52 ideas
| 7834 | Great philosophies are confessions by the author, growing out of moral intentions [Nietzsche] |
| Full Idea: It has gradually become clear to me what every great philosophy has hitherto been: a confession on the part of its author, and a kind of involuntary and unconscious memoir, ...with moral intentions being the real germ of its life. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §006) | |
| A reaction: This attitude is what places Nietzsche as the parent of post-modernism, and is the reason why most 'continental' philosophers seem to have given up the attempt to simply reason about life. It is anti-Enlightenment, and it is wicked. |
| 7080 | Metaphysics divided the old unified Greek world into two [Nietzsche, by Critchley] |
| Full Idea: Nietzsche famously defines metaphysics as the division of one world into two; the unity of the mythical pre-philosophical experience of the world is sundered, with Plato, into being and seeming, reality and appearance, supersensible and sensible. | |
| From: report of Friedrich Nietzsche (Beyond Good and Evil [1886]) by Simon Critchley - Continental Philosophy - V. Short Intro | |
| A reaction: (Critchley doesn't give a reference; Idea 2860 is close). This is the discredited status that metaphysics gradually acquired after Kant, but I see modern metaphysics as reuniting human thought by digging down to the foundations to reveal roots and links. |
| 11090 | Why do we want truth, rather than falsehood or ignorance? The value of truth is a problem [Nietzsche] |
| Full Idea: What really is it in us that wants 'the truth'? ...Granted we want truth: why not rather untruth? And uncertainty? Even ignorance? The problem of the value of truth stepped before us. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §001) | |
| A reaction: I think this is one of the great moments in philosophy, when something that has been taken for granted, as a kind of mantra, is suddenly looked in the face and challenged. Truth at all costs? What sacrifices would you make for truth? |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle. |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| Full Idea: It is surely wise to identify the positions in the natural numbers structure with their counterparts in the integer, rational, real and complex number structures. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
| A reaction: The point is that this might be denied, since 3, 3/1, 3.00.., and -3*i^2 are all arrived at by different methods of construction. Natural 3 has a predecessor, but real 3 doesn't. I agree, intuitively, with Shapiro. Russell (1919) disagreed. |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| Full Idea: A sequence a1,a2,... of rational numbers is 'Cauchy' if for each rational number ε>0 there is a natural number N such that for all natural numbers m, n, if m>N and n>N then -ε < am - an < ε. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 7.2 n4) | |
| A reaction: The sequence is 'Cauchy' if N exists. |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| Full Idea: There is a dedicated contingent who hold that the category of 'categories' is the proper foundation for mathematics. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.3 n7) | |
| A reaction: He cites Lawvere (1966) and McLarty (1993), the latter presenting the view as a form of structuralism. I would say that the concept of a category will need further explication, and probably reduce to either sets or relations or properties. |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| Full Idea: Zermelo said that for each number n, its successor is the singleton of n, so 3 is {{{null}}}, and 1 is not a member of 3. Von Neumann said each number n is the set of numbers less than n, so 3 is {null,{null},{null,{null}}}, and 1 is a member of 3. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
| A reaction: See Idea 645 - Zermelo could save Plato from the criticisms of Aristotle! These two accounts are cited by opponents of the set-theoretical account of numbers, because it seems impossible to arbitrate between them. |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| Full Idea: The structuralist vigorously rejects any sort of ontological independence among the natural numbers; the essence of a natural number is its relations to other natural numbers. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
| A reaction: This seems to place the emphasis on ordinals (what order?) rather than on cardinality (how many?). I am strongly inclined to think that this is the correct view, though you can't really have relations if there is nothing to relate. |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| Full Idea: A 'system' is a collection of objects with certain relations among them; a 'pattern' or 'structure' is the abstract form of a system, highlighting the interrelationships and ignoring any features they do not affect how they relate to other objects. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
