26 ideas
23250 | Desired responsible actions result either from rational or from irrational desire [Aristotle] |
5847 | It is the role of dialectic to survey syllogisms [Aristotle] |
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] |
13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
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] |
13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
5862 | A single counterexample is enough to prove that a truth is not necessary [Aristotle] |
5854 | Nobody fears a disease which nobody has yet caught [Aristotle] |
5849 | Rhetoric is a political offshoot of dialectic and ethics [Aristotle] |
5851 | Pentathletes look the most beautiful, because they combine speed and strength [Aristotle] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
5858 | Men are physically prime at thirty-five, and mentally prime at forty-nine [Aristotle] |
5855 | We all feel universal right and wrong, independent of any community or contracts [Aristotle] |
5850 | Happiness is composed of a catalogue of internal and external benefits [Aristotle] |
5856 | Self-interest is a relative good, but nobility an absolute good [Aristotle] |
5853 | The best virtues are the most useful to others [Aristotle] |
5848 | All good things can be misused, except virtue [Aristotle] |
5857 | The young feel pity from philanthropy, but the old from self-concern [Aristotle] |
5859 | Rich people are mindlessly happy [Aristotle] |
5852 | The four constitutions are democracy (freedom), oligarchy (wealth), aristocracy (custom), tyranny (security) [Aristotle] |
1660 | It is noble to avenge oneself on one's enemies, and not come to terms with them [Aristotle] |
5861 | People assume events cause what follows them [Aristotle] |