Combining Texts

All the ideas for 'The Sign of Four', 'Elements of Set Theory' and 'Treatise 2: Virtue or Moral Good'

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23 ideas

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
13201 ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
13206 A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
13204 The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
13200 Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
13199 The empty set may look pointless, but many sets can be constructed from it [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
13203 The singleton is defined using the pairing axiom (as {x,x}) [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13202 Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13205 We can only define functions if Choice tells us which items are involved [Enderton]
14. Science / C. Induction / 1. Induction
22200 If you eliminate the impossible, the truth will remain, even if it is weird [Conan Doyle]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
6248 Reason is too slow and doubtful to guide all actions, which need external and moral senses [Hutcheson]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
6238 We approve of actions by a superior moral sense [Hutcheson]
6239 We dislike a traitor, even if they give us great benefit [Hutcheson]
6240 The moral sense is not an innate idea, but an ability to approve or disapprove in a disinterested way [Hutcheson]
6242 We cannot choose our moral feelings, otherwise bribery could affect them [Hutcheson]
6247 Everyone feels uneasy when seeing others in pain, unless the others are evil [Hutcheson]
22. Metaethics / B. Value / 2. Values / f. Altruism
6244 Human nature seems incapable of universal malice, except what results from self-love [Hutcheson]
22. Metaethics / B. Value / 2. Values / i. Self-interest
6243 As death approaches, why do we still care about family, friends or country? [Hutcheson]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
6246 My action is not made good by a good effect, if I did not foresee and intend it [Hutcheson]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
6241 Contempt of danger is just madness if it is not in some worthy cause [Hutcheson]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
6245 That action is best, which procures the greatest happiness for the greatest number [Hutcheson]
25. Social Practice / C. Rights / 1. Basis of Rights
6251 The loss of perfect rights causes misery, but the loss of imperfect rights reduces social good [Hutcheson]
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
6250 We say God is good if we think everything he does aims at the happiness of his creatures [Hutcheson]
28. God / A. Divine Nature / 6. Divine Morality / d. God decrees morality
6249 If goodness is constituted by God's will, it is a tautology to say God's will is good [Hutcheson]