145 ideas
| 23889 | Among the Greeks Aristotle is the only philosopher in the modern style [Weil] |
| 23881 | All thought about values is philosophical, and thought about anything else is not philosophy [Weil] |
| 23885 | Philosophy aims to change the soul, not to accumulate knowledge [Weil] |
| 23886 | Systems are not unique to each philosopher. The platonist tradition is old and continuous [Weil] |
| 23884 | Truth is a value of thought [Weil] |
| 23755 | Genius and love of truth are always accompanied by great humility [Weil] |
| 23877 | Most people won't question an idea's truth if they depend on it [Weil] |
| 23825 | We seek truth only because it is good [Weil] |
| 23853 | Truth is not a object we love - it is the radiant manifestation of reality [Weil] |
| 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] |
| 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] |
| 15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
| 15947 | The infinite is extrapolation from the experience of indefinitely large size [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] |
| 23855 | Creation produced a network or web of determinations [Weil] |
| 23900 | Chance is compatible with necessity, and the two occur together [Weil] |
| 23888 | Knowledge is beyond question, as an unavoidable component of thinking [Weil] |
| 23747 | What is sacred is not a person, but the whole physical human being [Weil] |
| 23756 | The mind is imprisoned and limited by language, restricting our awareness of wider thoughts [Weil] |
| 23878 | Weakness of will is the inadequacy of the original impetus to carry through the action [Weil] |
| 23899 | The secret of art is that beauty is a just blend of unity and its opposite [Weil] |
| 23832 | We both desire what is beautiful, and want it to remain as it is [Weil] |
| 23848 | The aesthete's treatment of beauty as amusement is sacreligious; beauty should nourish [Weil] |
| 23758 | Beauty is an attractive mystery, leaving nothing to be desired [Weil] |
| 23887 | Art (like philosophy) establishes a relation between world and self, and between oneself and others [Weil] |
| 23903 | When we admire a work, we see ourselves as its creator [Weil] |
| 23898 | Those who say immorality is not an aesthetic criterion must show that all criteria are aesthetic [Weil] |
| 23814 | Every human yearns for an unattainable transcendent good [Weil] |
| 23826 | Beauty, goodness and truth are only achieved by applying full attention [Weil] |
| 23854 | Beauty is the proof of what is good [Weil] |
| 23824 | Where human needs are satisfied we find happiness, friendship and beauty [Weil] |
| 23879 | In a violent moral disagreement, it can't be that both sides are just following social morality [Weil] |
| 23882 | Ends, unlike means, cannot be defined, which is why people tend to pursue means [Weil] |
| 23760 | All we need are the unity of justice, truth and beauty [Weil] |
| 23883 | Minds essentially and always strive towards value [Weil] |
| 23748 | The sacred in every human is their expectation of good rather than evil [Weil] |
| 23759 | Everything which originates in love is beautiful [Weil] |
| 23762 | Evil is transmitted by comforts and pleasures, but mostly by doing harm to people [Weil] |
| 23808 | There are two goods - the absolute good we want, and the reachable opposite of evil [Weil] |
| 23833 | The good is a nothingness, and yet real [Weil] |
| 23865 | Morality would improve if people could pursue private interests [Weil] |
| 22725 | When players don't meet again, defection is the best strategy [Axelrod] |
| 22724 | Good strategies avoid conflict, respond to hostility, forgive, and are clear [Axelrod] |
| 23896 | We see our character as a restricting limit, but also as an unshakable support [Weil] |
| 23894 | The concept of character is at the centre of morality [Weil] |
| 23893 | We don't see character in a single moment, but only over a period of time [Weil] |
| 23895 | We modify our character by placing ourselves in situations, or by attending to what seems trivial [Weil] |
| 23837 | Respect is our only obligation, which can only be expressed through deeds, not words [Weil] |
| 23815 | We cannot equally respect what is unequal, so equal respect needs a shared ground [Weil] |
| 23834 | Friendship is partly universal - the love of a person is like the ideal of loving everyone [Weil] |
| 23823 | Life needs risks to avoid sickly boredom [Weil] |
| 23844 | The most important human need is to have multiple roots [Weil] |
| 23838 | The need for order stands above all others, and is understood via the other needs [Weil] |
| 23836 | Obligations only bind individuals, not collectives [Weil] |
| 23840 | A citizen should be able to understand the whole of society [Weil] |
| 23822 | We all need to partipate in public tasks, and take some initiative [Weil] |
| 23843 | Even the poorest should feel collective ownership, and participation in grand display [Weil] |
| 23846 | Culture is an instrument for creating an ongoing succession of teachers [Weil] |
| 23857 | People in power always try to increase their power [Weil] |
| 23866 | In oppressive societies the scope of actual control is extended by a religion of power [Weil] |
