Combining Texts

All the ideas for 'Set Theory', 'Kant and the Critique of Pure Reason' and 'Actualism and Thisness'

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18 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / c. Eighteenth century philosophy
21463 Hamann, Herder and Jacobi were key opponents of the Enlightenment [Gardner]
21459 Kant halted rationalism, and forced empiricists to worry about foundations [Gardner]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
21460 Only Kant and Hegel have united nature, morals, politics, aesthetics and religion [Gardner]
2. Reason / E. Argument / 2. Transcendental Argument
21443 Transcendental proofs derive necessities from possibilities (e.g. possibility of experiencing objects) [Gardner]
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]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
21444 Modern geoemtry is either 'pure' (and formal), or 'applied' (and a posteriori) [Gardner]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
21453 Leibnizian monads qualify as Kantian noumena [Gardner]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
16463 Adams says actual things have haecceities, but not things that only might exist [Adams,RM, by Stalnaker]