Combining Texts

All the ideas for 'Set Theory', 'Maxims and Reflections' and 'Treatise 4: The Moral Sense'

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24 ideas

2. Reason / A. Nature of Reason / 1. On Reason
6253 Reason is our power of finding out true propositions [Hutcheson]
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]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
7544 Many people imagine that to experience is to understand [Goethe]
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
7541 Man never understands how anthropomorphic he is [Goethe]
16. Persons / C. Self-Awareness / 2. Knowing the Self
7543 We gain self-knowledge through action, not thought - especially when doing our duty [Goethe]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
7540 Beauty is a manifestation of secret natural laws [Goethe]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
6256 Can't the moral sense make mistakes, as the other senses do? [Hutcheson]
22. Metaethics / C. The Good / 2. Happiness / a. Nature of happiness
6252 Happiness is a pleasant sensation, or continued state of such sensations [Hutcheson]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
7538 The happiest people link the beginning and end of life [Goethe]
23. Ethics / D. Deontological Ethics / 1. Deontology
6257 You can't form moral rules without an end, which needs feelings and a moral sense [Hutcheson]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
7542 The best form of government teaches us to govern ourselves [Goethe]
25. Social Practice / C. Rights / 1. Basis of Rights
7539 To get duties from people without rights, you must pay them well [Goethe]
28. God / A. Divine Nature / 6. Divine Morality / a. Divine morality
6254 We are asked to follow God's ends because he is our benefactor, but why must we do that? [Hutcheson]
6255 Why may God not have a superior moral sense very similar to ours? [Hutcheson]