213 ideas
9199 | Wisdom for one instant is as good as wisdom for eternity [Chrysippus] |
14519 | It is a great good to show reverence for a wise man [Epicurus] |
20853 | Wise men should try to participate in politics, since they are a good influence [Chrysippus, by Diog. Laertius] |
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] |
20772 | Three branches of philosophy: first logic, second ethics, third physics (which ends with theology) [Chrysippus] |
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] |
5969 | Chrysippus said the uncaused is non-existent [Chrysippus, by Plutarch] |
2670 | Epicurus despises and laughs at the whole of dialectic [Epicurus, by Cicero] |
14040 | Observation and applied thought are always true [Epicurus] |
21388 | The causes of future true events must exist now, so they will happen because of destiny [Chrysippus, by Cicero] |
20780 | Graspable presentations are criteria of facts, and are molded according to their objects [Chrysippus, by Diog. Laertius] |
20793 | How could you ever know that the presentation is similar to the object? [Sext.Empiricus on Chrysippus] |
9535 | 'Contradictory' propositions always differ in truth-value [Lemmon] |
8077 | Stoic propositional logic is like chemistry - how atoms make molecules, not the innards of atoms [Chrysippus, by Devlin] |
9509 | That proposition that both P and Q is their 'conjunction', written P∧Q [Lemmon] |
9512 | We write the 'negation' of P (not-P) as ¬ [Lemmon] |
9513 | We write 'P if and only if Q' as P↔Q; it is also P iff Q, or (P→Q)∧(Q→P) [Lemmon] |
9514 | If A and B are 'interderivable' from one another we may write A -||- B [Lemmon] |
9511 | We write the conditional 'if P (antecedent) then Q (consequent)' as P→Q [Lemmon] |
9510 | That proposition that either P or Q is their 'disjunction', written P∨Q [Lemmon] |
9508 | The sign |- may be read as 'therefore' [Lemmon] |
9517 | The 'scope' of a connective is the connective, the linked formulae, and the brackets [Lemmon] |
9533 | A 'implies' B if B is true whenever A is true (so that A→B is tautologous) [Lemmon] |
9528 | A wff is a 'tautology' if all assignments to variables result in the value T [Lemmon] |
9518 | A 'theorem' is the conclusion of a provable sequent with zero assumptions [Lemmon] |
9532 | 'Subcontrary' propositions are never both false, so that A∨B is a tautology [Lemmon] |
9530 | A wff is 'contingent' if produces at least one T and at least one F [Lemmon] |
9519 | A 'substitution-instance' is a wff formed by consistent replacing variables with wffs [Lemmon] |
9529 | A wff is 'inconsistent' if all assignments to variables result in the value F [Lemmon] |
9531 | 'Contrary' propositions are never both true, so that ¬(A∧B) is a tautology [Lemmon] |
9534 | Two propositions are 'equivalent' if they mirror one another's truth-value [Lemmon] |
9516 | A 'well-formed formula' follows the rules for variables, ¬, →, ∧, ∨, and ↔ [Lemmon] |
9402 | RAA: If assuming A will prove B∧¬B, then derive ¬A [Lemmon] |
9395 | MTT: Given ¬B and A→B, we derive ¬A [Lemmon] |
9400 | ∨I: Given either A or B separately, we may derive A∨B [Lemmon] |
9401 | ∨E: Derive C from A∨B, if C can be derived both from A and from B [Lemmon] |
9396 | DN: Given A, we may derive ¬¬A [Lemmon] |
9393 | A: we may assume any proposition at any stage [Lemmon] |
9399 | ∧E: Given A∧B, we may derive either A or B separately [Lemmon] |
9398 | ∧I: Given A and B, we may derive A∧B [Lemmon] |
9397 | CP: Given a proof of B from A as assumption, we may derive A→B [Lemmon] |
9394 | MPP: Given A and A→B, we may derive B [Lemmon] |
9521 | 'Modus tollendo ponens' (MTP) says ¬P, P ∨ Q |- Q [Lemmon] |
9522 | 'Modus ponendo tollens' (MPT) says P, ¬(P ∧ Q) |- ¬Q [Lemmon] |
9525 | We can change conditionals into negated conjunctions with P→Q -||- ¬(P ∧ ¬Q) [Lemmon] |
9524 | We can change conditionals into disjunctions with P→Q -||- ¬P ∨ Q [Lemmon] |
9523 | De Morgan's Laws make negated conjunctions/disjunctions into non-negated disjunctions/conjunctions [Lemmon] |
9527 | The Distributive Laws can rearrange a pair of conjunctions or disjunctions [Lemmon] |
9526 | We can change conjunctions into negated conditionals with P→Q -||- ¬(P → ¬Q) [Lemmon] |
20791 | Chrysippus has five obvious 'indemonstrables' of reasoning [Chrysippus, by Diog. Laertius] |
9537 | Truth-tables are good for showing invalidity [Lemmon] |
9538 | A truth-table test is entirely mechanical, but this won't work for more complex logic [Lemmon] |
9536 | If any of the nine rules of propositional logic are applied to tautologies, the result is a tautology [Lemmon] |
