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Ideas of JC Beall / G Restall, by Text
[Australian, fl. 2005, Professors at the Universities of Connecticut and Melbourne]
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 nonlogical 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

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 outofdate

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

13243

Excluded middle must be true for some situation, not for all situations

5.2

p.53

13242

It's 'relevantly' valid if all those situations make it true

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 truthconditions 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 nonempty, 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
