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]].
green numbers give full details |
back to texts
|
expand these ideas
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
|
15411
|
We only need to study mathematical models, since all other models are isomorphic to these
|
|
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
|
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'
|
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
|
15419
|
General consensus is S5 for logical modality of validity, and S4 for proof
|
|
15417
|
Logical necessity has two sides - validity and demonstrability - which coincide in classical logic
|
10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
|
15422
|
Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth)
|
|
15423
|
It is doubtful whether the negation of a conditional has any clear meaning
|