29 ideas
2653 | If the parts of the universe are subject to the law of nature, the whole universe must also be subject to it [Cicero] |
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] |
2628 | Why would mind mix with matter if it didn't need it? [Cicero] |
20814 | Eloquence educates, exhorts, comforts, distracts and unites us, and raises us from savagery [Cicero] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
2640 | We have the death penalty, but still have thousands of robbers [Cicero] |
2652 | Some regard nature simply as an irrational force that imparts movement [Cicero] |
2645 | Why shouldn't the gods fear their own destruction? [Cicero] |
2627 | I wonder whether loss of reverence for the gods would mean the end of all virtue [Cicero] |
2651 | God doesn't obey the laws of nature; they are subject to the law of God [Cicero] |
2634 | It seems clear to me that we have an innate idea of the divine [Cicero] |
2636 | Many primitive people know nothing of the gods [Cicero] |
2647 | It is obvious from order that someone is in charge, as when we visit a gymnasium [Cicero] |
2655 | If the barbarians of Britain saw a complex machine, they would be baffled, but would know it was designed [Cicero] |
2656 | Chance is no more likely to create the world than spilling lots of letters is likely to create a famous poem [Cicero] |
2650 | If a person cannot feel the power of God when looking at the stars, they are probably incapable of feeling [Cicero] |
2657 | If everything with regular movement and order is divine, then recurrent illnesses must be divine [Cicero] |
2638 | Either the gods are identical, or one is more beautiful than another [Cicero] |
2635 | The gods are happy, so virtuous, so rational, so must have human shape [Cicero] |
2641 | Why believe in gods if you have never seen them? [Cicero] |
2659 | The lists of good men who have suffered and bad men who have prospered are endless [Cicero] |
2658 | The gods blame men for having vices, but they could have given us enough reason to avoid them [Cicero] |