| A reaction: Note that 'ignoring' features is a psychological account of abstraction, which (thanks to Frege and Geach) is supposed to be taboo - but which I suspect is actually indispensable in any proper account of thought and concepts. |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| Full Idea: The thesis that principles of arithmetic are derivable from the laws of logic runs against a now common view that logic itself has no ontology. There are no particular logical objects. From this perspective logicism is a non-starter. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 5.1) | |
| A reaction: This criticism strikes me as utterly devastating. There are two routes to go: prove that logic does have an ontology of objects (what would they be?), or - better - deny that arithmetic contains any 'objects'. Or give up logicism. |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| Full Idea: Term Formalism is the view that mathematics is just about characters or symbols - the systems of numerals and other linguistic forms. ...This will cover integers and rational numbers, but what are real numbers supposed to be, if they lack names? | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.1) | |
| A reaction: Real numbers (such as pi and root-2) have infinite decimal expansions, so we can start naming those. We could also start giving names like 'Harry' to other reals, though it might take a while. OK, I give up. |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| Full Idea: Game Formalism likens mathematics to chess, where the 'content' of mathematics is exhausted by the rules of operating with its language. ...This, however, leaves the problem of why the mathematical games are so useful to the sciences. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.2) | |
| A reaction: This thought pushes us towards structuralism. It could still be a game, but one we learned from observing nature, which plays its own games. Chess is, after all, modelled on warfare. |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| Full Idea: The Deductivist version of formalism (sometimes called 'if-thenism') says that the practice of mathematics consists of determining logical consequences of otherwise uninterpreted axioms. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.2) | |
| A reaction: [Hilbert is the source] More plausible than Term or Game Formalism (qv). It still leaves the question of why it seems applicable to nature, and why those particular axioms might be chosen. In some sense, though, it is obviously right. |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| Full Idea: Critics commonly complain that the intuitionist restrictions cripple the mathematician. On the other hand, intuitionist mathematics allows for many potentially important distinctions not available in classical mathematics, and is often more subtle. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 7.1) | |
| A reaction: The main way in which it cripples is its restriction on talk of infinity ('Cantor's heaven'), which was resented by Hilbert. Since high-level infinities are interesting, it would be odd if we were not allowed to discuss them. |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| Full Idea: I classify conceptualists according to what they say about properties or concepts. If someone classified properties as existing independent of language I would classify her as a realist in ontology of mathematics. Or they may be idealists or nominalists. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 2.2.1) | |
| A reaction: In other words, Shapiro wants to eliminate 'conceptualist' as a useful label in philosophy of mathematics. He's probably right. All thought involves concepts, but that doesn't produce a conceptualist theory of, say, football. |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| Full Idea: A definition of a mathematical entity is 'impredicative' if it refers to a collection that contains the defined entity. The definition of 'least upper bound' is impredicative as it refers to upper bounds and characterizes a member of this set. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: The big question is whether mathematics can live with impredicative definitions, or whether they threaten to be viciously circular, and undermine the whole enterprise. |
| 7079 | Nietzsche resists nihilism through new values, for a world of becoming, without worship [Nietzsche, by Critchley] |
| Full Idea: Nietzsche's work is a resistance to nihilism. This is why he insists that new categories and values are required that would permit us to endure this world of becoming without either falling into despair or inventing some new god and bowing before it. | |
| From: report of Friedrich Nietzsche (Beyond Good and Evil [1886]) by Simon Critchley - Continental Philosophy - V. Short Intro | |
| A reaction: The trouble is that all Nietzsche offers is the invention of values out of nothing by some wretched Germanic übermensch who is obsessed with militarism and dominance. If values don't grow out of human nature, then 'all is permitted'. |
