Combining Texts

All the ideas for 'Set Theory', 'Response to David Armstrong' and 'The Tragedy of Reason'

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28 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
1606 You have to be a Platonist to debate about reality, so every philosopher is a Platonist [Roochnik]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / b. Philosophy as transcendent
1595 Philosophy aims to satisfy the chief human desire - the articulation of beauty itself [Roochnik]
2. Reason / A. Nature of Reason / 2. Logos
1571 'Logos' ranges from thought/reasoning, to words, to rational structures outside thought [Roochnik]
1572 In the seventeenth century the only acceptable form of logos was technical knowledge [Roochnik]
1573 The hallmark of a person with logos is that they give reasons why one opinion is superior to another [Roochnik]
1592 Logos cannot refute the relativist, and so must admit that it too is a matter of desire (for truth and agreement) [Roochnik]
1593 Human desire has an ordered structure, with logos at the pinnacle [Roochnik]
1603 Logos is not unconditionally good, but good if there is another person willing to engage with it [Roochnik]
2. Reason / A. Nature of Reason / 4. Aims of Reason
1598 We prefer reason or poetry according to whether basics are intelligible or not [Roochnik]
2. Reason / A. Nature of Reason / 8. Naturalising Reason
1584 Modern science, by aiming for clarity about the external world, has abandoned rationality in the human world [Roochnik]
2. Reason / A. Nature of Reason / 9. Limits of Reason
1591 Unfortunately for reason, argument can't be used to establish the value of argument [Roochnik]
1599 Attempts to suspend all presuppositions are hopeless, because a common ground must be agreed for the process [Roochnik]
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 / D. Theories of Reality / 3. Reality
1605 Reality can be viewed neutrally, or as an object of desire [Roochnik]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
18398 Space, time, and some other basics, are not causal powers [Ellis]
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
1577 Relativism is a disease which destroys the possibility of rational debate [Roochnik]
19. Language / F. Communication / 1. Rhetoric
1578 If relativism is the correct account of human values, then rhetoric is more important than reasoning [Roochnik]
1596 Reasoning aims not at the understanding of objects, but at the desire to give beautiful speeches [Roochnik]