139 ideas
| 20866 | Wise men participate in politics, especially if it shows moral progress [Stoic school, by Stobaeus] |
| 20854 | Wise men are never astonished at things which other people take to be wonders [Stoic school, by Diog. Laertius] |
| 20815 | No wise man has yet been discovered [Stoic school, by Cicero] |
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| 20806 | Stoic physics concerns cosmos, elements and causes (with six detailed divisions) [Stoic school, by Diog. Laertius] |
| 20839 | Ethics studies impulse, good, passion, virtue, goals, value, action, appropriateness, encouragement [Stoic school, by Diog. Laertius] |
| 20867 | True philosophising is not memorising ideas, but living by them [Stoic school, by Stobaeus] |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| 21675 | Some facts are indispensable for an effect, and others actually necessitate the effect [Stoic school, by Cicero] |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| 20775 | Stoics study canons, criteria and definitions, in order to find the truth [Stoic school, by Diog. Laertius] |
| 21393 | Stoics believed that rational capacity in man (logos) is embodied in the universe [Stoic school, by Long] |
| 21810 | The Stoics distinguished spoken logos from logos within the mind [Stoic school, by Plotinus] |
| 20776 | Dialectics is mastery of question and answer form [Stoic school, by Diog. Laertius] |
| 20849 | Falsehoods corrupt a mind, producing passions and instability [Stoic school, by Diog. Laertius] |
| 20823 | The truth bearers are said to be the signified, or the signifier, or the meaning of the signifier [Stoic school, by Sext.Empiricus] |
| 13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
| 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] |
| 20778 | Stoics like syllogisms, for showing what is demonstrative, which corrects opinions [Stoic school, by Diog. Laertius] |
| 13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
| 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] |
| 21400 | Stoics avoided universals by paraphrasing 'Man is...' as 'If something is a man, then it is...' [Stoic school, by Long] |
| 20788 | The contradictory of a contradictory is an affirmation [Stoic school, by Diog. Laertius] |
| 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] |
| 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] |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| 21594 | Stoics applied bivalence to sorites situations, so everyone is either vicious or wholly virtuous [Stoic school, by Williamson] |
| 20824 | Stoics have four primary categories: substrates, qualities, dispositions, relative dispositions [Stoic school, by Simplicius] |
| 20817 | Platonic Forms are just our thoughts [Stoic school, by Ps-Plutarch] |
| 6037 | Stoics say matter has qualities, and substance underlies it, with no form or qualities [Stoic school, by Chalcidius] |
| 20825 | How is divisibility possible, if stoics say things remain united when they are divided? [Alexander on Stoic school] |
| 20826 | How is separateness possible, if separated things are always said to be united? [Alexander on Stoic school] |
| 20872 | Stoics say wholes are more than parts, but entirely consist of parts [Stoic school, by Sext.Empiricus] |
| 20790 | A proposition is possible if it is true when nothing stops it being true [Stoic school, by Diog. Laertius] |
| 20789 | Conditionals are false if the falsehood of the conclusion does not conflict with the antecedent [Stoic school, by Diog. Laertius] |
| 20783 | Knowledge is a secure grasp of presentations which cannot be reversed by argument [Stoic school, by Diog. Laertius] |
| 20868 | Two sorts of opinion: either poorly grounded belief, or weak belief [Stoic school, by Stobaeus] |
| 20784 | There are non-sensible presentations, which come to us through the intellect [Stoic school, by Diog. Laertius] |
| 13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
| 20803 | Stoics say we are born like a blank sheet of paper; the first concepts on it are sensations [Stoic school, by Ps-Plutarch] |
| 6025 | At birth the soul is a blank sheet ready to be written on [Stoic school, by Aetius] |
| 13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
| 20781 | Non-graspable presentations are from what doesn't exist, or are not clear and distinct [Stoic school, by Diog. Laertius] |
| 20792 | Stoic perception is a presentation to which one voluntarily assents [Stoic school, by Stobaeus] |
| 20805 | All our concepts come from experience, directly, or by expansion, reduction or compounding [Stoic school, by Sext.Empiricus] |
| 20782 | Dialectic is a virtue which contains other virtues [Stoic school, by Diog. Laertius] |
| 1772 | For Stoics knowledge is an assertion which never deviates from the truth [Stoic school, by Diog. Laertius] |
| 20779 | Demonstration derives what is less clear from what is clear [Stoic school, by Diog. Laertius] |
| 23251 | The Stoics think that soul in the narrow sense is nothing but reason [Stoic school, by Frede,M] |
| 20809 | Eight parts of the soul: five senses, seeds, speech and reason [Stoic school, by Diog. Laertius] |
| 23267 | Stoics say the soul is a mixture of air and fire [Stoic school, by Galen] |
| 23321 | Division of the soul divides a person, reducing responsibility for the nonrational part [Stoic school, by Frede,M] |
| 20785 | Our conceptions arise from experience, similarity, analogy, transposition, composition and opposition [Stoic school, by Diog. Laertius] |
| 7502 | For Stoics the true self is defined by what I can be master of [Stoic school, by Foucault] |
| 23327 | Stoics expanded the idea of compulsion, and contracted what counts as one's own actions [Stoic school, by Frede,M] |
