Ideas of JC Beall / G Restall, by Theme
[Australian, fl. 2005, Professors at the Universities of Connecticut and Melbourne]
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3. Truth / A. Truth Problems / 1. Truth
13252

Some truths have true negations

3. Truth / B. Truthmakers / 5. What Makes Truths / b. Objects make truths
13247

A truthmaker is an object which entails a sentence

4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
10688

'Equivocation' is when terms do not mean the same thing in premises and conclusion

4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
13249

(∀x)(A v B)  (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically

4. Formal Logic / E. Nonclassical Logics / 5. Relevant Logic
13243

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

13242

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

13246

Relevant logic does not abandon classical logic

13245

Relevant consequence says invalidity is the conclusion not being 'in' the premises

13254

A doesn't imply A  that would be circular

13255

Relevant logic may reject transitivity

4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
13250

Free logic terms aren't existential; classical is nonempty, with referring names

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
13235

Logic studies consequence; logical truths are consequences of everything, or nothing

13238

Syllogisms are only logic when they use variables, and not concrete terms

5. Theory of Logic / A. Overview of Logic / 2. History of Logic
13234

The view of logic as knowing a body of truths looks outofdate

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

13232

Logic studies arguments, not formal languages; this involves interpretations

5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
13241

The model theory of classical predicate logic is mathematics

5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10691

Logical consequence needs either proofs, or absence of counterexamples

13253

There are several different consequence relations

5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence =
10695

Logical consequence is either necessary truth preservation, or preservation based on interpretation

13240

A sentence follows from others if they always model it

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

13236

Logical truth is much more important if mathematics rests on it, as logicism claims

5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10693

Models are mathematical structures which interpret the nonlogical primitives

5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / d. The Preface paradox
13237

Preface Paradox affirms and denies the conjunction of propositions in the book

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

10. Modality / A. Necessity / 3. Types of Necessity
13244

Relevant necessity is always true for some situation (not all situations)

18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
13239

Judgement is always predicating a property of a subject

19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
13248

We can rest truthconditions on situations, rather than on possible worlds

19. Language / D. Propositions / 1. Propositions
13233

Propositions commit to content, and not to any way of spelling it out
