32 ideas
501 | Reason is a more powerful persuader than gold [Democritus (attr)] |
3338 | Numbers have been defined in terms of 'successors' to the concept of 'zero' [Peano, by Blackburn] |
13949 | All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano] |
18113 | PA concerns any entities which satisfy the axioms [Peano, by Bostock] |
17634 | Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell] |
5897 | 0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew] |
15653 | We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano] |
17635 | Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano] |
514 | Beauty is merely animal without intelligence [Democritus (attr)] |
525 | Behave well when alone, and feel shame in you own eyes [Democritus (attr)] |
502 | Good breeding in men means having a good character [Democritus (attr)] |
507 | Virtuous love consists of decorous desire for the beautiful [Democritus (attr)] |
505 | Good and true are the same for everyone, but pleasures differ [Democritus (attr)] |
521 | We should only choose pleasures which are concerned with the beautiful [Democritus (attr)] |
508 | Only accept beneficial pleasures [Democritus (attr)] |
520 | The great pleasures come from the contemplation of noble works [Democritus (attr)] |
522 | Moderation brings more pleasures, and so increases pleasure [Democritus (attr)] |
506 | Immoderate desire is the mark of a child, not an adult [Democritus (attr)] |
523 | It is as brave to master pleasure as to overcome the enemy [Democritus (attr)] |
497 | Be virtuous from duty, not from fear [Democritus (attr)] |
518 | A bad life is just a drawn-out death [Democritus (attr)] |
503 | Virtue doesn't just avoid evil, but also doesn't desire it [Democritus (attr)] |
499 | Repentance of shameful deeds is salvation [Democritus (attr)] |
524 | Virtue comes more from practice than from nature [Democritus (attr)] |
519 | One must avoid even speaking of evil deeds [Democritus (attr)] |
500 | The wrongdoer is more unfortunate than the person wronged [Democritus (attr)] |
1539 | The endless desire for money is a crueller slavery than poverty [Democritus (attr)] |
526 | Small appetite makes poverty equal to wealth [Democritus (attr)] |
511 | It is better to have one intelligent friend than many unintelligent [Democritus (attr)] |
498 | It is a great thing, when one is in adversity, to think of duty [Democritus (attr)] |
1541 | It is better to be poor in a democracy than be rich without freedom [Democritus (attr)] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |