Combining Texts

All the ideas for 'Causal Explanation', 'Set Theory' and 'Reference and Generality (3rd ed)'

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28 ideas

3. Truth / A. Truth Problems / 6. Verisimilitude
15557 Verisimilitude has proved hard to analyse, and seems to have several components [Lewis]
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]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
12154 Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting? [Geach, by Perry]
8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived
15554 A disposition needs a causal basis, a property in a certain causal role. Could the disposition be the property? [Lewis]
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
8969 We should abandon absolute identity, confining it to within some category [Geach, by Hawthorne]
9. Objects / F. Identity among Objects / 3. Relative Identity
16075 Denial of absolute identity has drastic implications for logic, semantics and set theory [Wasserman on Geach]
12152 Identity is relative. One must not say things are 'the same', but 'the same A as' [Geach]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
16073 Leibniz's Law is incomplete, since it includes a non-relativized identity predicate [Geach, by Wasserman]
10. Modality / B. Possibility / 7. Chance
15560 We can explain a chance event, but can never show why some other outcome did not occur [Lewis]
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
15559 Does a good explanation produce understanding? That claim is just empty [Lewis]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
15556 Science may well pursue generalised explanation, rather than laws [Lewis]
14. Science / D. Explanation / 2. Types of Explanation / f. Necessity in explanations
15558 A good explanation is supposed to show that the event had to happen [Lewis]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
4809 Lewis endorses the thesis that all explanation of singular events is causal explanation [Lewis, by Psillos]
14321 To explain an event is to provide some information about its causal history [Lewis]
26. Natural Theory / C. Causation / 2. Types of cause
15555 Explaining match lighting in general is like explaining one lighting of a match [Lewis]
26. Natural Theory / C. Causation / 8. Particular Causation / d. Selecting the cause
15551 Ways of carving causes may be natural, but never 'right' [Lewis]
15552 We only pick 'the' cause for the purposes of some particular enquiry. [Lewis]
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
15553 Causal dependence is counterfactual dependence between events [Lewis]