53 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| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 30 [25]) |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| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [086]) | |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| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 32 [67]) | |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| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [052]) | |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| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 29 [205]) |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| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 30 [17]) |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. |
| 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. |
| 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. |
| 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]) |
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| Full Idea: The intuitionist rejection of double negation elimination undermines the important reductio ad absurdum proof in classical mathematics. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3) |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| Full Idea: In intuitionist logic double negation elimination fails. After all, proving that there is no proof that there can't be a proof of S is not the same thing as having a proof of S. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3) | |
| A reaction: I do like people like Colyvan who explain things clearly. All of this difficult stuff is understandable, if only someone makes the effort to explain it properly. |
| 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. |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| Full Idea: The law of excluded middle (for every proposition P, either P or not-P) must be carefully distinguished from its semantic counterpart bivalence, that every proposition is either true or false. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3) | |
| A reaction: So excluded middle makes no reference to the actual truth or falsity of P. It merely says P excludes not-P, and vice versa. |
| 17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
| Full Idea: Löwenheim proved that if a first-order sentence has a model at all, it has a countable model. ...Skolem generalised this result to systems of first-order sentences. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 2.1.2) |
| 17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
| Full Idea: A set of axioms is said to be 'categorical' if all models of the axioms in question are isomorphic. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 2.1.2) | |
| A reaction: The best example is the Peano Axioms, which are 'true up to isomorphism'. Set theory axioms are only 'quasi-isomorphic'. |
| 17928 | Ordinal numbers represent order relations [Colyvan] |
| Full Idea: Ordinal numbers represent order relations. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.2.3 n17) |
| 17923 | Intuitionists only accept a few safe infinities [Colyvan] |
| Full Idea: For intuitionists, all but the smallest, most well-behaved infinities are rejected. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3) | |
| A reaction: The intuitionist idea is to only accept what can be clearly constructed or proved. |
| 17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
| Full Idea: The problem with infinitesimals is that in some places they behaved like real numbers close to zero but in other places they behaved like zero. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 7.1.2) | |
| A reaction: Colyvan gives an example, of differentiating a polynomial. |
| 17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
| Full Idea: Given Dedekind's reduction of real numbers to sequences of rational numbers, and other known reductions in mathematics, it was tempting to see basic arithmetic as the foundation of mathematics. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.1) | |
| A reaction: The reduction is the famous Dedekind 'cut'. Nowadays theorists seem to be more abstract (Category Theory, for example) instead of reductionist. |
| 17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
| Full Idea: Transfinite inductions are inductive proofs that include an extra step to show that if the statement holds for all cases less than some limit ordinal, the statement also holds for the limit ordinal. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1 n11) |
| 17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
| Full Idea: Most mathematical proofs, outside of set theory, do not explicitly state the set theory being employed. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 7.1.1) |
| 17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
| Full Idea: Structuralism is able to explain why mathematicians are typically only interested in describing the objects they study up to isomorphism - for that is all there is to describe. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 3.1.2) |
| 17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
| Full Idea: In re structuralism does not posit anything other than the kinds of structures that are in fact found in the world. ...The problem is that the world may not provide rich enough structures for the mathematics. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 3.1.2) | |
| A reaction: You can perceive a repeating pattern in the world, without any interest in how far the repetitions extend. |
| 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. |
| 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. |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| Full Idea: Those who see probabilities as ratios of frequencies can't use Bayes's Theorem if there is no objective prior probability. Those who accept prior probabilities tend to opt for a subjectivist account, where probabilities are degrees of belief. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 9.1.8) | |
| A reaction: [compressed] |
| 17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
| Full Idea: Mathematics can demonstrate structural similarities between systems (e.g. missing population periods and the gaps in the rings of Saturn). | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 6.3.2) | |
| A reaction: [Colyvan expounds the details of his two examples] It is these sorts of results that get people enthusiastic about the mathematics embedded in nature. A misunderstanding, I think. |
| 17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
| Full Idea: Mathematics can show that under a broad range of conditions, something initially surprising must occur (e.g. the hexagonal structure of honeycomb). | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 6.3.2) |
| 17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
| Full Idea: Another style of proof often cited as unexplanatory are brute-force methods such as proof by cases (or proof by exhaustion). | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1) |
| 17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
| Full Idea: One kind of proof that is thought to be unexplanatory is the 'reductio' proof. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1) | |
| A reaction: Presumably you generate a contradiction, but are given no indication of why the contradiction has arisen? Tracking back might reveal the source of the problem? Colyvan thinks reductio can be explanatory. |
| 17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
| Full Idea: It might be argued that any proof by induction is revealing the explanation of the theorem, namely, that it holds by virtue of the structure of the natural numbers. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1) | |
| A reaction: This is because induction characterises the natural numbers, in the Peano Axioms. |
| 17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
| Full Idea: The proof of the four-colour theorem raises questions about whether a 'proof' that no one understands is a proof. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 9.1.6) | |
| A reaction: The point is that the theorem (that you can colour countries on a map with just four colours) was proved with the help of a computer. |
| 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. |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| Full Idea: One type of generalisation in mathematics extends a system to go beyond what is was originally set up for; another kind involves abstracting away from some details in order to capture similarities between different systems. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.2) |
| 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. |
| 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! |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 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. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |
| 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. |