79 ideas
14857 | The highest wisdom has the guise of simplicity [Nietzsche] |
14854 | Deep thinkers know that they are always wrong [Nietzsche] |
14833 | Comedy is a transition from fear to exuberance [Nietzsche] |
22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
14853 | Truth finds fewest champions not when it is dangerous, but when it is boring [Nietzsche] |
24075 | Convictions, more than lies, are the great enemy of truth [Nietzsche] |
10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
14858 | Being certain presumes that there are absolute truths, and means of arriving at them [Nietzsche] |
14830 | Intuition only recognises what is possible, not what exists or is certain [Nietzsche] |
20378 | Just as skin hides the horrors of the body, vanity conceals the passions of the soul [Nietzsche] |
9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
14820 | People always do what they think is right, according to the degree of their intellect [Nietzsche] |
14856 | Our judgment seems to cause our nature, but actually judgment arises from our nature [Nietzsche] |
14842 | Why are the strong tastes of other people so contagious? [Nietzsche] |
14835 | Artists are not especially passionate, but they pretend to be [Nietzsche] |
22473 | Nietzsche said the will doesn't exist, so it can't ground moral responsibility [Nietzsche, by Foot] |
14807 | The history of morality rests on an error called 'responsibility', which rests on an error called 'free will' [Nietzsche] |
14823 | Ceasing to believe in human responsibility is bitter, if you had based the nobility of humanity on it [Nietzsche] |
14824 | It is absurd to blame nature and necessity; we should no more praise actions than we praise plants or artworks [Nietzsche] |
14812 | Intellect is tied to morality, because it requires good memory and powerful imagination [Nietzsche] |
14810 | Originally it was the rulers who requited good for good and evil for evil who were called 'good' [Nietzsche] |
6017 | Nomos is king [Pindar] |
14831 | No one has ever done anything that was entirely for other people [Nietzsche] |
14855 | Simultaneous love and respect are impossible; love has no separation or rank, but respect admits power [Nietzsche] |
14815 | We get enormous pleasure from tales of noble actions [Nietzsche] |
14849 | We can only achieve happy moments, not happy eras [Nietzsche] |
14818 | First morality is force, then custom, then acceptance, then instinct, then a pleasure - and finally 'virtue' [Nietzsche] |
20103 | You are mastered by your own virtues, but you must master them, and turn them into tools [Nietzsche] |
14817 | The 'good' man does the moral thing as if by nature, easily and gladly, after a long inheritance [Nietzsche] |
14809 | All societies of good men give a priority to gratitude [Nietzsche] |
14816 | Justice (fairness) originates among roughly equal powers (as the Melian dialogues show) [Nietzsche] |
20112 | Pity consoles those who suffer, because they see that they still have the power to hurt [Nietzsche] |
14821 | Apart from philosophers, most people rightly have a low estimate of pity [Nietzsche] |
14841 | Many people are better at having good friends than being a good friend [Nietzsche] |
14843 | Women can be friends with men, but only some physical antipathy will maintain it [Nietzsche] |
14811 | In Homer it is the contemptible person, not the harmful person, who is bad [Nietzsche] |
20111 | We could live more naturally, relishing the spectacle, and not thinking we are special [Nietzsche] |
14844 | People do not experience boredom if they have never learned to work properly [Nietzsche] |
14808 | Over huge periods of time human character would change endlessly [Nietzsche] |
14822 | If self-defence is moral, then so are most expressions of 'immoral' egoism [Nietzsche] |
14838 | The state aims to protect individuals from one another [Nietzsche] |
14852 | Culture cannot do without passions and vices [Nietzsche] |
14846 | If we want the good life for the greatest number, we must let them decide on the good life [Nietzsche] |
14819 | Slavery cannot be judged by our standards, because the sense of justice was then less developed [Nietzsche] |
14847 | Laws that are well thought out, or laws that are easy to understand? [Nietzsche] |
14814 | Execution is worse than murder, because we are using the victim, and really we are the guilty [Nietzsche] |
14836 | People will enthusiastically pursue an unwanted war, once sacrifices have been made [Nietzsche] |
14845 | Don't crush girls with dull Gymnasium education, the way we have crushed boys! [Nietzsche] |
14848 | Education in large states is mediocre, like cooking in large kitchens [Nietzsche] |
14839 | Interest in education gains strength when we lose interest in God [Nietzsche] |
14834 | Teachers only gather knowledge for their pupils, and can't be serious about themselves [Nietzsche] |
14825 | In religious thought nature is a complex of arbitrary acts by conscious beings [Nietzsche] |
14826 | Modern man wants laws of nature in order to submit to them [Nietzsche] |
14827 | The Greeks saw the gods not as their masters, but as idealised versions of themselves [Nietzsche] |
14813 | Science rejecting the teaching of Christianity in favour of Epicurus shows the superiority of the latter [Nietzsche] |
14832 | The Sermon on the Mount is vanity - praying to one part of oneself, and demonising the rest [Nietzsche] |
14850 | Christ was the noblest human being [Nietzsche] |
14837 | Christ seems warm hearted, and suppressed intellect in favour of the intellectually weak [Nietzsche] |
14828 | Religion is tempting if your life is boring, but you can't therefore impose it on the busy people [Nietzsche] |