Beall / G Restall, by Text

[Australian, fl. 2005, Professors at the Universities of Connecticut and Melbourne]

2005 Logical Consequence
Intro p.1 10688 'Equivocation' is when terms do not mean the same thing in premises and conclusion
2 p.4 10689 A step is a 'material consequence' if we need contents as well as form
2 p.5 10690 Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought
2 p.7 10695 Logical consequence is either necessary truth preservation, or preservation based on interpretation
3 p.6 10691 Logical consequence needs either proofs, or absence of counterexamples
3 p.6 10693 Models are mathematical structures which interpret the non-logical primitives
3 p.6 10692 Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite
4 p.8 10696 A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises
2006 Logical Pluralism
2.1 p.8 13232 Logic studies arguments, not formal languages; this involves interpretations
2.1 p.12 13233 Propositions commit to content, and not to any way of spelling it out
2.2 p.12 13234 The view of logic as knowing a body of truths looks out-of-date
2.2 p.13 13235 Logic studies consequence; logical truths are consequences of everything, or nothing
2.2 p.13 13236 Logical truth is much more important if mathematics rests on it, as logicism claims
2.4 p.16 13237 Preface Paradox affirms and denies the conjunction of propositions in the book
2.5 p.19 13238 Syllogisms are only logic when they use variables, and not concrete terms
2.5 p.21 13239 Judgement is always predicating a property of a subject
3.2 p.29 13240 A sentence follows from others if they always model it
4.2.1 p.40 13241 The model theory of classical predicate logic is mathematics
5.2 p.53 13244 Relevant necessity is always true for some situation (not all situations)
5.2 p.53 13242 It's 'relevantly' valid if all those situations make it true
5.2 p.53 13243 Excluded middle must be true for some situation, not for all situations
5.3.3 p.55 13245 Relevant consequence says invalidity is the conclusion not being 'in' the premises
5.4 p.55 13246 Relevant logic does not abandon classical logic
5.5.3 p.57 13247 A truthmaker is an object which entails a sentence
5.5.4 p.58 13248 We can rest truth-conditions on situations, rather than on possible worlds
6.1.2 p.64 13249 (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically
7.1 p.75 13250 Free logic terms aren't existential; classical is non-empty, with referring names
7.4 p.79 13252 Some truths have true negations
8 p.88 13253 There are several different consequence relations
8 p.91 13254 A doesn't imply A - that would be circular
8 p.91 13255 Relevant logic may reject transitivity