Combining Texts

All the ideas for 'Community and Citizenship', 'Set Theory' and 'Against the Physicists (two books)'

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33 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]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
22744 Parts are not parts if their whole is nothing more than the parts [Sext.Empiricus]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
22748 Some say motion is perceived by sense, but others say it is by intellect [Sext.Empiricus]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
22746 If we try to conceive of a line with no breadth, it ceases to exist, and so has no length [Sext.Empiricus]
17. Mind and Body / D. Property Dualism / 4. Emergentism
22741 The incorporeal is not in the nature of body, and so could not emerge from it [Sext.Empiricus]
24. Political Theory / B. Nature of a State / 4. Citizenship
22817 Citizenship involves a group of mutually supporting rights, which create community and equality [Miller,D]
24. Political Theory / D. Ideologies / 14. Nationalism
22816 Socialists reject nationality as a false source of identity [Miller,D]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
22747 A man walking backwards on a forwards-moving ship is moving in a fixed place [Sext.Empiricus]
27. Natural Reality / D. Time / 2. Passage of Time / c. Tenses and time
22749 Time doesn't end with the Universe, because tensed statements about destruction remain true [Sext.Empiricus]
27. Natural Reality / D. Time / 3. Parts of Time / c. Intervals
22750 Time is divisible, into past, present and future [Sext.Empiricus]
27. Natural Reality / D. Time / 3. Parts of Time / e. Present moment
22742 Socrates either dies when he exists (before his death) or when he doesn't (after his death) [Sext.Empiricus]
22751 If the present is just the limit of the past or the future, it can't exist because they don't exist [Sext.Empiricus]
28. God / A. Divine Nature / 2. Divine Nature
22730 All men agree that God is blessed, imperishable, happy and good [Sext.Empiricus]
22739 God must suffer to understand suffering [Sext.Empiricus]
28. God / A. Divine Nature / 3. Divine Perfections
22738 The Divine must lack the virtues of continence and fortitude, because they are not needed [Sext.Empiricus]
28. God / B. Proving God / 1. Proof of God
22734 God is defended by agreement, order, absurdity of denying God, and refutations [Sext.Empiricus]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
22736 God's sensations imply change, and hence perishing, which is absurd, so there is no such God [Sext.Empiricus]
22740 God without virtue is absurd, but God's virtues will be better than God [Sext.Empiricus]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
22735 The original substance lacked motion or shape, and was given these by a cause [Sext.Empiricus]
28. God / C. Attitudes to God / 4. God Reflects Humanity
22732 The perfections of God were extrapolations from mankind [Sext.Empiricus]
28. God / C. Attitudes to God / 5. Atheism
22728 Gods were invented as watchers of people's secret actions [Sext.Empiricus]
22737 An incorporeal God could do nothing, and a bodily god would perish, so there is no God [Sext.Empiricus]
29. Religion / A. Polytheistic Religion / 1. Animism
22731 It is mad to think that what is useful to us, like lakes and rivers, are gods [Sext.Empiricus]