Ideas from 'Logical Pluralism' by JC Beall / G Restall [2006], by Theme Structure
[found in 'Logical Pluralism' by Beall,J/Restall,G [OUP 2006,978-0-19-928841-0]].
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3. Truth / A. Truth Problems / 1. Truth
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13252
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Some truths have true negations
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3. Truth / B. Truthmakers / 5. What Makes Truths / b. Objects make truths
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13247
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A truthmaker is an object which entails a sentence
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4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
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13249
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(∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically
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4. Formal Logic / E. Nonclassical Logics / 5. Relevant Logic
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13242
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It's 'relevantly' valid if all those situations make it true
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13243
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Excluded middle must be true for some situation, not for all situations
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13245
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Relevant consequence says invalidity is the conclusion not being 'in' the premises
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13246
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Relevant logic does not abandon classical logic
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13254
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A doesn't imply A - that would be circular
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13255
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Relevant logic may reject transitivity
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4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
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13250
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Free logic terms aren't existential; classical is non-empty, with referring names
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5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
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13235
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Logic studies consequence; logical truths are consequences of everything, or nothing
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13238
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Syllogisms are only logic when they use variables, and not concrete terms
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5. Theory of Logic / A. Overview of Logic / 2. History of Logic
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13234
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The view of logic as knowing a body of truths looks out-of-date
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5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
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13232
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Logic studies arguments, not formal languages; this involves interpretations
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5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
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13241
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The model theory of classical predicate logic is mathematics
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5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
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13253
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There are several different consequence relations
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5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
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13240
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A sentence follows from others if they always model it
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
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13236
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Logical truth is much more important if mathematics rests on it, as logicism claims
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / d. The Preface paradox
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13237
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Preface Paradox affirms and denies the conjunction of propositions in the book
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10. Modality / A. Necessity / 3. Types of Necessity
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13244
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Relevant necessity is always true for some situation (not all situations)
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18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
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13239
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Judgement is always predicating a property of a subject
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19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
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13248
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We can rest truth-conditions on situations, rather than on possible worlds
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19. Language / D. Propositions / 1. Propositions
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13233
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Propositions commit to content, and not to any way of spelling it out
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