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
13245 Relevant consequence says invalidity is the conclusion not being 'in' the premises
13246 Relevant logic does not abandon classical logic
13254 A doesn't imply A - that would be circular
13255 Relevant logic may reject transitivity
13242 It's 'relevantly' valid if all those situations make it true
4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
13250 Free logic terms aren't existential; classical is non-empty, 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13234 The view of logic as knowing a body of truths looks out-of-date
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 non-logical 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 truth-conditions 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