143 ideas
| 14519 | It is a great good to show reverence for a wise man [Epicurus] |
| 22733 | Epicurus accepted God in his popular works, but not in his writings on nature [Epicurus, by Sext.Empiricus] |
| 14518 | In the study of philosophy, pleasure and knowledge arrive simultaneously [Epicurus] |
| 14052 | Begin philosophy when you are young, and keep going when you are old [Epicurus] |
| 13291 | Slavery to philosophy brings true freedom [Epicurus] |
| 22758 | Philosophy aims at a happy life, through argument and discussion [Epicurus] |
| 14523 | We should come to philosophy free from any taint of culture [Epicurus] |
| 22240 | The aim of medicine is removal of sickness, and philosophy similarly removes our affections [Epicurus] |
| 1484 | We should say nothing of the whole if our contact is with the parts [Epicurus, by Plutarch] |
| 14027 | If we are to use words in enquiry, we need their main, unambiguous and uncontested meanings [Epicurus] |
| 2670 | Epicurus despises and laughs at the whole of dialectic [Epicurus, by Cicero] |
| 9955 | Contextual definitions replace a complete sentence containing the expression [George/Velleman] |
| 10031 | Impredicative definitions quantify over the thing being defined [George/Velleman] |
| 14040 | Observation and applied thought are always true [Epicurus] |
| 10098 | The 'power set' of A is all the subsets of A [George/Velleman] |
| 10099 | The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}} [George/Velleman] |
| 10101 |
Cartesian Product A x B: the set of all ordered pairs |
| 10103 | Grouping by property is common in mathematics, usually using equivalence [George/Velleman] |
| 10104 | 'Equivalence' is a reflexive, symmetric and transitive relation; 'same first letter' partitions English words [George/Velleman] |
| 10096 | Even the elements of sets in ZFC are sets, resting on the pure empty set [George/Velleman] |
| 10097 | Axiom of Extensionality: for all sets x and y, if x and y have the same elements then x = y [George/Velleman] |
| 10100 | Axiom of Pairing: for all sets x and y, there is a set z containing just x and y [George/Velleman] |
| 17900 | The Axiom of Reducibility made impredicative definitions possible [George/Velleman] |
| 10109 | ZFC can prove that there is no set corresponding to the concept 'set' [George/Velleman] |
| 10108 | As a reduction of arithmetic, set theory is not fully general, and so not logical [George/Velleman] |
| 21668 | Epicurus rejected excluded middle, because accepting it for events is fatalistic [Epicurus, by Cicero] |
| 10111 | Asserting Excluded Middle is a hallmark of realism about the natural world [George/Velleman] |
| 21676 | Epicureans say disjunctions can be true whiile the disjuncts are not true [Epicurus, by Cicero] |
| 10129 | A 'model' is a meaning-assignment which makes all the axioms true [George/Velleman] |
| 10105 | Differences between isomorphic structures seem unimportant [George/Velleman] |
| 10119 | Consistency is a purely syntactic property, unlike the semantic property of soundness [George/Velleman] |
| 10126 | A 'consistent' theory cannot contain both a sentence and its negation [George/Velleman] |
| 10120 | Soundness is a semantic property, unlike the purely syntactic property of consistency [George/Velleman] |
| 10127 | A 'complete' theory contains either any sentence or its negation [George/Velleman] |
| 10106 | Rational numbers give answers to division problems with integers [George/Velleman] |
| 10102 | The integers are answers to subtraction problems involving natural numbers [George/Velleman] |
| 10107 | Real numbers provide answers to square root problems [George/Velleman] |
| 9946 | Logicists say mathematics is applicable because it is totally general [George/Velleman] |
| 10125 | The classical mathematician believes the real numbers form an actual set [George/Velleman] |
| 17899 | Second-order induction is stronger as it covers all concepts, not just first-order definable ones [George/Velleman] |
| 10128 | The Incompleteness proofs use arithmetic to talk about formal arithmetic [George/Velleman] |
| 17902 | A successor is the union of a set with its singleton [George/Velleman] |
| 10133 | Frege's Theorem shows the Peano Postulates can be derived from Hume's Principle [George/Velleman] |
| 10130 | Set theory can prove the Peano Postulates [George/Velleman] |
| 10089 | Talk of 'abstract entities' is more a label for the problem than a solution to it [George/Velleman] |
| 10131 | If mathematics is not about particulars, observing particulars must be irrelevant [George/Velleman] |
| 10092 | In the unramified theory of types, the types are objects, then sets of objects, sets of sets etc. [George/Velleman] |
| 10094 | The theory of types seems to rule out harmless sets as well as paradoxical ones. [George/Velleman] |
