125 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] |
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] |
21675 | Some facts are indispensable for an effect, and others actually necessitate the effect [Stoic school, by Cicero] |
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] |
20778 | Stoics like syllogisms, for showing what is demonstrative, which corrects opinions [Stoic school, by Diog. Laertius] |
15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
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] |
15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
15940 | The intuitionist endorses only the potential infinite [Lavine] |
15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
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] |
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] |
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] |
23321 | Division of the soul divides a person, reducing responsibility for the nonrational part [Stoic school, by Frede,M] |
23267 | Stoics say the soul is a mixture of air and fire [Stoic school, by Galen] |
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] |
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] |
22086 | The most important aspect of a human being is not reason, but passion [Kierkegaard, by Carlisle] |
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] |
13296 | The cosmos has two elements - passive matter, and active cause (or reason) which shapes it [Stoic school, by Seneca] |
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 ] |