149 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] |
9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
9705 | 'fld R' indicates the 'field' of all objects in the relation [Enderton] |
9704 | 'ran R' indicates the 'range' of objects being related to [Enderton] |
9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton] |
9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
9699 | The 'powerset' of a set is all the subsets of a given set [Enderton] |
9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
9701 | A 'relation' is a set of ordered pairs [Enderton] |
9706 | A 'function' is a relation in which each object is related to just one other object [Enderton] |
9708 | A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton] |
9709 | A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton] |
9711 | A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton] |
9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton] |
9717 | A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton] |
13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
9721 | A logical truth or tautology is a logical consequence of the empty set [Enderton] |
9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
9720 | A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton] |
9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
9996 | Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton] |
9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
23855 | Creation produced a network or web of determinations [Weil] |
23900 | Chance is compatible with necessity, and the two occur together [Weil] |
9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
23888 | Knowledge is beyond question, as an unavoidable component of thinking [Weil] |
20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
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] |
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] |
23816 | Attention to a transcendent reality motivates a duty to foster the good of humanity [Weil] |
23754 | The only choice is between supernatural good, or evil [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] |