Combining Texts

All the ideas for 'Set Theory', 'works' and 'The Structure of Empirical Knowledge'

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21 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]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
21506 A coherence theory of justification can combine with a correspondence theory of truth [Bonjour]
21509 There will always be a vast number of equally coherent but rival systems [Bonjour]
21503 Empirical coherence must attribute reliability to spontaneous experience [Bonjour]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
21511 A well written novel cannot possibly match a real belief system for coherence [Bonjour]
21510 The objection that a negated system is equally coherent assume that coherence is consistency [Bonjour]
21505 A coherent system can be justified with initial beliefs lacking all credibility [Bonjour]
21504 The best explanation of coherent observations is they are caused by and correspond to reality [Bonjour]
14. Science / A. Basis of Science / 5. Anomalies
21508 Anomalies challenge the claim that the basic explanations are actually basic [Bonjour]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / b. Heat
20645 Heat is a state of vibration, not a substance [Joule]
20972 Joule showed that energy converts to heat, and heat to energy [Joule, by Papineau]