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
Excluded middle must be true for some situation, not for all situations
It's 'relevantly' valid if all those situations make it true
Relevant logic does not abandon classical logic
Relevant consequence says invalidity is the conclusion not being 'in' the premises
A doesn't imply A - that would be circular
Relevant logic may reject transitivity
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The view of logic as knowing a body of truths looks out-of-date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