Combining Texts

All the ideas for 'Set Theory', 'Causality and Determinism' and 'The Problem of the Essential Indexical'

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23 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]
11. Knowledge Aims / A. Knowledge / 4. Belief / b. Elements of beliefs
12149 Indexicals are a problem for beliefs being just subject-proposition relations [Perry]
16. Persons / F. Free Will / 3. Constraints on the will
8353 Freedom involves acting according to an idea [Anscombe]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
8352 To believe in determinism, one must believe in a system which determines events [Anscombe]
19. Language / C. Assigning Meanings / 9. Indexical Semantics
12151 If we replace 'I' in sentences about me, they are different beliefs and explanations of behaviour [Perry]
18412 Indexicals individuate certain belief states, helping in explanation and prediction [Perry]
19. Language / D. Propositions / 6. Propositions Critique
12150 Indexicals reveal big problems with the traditional idea of a proposition [Perry]
26. Natural Theory / C. Causation / 5. Direction of causation
8351 With diseases we easily trace a cause from an effect, but we cannot predict effects [Anscombe]
26. Natural Theory / C. Causation / 6. Causation as primitive
4777 The word 'cause' is an abstraction from a group of causal terms in a language (scrape, push..) [Anscombe]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
10363 Causation is relative to how we describe the primary relata [Anscombe, by Schaffer,J]
26. Natural Theory / C. Causation / 8. Particular Causation / c. Conditions of causation
8350 Since Mill causation has usually been explained by necessary and sufficient conditions [Anscombe]
27. Natural Reality / D. Time / 2. Passage of Time / c. Tenses and time
15203 Tense is essential for thought and action [Perry, by Le Poidevin]
15204 Actual tensed sentences cannot be tenseless, because they can cite their own context [Perry, by Le Poidevin]