Combining Texts

All the ideas for 'fragments/reports', 'Set Theory' and 'Mental Files in Flux'

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22 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 / A. Overview of Logic / 4. Pure Logic
22246 A train of reasoning must be treated as all happening simultaneously [Recanati]
7. Existence / A. Nature of Existence / 3. Being / d. Non-being
18933 Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius]
18. Thought / A. Modes of Thought / 9. Indexical Thought
22247 Indexicality is not just a feature of language; examples show it also occurs in thought [Recanati]
22248 How can we communicate indexical thoughts to people not in the right context? [Recanati]
18. Thought / B. Mechanics of Thought / 5. Mental Files
22242 Mental files are concepts, which are either collections or (better) containers [Recanati]
22243 The Frege case of believing a thing is both F and not-F is explained by separate mental files [Recanati]
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
22245 A linguistic expression refers to what its associated mental file refers to [Recanati]
19. Language / D. Propositions / 4. Mental Propositions
22250 There are speakers' thoughts and hearers' thoughts, but no further thought attached to the utterance [Recanati]
19. Language / F. Communication / 1. Rhetoric
9866 Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato]
5864 Destroy seriousness with laughter, and laughter with seriousness [Gorgias]
19. Language / F. Communication / 5. Pragmatics / a. Contextual meaning
22249 The Naive view of communication is that hearers acquire exactly the thoughts of the speaker [Recanati]