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All the ideas for 'Posthumous notes', 'Classes and Attributes' and 'Philosophical Logic'

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30 ideas

4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic
With four tense operators, all complex tenses reduce to fourteen basic cases [Burgess]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
The temporal Barcan formulas fix what exists, which seems absurd [Burgess]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Is classical logic a part of intuitionist logic, or vice versa? [Burgess]
It is still unsettled whether standard intuitionist logic is complete [Burgess]
4. Formal Logic / E. Nonclassical Logics / 5. Relevant Logic
Relevance logic's → is perhaps expressible by 'if A, then B, for that reason' [Burgess]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
Technical people see logic as any formal system that can be studied, not a study of argument validity [Burgess]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
The Cut Rule expresses the classical idea that entailment is transitive [Burgess]
Classical logic neglects the non-mathematical, such as temporality or modality [Burgess]
Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess]
5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
Philosophical logic is a branch of logic, and is now centred in computer science [Burgess]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Formalising arguments favours lots of connectives; proving things favours having very few [Burgess]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / e. or
Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths [Burgess]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
All occurrences of variables in atomic formulas are free [Burgess]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
The denotation of a definite description is flexible, rather than rigid [Burgess]
5. Theory of Logic / H. Proof Systems / 1. Proof Systems
'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components [Burgess]
5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi
We can build one expanding sequence, instead of a chain of deductions [Burgess]
The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics [Burgess]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
We only need to study mathematical models, since all other models are isomorphic to these [Burgess]
Models leave out meaning, and just focus on truth values [Burgess]
We aim to get the technical notion of truth in all models matching intuitive truth in all instances [Burgess]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess]
8. Modes of Existence / B. Properties / 11. Properties as Sets
While no two classes coincide in membership, there are distinct but coextensive attributes [Cartwright,R]
10. Modality / A. Necessity / 4. De re / De dicto modality
De re modality seems to apply to objects a concept intended for sentences [Burgess]
10. Modality / A. Necessity / 6. Logical Necessity
Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess]
General consensus is S5 for logical modality of validity, and S4 for proof [Burgess]
10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess]
It is doubtful whether the negation of a conditional has any clear meaning [Burgess]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
Transcendental philosophy is the subject becoming the originator of unified reality [Kant]