Combining Texts

All the ideas for 'Set Theory', 'Truth and Meaning' and 'Reply to First Objections'

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19 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]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
7332 There is a huge range of sentences of which we do not know the logical form [Davidson]
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
16634 I can't be unaware of anything which is in me [Descartes]
19. Language / C. Assigning Meanings / 4. Compositionality
7772 Compositionality explains how long sentences work, and truth conditions are the main compositional feature [Davidson, by Lycan]
19. Language / C. Assigning Meanings / 5. Fregean Semantics
7327 Davidson thinks Frege lacks an account of how words create sentence-meaning [Davidson, by Miller,A]
19. Language / C. Assigning Meanings / 9. Indexical Semantics
7769 You can state truth-conditions for "I am sick now" by relativising it to a speaker at a time [Davidson, by Lycan]
19. Language / F. Communication / 6. Interpreting Language / b. Indeterminate translation
6179 Should we assume translation to define truth, or the other way around? [Blackburn on Davidson]
23. Ethics / F. Existentialism / 5. Existence-Essence
3635 Essence must be known before we discuss existence [Descartes]
28. God / B. Proving God / 3. Proofs of Evidence / a. Cosmological Proof
3634 We can't prove a first cause from our inability to grasp infinity [Descartes]