49 ideas
| 14888 | Wisdom prevents us from being ruled by the moment [Nietzsche] |
| Full Idea: The most important thing about wisdom is that it prevents human beings from being ruled by the moment. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 30 [25]) |
| 14863 | Unlike science, true wisdom involves good taste [Nietzsche] |
| Full Idea: Inherent in wisdom [sophia] is discrimination, the possession of good taste: whereas science, lacking such a refined sense of taste, gobbles up anything that is worth knowing. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [086]) | |
| A reaction: This is blatantly unfair to science, which may lack 'taste', but at least prefers deep theories with wide-ranging explanatory power to narrow local theories. Maybe the line across the philosophical community is the one picking out those with taste? |
| 14890 | Suffering is the meaning of existence [Nietzsche] |
| Full Idea: Suffering is the meaning of existence. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 32 [67]) | |
| A reaction: This doesn't mean that he is advocating suffering. The context of his remark is that the pursuit of truth involves suffering. |
| 14861 | Philosophy ennobles the world, by producing an artistic conception of our knowledge [Nietzsche] |
| Full Idea: Philosophy is indispensable for education because it draws knowledge into an artistic conception of the world, and thereby ennobles it. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [052]) | |
| A reaction: I take this to be an unusual way of saying that philosophy aims at the unification of knowledge, which is roughly my own view. It has hard for us to keep believing that life could be 'ennobled'. |
| 14885 | The first aim of a philosopher is a life, not some works [Nietzsche] |
| Full Idea: The philosopher's product is his life (first, before his works). It is his work of art. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 29 [205]) |
| 14887 | You should only develop a philosophy if you are willing to live by it [Nietzsche] |
| Full Idea: One should have a philosophy only to the extent that one is capable of living according to this philosophy: so that everything does not become mere words. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 30 [17]) |
| 14889 | Philosophy is pointless if it does not advocate, and live, a new way of life [Nietzsche] |
| Full Idea: As long as philosophers do not muster the courage to advocate a lifestyle structured in an entirely different way and demonstrate it by their own example, they will come to nothing. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 31 [10]) | |
| A reaction: This is a pretty tough requirement for the leading logicians and metaphysicians of our day, but they must face their marginality. The public will only be interested in philosophers who advocate new ways of living. |
| 14862 | Philosophy is more valuable than much of science, because of its beauty [Nietzsche] |
| Full Idea: The reason why unprovable philosophizing still has some value - more value, in fact, than many a scientific proposition - lies in the aesthetic value of such philosophizing, that is, in its beauty and sublimity. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [076]) | |
| A reaction: I am increasingly inclined to agree. I love wide-ranging and ambitious works of metaphysics, each of which is a unique creation of the human intellect (and with which no other individual will ever entirely agree). A great short paper is also beautiful. |
| 14876 | Philosophy is always secondary, because it cannot support a popular culture [Nietzsche] |
| Full Idea: It is not possible to base a popular culture on philosophy. Thus, with regard to culture, philosophy never can have primary, but always only secondary, significance. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 23 [14]) | |
| A reaction: It is the brilliance of Christianity as a set of ideas that it is simple enough to found a popular culture. A complex theology would make that impossible. Luther brought it back to its roots, when the priesthood lost touch with the people. |
| 14878 | It would better if there was no thought [Nietzsche] |
| Full Idea: It would be better if thought did not exist at all. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 29 [004]) |
| 14881 | Why do people want philosophers? [Nietzsche] |
| Full Idea: Why do human beings even want philosophers? | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 29 [019]) | |
| A reaction: It is not clear, of course, that they do want philosophers. The standard attitude to them seems to be a mixture of contempt and fear. |
| 14860 | Kant has undermined our belief in metaphysics [Nietzsche] |
| Full Idea: In a certain sense, Kant's influence was detrimental; for the belief in metaphysics has been lost. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [028]) | |
| A reaction: As I understand it, there are two interpretations of Kant, one of which is fairly thoroughly anti-metaphysical, and another which is less so. Also one path leads to idealism and the other doesn't, but I need to research that. |
| 14859 | If philosophy controls science, then it has to determine its scope, and its value [Nietzsche] |
| Full Idea: The philosophy that is in control of science must also consider the extent to which science should be allowed to develop; it must determine its value! | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [024]) |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| Full Idea: While truth can be defined in a relative way, as truth in one particular model, a non-relative notion of truth is implied, as truth in all models. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: [The article is actually discussing arithmetic] This idea strikes me as extremely important. True-in-all-models is usually taken to be tautological, but it does seem to give a more universal notion of truth. See semantic truth, Tarski, Davidson etc etc. |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| Full Idea: In standard ZFC ('Zermelo-Fraenkel with Choice') set theory we deal merely with pure sets, not with additional urelements. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: The 'urelements' would the actual objects that are members of the sets, be they physical or abstract. This idea is crucial to understanding philosophy of mathematics, and especially logicism. Must the sets exist, just as the urelements do? |