| 21982 | I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L] |
| Full Idea: "I see nobody on the road," said Alice. - "I only wish I had such eyes," the King remarked. ..."To be able to see Nobody! ...Why, it's as much as I can do to see real people." | |
| From: Lewis Carroll (C.Dodgson) (Through the Looking Glass [1886], p.189), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7 | |
| A reaction: [Moore quotes this, inevitably, in a chapter on Hegel] This may be a better candidate for the birth of philosophy of language than Frege's Groundwork. |
| 2878 | We see an approximation of a tree, not the full detail [Nietzsche] |
| Full Idea: We do not see a tree exactly and entire with regard to its leaves, branches, colour and shape; it is so much easier for us to see an approximation of a tree. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §192) |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| Full Idea: Rationalism is a long-standing school that can be characterized as an attempt to extend the perceived methodology of mathematics to all of knowledge. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.1) | |
| A reaction: Sometimes called 'Descartes's Dream', or the 'Enlightenment Project', the dream of proving everything. Within maths, Hilbert's Programme aimed for the same certainty. Idea 22 is the motto for the opposition to this approach. |
| 20140 | We shouldn't object to a false judgement, if it enhances and preserves life [Nietzsche] |
| Full Idea: The falseness of a judgement is to us not necessarily an objection to a judgement. To what extent is it life-advancing, life-preserving, species-preserving. Our fundamental tendency is to assert that our falsest judgements are the most indispensable. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §004) | |
| A reaction: This is the standard objection to pragmatism, that what is false may still be useful, and that clever blighter Nietzsche embraces the idea! |
| 2877 | Morality becomes a problem when we compare many moralities [Nietzsche] |
| Full Idea: The real problems of morality come into view only if we compare many moralities. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §186) |
| 20355 | The ranking of a person's innermost drives reveals their true nature [Nietzsche] |
| Full Idea: To know 'who he is', we must know the order of rank the innermost drives of his nature stand in relative to one another. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §006) | |
| A reaction: This is clearly an essentialist view of a person, as having a 'nature', which is 'inner', and which we can try to specify. Ranking drives and values seems a good proposal for getting at it. I'm also intrigued by what people find interesting. |
| 2291 | A thought comes when 'it' wants, not when 'I' want [Nietzsche] |
| Full Idea: A thought comes when 'it' wants, not when 'I' want. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §017) | |
| A reaction: A wonderful remark (which I have since found in Schopenhauer). I don't see how the most enthusiastic free will libertarian can deny it. |
| 2871 | Wanting 'freedom of will' is wanting to pull oneself into existence out of the swamp of nothingness by one's own hair [Nietzsche] |
| Full Idea: The desire for 'freedom of will' is nothing less than the desire to pull oneself into existence out of the swamp of nothingness by one's own hair. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §021) |
| 20381 | It is psychology which reveals the basic problems [Nietzsche] |
| Full Idea: Psychology is now once again the road to the fundamental problems. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §023) | |
| A reaction: This may become the epigraph of my great book, which will have as working title 'The Psychology of Metaphysics'. If you trawl through this collection, you will see where I am going! (A tough job, but easier than reading Hegel). |
| 2860 | The most boring and dangerous of all errors is Plato's invention of pure spirit and goodness [Nietzsche] |
| Full Idea: The worst, most wearisomely protracted and most dangerous of all errors hitherto has been a dogmatist's error, namely Plato's invention of pure spirit and the good in itself. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], Pref) | |
| A reaction: A landmark observation about the history of philosophy. Imagine if all the Aristotle had survived, but all the Plato had been lost. |
| 1568 | Nietzsche felt that Plato's views downgraded the human body and its brevity of life [Nietzsche, by Roochnik] |
| Full Idea: Nietzsche believed that by elevating the importance of the mind, Plato downplayed the wonders of the body, and by searching for a timeless Truth he degraded the indisputable fact of human temporality. | |
| From: report of Friedrich Nietzsche (Beyond Good and Evil [1886], Pref) by David Roochnik - The Tragedy of Reason Prol. X | |
| A reaction: Both ideas are very important. The second is widely misunderstood. Nietzsche was not a denier of truth. He asked us to scrutinise the role and value we assign to truth. |
