41 ideas
14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
14240 | The empty set is something, not nothing! [Oliver/Smiley] |
14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
16661 | There are two sorts of category - referring to things, and to circumstances of things [Boethius] |
15035 | If universals are not separate, we can isolate them by abstraction [Boethius, by Panaccio] |
14665 | We can call the quality of Plato 'Platonity', and say it is a quality which only he possesses [Boethius] |
16066 | Additional or removal of any part changes a thing, so people are never the same person [Epicharmus] |
23308 | Reasoning relates to understanding as time does to eternity [Boethius, by Sorabji] |
436 | A dog seems handsome to another a dog, and even a pig to another pig [Epicharmus] |
5771 | Knowledge of present events doesn't make them necessary, so future events are no different [Boethius] |
5767 | Rational natures require free will, in order to have power of judgement [Boethius] |
5768 | God's universal foreknowledge seems opposed to free will [Boethius] |
5769 | Does foreknowledge cause necessity, or necessity cause foreknowledge? [Boethius] |
5762 | The wicked want goodness, so they would not be wicked if they obtained it [Boethius] |
5770 | Rewards and punishments are not deserved if they don't arise from free movement of the mind [Boethius] |
5764 | When people fall into wickedness they lose their human nature [Boethius] |
5756 | Happiness is a good which once obtained leaves nothing more to be desired [Boethius] |
442 | Pleasures are like pirates - if you are caught they drown you in a sea of pleasures [Epicharmus] |
440 | Hands wash hands; give that you may get [Epicharmus] |
5763 | The bad seek the good through desire, but the good through virtue, which is more natural [Boethius] |
5759 | Varied aims cannot be good because they differ, but only become good when they unify [Boethius] |
441 | Against a villain, villainy is not a useless weapon [Epicharmus] |
5754 | You can't control someone's free mind, only their body and possessions [Boethius] |
439 | God knows everything, and nothing is impossible for him [Epicharmus] |
16692 | Divine eternity is the all-at-once and complete possession of unending life [Boethius] |
5752 | Where does evil come from if there is a god; where does good come from if there isn't? [Boethius] |
5758 | God is the good [Boethius] |
5757 | God is the supreme good, so no source of goodness could take precedence over God [Boethius] |
5760 | The power through which creation remains in existence and motion I call 'God' [Boethius] |
5753 | The regular events of this life could never be due to chance [Boethius] |
5765 | The reward of the good is to become gods [Boethius] |
5761 | God can do anything, but he cannot do evil, so evil must be nothing [Boethius] |
5766 | If you could see the plan of Providence, you would not think there was evil anywhere [Boethius] |
443 | Human logos is an aspect of divine logos, and is sufficient for successful living [Epicharmus] |