| 14880 | Logic is just slavery to language [Nietzsche] |
| Full Idea: Logic is merely slavery in the fetters of language. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 29 [008]) | |
| A reaction: I don't think I agree with this, but I still like it. |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| Full Idea: In second-order logic there are three kinds of variables, for objects, for functions, and for predicates or sets. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: It is interesting that a predicate seems to be the same as a set, which begs rather a lot of questions. For those who dislike second-order logic, there seems nothing instrinsically wicked in having variables ranging over innumerable multi-order types. |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| Full Idea: 'Analysis' is the theory of the real numbers. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: 'Analysis' began with the infinitesimal calculus, which later built on the concept of 'limit'. A continuum of numbers seems to be required to make that work. |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| Full Idea: The difficulties for a nominalistic mereological approach to arithmetic is that an infinity of physical objects are needed (space-time points? strokes?), and it must define functions, such as 'successor'. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: Many ontologically austere accounts of arithmetic are faced with the problem of infinity. The obvious non-platonist response seems to be a modal or if-then approach. To postulate infinite abstract or physical entities so that we can add 3 and 2 is mad. |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| Full Idea: A common formulation of Peano Arithmetic uses 2nd-order logic, the constant '1', and a one-place function 's' ('successor'). Three axioms then give '1 is not a successor', 'different numbers have different successors', and induction. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: This is 'second-order' Peano Arithmetic, though it is at least as common to formulate in first-order terms (only quantifying over objects, not over properties - as is done here in the induction axiom). I like the use of '1' as basic instead of '0'! |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| Full Idea: The merits of basing an account of mathematics on set theory are that it allows for a comprehensive unified treatment of many otherwise separate branches of mathematics, and that all assumption, including existence, are explicit in the axioms. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I am forming the impression that set-theory provides one rather good model (maybe the best available) for mathematics, but that doesn't mean that mathematics is set-theory. The best map of a landscape isn't a landscape. |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| Full Idea: Structuralism has emerged from the development of abstract algebra (such as group theory), the creation of axiom systems, the introduction of set theory, and Bourbaki's encyclopaedic survey of set theoretic structures. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: In other words, mathematics has gradually risen from one level of abstraction to the next, so that mathematical entities like points and numbers receive less and less attention, with relationships becoming more prominent. |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| Full Idea: Relativist Structuralism simply picks one particular model of axiomatised arithmetic (i.e. one particular interpretation that satisfies the axioms), and then stipulates what the elements, functions and quantifiers refer to. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: The point is that a successful model can be offered, and it doesn't matter which one, like having any sort of aeroplane, as long as it flies. I don't find this approach congenial, though having a model is good. What is the essence of flight? |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| Full Idea: The term 'structure' has two uses in the literature, what can be called 'particular structures' (which are particular relational systems), but also what can be called 'universal structures' - what particular systems share, or what they instantiate. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §6) | |
| A reaction: This is a very helpful distinction, because it clarifies why (rather to my surprise) some structuralists turn out to be platonists in a new guise. Personal my interest in structuralism has been anti-platonist from the start. |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| Full Idea: According to 'pattern' structuralism, what we study are not the various particular isomorphic models of arithmetic, but something in addition to them: a corresponding pattern. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §7) | |
| A reaction: Put like that, we have to feel a temptation to wield Ockham's Razor. It's bad enough trying to give the structure of all the isomorphic models, without seeking an even more abstract account of underlying patterns. But patterns connect to minds.. |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| Full Idea: There are four main variants of structuralism in the philosophy of mathematics - formalist structuralism, relativist structuralism, universalist structuralism (with modal variants), and pattern structuralism. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §9) | |
