78 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] |
15716 | If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert] |
18844 | You would cripple mathematics if you denied Excluded Middle [Hilbert] |
17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
12456 | I aim to establish certainty for mathematical methods [Hilbert] |
12461 | We believe all mathematical problems are solvable [Hilbert] |
13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
12462 | Only the finite can bring certainty to the infinite [Hilbert] |
12455 | The idea of an infinite totality is an illusion [Hilbert] |
12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
22293 | Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter] |
12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
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] |
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] |
13554 | True greatness is never allowing events to disturb you [Seneca] |
13305 | Character is ruined by not looking back over our pasts, since the future rests on the past [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] |
13553 | Anger is a vice which afflicts good men as well as bad [Seneca] |
13312 | Excessive curiosity is a form of intemperance [Seneca] |
13552 | Anger is an extreme vice, threatening sanity, and gripping whole states [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] |
13563 | Why does your wife wear in her ears the income of a wealthy house? [Seneca] |
13565 | If wealth was a good, it would make men good [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] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
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] |