Combining Texts

All the ideas for 'Lectures on the History of Philosophy', 'Set Theory' and 'The Later Works (17 vols, ed Boydston)'

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23 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
21757 Philosophy is the conceptual essence of the shape of history [Hegel]
22864 Philosophy is the study and criticsm of cultural beliefs, to achieve new possibilities [Dewey]
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]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
22873 Liberalism should improve the system, and not just ameliorate it [Dewey]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
22869 Knowledge is either the product of competent enquiry, or it is meaningless [Dewey]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
22867 The quest for certainty aims for peace, and avoidance of the stress of action [Dewey]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
22870 No belief can be so settled that it is not subject to further inquiry [Dewey]
15. Nature of Minds / A. Nature of Mind / 1. Mind / a. Mind
22866 Mind is never isolated, but only exists in its interactions [Dewey]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
22872 Liberals aim to allow individuals to realise their capacities [Dewey]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
22880 The things in civilisation we prize are the products of other members of our community [Dewey]
28. God / A. Divine Nature / 2. Divine Nature
22879 'God' is an imaginative unity of ideal values [Dewey]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
22877 We should try attaching the intensity of religious devotion to intelligent social action [Dewey]
22878 Religions are so shockingly diverse that they have no common element [Dewey]