| A reaction: I'm not sure where Chihara's later book fits into this, though it is at the nominalist end of the spectrum. Shapiro and Resnik do patterns (the latter more loosely); Hellman does modal universalism; Quine does the relativist version. Dedekind? |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| Full Idea: Formalist Structuralism endorses structural methodology in mathematics, but rejects semantic and metaphysical problems as either meaningless, or purely formal, or as inference relations. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §3) | |
| A reaction: [very compressed] I find the third option fairly congenial, certainly in preference to rather platonist accounts of structuralism. One still needs to distinguish the mathematical from the non-mathematical in the inference relations. |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| Full Idea: It is tempting to take a modal turn, and quantify over all possible objects, because if there are only a finite number of actual objects, then there are no models (of the right sort) for Peano Arithmetic, and arithmetic is vacuously true. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: [compressed; Geoffrey Hellman is the chief champion of this view] The article asks whether we are not still left with the puzzle of whether infinitely many objects are possible, instead of existent. |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| Full Idea: Universalist Structuralism is a semantic thesis, that an arithmetical statement asserts a universal if-then statement. We build an if-then statement (using quantifiers) into the structure, and we generalise away from any one particular model. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: There remains the question of what is distinctively mathematical about the highly generalised network of inferences that is being described. Presumable the axioms capture that, but why those particular axioms? Russell is cited as an originator. |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| Full Idea: Universalist Structuralism is eliminativist about abstract objects, in a distinctive form. Instead of treating the base element (say '1') as an ambiguous referring expression (the Relativist approach), it is a variable which is quantified out. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: I am a temperamental eliminativist on this front (and most others) so this is tempting. I am also in love with the concept of a 'variable', which I take to be utterly fundamental to all conceptual thought, even in animals, and not just a trick of algebra. |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| Full Idea: Relativist Structuralism must first assume the existence of an infinite set, otherwise there would be no model to pick, and arithmetical terms would have no reference. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: See Idea 10169 for Relativist Structuralism. They point out that ZFC has an Axiom of Infinity. |
| 14869 | If some sort of experience is at the root of matter, then human knowledge is close to its essence [Nietzsche] |
| Full Idea: If pleasure, displeasure, sensation, memory, reflex movements are all part of the essence of matter, then human knowledge penetrates far more deeply into the essence of things. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [161]) | |
| A reaction: I don't think Nietzsche is thinking of monads at this point, but his idea certainly applies to them. Leibniz rested his whole theory on the close analogy between how minds work and how matter must also work. |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| Full Idea: One way for a nominalist to reject appeal to all abstract objects, including sets, is to only appeal to nominalistically acceptable objects, including mereological sums. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I'm suddenly thinking that this looks very interesting and might be the way to go. The issue seems to be whether mereological sums should be seen as constrained by nature, or whether they are unrestricted. See Mereology in Ontology...|Intrinsic Identity. |
| 14875 | Belief matters more than knowledge, and only begins when knowledge ceases [Nietzsche] |
| Full Idea: The human being starts to believe when he ceases to know. …Knowledge is not as important for the welfare of human beings as is belief. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 21 [13]) | |
| A reaction: The first idea is now associated with Williamson (and Hossack). The second is something like the pragmatic view of belief espoused by Ramsey. |
| 14866 | It always remains possible that the world just is the way it appears [Nietzsche] |
| Full Idea: Against Kant we can still object, even if we accept all his propositions, that it is still possible that the world is as it appears to us. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [125]) | |
| A reaction: This little thought at least seems to be enough to block the slide from phenomenalism into total idealism. The idea that direct realism can never be ruled out, even if it is false, is very striking. |
| 14872 | Our knowledge is illogical, because it rests on false identities between things [Nietzsche] |
| Full Idea: Every piece of knowledge that is beneficial to us involves an identification of nonidentical things, of things that are similar, which means that it is essentially illogical. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [236]) | |
| A reaction: I take the thought to be that no two tigers are alike, but we call them all 'tigers' and merge them into a type, and then all our knowledge is based on this distortion. A wonderful idea. I love particulars You should love particulars. |
| 14879 | The most extreme scepticism is when you even give up logic [Nietzsche] |
| Full Idea: Even skepticism contains a belief: the belief in logic. The most extreme position is hence the abandoning of logic. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 29 [008]) | |
| A reaction: Some might say that flirting with non-classical logic (as in Graham Priest) is precisely travelling down this road. You could also be sceptical about meaning in language, so you couldn't articulate your abandonment of logic. |