| 2883 | Noble people see themselves as the determiners of values [Nietzsche] |
| Full Idea: The noble type of man feels himself to be the determiner of values. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §260) | |
| A reaction: So do criminals |
| 23440 | Nietzsche's judgement of actions by psychology instead of outcome was poisonous [Foot on Nietzsche] |
| Full Idea: Nietzsche wants to judge actions not by what is done, but by the nature of the person who does them, and that is poisonous. We have to be horrified by what is done by Hitler and Stalin, without inquiring into their psychology. | |
| From: comment on Friedrich Nietzsche (Beyond Good and Evil [1886]) by Philippa Foot - Interview with Philippa Foot p.37 | |
| A reaction: She says morality should focus on social needs, not on spontaneity, energy and passion. Nietzsche was very much a product of romanticism. Some of Nietzsche's heroes are military conquerors, so I think she is right. |
| 2875 | That which is done out of love always takes place beyond good and evil [Nietzsche] |
| Full Idea: That which is done out of love always takes place beyond good and evil. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §153) | |
| A reaction: He is referring to the conventional morality of his contemporary society. Nietzsche clearly thought that actions motivated by love are intrinsically good. (Apart from murders by the jealous!). |
| 2868 | Nature is totally indifferent, so you should try to be different from it, not live by it [Nietzsche] |
| Full Idea: You Stoics want to "live according to nature"? Oh you noble Stoics, what fraudulent words! Nature is prodigal and indifferent beyond measure - how could you live by such indifference? Living is wanting to be other than nature. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §009) | |
| A reaction: I think this is simply indicative of the slide from optimism to pessimism about nature in the intervening centuries. Stoics thought nature rational. See 'King Lear' for the transition. |
| 2882 | Morality originally judged people, and actions only later on [Nietzsche] |
| Full Idea: Designation of moral values was everywhere first applied to human beings, and only later and derivatively to actions. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §260) | |
| A reaction: Nietzsche was a great expert on ethics in the ancient world, so you should trust him on this one. In ordinary life assessment of people is what counts. Actions are for law courts. |
| 2872 | In the earliest phase of human history only consequences mattered [Nietzsche] |
| Full Idea: Throughout the longest part of history ('prehistoric times') the value or non-value of an action was derived from its consequences. …but now men are unanimous that the value of an action is in the intention behind it. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §032) | |
| A reaction: This seems to be Kant's fault. No one thinks that a reckless or malicios action is innocent if no actual harm results. |
| 2885 | The noble soul has reverence for itself [Nietzsche] |
| Full Idea: The noble soul has reverence for itself. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §287) |
| 20134 | Moralities extravagantly address themselves to 'all', by falsely generalising [Nietzsche] |
| Full Idea: All moralities are baroque and unreasonable ...because they address themselves to 'all', because they generalise where one must not generalise. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §198) | |
| A reaction: 'Particularism' is a recent label, but one finds passing remarks from many earlier philosophers which support that approach to ethics. No one was ever more opposed to strict moral rules than Nietzsche. |
| 2881 | Virtue has been greatly harmed by the boringness of its advocates [Nietzsche] |
| Full Idea: May I be forgiven for the discovery that 'virtue' has been harmed by nothing more than it has been by the boringness of its advocates. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §228) |
| 20382 | The four virtues are courage, insight, sympathy, solitude [Nietzsche] |
| Full Idea: To remain master of one's four virtues: courage, insight, sympathy, solitude. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §284) | |
| A reaction: Compare this with 'Daybreak (Dawn)' 556. Solitude is the surprising addition, defended as the urge to 'cleanliness', when since humanity is 'unclean'. |
| 2879 | In ancient Rome pity was considered neither good nor bad [Nietzsche] |
| Full Idea: An act of pity was during the finest age of Rome considered neither good nor bad. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §201) |
| 2859 | The idea of the categorical imperative is just that we should all be very obedient [Nietzsche] |
| Full Idea: What does the claim that there exists in us a categorical imperative say of the man who asserts it? …that 'what is worthy of respect in me is that I know how to obey - and things ought to be no different with you'. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §187) |
