61 ideas
7834 | Great philosophies are confessions by the author, growing out of moral intentions [Nietzsche] |
7080 | Metaphysics divided the old unified Greek world into two [Nietzsche, by Critchley] |
11090 | Why do we want truth, rather than falsehood or ignorance? The value of truth is a problem [Nietzsche] |
10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
10857 | Set theory made a closer study of infinity possible [Clegg] |
10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
10871 | Axiom of Existence: there exists at least one set [Clegg] |
10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
10860 | An ordinal number is defined by the set that comes before it [Clegg] |
10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
7079 | Nietzsche resists nihilism through new values, for a world of becoming, without worship [Nietzsche, by Critchley] |
2878 | We see an approximation of a tree, not the full detail [Nietzsche] |
20140 | We shouldn't object to a false judgement, if it enhances and preserves life [Nietzsche] |
2877 | Morality becomes a problem when we compare many moralities [Nietzsche] |
13195 | To explain a house we must describe its use, as well as its parts [Leibniz] |
13193 | Active force is not just potential for action, since it involves a real effort or striving [Leibniz] |
20355 | The ranking of a person's innermost drives reveals their true nature [Nietzsche] |
2291 | A thought comes when 'it' wants, not when 'I' want [Nietzsche] |
2871 | Wanting 'freedom of will' is wanting to pull oneself into existence out of the swamp of nothingness by one's own hair [Nietzsche] |
20381 | It is psychology which reveals the basic problems [Nietzsche] |
2860 | The most boring and dangerous of all errors is Plato's invention of pure spirit and goodness [Nietzsche] |
1568 | Nietzsche felt that Plato's views downgraded the human body and its brevity of life [Nietzsche, by Roochnik] |
2883 | Noble people see themselves as the determiners of values [Nietzsche] |
23440 | Nietzsche's judgement of actions by psychology instead of outcome was poisonous [Foot on Nietzsche] |
2875 | That which is done out of love always takes place beyond good and evil [Nietzsche] |
2868 | Nature is totally indifferent, so you should try to be different from it, not live by it [Nietzsche] |
2882 | Morality originally judged people, and actions only later on [Nietzsche] |
2872 | In the earliest phase of human history only consequences mattered [Nietzsche] |
2885 | The noble soul has reverence for itself [Nietzsche] |
20134 | Moralities extravagantly address themselves to 'all', by falsely generalising [Nietzsche] |
2881 | Virtue has been greatly harmed by the boringness of its advocates [Nietzsche] |
20382 | The four virtues are courage, insight, sympathy, solitude [Nietzsche] |
2879 | In ancient Rome pity was considered neither good nor bad [Nietzsche] |
2859 | The idea of the categorical imperative is just that we should all be very obedient [Nietzsche] |
2884 | The morality of slaves is the morality of utility [Nietzsche] |
2880 | The greatest possibilities in man are still unexhausted [Nietzsche] |
2876 | The thought of suicide is a great reassurance on bad nights [Nietzsche] |
7078 | The freedom of the subject means the collapse of moral certainty [Nietzsche, by Critchley] |
2874 | Man is the animal whose nature has not yet been fixed [Nietzsche] |
6869 | Nietzsche thinks the human condition is to overcome and remake itself [Nietzsche, by Ansell Pearson] |
20137 | The great person engages wholly with life, and is happy to endlessly relive the life they created [Nietzsche] |
20139 | Only aristocratic societies can elevate the human species [Nietzsche] |
20373 | A healthy aristocracy has no qualms about using multitudes of men as instruments [Nietzsche] |
22394 | Democracy diminishes mankind, making them mediocre and lowering their value [Nietzsche] |
13194 | God's laws would be meaningless without internal powers for following them [Leibniz] |
13196 | All qualities of bodies reduce to forces [Leibniz] |
13192 | Power is passive force, which is mass, and active force, which is entelechy or form [Leibniz] |
2867 | Christianity is Platonism for the people [Nietzsche] |