71 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] |
| 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] |
| 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] |
| 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] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| 2867 | Christianity is Platonism for the people [Nietzsche] |