Combining Texts

All the ideas for 'Set Theory', 'Truth and Meaning' and 'Nihilism without Self-Contradiction'

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19 ideas

2. Reason / F. Fallacies / 7. Ad Hominem
14231 We should always apply someone's theory of meaning to their own utterances [Liggins]
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]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
14232 We normally formalise 'There are Fs' with singular quantification and predication, but this may be wrong [Liggins]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
14233 Nihilists needn't deny parts - they can just say that some of the xs are among the ys [Liggins]
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]