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All the ideas for 'Philosophical Logic', 'Deriving Kripkean Claims with Abstract Objects' and 'Logical Necessity'

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41 ideas

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
12204 The logic of metaphysical necessity is S5 [Rumfitt]
4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic
15413 With four tense operators, all complex tenses reduce to fourteen basic cases [Burgess]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
15415 The temporal Barcan formulas fix what exists, which seems absurd [Burgess]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
15430 Is classical logic a part of intuitionist logic, or vice versa? [Burgess]
15431 It is still unsettled whether standard intuitionist logic is complete [Burgess]
4. Formal Logic / E. Nonclassical Logics / 5. Relevant Logic
15429 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
15404 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
15405 Classical logic neglects the non-mathematical, such as temporality or modality [Burgess]
15427 The Cut Rule expresses the classical idea that entailment is transitive [Burgess]
15421 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
15403 Philosophical logic is a branch of logic, and is now centred in computer science [Burgess]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
12195 Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt]
12199 There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt]
12201 We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt]
5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
12194 Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' [Rumfitt]
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 [Burgess]
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 [Burgess]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
15409 All occurrences of variables in atomic formulas are free [Burgess]
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 [Burgess]
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 [Burgess]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
12198 Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [Rumfitt]
5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi
15425 The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess]
15426 We can build one expanding sequence, instead of a chain of deductions [Burgess]
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 [Burgess]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
15418 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
15412 Models leave out meaning, and just focus on truth values [Burgess]
15411 We only need to study mathematical models, since all other models are isomorphic to these [Burgess]
15416 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
15428 The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
10558 Abstract objects are actually constituted by the properties by which we conceive them [Zalta]
10. Modality / A. Necessity / 3. Types of Necessity
14532 A distinctive type of necessity is found in logical consequence [Rumfitt, by Hale/Hoffmann,A]
10. Modality / A. Necessity / 4. De re / De dicto modality
15420 De re modality seems to apply to objects a concept intended for sentences [Burgess]
10. Modality / A. Necessity / 6. Logical Necessity
15419 General consensus is S5 for logical modality of validity, and S4 for proof [Burgess]
15417 Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess]
12193 Logical necessity is when 'necessarily A' implies 'not-A is contradictory' [Rumfitt]
12200 A logically necessary statement need not be a priori, as it could be unknowable [Rumfitt]
12202 Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not [Rumfitt]
10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
15422 Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess]
15423 It is doubtful whether the negation of a conditional has any clear meaning [Burgess]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
12203 If a world is a fully determinate way things could have been, can anyone consider such a thing? [Rumfitt]
18. Thought / E. Abstraction / 2. Abstracta by Selection
10557 Abstract objects are captured by second-order modal logic, plus 'encoding' formulas [Zalta]