Combining Texts

All the ideas for 'fragments/reports', 'Set Theory' and 'The Elements of Law'

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21 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / b. Seventeenth century philosophy
7396 Hobbes created English-language philosophy [Hobbes, by Tuck]
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 / B. Perception / 4. Sense Data / a. Sense-data theory
16638 The qualities of the world are mere appearances; reality is the motions which cause them [Hobbes]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
16688 Evidence is conception, which is imagination, which proceeds from the senses [Hobbes]
7405 Experience can't prove universal truths [Hobbes]
20. Action / C. Motives for Action / 1. Acting on Desires
7408 It is an error that reason should control the passions, which give right guidance on their own [Hobbes, by Tuck]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
7407 Good and evil are what please us; goodness and badness the powers causing them [Hobbes]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
7410 Self-preservation is basic, and people judge differently about that, implying ethical relativism [Hobbes, by Tuck]
22. Metaethics / C. The Good / 1. Goodness / c. Right and good
7409 Hobbes shifted from talk of 'the good' to talk of 'rights' [Hobbes, by Tuck]
28. God / C. Attitudes to God / 4. God Reflects Humanity
7411 The attributes of God just show our inability to conceive his nature [Hobbes]