Combining Texts

All the ideas for 'works', 'Set Theory' and 'Universals'

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27 ideas

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]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
4444 One moderate nominalist view says that properties and relations exist, but they are particulars [Armstrong]
8. Modes of Existence / B. Properties / 13. Tropes / b. Critique of tropes
4445 If properties and relations are particulars, there is still the problem of how to classify and group them [Armstrong]
8. Modes of Existence / D. Universals / 1. Universals
4448 Should we decide which universals exist a priori (through words), or a posteriori (through science)? [Armstrong]
8. Modes of Existence / D. Universals / 4. Uninstantiated Universals
4446 It is claimed that some universals are not exemplified by any particular, so must exist separately [Armstrong]
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
4440 'Resemblance Nominalism' finds that in practice the construction of resemblance classes is hard [Armstrong]
4439 'Resemblance Nominalism' says properties are resemblances between classes of particulars [Armstrong]
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
4431 'Predicate Nominalism' says that a 'universal' property is just a predicate applied to lots of things [Armstrong]
8. Modes of Existence / E. Nominalism / 4. Concept Nominalism
4433 Concept and predicate nominalism miss out some predicates, and may be viciously regressive [Armstrong]
4432 'Concept Nominalism' says a 'universal' property is just a mental concept applied to lots of things [Armstrong]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
4436 'Class Nominalism' may explain properties if we stick to 'natural' sets, and ignore random ones [Armstrong]
4434 'Class Nominalism' says that properties or kinds are merely membership of a set (e.g. of white things) [Armstrong]
4435 'Class Nominalism' cannot explain co-extensive properties, or sets with random members [Armstrong]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
4437 'Mereological Nominalism' sees whiteness as a huge white object consisting of all the white things [Armstrong]
4438 'Mereological Nominalism' may work for whiteness, but it doesn't seem to work for squareness [Armstrong]
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
16713 Philosophers are the forefathers of heretics [Tertullian]
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
6610 I believe because it is absurd [Tertullian]