89 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] |
| 17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
| 10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
| 21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
| 17751 | Gödel proved the completeness of first order predicate logic in 1930 [Gödel, by Walicki] |
| 8679 | We perceive the objects of set theory, just as we perceive with our senses [Gödel] |
| 17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
| 9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
| 21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
| 9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
| 10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
| 10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
| 10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
| 17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
| 10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
| 19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
| 17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
| 10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
| 17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
| 10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
| 18062 | Set-theory paradoxes are no worse than sense deception in physics [Gödel] |
| 10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
| 10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
| 10868 | The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg] |
| 13517 | If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD] |
| 17885 | Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner] |
| 10614 | The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel] |
| 3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
| 10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
| 9590 | Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman] |
| 11069 | Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna] |
| 10118 | First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman] |
| 10122 | Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman] |
| 10611 | There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P] |
| 10867 | 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg] |
| 10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
| 10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
| 10271 | Basic mathematics is related to abstract elements of our empirical ideas [Gödel] |
| 10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
| 8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
| 12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
| 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] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 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] |