102 ideas
| 9199 | Wisdom for one instant is as good as wisdom for eternity [Chrysippus] |
| 20853 | Wise men should try to participate in politics, since they are a good influence [Chrysippus, by Diog. Laertius] |
| 20772 | Three branches of philosophy: first logic, second ethics, third physics (which ends with theology) [Chrysippus] |
| 5969 | Chrysippus said the uncaused is non-existent [Chrysippus, by Plutarch] |
| 9955 | Contextual definitions replace a complete sentence containing the expression [George/Velleman] |
| 10031 | Impredicative definitions quantify over the thing being defined [George/Velleman] |
| 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] |
| 8077 | Stoic propositional logic is like chemistry - how atoms make molecules, not the innards of atoms [Chrysippus, by Devlin] |
| 20791 | Chrysippus has five obvious 'indemonstrables' of reasoning [Chrysippus, by Diog. Laertius] |
| 10098 | The 'power set' of A is all the subsets of A [George/Velleman] |
| 10101 |
Cartesian Product A x B: the set of all ordered pairs |
| 10099 | The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}} [George/Velleman] |
| 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] |
| 8078 | Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin] |
| 6023 | Every proposition is either true or false [Chrysippus, by Cicero] |
| 10111 | Asserting Excluded Middle is a hallmark of realism about the natural world [George/Velleman] |
| 10129 | A 'model' is a meaning-assignment which makes all the axioms true [George/Velleman] |
| 10105 | Differences between isomorphic structures seem unimportant [George/Velleman] |
| 10126 | A 'consistent' theory cannot contain both a sentence and its negation [George/Velleman] |
| 10119 | Consistency is a purely syntactic property, unlike the semantic property of soundness [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] |
| 5992 | Chrysippus says action is the criterion for existence, which must be physical [Chrysippus, by Tieleman] |
| 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] |
| 16058 | Dion and Theon coexist, but Theon lacks a foot. If Dion loses a foot, he ousts Theon? [Chrysippus, by Philo of Alexandria] |
| 16059 | Change of matter doesn't destroy identity - in Dion and Theon change is a condition of identity [Chrysippus, by Long/Sedley] |
| 1875 | Dogs show reason in decisions made by elimination [Chrysippus, by Sext.Empiricus] |
| 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] |
| 20808 | Everything is fated, either by continuous causes or by a supreme rational principle [Chrysippus, by Diog. Laertius] |
| 20835 | Chrysippus is wrong to believe in non-occurring future possibilities if he is a fatalist [Plutarch on Chrysippus] |
| 20836 | The Lazy Argument responds to fate with 'why bother?', but the bothering is also fated [Chrysippus, by Cicero] |
| 20837 | Fate is an eternal and fixed chain of causal events [Chrysippus] |
| 21679 | When we say events are fated by antecedent causes, do we mean principal or auxiliary causes? [Chrysippus] |
| 5971 | Destiny is only a predisposing cause, not a sufficient cause [Chrysippus, by Plutarch] |
| 10110 | Corresponding to every concept there is a class (some of them sets) [George/Velleman] |
| 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] |
| 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] |
| 22688 | The Aristotelian idea that choices can be perceived needs literary texts to expound it [Nussbaum] |
| 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] |
| 5972 | Living happily is nothing but living virtuously [Chrysippus, by Plutarch] |
| 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] |
| 20845 | There are shameful pleasures, and nothing shameful is good, so pleasure is not a good [Chrysippus, by Diog. Laertius] |
| 5967 | People need nothing except corn and water [Chrysippus, by Plutarch] |
| 5966 | All virtue is good, but not always praised (as in not lusting after someone ugly) [Chrysippus] |
| 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] |
| 20842 | Rational animals begin uncorrupted, but externals and companions are bad influences [Chrysippus, by Diog. Laertius] |
| 20856 | Justice, the law, and right reason are natural and not conventional [Chrysippus, 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] |
| 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] |
| 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] |
| 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] |
| 3042 | Stoics teach that law is identical with right reason, which is the will of Zeus [Chrysippus, by Diog. Laertius] |
| 5965 | The source of all justice is Zeus and the universal nature [Chrysippus] |
| 1782 | Stoics teach that God is a unity, variously known as Mind, or Fate, or Jupiter [Chrysippus, by Diog. Laertius] |
| 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] |