Combining Texts

All the ideas for 'fragments/reports', 'Set Theory' and 'Just and Unjust Wars'

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38 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
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
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
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
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
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
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
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
Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
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
Constructibility: V = L (all sets are constructible) [Kunen]
20. Action / C. Motives for Action / 4. Responsibility for Actions
Criminal responsibility can be fully assigned to each member of a group [Walzer]
20. Action / C. Motives for Action / 5. Action Dilemmas / b. Double Effect
Double Effect needs a double intention - to achieve the good, and minimise the evil [Walzer]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
Deep ethical theory is very controversial, but we have to live with higher ethical practice [Walzer]
25. Social Practice / C. Rights / 1. Basis of Rights
If whole states possess rights, there can be social relations between states [Walzer]
25. Social Practice / E. Policies / 1. War / a. Just wars
States can rightly pre-empt real and serious threats [Walzer]
Just wars are self-defence, or a rightful intercession in another's troubles [Walzer]
The aim of reprisals is to enforce the rules of war [Walzer]
Reprisal is defensible, as an alternative to war [Walzer]
With nuclear weapons we have a permanent supreme emergency (which is unstable) [Walzer]
States need not endure attacks passively, and successful reprisals are legitimate [Walzer]
Nuclear bombs are not for normal war; they undermine the 'just war', with a new morality [Walzer]
Even non-violent intrusive acts between states count as aggression, if they justify resistance [Walzer]
The only good reason for fighting is in defence of rights [Walzer]
25. Social Practice / E. Policies / 1. War / b. Justice in war
For moral reasons, a just war must be a limited war [Walzer]
Napoleon said 'I don't care about the deaths of a million men' [Walzer]
Jus ad bellum and Jus in bello are independent; unjust wars can be fought in a just way [Walzer]
25. Social Practice / E. Policies / 1. War / c. Combatants
The duties and moral status of loyal and obedient soldiers is the same in defence and aggression [Walzer]
We can't blame soldiers for anything they do which clearly promotes victory [Walzer]
Rejecting Combatant Equality allows just soldiers to be harsher, even to the extreme [Walzer]
Kidnapped sailors and volunteers have different obligations to the passengers [Walzer]
Even aggressor soldiers are not criminals, so they have equal rights with their opponents [Walzer]
25. Social Practice / E. Policies / 1. War / d. Non-combatants
Soldiers will only protect civilians if they feel safe from them [Walzer]
What matters in war is unacceptable targets, not unacceptable weapons [Walzer]
If the oppressor is cruel, nonviolence is either surrender, or a mere gesture [Walzer]
25. Social Practice / E. Policies / 1. War / e. Peace
We can only lead war towards peace if we firmly enforce the rules of war [Walzer]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]