| 7672 | The free will problem was invented by the Stoics [Stoic school, by Berlin] |
| 23315 | The nearest to ancient determinism is Stoic fate, but that is controlled by a sympathetic God [Stoic school, by Frede,M] |
| 4014 | Stoics classify passions according to the opinion of good and bad which they imply [Stoic school, by Taylor,C] |
| 23988 | There are four basic emotions: pleasure or delight, distress, appetite, and fear [Stoic school, by Cicero] |
| 6594 | Stoics said that correct judgement needs an invincible criterion of truth [Stoic school, by Fogelin] |
| 20804 | Concepts are intellectual phantasms [Stoic school, by Ps-Plutarch] |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| 20786 | Predicates are incomplete 'lekta' [Stoic school, by Diog. Laertius] |
| 23322 | Humans have rational impressions, which are conceptual, and are true or false [Stoic school, by Frede,M] |
| 20777 | Rhetoric has three types, four modes, and four sections [Stoic school, by Diog. Laertius] |
| 23323 | Earlier Stoics speak of assent, but not of choice, let alone of a will [Stoic school, by Frede,M] |
| 23305 | Stoics said responsibility depends on rationality [Stoic school, by Sorabji] |
| 1907 | Stoics use 'kalon' (beautiful) as a synonym for 'agathon' (good) [Bury on Stoic school] |
| 22757 | Stoics say that folly alone is evil [Stoic school, by Sext.Empiricus] |
| 20846 | Prime values apply to the life in agreement; useful values apply to the natural life [Stoic school, by Diog. Laertius] |
| 20847 | The appraiser's value is what is set by someone experienced in the facts [Stoic school, by Diog. Laertius] |
| 20870 | The goal is to live consistently with the constitution of a human being [Stoic school, by Clement] |
| 22238 | Stoics said health is an 'indifferent', but they still considered it preferable [Stoic school, by Pormann] |
| 20861 | The health of the soul is a good blend of beliefs [Stoic school, by Stobaeus] |
| 3553 | Stoic morality says that one's own happiness will lead to impartiality [Stoic school, by Annas] |
| 20851 | Virtuous men do not feel sexual desire, which merely focuses on physical beauty [Stoic school, by Diog. Laertius] |
| 7499 | Stoicism was an elitist option to lead a beautiful life [Stoic school, by Foucault] |
| 20843 | Final goods: confidence, prudence, freedom, enjoyment and no pain, good spirits, virtue [Stoic school, by Diog. Laertius] |
| 22753 | Happiness for the Stoics was an equable flow of life [Stoic school, by Sext.Empiricus] |
| 20865 | Happiness is the end and goal, achieved by living virtuously, in agreement, and according to nature [Stoic school, by Stobaeus] |
| 20840 | Stoics say pleasure is at most a byproduct of finding what is suitable for us [Stoic school, by Diog. Laertius] |
| 20852 | Rapture is a breakdown of virtue [Stoic school, by Diog. Laertius] |
| 6895 | If humans are citizens of the world (not just a state) then virtue is all good human habits [Stoic school, by Mautner] |
| 20848 | An appropriate action is one that can be defended, perhaps by its consistency. [Stoic school, by Diog. Laertius] |
| 20844 | Honour is just, courageous, orderly or knowledgeable. It is praiseworthy, or functions well [Stoic school, by Diog. Laertius] |
| 4012 | The Stoics rejected entirely the high value that had been placed on contemplation [Stoic school, by Taylor,C] |
| 5073 | Stoics do not despise external goods, but subject them to reason, and not to desire [Taylor,R on Stoic school] |
| 20862 | Crafts like music and letters are virtuous conditions, and they accord with virtue [Stoic school, by Stobaeus] |
| 5072 | For Stoics, obligations are determined by social role [Taylor,R on Stoic school] |
| 21396 | Man is distinguished by knowing conditional truths, because impressions are connected [Stoic school, by Long] |
| 1781 | Stoics favour a mixture of democracy, monarchy and aristocracy [Stoic school, by Diog. Laertius] |
| 21384 | The Stoics saw the whole world as a city [Stoic school, by Long] |
| 20859 | The best government blends democracy, monarchy and aristocracy [Stoic school, by Diog. Laertius] |
| 3561 | Stoics originated the concept of natural law, as agreed correct reasoning [Stoic school, by Annas] |
| 3046 | Stoics say a wise man will commit suicide if he has a good enough reason [Stoic school, by Diog. Laertius] |
| 20858 | Suicide is reasonable, for one's country or friends, or because of very bad health [Stoic school, by Diog. Laertius] |
| 3556 | Stoic 'nature' is deterministic, physical and teleological [Stoic school, by Annas] |
| 22743 | Unlike Epicurus, Stoics distinguish the Whole from the All, with the latter including the void [Stoic school, by Sext.Empiricus] |
| 14586 | Physical causation consists in transference of conserved quantities [Dowe, by Mumford/Anjum] |
| 4787 | Causation interaction is an exchange of conserved quantities, such as mass, energy or charge [Dowe, by Psillos] |
| 13296 | The cosmos has two elements - passive matter, and active cause (or reason) which shapes it [Stoic school, by Seneca] |
| 4788 | Dowe commends the Conserved Quantity theory as it avoids mention of counterfactuals [Dowe, by Psillos] |
| 20827 | The cosmos is regularly consumed and reorganised by the primary fire [Stoic school, by Aristocles] |
| 7815 | Early Stoics called the logos 'god', meaning not a being, but the principle of the universe [Stoic school] |
| 6038 | Stoics say god is matter, or an inseparable quality of it, or is the power within it [Stoic school, by Chalcidius] |
| 20829 | Virtuous souls endure till the end, foolish souls for a short time, animal souls not at all [Stoic school, by Eusebius] |
| 6039 | Stoics say virtuous souls last till everything ends in fire, but foolish ones fade away [Stoic school, by ] |