| 2884 | The morality of slaves is the morality of utility [Nietzsche] |
| Full Idea: Slave morality is essentially the morality of utility. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §261) |
| 2880 | The greatest possibilities in man are still unexhausted [Nietzsche] |
| Full Idea: The greatest possibilities in man are still unexhausted. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §203) |
| 2876 | The thought of suicide is a great reassurance on bad nights [Nietzsche] |
| Full Idea: The thought of suicide is a powerful solace: by means of it one gets through many a bad night. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §157) |
| 7078 | The freedom of the subject means the collapse of moral certainty [Nietzsche, by Critchley] |
| Full Idea: In the 1880s Nietzsche diagnosed the concept of nihilism for a whole range of continental thinkers: the recognition of the subject's freedom goes hand in hand with the collapse of moral certainty in the world. | |
| From: report of Friedrich Nietzsche (Beyond Good and Evil [1886]) by Simon Critchley - Continental Philosophy - V. Short Intro Ch.5 | |
| A reaction: Avoiding this dilemma is just one of the many bonuses offered to those who abandon the idea of free will. The fact that one can decide to be wicked doesn't bring an end to morality. Philosophers should think more concretely about human life. |
| 2874 | Man is the animal whose nature has not yet been fixed [Nietzsche] |
| Full Idea: Man is the animal whose nature has not yet been fixed. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §062) |
| 6869 | Nietzsche thinks the human condition is to overcome and remake itself [Nietzsche, by Ansell Pearson] |
| Full Idea: Nietzsche thinks that the human condition is precisely to overcome itself; we continually remake ourselves. | |
| From: report of Friedrich Nietzsche (Beyond Good and Evil [1886]) by Keith Ansell Pearson - Interview with Baggini and Stangroom p.261 | |
| A reaction: This is why I think of Nietzsche as a straightforwardly existentialist philosopher. There is a crucial distinction between 'remaking' ourselves and 'realising all our possibilities'. The latter seems right. Which view did Nietzsche take? |
| 20137 | The great person engages wholly with life, and is happy to endlessly relive the life they created [Nietzsche] |
| Full Idea: There is an ideal ...of the most exuberant, most living and most world-affirming man, who has not only learned to get on and treat with all that was and is, but who wants to have it again as it was and is to all eternity. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §056) | |
| A reaction: This seems to be the main point of the idea of eternal recurrence. Could we inculcate this vision into the teenagers of our nation - that they should each try to design for themselves a life which they would be happy to endlessly repeat? Hm. |
| 20139 | Only aristocratic societies can elevate the human species [Nietzsche] |
| Full Idea: Every elevation of the type 'man' has thitherto been the work of an aristocratic society - and so it will always be: a society which believes in a long scale of orders of rank and differences of worth between man and man, and needs slavery in some sense. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §257) | |
| A reaction: The aim of 'elevating the type "man"' does not figure in works of political philosophy very much! I doubt whether one could base a political party on the idea, and win a general election. Could the people still be sold the idea of aristocracy? |
| 20373 | A healthy aristocracy has no qualms about using multitudes of men as instruments [Nietzsche] |
| Full Idea: A good and healthy aristocracy ...accepts with a good conscience the sacrifice of innumerable men who for its sake have to be suppressed and reduced to imperfect men, to slaves and instruments. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §258) | |
| A reaction: Something similar might be said of a democracy - that a slavelike workforce is needed to create the great universal goods we all want and need. Do the aristocrats want sacrifices for great art, or for wild parties and fox hunting? |
| 22394 | Democracy diminishes mankind, making them mediocre and lowering their value [Nietzsche] |
| Full Idea: To us the democratic movement is ...a form of decay, namely the diminution, of man, making him mediocre and lowering his value. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], §203), quoted by Philippa Foot - Nietzsche: the Revaluation of Values p.88 | |
| A reaction: It is not clear how a society of natural aristocrats followed by sheep would increase the value of mankind. Nor if the talented people are given total freedom, and the rest of us are servants. The value of humanity cannot reside in a few individuals. |
| 2867 | Christianity is Platonism for the people [Nietzsche] |
| Full Idea: Christianity is Platonism for the people. | |
| From: Friedrich Nietzsche (Beyond Good and Evil [1886], Pref) |