82 ideas
| 13310 | Wisdom does not lie in books, and unread people can also become wise [Seneca] |
| 13560 | A wise man is not subservient to anything [Seneca] |
| 13295 | Wise people escape necessity by willing it [Seneca] |
| 13317 | Philosophy aims at happiness [Seneca] |
| 13293 | What philosophy offers humanity is guidance [Seneca] |
| 13309 | That something is a necessary condition of something else doesn't mean it caused it [Seneca] |
| 13313 | Even philosophers have got bogged down in analysing tiny bits of language [Seneca] |
| 9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
| 9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
| 9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
| 9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
| 9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
| 9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
| 9605 | If a proposition is false, then its negation is true [Brown,JR] |
| 9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
| 9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
| 9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
| 9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
| 9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
| 9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
| 9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
| 9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
| 9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
| 9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
| 9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
| 9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
| 9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
| 9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
| 9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
| 9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
| 9630 | The most brilliant formalist was Hilbert [Brown,JR] |
| 9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
| 9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
| 9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
| 9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
| 9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
| 13297 | To the four causes Plato adds a fifth, the idea which guided the event [Seneca] |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| 13307 | If everything can be measured, try measuring the size of a man's soul [Seneca] |
| 9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
| 9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
| 9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
| 21399 | Referring to a person, and speaking about him, are very different [Seneca] |
| 13558 | The supreme good is harmony of spirit [Seneca] |
| 13325 | Trouble in life comes from copying other people, which is following convention instead of reason [Seneca] |
| 22239 | Humans acquired the concept of virtue from an analogy with bodily health and strength [Seneca, by Allen] |
| 13294 | We know death, which is like before birth; ceasing to be and never beginning are the same [Seneca] |
| 13299 | Living is nothing wonderful; what matters is to die well [Seneca] |
| 13300 | It is as silly to lament ceasing to be as to lament not having lived in the remote past [Seneca] |
| 13321 | Is anything sweeter than valuing yourself more when you find you are loved? [Seneca] |
| 13292 | Selfishness does not produce happiness; to live for yourself, live for others [Seneca] |
| 13550 | To be always happy is to lack knowledge of one half of nature [Seneca] |
| 13303 | A man is as unhappy as he has convinced himself he is [Seneca] |
| 13302 | Life is like a play - it is the quality that matters, not the length [Seneca] |
| 13301 | We are scared of death - except when we are immersed in pleasure! [Seneca] |
| 13323 | The whole point of pleasure-seeking is novelty, and abandoning established ways [Seneca] |
| 13318 | Nature doesn't give us virtue; we must unremittingly pursue it, as a training and an art [Seneca] |
| 13324 | Living contrary to nature is like rowing against the stream [Seneca] |
| 13559 | I seek virtue, because it is its own reward [Seneca] |
| 13305 | Character is ruined by not looking back over our pasts, since the future rests on the past [Seneca] |
| 13554 | True greatness is never allowing events to disturb you [Seneca] |
| 13561 | Virtue is always moderate, so excess need not be feared [Seneca] |
| 13562 | It is shameful to not even recognise your own slaves [Seneca] |
| 13556 | Every night I critically review how I have behaved during the day [Seneca] |
| 13308 | It's no good winning lots of fights, if you are then conquered by your own temper [Seneca] |
| 13552 | Anger is an extreme vice, threatening sanity, and gripping whole states [Seneca] |
| 13312 | Excessive curiosity is a form of intemperance [Seneca] |
| 13553 | Anger is a vice which afflicts good men as well as bad [Seneca] |
| 13549 | Nothing bad can happen to a good man [Seneca] |
| 13564 | There is far more scope for virtue if you are wealthy; poverty only allows endurance [Seneca] |
| 13565 | If wealth was a good, it would make men good [Seneca] |
| 13563 | Why does your wife wear in her ears the income of a wealthy house? [Seneca] |
| 13315 | To govern used to mean to serve, not to rule; rulers did not test their powers over those who bestowed it [Seneca] |
| 13557 | Unfortunately the majority do not tend to favour what is best [Seneca] |
| 13290 | One joy of learning is making teaching possible [Seneca] |
| 13322 | Both teachers and pupils should aim at one thing - the improvement of the pupil [Seneca] |
| 13298 | Suicide may be appropriate even when it is not urgent, if there are few reasons against it [Seneca] |
| 13319 | If we control our own death, no one has power over us [Seneca] |
| 13320 | Sometimes we have a duty not to commit suicide, for those we love [Seneca] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
| 13548 | The ocean changes in volume in proportion to the attraction of the moon [Seneca] |
| 13311 | Does time exist on its own? Did anything precede it? Did it pre-exist the cosmos? [Seneca] |