Combining Philosophers

All the ideas for Eubulides, Kenneth Kunen and R Keefe / P Smith

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32 ideas

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
9065 S5 collapses iterated modalities (◊□P→□P, and ◊◊P→◊P) [Keefe/Smith]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13030 Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
13032 Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
13033 Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13037 Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
13038 Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13034 Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
13039 Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13036 Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
13029 Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
13031 Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
13040 Constructibility: V = L (all sets are constructible) [Kunen]
5. Theory of Logic / L. Paradox / 1. Paradox
6007 If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
6006 If you say truly that you are lying, you are lying [Eubulides, by Dancy,R]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
6008 Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R]
7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
9064 Objects such as a cloud or Mount Everest seem to have fuzzy boundaries in nature [Keefe/Smith]
7. Existence / D. Theories of Reality / 10. Vagueness / c. Vagueness as ignorance
9044 If someone is borderline tall, no further information is likely to resolve the question [Keefe/Smith]
9048 The simplest approach, that vagueness is just ignorance, retains classical logic and semantics [Keefe/Smith]
9055 The epistemic view of vagueness must explain why we don't know the predicate boundary [Keefe/Smith]
7. Existence / D. Theories of Reality / 10. Vagueness / f. Supervaluation for vagueness
9049 Supervaluationism keeps true-or-false where precision can be produced, but not otherwise [Keefe/Smith]
9056 Vague statements lack truth value if attempts to make them precise fail [Keefe/Smith]
9058 Some of the principles of classical logic still fail with supervaluationism [Keefe/Smith]
9059 The semantics of supervaluation (e.g. disjunction and quantification) is not classical [Keefe/Smith]
9060 Supervaluation misunderstands vagueness, treating it as a failure to make things precise [Keefe/Smith]
7. Existence / D. Theories of Reality / 10. Vagueness / g. Degrees of vagueness
9050 A third truth-value at borderlines might be 'indeterminate', or a value somewhere between 0 and 1 [Keefe/Smith]
9061 People can't be placed in a precise order according to how 'nice' they are [Keefe/Smith]
9062 If truth-values for vagueness range from 0 to 1, there must be someone who is 'completely tall' [Keefe/Smith]
9063 How do we decide if my coat is red to degree 0.322 or 0.321? [Keefe/Smith]
8. Modes of Existence / A. Relations / 4. Formal Relations / b. Equivalence relation
18465 An 'equivalence' relation is one which is reflexive, symmetric and transitive [Kunen]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
9045 Vague predicates involve uncertain properties, uncertain objects, and paradoxes of gradual change [Keefe/Smith]
9047 Many vague predicates are multi-dimensional; 'big' involves height and volume; heaps include arrangement [Keefe/Smith]
9053 If there is a precise borderline area, that is not a case of vagueness [Keefe/Smith]