9539 | Propositional logic is complete, since all of its tautologous sequents are derivable [Lemmon] |
13909 | Write '(∀x)(...)' to mean 'take any x: then...', and '(∃x)(...)' to mean 'there is an x such that....' [Lemmon] |
13902 | 'Gm' says m has property G, and 'Pmn' says m has relation P to n [Lemmon] |
13911 | The 'symbols' are bracket, connective, term, variable, predicate letter, reverse-E [Lemmon] |
13910 | Our notation uses 'predicate-letters' (for 'properties'), 'variables', 'proper names', 'connectives' and 'quantifiers' [Lemmon] |
13904 | Universal Elimination (UE) lets us infer that an object has F, from all things having F [Lemmon] |
13906 | With finite named objects, we can generalise with &-Intro, but otherwise we need ∀-Intro [Lemmon] |
13908 | UE all-to-one; UI one-to-all; EI arbitrary-to-one; EE proof-to-one [Lemmon] |
13901 | Predicate logic uses propositional connectives and variables, plus new introduction and elimination rules [Lemmon] |
13903 | Universal elimination if you start with the universal, introduction if you want to end with it [Lemmon] |
13905 | If there is a finite domain and all objects have names, complex conjunctions can replace universal quantifiers [Lemmon] |
13900 | 'Some Frenchmen are generous' is rendered by (∃x)(Fx→Gx), and not with the conditional → [Lemmon] |
8078 | Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin] |
9520 | The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon] |
21668 | Epicurus rejected excluded middle, because accepting it for events is fatalistic [Epicurus, by Cicero] |
6023 | Every proposition is either true or false [Chrysippus, by Cicero] |
21676 | Epicureans say disjunctions can be true whiile the disjuncts are not true [Epicurus, by Cicero] |
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] |
5992 | Chrysippus says action is the criterion for existence, which must be physical [Chrysippus, by Tieleman] |
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] |
21673 | There are simple and complex facts; the latter depend on further facts [Chrysippus, by Cicero] |
16652 | Stoics categories are Substrate, Quality, Disposition, and Relation [Chrysippus, by Pasnau] |
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] |
16058 | Dion and Theon coexist, but Theon lacks a foot. If Dion loses a foot, he ousts Theon? [Chrysippus, by Philo of Alexandria] |
14047 | Bodies have impermanent properties, and permanent ones which define its conceived nature [Epicurus] |
16059 | Change of matter doesn't destroy identity - in Dion and Theon change is a condition of identity [Chrysippus, by Long/Sedley] |
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] |
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] |
1487 | When entering a dark room it is colourless, but colour gradually appears [Epicurus] |
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] |
1875 | Dogs show reason in decisions made by elimination [Chrysippus, by Sext.Empiricus] |
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] |
20834 | Chrysippus allows evil to say it is fated, or even that it is rational and natural [Plutarch on Chrysippus] |
20833 | A swerve in the atoms would be unnatural, like scales settling differently for no reason [Chrysippus, by Plutarch] |
20835 | Chrysippus is wrong to believe in non-occurring future possibilities if he is a fatalist [Plutarch on Chrysippus] |
14521 | If everything is by necessity, then even denials of necessity are by necessity [Epicurus] |
20808 | Everything is fated, either by continuous causes or by a supreme rational principle [Chrysippus, by Diog. Laertius] |
20837 | Fate is an eternal and fixed chain of causal events [Chrysippus] |
14062 | Sooner follow mythology, than accept the 'fate' of natural philosophers [Epicurus] |
20836 | The Lazy Argument responds to fate with 'why bother?', but the bothering is also fated [Chrysippus, by Cicero] |
21679 | When we say events are fated by antecedent causes, do we mean principal or auxiliary causes? [Chrysippus] |
1837 | We should not refer things to irresponsible necessity, but either to fortune or to our own will [Epicurus] |
5971 | Destiny is only a predisposing cause, not a sufficient cause [Chrysippus, by Plutarch] |
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] |
20787 | A proposition is what can be asserted or denied on its own [Chrysippus] |
20850 | Passions are judgements; greed thinks money is honorable, and likewise drinking and lust [Chrysippus, by Diog. Laertius] |
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] |
20869 | The highest degree of morality performs all that is appropriate, omitting nothing [Chrysippus] |
