Combining Texts

All the ideas for 'Set Theory', 'Process and Reality' and 'Abortion and the Doctrine of Double Effect'

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22 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / c. Classical philosophy
7719 European philosophy consists of a series of footnotes to Plato [Whitehead]
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 / G. Quantification / 2. Domain of Quantification
10656 With 'extensive connection', boundary elements are not included in domains [Whitehead, by Varzi]
7. Existence / B. Change in Existence / 2. Processes
15389 In Whitehead 'processes' consist of events beginning and ending [Whitehead, by Simons]
20. Action / C. Motives for Action / 5. Action Dilemmas / b. Double Effect
22384 A 'double effect' is a foreseen but not desired side-effect, which may be forgivable [Foot]
22385 The doctrine of double effect can excuse an outcome because it wasn't directly intended [Foot]
22386 Double effect says foreseeing you will kill someone is not the same as intending it [Foot]
22387 Without double effect, bad men can make us do evil by threatening something worse [Foot]
22388 Double effect seems to rely on a distinction between what we do and what we allow [Foot]
25. Social Practice / F. Life Issues / 3. Abortion
22383 Abortion is puzzling because we do and don't want the unborn child to have rights [Foot]
26. Natural Theory / C. Causation / 1. Causation
15247 Whitehead held that perception was a necessary feature of all causation [Whitehead, by Harré/Madden]
27. Natural Reality / C. Space / 3. Points in Space
16962 Whitehead replaced points with extended regions [Whitehead, by Quine]