| 23812 | Force is what turns man into a thing, and ultimately into a corpse [Weil] |
| 23831 | The essence of power is illusory prestige [Weil] |
| 23839 | A lifelong head of society should only be a symbol, not a ruler [Weil] |
| 23871 | No central authority can initiate decentralisation [Weil] |
| 23856 | Spontaneous movements are powerless against organised repression [Weil] |
| 23867 | After a bloody revolution the group which already had the power comes to the fore [Weil] |
| 23830 | A group is only dangerous if it endorses an abstract entity [Weil] |
| 23870 | Decentralisation is only possible by co-operation between strong and weak - which is absurd [Weil] |
| 23809 | Our only social duty is to try to limit evil [Weil] |
| 23829 | National leaders want to preserve necessary order - but always the existing order [Weil] |
| 23817 | We need both equality (to attend to human needs) and hierarchy (as a scale of responsibilities) [Weil] |
| 23842 | Party politics in a democracy can't avoid an anti-democratic party [Weil] |
| 23859 | True democracy is the subordination of society to the individual [Weil] |
| 23863 | Only individual people of good will can achieve social progress [Weil] |
| 23869 | In the least evil societies people can think, control community life, and be autonomous [Weil] |
| 23847 | Socialism tends to make a proletariat of the whole population [Weil] |
| 23750 | It is not more money which the wretched members of society need [Weil] |
| 23807 | The collective is the one and only object of false idolatry [Weil] |
| 23749 | The problem of the collective is not suppression of persons, but persons erasing themselves [Weil] |
| 23861 | Marx showed that capitalist oppression, because of competition, is unstoppable [Weil] |
| 23897 | Once money is the main aim, society needs everyone to think wealth is possible [Weil] |
| 23845 | The capitalists neglect the people and the nation, and even their own interests [Weil] |
| 23828 | National prestige consists of behaving as if you could beat the others in a war [Weil] |
| 23810 | Charity is the only love, and you can feel that for a country (a place with traditions), but not a nation [Weil] |
| 23811 | If effort is from necessity rather than for a good, it is slavery [Weil] |
| 23868 | The pleasure of completing tasks motivates just as well as the whip of slavery [Weil] |
| 23819 | Deliberate public lying should be punished [Weil] |
| 23818 | We have liberty in the space between nature and accepted authority [Weil] |
| 23901 | Relationships depend on equality, so unequal treatment kills them [Weil] |
| 23753 | People absurdly claim an equal share of things which are essentially privileged [Weil] |
| 23841 | By making money the sole human measure, inequality has become universal [Weil] |
| 23864 | Inequality could easily be mitigated, if it were not for the struggle for power [Weil] |
| 23835 | People have duties, and only have rights because of the obligations of others to them [Weil] |
| 23751 | Rights are asserted contentiously, and need the backing of force [Weil] |
| 23752 | Giving centrality to rights stifles all impulses of charity [Weil] |
| 23820 | People need personal and collective property, and a social class lacking property is shameful [Weil] |
| 23813 | Only people who understand force, and don't respect it, are capable of justice [Weil] |
| 23757 | The spirit of justice needs the full attention of truth, and that attention is love [Weil] |
| 23761 | Justice (concerning harm) is distinct from rights (concerning inequality) [Weil] |
| 23852 | To punish people we must ourselves be innocent - but that undermines the desire to punish [Weil] |
| 23764 | The only thing in society worse than crime is repressive justice [Weil] |
| 23821 | Crime should be punished, to bring the perpetrator freely back to morality [Weil] |
| 23763 | Punishment aims at the good for men who don't desire it [Weil] |
| 23827 | Modern wars are fought in the name of empty words which are given capital letters [Weil] |
| 23880 | When war was a profession, customary morality justified any act of war [Weil] |
| 23850 | The soldier-civilian distinction should be abolished; every citizen is committed to a war [Weil] |
| 23858 | War is perpetuated by its continual preparations [Weil] |
| 23851 | Education is essentially motivation [Weil] |
| 23873 | Dividing history books into separate chapters is disastrous [Weil] |
| 23860 | Even if a drowning man is doomed, he should keep swimming to the last [Weil] |
| 23754 | The only choice is between supernatural good, or evil [Weil] |
| 23816 | Attention to a transcendent reality motivates a duty to foster the good of humanity [Weil] |
| 23892 | The only legitimate proof of God by order derives from beauty [Weil] |
| 23904 | The cruelty of the Old Testament put me off Christianity [Weil] |
| 23849 | Religion should quietly suffuse all human life with its light [Weil] |
| 23902 | I attach little importance to immortality, which is an undecidable fact, and irrelevant to us [Weil] |
| 23765 | The soul is the intrinsic value of a human [Weil] |