3044 | Stoics say that beauty and goodness are equivalent and linked [Chrysippus, by Diog. Laertius] |
7814 | It was Epicurus who made the question of the will's freedom central to ethics [Epicurus, by Grayling] |
20838 | Fate initiates general causes, but individual wills and characters dictate what we do [Chrysippus] |
20813 | Human purpose is to contemplate and imitate the cosmos [Chrysippus] |
3045 | Stoics say justice is a part of nature, not just an invented principle [Chrysippus, by Diog. Laertius] |
20774 | Only nature is available to guide action and virtue [Chrysippus] |
20864 | Live in agreement, according to experience of natural events [Chrysippus] |
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] |
5972 | Living happily is nothing but living virtuously [Chrysippus, by Plutarch] |
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] |
1777 | Pleasure is not the good, because there are disgraceful pleasures [Chrysippus, by Diog. Laertius] |
5973 | Justice can be preserved if pleasure is a good, but not if it is the goal [Chrysippus, by Plutarch] |
14057 | All pleasures are good, but it is not always right to choose them [Epicurus] |
1833 | Pleasure is the first good in life [Epicurus] |
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] |
20845 | There are shameful pleasures, and nothing shameful is good, so pleasure is not a good [Chrysippus, by Diog. Laertius] |
3563 | Pleasure and virtue entail one another [Epicurus] |
5967 | People need nothing except corn and water [Chrysippus, by Plutarch] |
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] |
5966 | All virtue is good, but not always praised (as in not lusting after someone ugly) [Chrysippus] |
14060 | Prudence is the greatest good, and more valuable than philosophy, because it produces virtue [Epicurus] |
20855 | Chrysippus says virtue can be lost (though Cleanthes says it is too secure for that) [Chrysippus, by Diog. Laertius] |
5970 | Chrysippus says nothing is blameworthy, as everything conforms with the best nature [Chrysippus, by Plutarch] |
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] |
20842 | Rational animals begin uncorrupted, but externals and companions are bad influences [Chrysippus, by Diog. Laertius] |
14515 | A law is not just if it is not useful in mutual associations [Epicurus] |
20856 | Justice, the law, and right reason are natural and not conventional [Chrysippus, by Diog. Laertius] |
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] |
1779 | We don't have obligations to animals as they aren't like us [Chrysippus, by Diog. Laertius] |
20857 | Justice is irrelevant to animals, because they are too unlike us [Chrysippus, by Diog. Laertius] |
20812 | Covers are for shields, and sheaths for swords; likewise, all in the cosmos is for some other thing [Chrysippus] |
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] |
21403 | The later Stoics identified the logos with an air-fire compound, called 'pneuma' [Chrysippus, by Long] |
20828 | Fire is a separate element, not formed with others (as was previously believed) [Chrysippus, by Stobaeus] |
5975 | Stoics say earth, air, fire and water are the primary elements [Chrysippus, by Plutarch] |
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] |
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] |
20819 | The past and the future subsist, but only the present exists [Chrysippus, by Plutarch] |
20818 | The present does not exist, so our immediate experience is actually part past and part future [Chrysippus, by Plutarch] |
20821 | Time is continous and infinitely divisible, so there cannot be a wholly present time [Chrysippus, by Stobaeus] |
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] |
3048 | Stoics say that God the creator is the perfection of all animals [Chrysippus, by Diog. Laertius] |
20773 | The origin of justice can only be in Zeus, and in nature [Chrysippus] |
5965 | The source of all justice is Zeus and the universal nature [Chrysippus] |
3042 | Stoics teach that law is identical with right reason, which is the will of Zeus [Chrysippus, by Diog. Laertius] |
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] |
1782 | Stoics teach that God is a unity, variously known as Mind, or Fate, or Jupiter [Chrysippus, by Diog. Laertius] |
14527 | If god answered prayers we would be destroyed, because we pray for others to suffer [Epicurus] |
20830 | Death can't separate soul from body, because incorporeal soul can't unite with body [Chrysippus] |
21404 | There is a rationale in terrible disasters; they are useful to the whole, and make good possible [Chrysippus] |