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2.2 p.12 The view of logic as knowing a body of truths looks out-of-date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