| 10095 | Type theory has only finitely many items at each level, which is a problem for mathematics [George/Velleman] |
| 17901 | Type theory prohibits (oddly) a set containing an individual and a set of individuals [George/Velleman] |
| 10114 | Bounded quantification is originally finitary, as conjunctions and disjunctions [George/Velleman] |
| 10134 | Much infinite mathematics can still be justified finitely [George/Velleman] |
| 10123 | The intuitionists are the idealists of mathematics [George/Velleman] |
| 10124 | Gödel's First Theorem suggests there are truths which are independent of proof [George/Velleman] |
| 14028 | Nothing comes to be from what doesn't exist [Epicurus] |
| 14029 | If disappearing things went to nothingness, nothing could return, and it would all be gone by now [Epicurus] |
| 14030 | The totality is complete, so there is no room for it to change, and nothing extraneous to change it [Epicurus] |
| 14048 | Astronomical movements are blessed, but they don't need the help of the gods [Epicurus] |
| 14044 | The perceived accidental properties of bodies cannot be conceived of as independent natures [Epicurus] |
| 14045 | Accidental properties give a body its nature, but are not themselves bodies or parts of bodies [Epicurus] |
| 14524 | Bodies are combinations of shape, size, resistance and weight [Epicurus] |
| 14046 | A 'body' is a conception of an aggregate, with properties defined by application conditions [Epicurus] |
| 14047 | Bodies have impermanent properties, and permanent ones which define its conceived nature [Epicurus] |
| 14039 | Above and below us will never appear to be the same, because it is inconceivable [Epicurus] |
| 14050 | We aim to dissolve our fears, by understanding their causes [Epicurus] |
| 1823 | We can't seek for things if we have no idea of them [Epicurus, by Diog. Laertius] |
| 1824 | To name something, you must already have an idea of what it is [Epicurus, by Diog. Laertius] |
| 14037 | Atoms only have shape, weight and size, and the properties which accompany shape [Epicurus] |
| 5949 | Epicurus says colours are relative to the eye, not intrinsic to bodies [Epicurus, by Plutarch] |
| 1821 | Sensations cannot be judged, because similar sensations have equal value, and different ones have nothing in common [Epicurus, by Diog. Laertius] |
| 1820 | The criteria of truth are senses, preconceptions and passions [Epicurus, by Diog. Laertius] |
| 1822 | Reason can't judge senses, as it is based on them [Epicurus, by Diog. Laertius] |
| 4549 | Epicurus denied knowledge in order to retain morality or hedonism as the highest values [Nietzsche on Epicurus] |
| 2668 | Epicurus says if one of a man's senses ever lies, none of his senses should ever be believed [Epicurus, by Cicero] |
| 6010 | Illusions are not false perceptions, as we accurately perceive the pattern of atoms [Epicurus, by Modrak] |
| 1487 | When entering a dark room it is colourless, but colour gradually appears [Epicurus] |
| 1482 | If two people disagree over taste, who is right? [Epicurus, by Plutarch] |
| 1483 | Bath water is too hot for some, too cold for others [Epicurus, by Plutarch] |
| 21386 | We should accept as explanations all the plausible ways in which something could come about [Epicurus] |
| 14526 | The rational soul is in the chest, and the non-rational soul is spread through the body [Epicurus] |
| 14041 | The soul is fine parts distributed through the body, resembling hot breath [Epicurus] |
| 6035 | Soul is made of four stuffs, giving warmth, rest, motion and perception [Epicurus, by Aetius] |
| 6018 | Epicurus was the first to see the free will problem, and he was a libertarian [Epicurus, by Long/Sedley] |
| 20922 | Epicurus showed that the swerve can give free motion in the atoms [Epicurus, by Diogenes of Oen.] |
| 14516 | There is no necessity to live with necessity [Epicurus] |
| 14521 | If everything is by necessity, then even denials of necessity are by necessity [Epicurus] |
| 14062 | Sooner follow mythology, than accept the 'fate' of natural philosophers [Epicurus] |
| 1837 | We should not refer things to irresponsible necessity, but either to fortune or to our own will [Epicurus] |
| 14042 | The soul cannot be incorporeal, because then it could neither act nor be acted upon [Epicurus] |
| 1909 | How can pleasure or judgement occur in a heap of atoms? [Sext.Empiricus on Epicurus] |
| 10110 | Corresponding to every concept there is a class (some of them sets) [George/Velleman] |
| 1836 | Prudence is more valuable than philosophy, because it avoids confusions of the soul [Epicurus] |
| 14061 | Our own choices are autonomous, and the basis for praise and blame [Epicurus] |
| 7814 | It was Epicurus who made the question of the will's freedom central to ethics [Epicurus, by Grayling] |
