Combining Texts

All the ideas for 'Set Theory', 'Essays on Intellectual Powers 2: Senses' and 'Does Moral Subjectivism Rest on a Mistake?'

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24 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]
7. Existence / A. Nature of Existence / 1. Nature of Existence
23634 Accepting the existence of anything presupposes the notion of existence [Reid]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
23635 Truths are self-evident to sensible persons who understand them clearly without prejudice [Reid]
12. Knowledge Sources / B. Perception / 1. Perception
7631 Sensation is not committed to any external object, but perception is [Reid]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / c. Primary qualities
23637 Primary qualities are the object of mathematics [Reid]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
23638 Secondary qualities conjure up, and are confused with, the sensations which produce them [Reid]
12. Knowledge Sources / B. Perception / 5. Interpretation
23639 It is unclear whether a toothache is in the mind or in the tooth, but the word has a single meaning [Reid]
12. Knowledge Sources / E. Direct Knowledge / 1. Common Sense
6492 Reid is seen as the main direct realist of the eighteenth century [Reid, by Robinson,H]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / a. Evidence
23641 People dislike believing without evidence, and try to avoid it [Reid]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
23642 If non-rational evidence reaches us, it is reason which then makes use of it [Reid]
18. Thought / E. Abstraction / 2. Abstracta by Selection
23640 Only mature minds can distinguish the qualities of a body [Reid]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / f. Ethical non-cognitivism
22485 Non-cognitivists give the conditions of use of moral sentences as facts about the speaker [Foot]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
22486 The mistake is to think good grounds aren't enough for moral judgement, which also needs feelings [Foot]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
22487 Moral arguments are grounded in human facts [Foot]