107 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] |
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| 20772 | Three branches of philosophy: first logic, second ethics, third physics (which ends with theology) [Chrysippus] |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| 5969 | Chrysippus said the uncaused is non-existent [Chrysippus, by Plutarch] |
| 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] |
| 13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
| 20793 | How could you ever know that the presentation is similar to the object? [Sext.Empiricus on Chrysippus] |
| 13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
| 13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
| 8077 | Stoic propositional logic is like chemistry - how atoms make molecules, not the innards of atoms [Chrysippus, by Devlin] |
| 13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
| 20791 | Chrysippus has five obvious 'indemonstrables' of reasoning [Chrysippus, by Diog. Laertius] |
| 13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
| 13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
| 13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
| 13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
| 13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
| 13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
| 13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
| 13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
| 13441 | Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
| 13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
| 13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
| 13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
| 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] |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| 13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
| 13505 | Model theory studies how set theory can model sets of sentences [Hart,WD] |
| 13511 | Model theory is mostly confined to first-order theories [Hart,WD] |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
| 13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
| 13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
| 13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
| 13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
| 9117 | The smallest heap has four objects: three on the bottom, one on the top [Hart,WD, by Sorensen] |
| 13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD] |
| 13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
| 13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
| 13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
| 13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
| 13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
| 5992 | Chrysippus says action is the criterion for existence, which must be physical [Chrysippus, by Tieleman] |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| 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] |
| 13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
| 13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
| 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] |
| 3449 | If parallelism is true, how does the mind know about the body? [Crease] |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| 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] |
| 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] |