| 14054 | Fearing death is absurd, because we are not present when it occurs [Epicurus] |
| 14053 | It is absurd to fear the pain of death when you are not even facing it [Epicurus] |
| 14055 | The wisdom that produces a good life also produces a good death [Epicurus] |
| 3562 | Fine things are worthless if they give no pleasure [Epicurus] |
| 1833 | Pleasure is the first good in life [Epicurus] |
| 14057 | All pleasures are good, but it is not always right to choose them [Epicurus] |
| 14058 | Pleasure is the goal, but as lack of pain and calm mind, not as depraved or greedy pleasure [Epicurus] |
| 1840 | Pleasure is the chief good because it is the most natural, especially for animals [Epicurus, by Diog. Laertius] |
| 14063 | Sooner a good decision going wrong, than a bad one turning out for the good [Epicurus] |
| 14522 | What happens to me if I obtain all my desires, and what if I fail? [Epicurus] |
| 14059 | The best life is not sensuality, but rational choice and healthy opinion [Epicurus] |
| 1835 | True pleasure is not debauchery, but freedom from physical and mental pain [Epicurus] |
| 1839 | Pains of the soul are worse than pains of the body, because it feels the past and future [Epicurus, by Diog. Laertius] |
| 1842 | Pleasures only differ in their duration and the part of the body affected [Epicurus] |
| 3557 | The end for Epicurus is static pleasure [Epicurus, by Annas] |
| 14056 | We only need pleasure when we have the pain of desire [Epicurus] |
| 3563 | Pleasure and virtue entail one another [Epicurus] |
| 1845 | Justice has no independent existence, but arises entirely from keeping contracts [Epicurus] |
| 3560 | Justice is merely a contract about not harming or being harmed [Epicurus] |
| 14060 | Prudence is the greatest good, and more valuable than philosophy, because it produces virtue [Epicurus] |
| 1841 | We choose virtue because of pleasure, not for its own sake [Epicurus, by Diog. Laertius] |
| 14517 | We value our own character, whatever it is, and we should respect the characters of others [Epicurus] |
| 14513 | Justice is a pledge of mutual protection [Epicurus] |
| 1829 | A wise man would be happy even under torture [Epicurus, by Diog. Laertius] |
| 1843 | Friendship is by far the most important ingredient of a complete and happy life [Epicurus] |
| 14515 | A law is not just if it is not useful in mutual associations [Epicurus] |
| 14520 | It is small-minded to find many good reasons for suicide [Epicurus] |
| 1831 | Wise men should partake of life even if they go blind [Epicurus, by Diog. Laertius] |
| 12044 | Only Epicurus denied purpose in nature, for the whole world, or for its parts [Epicurus, by Annas] |
| 14032 | Totality has no edge; an edge implies a contrast beyond the edge, and there can't be one [Epicurus] |
| 14033 | Bodies are unlimited as well as void, since the two necessarily go together [Epicurus] |
| 14034 | There exists an infinity of each shape of atom, but the number of shapes is beyond our knowledge [Epicurus] |
| 14035 | Atoms just have shape, size and weight; colour results from their arrangement [Epicurus] |
| 14038 | There cannot be unlimited division, because it would reduce things to non-existence [Epicurus] |
| 20907 | Democritus says atoms have size and shape, and Epicurus added weight [Epicurus, by Ps-Plutarch] |
| 21669 | Atoms don't swerve by being struck, because they move in parallel, so the swerve is uncaused [Cicero on Epicurus] |
| 21680 | What causes atomic swerves? Do they draw lots? What decides the size or number of swerves? [Cicero on Epicurus] |
| 8338 | A phenomenalist about objects has to be a regularity theorist about causation [Strawson,G] |
| 14049 | We aim to know the natures which are observed in natural phenomena [Epicurus] |
| 14043 | The void cannot interact, but just gives the possibility of motion [Epicurus] |
| 14031 | Space must exist, since movement is obvious, and there must be somewhere to move in [Epicurus] |
| 14525 | Stoics say time is incorporeal and self-sufficient; Epicurus says it is a property of properties of things [Epicurus] |
| 14051 | A cosmos is a collection of stars and an earth, with some sort of boundary, movement and shape [Epicurus] |
| 14036 | There are endless cosmoi, some like and some unlike this one [Epicurus] |
| 2637 | For Epicureans gods are made of atoms, and are not eternal [Epicurus, by Cicero] |
| 2633 | Epicurus saw that gods must exist, because nature has imprinted them on human minds [Epicurus, by Cicero] |
| 1828 | God does not intervene in heavenly movements, but is beyond all action and perfectly happy [Epicurus] |
| 2639 | Some say Epicurus only pretended to believe in the gods, so as not to offend Athenians [Epicurus, by Cicero] |
| 14527 | If god answered prayers we would be destroyed, because we pray for others to suffer [Epicurus] |