Ideas from 'Philosophical Logic' by John P. Burgess [2009], by Theme Structure
[found in 'Philosophical Logic' by Burgess,John P. [Princeton 2009,978-0-691-13789-6]].
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4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic
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15413
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With four tense operators, all complex tenses reduce to fourteen basic cases
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4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
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15415
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The temporal Barcan formulas fix what exists, which seems absurd
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4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
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15430
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Is classical logic a part of intuitionist logic, or vice versa?
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15431
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It is still unsettled whether standard intuitionist logic is complete
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4. Formal Logic / E. Nonclassical Logics / 5. Relevant Logic
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15429
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Relevance logic's → is perhaps expressible by 'if A, then B, for that reason'
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5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
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15404
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Technical people see logic as any formal system that can be studied, not a study of argument validity
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5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
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15405
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Classical logic neglects the non-mathematical, such as temporality or modality
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15421
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Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them
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15427
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The Cut Rule expresses the classical idea that entailment is transitive
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5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
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15403
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Philosophical logic is a branch of logic, and is now centred in computer science
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
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15407
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Formalising arguments favours lots of connectives; proving things favours having very few
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / e. or
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15424
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Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths
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5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
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15409
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All occurrences of variables in atomic formulas are free
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5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
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15414
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The denotation of a definite description is flexible, rather than rigid
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5. Theory of Logic / H. Proof Systems / 1. Proof Systems
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15406
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'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components
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5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi
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15425
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The sequent calculus makes it possible to have proof without transitivity of entailment
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15426
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We can build one expanding sequence, instead of a chain of deductions
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
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15408
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'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics
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5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
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15418
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Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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15411
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We only need to study mathematical models, since all other models are isomorphic to these
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15412
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Models leave out meaning, and just focus on truth values
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15416
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We aim to get the technical notion of truth in all models matching intuitive truth in all instances
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
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15428
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The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut'
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10. Modality / A. Necessity / 4. De re / De dicto modality
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15420
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De re modality seems to apply to objects a concept intended for sentences
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10. Modality / A. Necessity / 6. Logical Necessity
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15417
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Logical necessity has two sides - validity and demonstrability - which coincide in classical logic
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15419
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General consensus is S5 for logical modality of validity, and S4 for proof
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10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
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15423
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It is doubtful whether the negation of a conditional has any clear meaning
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15422
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Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth)
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