Combining Texts

All the ideas for 'The Middle Works (15 vols, ed Boydston)', 'Knowledge First (and reply)' and 'Set Theory'

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28 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]
11. Knowledge Aims / A. Knowledge / 3. Value of Knowledge
22868 The value and truth of knowledge are measured by success in activity [Dewey]
11. Knowledge Aims / A. Knowledge / 7. Knowledge First
19527 We don't acquire evidence and then derive some knowledge, because evidence IS knowledge [Williamson]
19528 Knowledge is prior to believing, just as doing is prior to trying to do [Williamson]
19529 Belief explains justification, and knowledge explains belief, so knowledge explains justification [Williamson]
19530 A neutral state of experience, between error and knowledge, is not basic; the successful state is basic [Williamson]
19531 Internalism about mind is an obsolete view, and knowledge-first epistemology develops externalism [Williamson]
19536 Knowledge-first says your total evidence IS your knowledge [Williamson]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / b. Direct realism
19526 Surely I am acquainted with physical objects, not with appearances? [Williamson]
16. Persons / B. Nature of the Self / 1. Self and Consciousness
22865 Habits constitute the self [Dewey]
19. Language / C. Assigning Meanings / 2. Semantics
19534 How does inferentialism distinguish the patterns of inference that are essential to meaning? [Williamson]
19535 Internalist inferentialism has trouble explaining how meaning and reference relate [Williamson]
19533 Inferentialist semantics relies on internal inference relations, not on external references [Williamson]
19. Language / C. Assigning Meanings / 7. Extensional Semantics
19532 Truth-conditional referential semantics is externalist, referring to worldly items [Williamson]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
22871 The good people are those who improve; the bad are those who deteriorate [Dewey]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
22876 Democracy is the development of human nature when it shares in the running of communal activities [Dewey]
22875 Democracy is not just a form of government; it is a mode of shared living [Dewey]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
22874 Individuality is only developed within groups [Dewey]