Combining Texts

All the ideas for 'The Sayings of Confucius', 'Anselm and Actuality' and 'Elements of Set Theory'

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17 ideas

4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
16456 For modality Lewis rejected boxes and diamonds, preferring worlds, and an index for the actual one [Lewis, by Stalnaker]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
13206 A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
13201 ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [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]
19. Language / F. Communication / 1. Rhetoric
7357 People who control others with fluent language often end up being hated [Kongzi (Confucius)]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / h. Against ethics
7358 All men prefer outward appearance to true excellence [Kongzi (Confucius)]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
7362 Humans are similar, but social conventions drive us apart (sages and idiots being the exceptions) [Kongzi (Confucius)]
23. Ethics / B. Contract Ethics / 2. Golden Rule
7360 Do not do to others what you would not desire yourself [Kongzi (Confucius)]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
7359 Excess and deficiency are equally at fault [Kongzi (Confucius)]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7363 The virtues of the best people are humility, maganimity, sincerity, diligence, and graciousness [Kongzi (Confucius)]
24. Political Theory / C. Ruling a State / 2. Leaders / d. Elites
7361 Men of the highest calibre avoid political life completely [Kongzi (Confucius)]
24. Political Theory / D. Ideologies / 3. Conservatism
23393 Confucianism assumes that all good developments have happened, and there is only one Way [Norden on Kongzi (Confucius)]