| 14873 | If we find a hypothesis that explains many things, we conclude that it explains everything [Nietzsche] |
| Full Idea: The feeling of certainty is the most difficult to develop. Initially one seeks explanation: if a hypothesis explains many things, we draw the conclusion that it explains everything. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [238]) | |
| A reaction: As so often, a wonderful warning from Nietzsche to other philosophers. They love to latch onto a Big Idea, and offer it as the answer to everything (especially, dare I say it, continental philosophers). |
| 14868 | Our primary faculty is perception of structure, as when looking in a mirror [Nietzsche] |
| Full Idea: The primary faculty seems to me to be the perception of structure, that is, based upon the mirror. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [153]) | |
| A reaction: The point about the mirror makes this such an intriguingly original idea. Personally I like very much the idea that structure is our prime perception. See Sider 2011 on structure. |
| 14870 | We experience causation between willing and acting, and thereby explain conjunctions of changes [Nietzsche] |
| Full Idea: The only form of causality of which we are aware is that between willing and acting - we transfer this to all things, and thereby explain the relationship between two changes that always occur together. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [209]) | |
| A reaction: This is a rather Humean view, of projecting our experience onto the world, but it may be that we really are experiencing real causation, just as it occurs between insentiate things. |
| 12727 | It's impossible, but imagine a body carrying on normally, but with no mind [Leibniz] |
| Full Idea: If it could be supposed that a body exists without a mind, then a man would do everything in the same way as if he did not have a mind, and men would speak and write the same things, without knowing what they do. ...But this supposition is impossible. | |
| From: Gottfried Leibniz (Paper of December 1676 [1676], A6.3.400), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 5 | |
| A reaction: This is clearly the zombie dream, three centuries before Robert Kirk's modern invention of the idea. Leibniz's reason for denying the possibility of zombies won't be the modern physicalist reason. |
| 14867 | It is just madness to think that the mind is supernatural (or even divine!) [Nietzsche] |
| Full Idea: To view 'spirit', the product of the brain, as supernatural. Even to deify it. What madness! | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [127]) | |
| A reaction: When I started philolosophy I was obliged to take mind-body dualism very seriously, but I have finally managed to drag myself to the shores of this lake of madness, where Nietzsche awaited with a helping hand. |
| 14884 | The shortest path to happiness is forgetfulness, the path of animals (but of little value) [Nietzsche] |
| Full Idea: If happiness were the goal, then animals would be the highest creatures. Their cynicism is grounded in forgetfulness: that is the shortest path to happiness, even if it is a happiness with little value. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 29 [143]) | |
| A reaction: I would be reluctant to describe an apparently contented cow as 'happy'. Is a comatose person happy? Maybe happiness is fulfilling one's nature, like a monkey swinging through trees? |
| 14886 | Education is contrary to human nature [Nietzsche] |
| Full Idea: Education runs contrary to the nature of a human being. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 30 [06]) | |
| A reaction: Tell me about it! |
| 14883 | We should evaluate the past morally [Nietzsche] |
| Full Idea: For the past I desire above all a moral evaluation. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 29 [096]) | |
| A reaction: There is a bit of a contradiction with Idea 14819, of only a few years later. He was always interested in a historical approach to morality, but I'm not sure if his ethics gives a decent basis for moral assessments of remote historical eras. |
| 14882 | Protest against vivisection - living things should not become objects of scientific investigation [Nietzsche] |
| Full Idea: Protest against vivisection of living things, that is, those things that are not yet dead should be allowed to live and not immediately be treated as an object for scientific investigation. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 29 [027]) | |
| A reaction: Wow. How many other people had come up with this idea in 1873? |
| 14865 | We do not know the nature of one single causality [Nietzsche] |
| Full Idea: We do not know the nature of one single causality. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [121]) |
| 14871 | Laws of nature are merely complex networks of relations [Nietzsche] |
| Full Idea: All laws of nature are only relations between x, y and z. We define laws of nature as relations to an x, y, and z, each of which in turn, is known to us only in relation to other x's, y's and z's. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [235]) | |
| A reaction: This could be interpreted in Armstrong's terms, as only identifying the x's, y's and z's by their universals, and then seeing laws as how those universal relate. I suspect, though, that Nietzsche has a Humean regularity pattern in mind. |
| 14864 | The Greeks lack a normative theology: each person has their own poetic view of things [Nietzsche] |
| Full Idea: The Greeks lack a normative theology: everyone has the right to deal with it in a poetic manner and he can believe whatever he wants. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [110]) | |
| A reaction: There is quite a lot of record of harshness towards atheists, and the trial of Socrates seems to have been partly over theology. However, no proper theological texts have come down, or records of the teachings of the priests. |