116 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] |
6123 | Empirical investigation can't discover if holes exist, or if two things share a colour [Merricks] |
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] |
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] |
15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [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] |
6143 | Prolonged events don't seem to endure or exist at any particular time [Merricks] |
6135 | A crumbling statue can't become vague, because vagueness is incoherent [Merricks] |
6145 | Intrinsic properties are those an object still has even if only that object exists [Merricks] |
6124 | I say that most of the objects of folk ontology do not exist [Merricks] |
6134 | Is swimming pool water an object, composed of its mass or parts? [Merricks] |
6125 | We can eliminate objects without a commitment to simples [Merricks] |
14229 | Merricks agrees that there are no composite objects, but offers a different semantics [Merricks, by Liggins] |
6142 | The 'folk' way of carving up the world is not intrinsically better than quite arbitrary ways [Merricks] |
14472 | If atoms 'arranged baseballwise' break a window, that analytically entails that a baseball did it [Merricks, by Thomasson] |
14469 | Overdetermination: the atoms do all the causing, so the baseball causes no breakage [Merricks] |
6137 | Clay does not 'constitute' a statue, as they have different persistence conditions (flaking, squashing) [Merricks] |
6141 | There is no visible difference between statues, and atoms arranged statuewise [Merricks] |
6127 | 'Unrestricted composition' says any two things can make up a third thing [Merricks] |
6131 | Composition as identity is false, as identity is never between a single thing and many things [Merricks] |
6132 | Composition as identity is false, as it implies that things never change their parts [Merricks] |
6130 | 'Composition' says things are their parts; 'constitution' says a whole substance is an object [Merricks] |
6138 | It seems wrong that constitution entails that two objects are wholly co-located [Merricks] |
6128 | Objects decompose (it seems) into non-overlapping parts that fill its whole region [Merricks] |
6136 | Eliminativism about objects gives the best understanding of the Sorites paradox [Merricks] |
6133 | If my counterpart is happy, that is irrelevant to whether I 'could' have been happy [Merricks] |
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] |
6150 | The 'warrant' for a belief is what turns a true belief into knowledge [Merricks] |
6144 | You hold a child in your arms, so it is not mental substance, or mental state, or software [Merricks] |
20378 | Just as skin hides the horrors of the body, vanity conceals the passions of the soul [Nietzsche] |
6140 | Maybe the word 'I' can only refer to persons [Merricks] |
6149 | Free will and determinism are incompatible, since determinism destroys human choice [Merricks] |
6148 | Human organisms can exercise downward causation [Merricks] |
6146 | Before Creation it is assumed that God still had many many mental properties [Merricks] |
6147 | The hypothesis of solipsism doesn't seem to be made incoherent by the nature of mental properties [Merricks] |
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] |
14807 | The history of morality rests on an error called 'responsibility', which rests on an error called 'free will' [Nietzsche] |
14824 | It is absurd to blame nature and necessity; we should no more praise actions than we praise plants or artworks [Nietzsche] |
14823 | Ceasing to believe in human responsibility is bitter, if you had based the nobility of humanity on it [Nietzsche] |
22473 | Nietzsche said the will doesn't exist, so it can't ground moral responsibility [Nietzsche, by Foot] |
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] |
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] |
14839 | Interest in education gains strength when we lose interest in God [Nietzsche] |
14848 | Education in large states is mediocre, like cooking in large kitchens [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] |