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All the ideas for 'Set Theory', 'The Metaphysics of Modality' and 'Reductive Theories of Modality'

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37 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
9218 Maybe what distinguishes philosophy from science is its pursuit of necessary truths [Sider]
1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
12027 There must be a plausible epistemological theory alongside any metaphysical theory [Forbes,G]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / a. Symbols of PL
12005 The symbol 'ι' forms definite descriptions; (ιx)F(x) says 'the x which is such that F(x)' [Forbes,G]
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 / E. Structures of Logic / 2. Logical Connectives / d. and
12010 Is the meaning of 'and' given by its truth table, or by its introduction and elimination rules? [Forbes,G]
7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
12023 Vagueness problems arise from applying sharp semantics to vague languages [Forbes,G]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
12017 In all instances of identity, there must be some facts to ensure the identity [Forbes,G]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
12024 If we combined two clocks, it seems that two clocks may have become one clock. [Forbes,G]
9. Objects / D. Essence of Objects / 3. Individual Essences
11885 Only individual essences will ground identities across worlds in other properties [Forbes,G, by Mackie,P]
12014 An individual essence is a set of essential properties which only that object can have [Forbes,G]
12015 Non-trivial individual essence is properties other than de dicto, or universal, or relational [Forbes,G]
9. Objects / D. Essence of Objects / 5. Essence as Kind
12013 Essential properties depend on a category, and perhaps also on particular facts [Forbes,G]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
12012 Essential properties are those without which an object could not exist [Forbes,G]
9. Objects / D. Essence of Objects / 11. Essence of Artefacts
12022 Same parts does not ensure same artefact, if those parts could constitute a different artefact [Forbes,G]
12025 Artefacts have fuzzy essences [Forbes,G]
9. Objects / E. Objects over Time / 12. Origin as Essential
12020 An individual might change their sex in a world, but couldn't have differed in sex at origin [Forbes,G]
9. Objects / F. Identity among Objects / 1. Concept of Identity
11888 Identities must hold because of other facts, which must be instrinsic [Forbes,G, by Mackie,P]
10. Modality / A. Necessity / 4. De re / De dicto modality
12003 De re modal formulae, unlike de dicto, are sensitive to transworld identities [Forbes,G]
10. Modality / C. Sources of Modality / 4. Necessity from Concepts
12028 De re necessity is a form of conceptual necessity, just as de dicto necessity is [Forbes,G]
10. Modality / E. Possible worlds / 1. Possible Worlds / c. Possible worlds realism
12008 Unlike places and times, we cannot separate possible worlds from what is true at them [Forbes,G]
12009 The problem with possible worlds realism is epistemological; we can't know properties of possible objects [Forbes,G]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
12007 Possible worlds are points of logical space, rather like other times than our own [Forbes,G]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
12011 Transworld identity concerns the limits of possibility for ordinary things [Forbes,G]
12016 The problem of transworld identity can be solved by individual essences [Forbes,G]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
12004 Counterpart theory is not good at handling the logic of identity [Forbes,G]
10. Modality / E. Possible worlds / 3. Transworld Objects / d. Haecceitism
12021 Haecceitism attributes to each individual a primitive identity or thisness [Forbes,G]
12029 We believe in thisnesses, because we reject bizarre possibilities as not being about that individual [Forbes,G]