Combining Texts

All the ideas for 'Set Theory', 'Ontological Categories' and 'talk'

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26 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]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
13134 We negate predicates but do not negate names [Westerhoff]
7. Existence / E. Categories / 1. Categories
13124 Categories can be ordered by both containment and generality [Westerhoff]
13117 How far down before we are too specialised to have a category? [Westerhoff]
13116 Maybe objects in the same category have the same criteria of identity [Westerhoff]
13118 Categories are base-sets which are used to construct states of affairs [Westerhoff]
13125 Categories are held to explain why some substitutions give falsehood, and others meaninglessness [Westerhoff]
13126 Categories systematize our intuitions about generality, substitutability, and identity [Westerhoff]
13130 Categories as generalities don't give a criterion for a low-level cut-off point [Westerhoff]
7. Existence / E. Categories / 2. Categorisation
13131 The aim is that everything should belong in some ontological category or other [Westerhoff]
7. Existence / E. Categories / 3. Proposed Categories
13123 All systems have properties and relations, and most have individuals, abstracta, sets and events [Westerhoff]
7. Existence / E. Categories / 5. Category Anti-Realism
13115 Ontological categories are like formal axioms, not unique and with necessary membership [Westerhoff]
13119 Categories merely systematise, and are not intrinsic to objects [Westerhoff]
13135 A thing's ontological category depends on what else exists, so it is contingent [Westerhoff]
9. Objects / D. Essence of Objects / 5. Essence as Kind
13129 Essential kinds may be too specific to provide ontological categories [Westerhoff]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
7417 God can't have silly perfections, but how do we decide which ones are 'silly'? [Joslin]