Combining Texts

All the ideas for 'Set Theory', 'Critique of the Gotha Program' and 'Conceptual truth and metaphysical necessity'

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24 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]
10. Modality / C. Sources of Modality / 4. Necessity from Concepts
16423 Conceptual possibilities are metaphysical possibilities we can conceive of [Stalnaker]
16422 The necessity of a proposition concerns reality, not our words or concepts [Stalnaker]
10. Modality / D. Knowledge of Modality / 3. A Posteriori Necessary
16421 Critics say there are just an a priori necessary part, and an a posteriori contingent part [Stalnaker]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
16429 A 'centred' world is an ordered triple of world, individual and time [Stalnaker]
18. Thought / C. Content / 6. Broad Content
16428 Meanings aren't in the head, but that is because they are abstract [Stalnaker]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
16432 One view says the causal story is built into the description that is the name's content [Stalnaker]
19. Language / C. Assigning Meanings / 10. Two-Dimensional Semantics
16430 Two-D says that a posteriori is primary and contingent, and the necessity is the secondary intension [Stalnaker]
16431 In one view, the secondary intension is metasemantic, about how the thinker relates to the content [Stalnaker]
24. Political Theory / C. Ruling a State / 4. Changing the State / c. Revolution
22971 In moving from capitalism to communism a revolutionary dictatorship of the proletariat is needed [Marx]
24. Political Theory / D. Ideologies / 9. Communism
22969 People who only have their labour power are the slaves of those permitting them to work [Marx]
22970 Freedom is making the state subordinate to its society [Marx]
22000 From each according to his ability, to each according to his need [Marx]
25. Social Practice / A. Freedoms / 2. Freedom of belief
22972 Bourgeois 'freedom of conscience' just tolerates all sorts of religious intolerance [Marx]