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
Some truths have true negations
3. Truth / B. Truthmakers / 5. What Makes Truths / b. Objects make truths
A truthmaker is an object which entails a sentence
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
'Equivocation' is when terms do not mean the same thing in premises and conclusion
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
(∀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
Relevant consequence says invalidity is the conclusion not being 'in' the premises
Relevant logic may reject transitivity
Relevant logic does not abandon classical logic
A doesn't imply A - that would be circular
Excluded middle must be true for some situation, not for all situations
It's 'relevantly' valid if all those situations make it true
4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
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
Logic studies consequence; logical truths are consequences of everything, or nothing
Syllogisms are only logic when they use variables, and not concrete terms
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
The view of logic as knowing a body of truths looks out-of-date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
Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought
Logic studies arguments, not formal languages; this involves interpretations
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
The model theory of classical predicate logic is mathematics
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
Logical consequence needs either proofs, or absence of counterexamples
There are several different consequence relations
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
Logical consequence is either necessary truth preservation, or preservation based on interpretation
A sentence follows from others if they always model it
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
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
A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises
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
Models are mathematical structures which interpret the non-logical primitives
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / d. The Preface paradox
Preface Paradox affirms and denies the conjunction of propositions in the book
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite
10. Modality / A. Necessity / 3. Types of Necessity
Relevant necessity is always true for some situation (not all situations)
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
Judgement is always predicating a property of a subject
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
We can rest truth-conditions on situations, rather than on possible worlds
19. Language / D. Propositions / 1. Propositions
Propositions commit to content, and not to any way of spelling it out