80 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] |
10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
18192 | Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy] |
7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
13547 | Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter] |
10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |
14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo] |
10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo] |
10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos] |
10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro] |
10267 | We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro] |
10698 | Plural forms have no more ontological commitment than to first-order objects [Boolos] |
7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
10833 | Many concepts can only be expressed by second-order logic [Boolos] |
10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
7295 | Maybe induction is only reliable IF reality is stable [Mitchell,A] |
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] |
8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
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] |
13322 | Both teachers and pupils should aim at one thing - the improvement of the pupil [Seneca] |
13290 | One joy of learning is making teaching possible [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] |
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] |