Combining Texts

All the ideas for 'Set Theory', 'The Mirage of Social Justice' and 'Penses'

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26 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason
6675 The heart has its reasons of which reason knows nothing [Pascal]
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 / C. Rationalism / 1. Rationalism
22011 The first principles of truth are not rational, but are known by the heart [Pascal]
19. Language / F. Communication / 1. Rhetoric
6681 We only want to know things so that we can talk about them [Pascal]
21. Aesthetics / C. Artistic Issues / 3. Artistic Representation
6676 Painting makes us admire things of which we do not admire the originals [Pascal]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
6680 It is a funny sort of justice whose limits are marked by a river [Pascal]
22. Metaethics / B. Value / 1. Nature of Value / d. Subjective value
6677 Imagination creates beauty, justice and happiness, which is the supreme good [Pascal]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
6678 We live for the past or future, and so are never happy in the present [Pascal]
23. Ethics / F. Existentialism / 3. Angst
20732 If man considers himself as lost and imprisoned in the universe, he will be terrified [Pascal]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
6682 Majority opinion is visible and authoritative, although not very clever [Pascal]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
6679 It is not good to be too free [Pascal]
25. Social Practice / D. Justice / 1. Basis of justice
20543 'Social justice' is a confused idea, and inequalities need no justification [Hayek, by Swift]
28. God / B. Proving God / 2. Proofs of Reason / d. Pascal's Wager
7455 Pascal knows you can't force belief, but you can make it much more probable [Pascal, by Hacking]
7457 Pascal is right, but relies on the unsupported claim of a half as the chance of God's existence [Hacking on Pascal]
7456 The libertine would lose a life of enjoyable sin if he chose the cloisters [Hacking on Pascal]
6684 If you win the wager on God's existence you win everything, if you lose you lose nothing [Pascal]