Ideas of John P. Burgess, by Theme

[American, b.1948, Studied at Berkeley. Teacher at Princeton University.]

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4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic
15413 With four tense operators, all complex tenses reduce to fourteen basic cases
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
15415 The temporal Barcan formulas fix what exists, which seems absurd
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
15430 Is classical logic a part of intuitionist logic, or vice versa?
15431 It is still unsettled whether standard intuitionist logic is complete
4. Formal Logic / E. Nonclassical Logics / 5. Relevant Logic
15429 Relevance logic's → is perhaps expressible by 'if A, then B, for that reason'
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
15404 Technical people see logic as any formal system that can be studied, not a study of argument validity
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
15405 Classical logic neglects the non-mathematical, such as temporality or modality
15421 Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them
15427 The Cut Rule expresses the classical idea that entailment is transitive
5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
15403 Philosophical logic is a branch of logic, and is now centred in computer science
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
15407 Formalising arguments favours lots of connectives; proving things favours having very few
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / e. or
15424 Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
15409 All occurrences of variables in atomic formulas are free
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
15414 The denotation of a definite description is flexible, rather than rigid
5. Theory of Logic / H. Proof Systems / 1. Proof Systems
15406 'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components
5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi
15425 The sequent calculus makes it possible to have proof without transitivity of entailment
15426 We can build one expanding sequence, instead of a chain of deductions
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
15408 'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
15418 Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
15416 We aim to get the technical notion of truth in all models matching intuitive truth in all instances
15412 Models leave out meaning, and just focus on truth values
15411 We only need to study mathematical models, since all other models are isomorphic to these
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
15428 The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut'
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10185 Set theory is the standard background for modern mathematics
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
10184 Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure
10189 There is no one relation for the real number 2, as relations differ in different models
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
10186 If set theory is used to define 'structure', we can't define set theory structurally
10187 Abstract algebra concerns relations between models, not common features of all the models
10188 How can mathematical relations be either internal, or external, or intrinsic?
10. Modality / A. Necessity / 4. De re / De dicto modality
15420 De re modality seems to apply to objects a concept intended for sentences
10. Modality / A. Necessity / 6. Logical Necessity
15417 Logical necessity has two sides - validity and demonstrability - which coincide in classical logic
15419 General consensus is S5 for logical modality of validity, and S4 for proof
10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
15423 It is doubtful whether the negation of a conditional has any clear meaning
15422 Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth)