Combining Texts

All the ideas for 'Set Theory', 'talk' and 'Logological Fragments I'

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41 ideas

1. Philosophy / C. History of Philosophy / 1. History of Philosophy
19579 The history of philosophy is just experiments in how to do philosophy [Novalis]
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
19583 Philosophy only begins when it studies itself [Novalis]
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 / E. Structures of Logic / 5. Functions in Logic
15105 F(x) walked into a bar. The barman said.. [Sommers,W]
5. Theory of Logic / L. Paradox / 2. Aporiai
19581 A problem is a solid mass, which the mind must break up [Novalis]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
19584 Whoever first counted to two must have seen the possibility of infinite counting [Novalis]
7. Existence / A. Nature of Existence / 3. Being / d. Non-being
12408 Sartre to Waitress: Coffee with no cream, please... [Sommers,W]
7. Existence / A. Nature of Existence / 3. Being / h. Dasein (being human)
22025 Novalis thought self-consciousness cannot disclose 'being', because we are temporal creatures [Novalis, by Pinkard]
7. Existence / D. Theories of Reality / 4. Anti-realism
12397 Said Plato: 'The things that we feel... [Sommers,W]
11. Knowledge Aims / B. Certain Knowledge / 5. Cogito Critique
12407 Barman to Descartes: Would you like another drink?... [Sommers,W]
12399 There was a young student called Fred... [Sommers,W]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
20963 A philosopher and his wife are out for a drive... [Sommers,W]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / c. Empirical idealism
12404 Dear Sir, Your astonishment's odd.... [Sommers,W]
12403 There once was a man who said: 'God... [Sommers,W]
12402 ..But if he's a student of Berkeley... [Sommers,W]
12409 The philosopher Berkeley once said.. [Sommers,W]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
22067 Poetry is true idealism, and the self-consciousness of the universe [Novalis]
12. Knowledge Sources / B. Perception / 1. Perception
14694 "My dog's got synaesthesia." How does he smell? ..... [Sommers,W]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
12401 A toper who spies in the distance... [Sommers,W]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
12410 There once was a man who said 'Damn!... [Sommers,W]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
9392 How do behaviourists greet each other? [Sommers,W]
19. Language / F. Communication / 4. Private Language
19585 Every person has his own language [Novalis]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / b. Defining ethics
19582 Morality and philosophy are mutually dependent [Novalis]
23. Ethics / F. Existentialism / 7. Existential Action
22027 Life isn't given to us like a novel - we write the novel [Novalis]
24. Political Theory / C. Ruling a State / 2. Leaders / d. Elites
12405 'If you're aristocratic,' said Nietzsche... [Sommers,W]
24. Political Theory / D. Ideologies / 2. Anarchism
9391 Why do anarchists drink herbal tea? [Sommers,W]
25. Social Practice / E. Policies / 5. Education / c. Teaching
19580 If the pupil really yearns for the truth, they only need a hint [Novalis]
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
12400 Cries the maid: 'You must marry me Hume!'... [Sommers,W]
16527 Causation - we all thought we knew it/ Till Hume came along and saw through it/…. [Sommers,W]
27. Natural Reality / D. Time / 1. Nature of Time / c. Idealist time
17592 The barman called 'Time!', and Augustine said..... [Sommers,W]
27. Natural Reality / D. Time / 2. Passage of Time / c. Tenses and time
15208 The past, present and future walked into a bar.... [Sommers,W]