48 ideas
| 13310 | Wisdom does not lie in books, and unread people can also become wise [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] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 10245 | One geometry cannot be more true than another [Poincaré] |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 13297 | To the four causes Plato adds a fifth, the idea which guided the event [Seneca] |
| 13307 | If everything can be measured, try measuring the size of a man's soul [Seneca] |
| 21399 | Referring to a person, and speaking about him, are very different [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] |
| 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] |
| 13305 | Character is ruined by not looking back over our pasts, since the future rests on the past [Seneca] |
| 13308 | It's no good winning lots of fights, if you are then conquered by your own temper [Seneca] |
| 13312 | Excessive curiosity is a form of intemperance [Seneca] |
| 13315 | To govern used to mean to serve, not to rule; rulers did not test their powers over those who bestowed it [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] |
| 13311 | Does time exist on its own? Did anything precede it? Did it pre-exist the cosmos? [Seneca] |