47 ideas
| 20121 | Grammar only reveals popular metaphysics [Nietzsche] |
| Full Idea: The snares of grammar are the metaphysics of the people. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
| A reaction: If you have this elitist view of metaphysics, then linguistic analysis is just a branch of anthropology. |
| 8623 | Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege] |
| Full Idea: Euclid gives proofs of many things which anyone would concede to him without question. ...The aim of proof is not merely to place the truth of a proposition beyond doubt, but also to afford us insight into the dependence of truths upon one another. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §02 | |
| A reaction: This connects nicely with Shoemaker's view of analysis (Idea 8559), which I will adopt as my general view. I've always thought of philosophy as the aspiration to wisdom through the cartography of concepts. |
| 24082 | Is the will to truth the desire to avoid deception? [Nietzsche] |
| Full Idea: This unconditional will to truth: what is it? Is it the will not to let oneself be deceived? Is it the will not to deceive? | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §344) | |
| A reaction: He is hunting for the evolutionary origin of the love of truth, in the needs of a community. In that sense, I would have thought it was just the pressure to get the facts right, because error is dangerous. Nice thought, though. |
| 13907 | If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon] |
| Full Idea: Euclid begins proofs about all triangles with 'let ABC be a triangle', but ABC is not a proper name. It names an arbitrarily selected triangle, and if that has a property, then we can conclude that all triangles have the property. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by E.J. Lemmon - Beginning Logic 3.2 | |
| A reaction: Lemmon adds the proviso that there must be no hidden assumptions about the triangle we have selected. You must generalise the properties too. Pick a triangle, any triangle, say one with three angles of 60 degrees; now generalise from it. |
| 6297 | Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik] |
| Full Idea: Euclid's geometry is a synthetic geometry; Descartes supplied an analytic version of Euclid's geometry, and we now have analytic versions of the early non-Euclidean geometries. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Michael D. Resnik - Maths as a Science of Patterns One.4 | |
| A reaction: I take it that the original Euclidean axioms were observations about the nature of space, but Descartes turned them into a set of pure interlocking definitions which could still function if space ceased to exist. |
| 9603 | An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR] |
| Full Idea: Assume a largest prime, then multiply the primes together and add one. The new number isn't prime, because we assumed a largest prime; but it can't be divided by a prime, because the remainder is one. So only a larger prime could divide it. Contradiction. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by James Robert Brown - Philosophy of Mathematics Ch.1 | |
| A reaction: Not only a very elegant mathematical argument, but a model for how much modern logic proceeds, by assuming that the proposition is false, and then deducing a contradiction from it. |
| 9894 | A unit is that according to which each existing thing is said to be one [Euclid] |
| Full Idea: A unit is that according to which each existing thing is said to be one. | |
| From: Euclid (Elements of Geometry [c.290 BCE], 7 Def 1) | |
| A reaction: See Frege's 'Grundlagen' §29-44 for a sustained critique of this. Frege is good, but there must be something right about the Euclid idea. If I count stone, paper and scissors as three, each must first qualify to be counted as one. Psychology creeps in. |
| 8738 | Postulate 2 says a line can be extended continuously [Euclid, by Shapiro] |
| Full Idea: Euclid's Postulate 2 says the geometer can 'produce a finite straight line continuously in a straight line'. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Stewart Shapiro - Thinking About Mathematics 4.2 | |
| A reaction: The point being that this takes infinity for granted, especially if you start counting how many points there are on the line. The Einstein idea that it might eventually come round and hit you on the back of the head would have charmed Euclid. |
| 22278 | Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid] |
| Full Idea: Euclid's axioms were insufficient to derive all the theorems of geometry: at various points in his proofs he appealed to properties that are obvious from the diagrams but do not follow from the stated axioms. | |
| From: comment on Euclid (Elements of Geometry [c.290 BCE]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 03 'aim' | |
| A reaction: I suppose if the axioms of a system are based on self-evidence, this would licence an appeal to self-evidence elsewhere in the system. Only pedants insist on writing down what is obvious to everyone! |
| 8673 | Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend] |
| Full Idea: Euclid's fifth 'parallel' postulate says if there is an infinite straight line and a point, then there is only one straight line through the point which won't intersect the first line. This axiom is independent of Euclid's first four (agreed) axioms. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Michèle Friend - Introducing the Philosophy of Mathematics 2.2 | |
| A reaction: This postulate was challenged in the nineteenth century, which was a major landmark in the development of modern relativist views of knowledge. |
| 10250 | Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid] |
| Full Idea: Euclid gives no principle of continuity, which would sanction an inference that if a line goes from the outside of a circle to the inside of circle, then it must intersect the circle at some point. | |
| From: comment on Euclid (Elements of Geometry [c.290 BCE]) by Stewart Shapiro - Philosophy of Mathematics 6.1 n2 | |
| A reaction: Cantor and Dedekind began to contemplate discontinuous lines. |
| 10302 | Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays] |
| Full Idea: Euclid postulates: One can join two points by a straight line; Hilbert states the axiom: Given any two points, there exists a straight line on which both are situated. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Paul Bernays - On Platonism in Mathematics p.259 |
| 14157 | Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid] |
| Full Idea: In descriptive geometry the first 26 propositions of Euclid hold. In projective geometry the 1st, 7th, 16th and 17th require modification (as a straight line is not a closed series). Those after 26 depend on the postulate of parallels, so aren't assumed. | |
| From: comment on Euclid (Elements of Geometry [c.290 BCE]) by Bertrand Russell - The Principles of Mathematics §388 |
| 1600 | Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik] |
| Full Idea: The best known example of Euclid's 'common notions' is "If equals are subtracted from equals the remainders are equal". These can be called axioms, and are what "the man who is to learn anything whatever must have". | |
| From: report of Euclid (Elements of Geometry [c.290 BCE], 72a17) by David Roochnik - The Tragedy of Reason p.149 |
| 20360 | We Germans value becoming and development more highly than mere being of what 'is' [Nietzsche] |
| Full Idea: We Germans are Hegelians insofar as we instinctively attribute a deeper sense and richer value to becoming and development than to what 'is'. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §357) | |
| A reaction: I always doubt Nietzsche's claims about 'we Germans' or 'we philosophers'. They say that, intellectually, everyone is either French or German, and my immediate response was to embrace being German. So becoming is where it's at. |
| 24077 | Necessity is thought to require an event, but is only an after-effect of the event [Nietzsche] |
| Full Idea: Necessity is supposed to be the cause of something coming to be: in truth it is often only an effect of what has come to be. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §205) | |
| A reaction: This sounds like an account of the traditional idea of destiny - which sees inevitability in some major event, which was previously unpredictable. |
| 20126 | The strength of knowledge is not its truth, but its entrenchment in our culture [Nietzsche] |
| Full Idea: The strength of knowledge does not depend on its degree of truth but on its age, on the degree to which it has been incoporated, in its character as a condition of life. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §110) | |
| A reaction: This seems to be the rather modern idea (in Foucault, perhaps) of knowledge as a central component of culture, rather than as an eternal revelation of facts. Note that he is talking about its 'strength', not its veracity or degree of support. |
| 20119 | We became increasingly conscious of our sense impressions in order to communicate them [Nietzsche] |
| Full Idea: The emergence of our sense impressions into our consciousness, the ability to fix them and, as it were, exhibit them externally, increased proportionally with the need to communicate them to others by means of signs. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
| A reaction: He says in the same section that such ideas (plus his thoughts on consciousness) are the essence of his 'Perspectivism'. In effect, knowledge is not an individual activity, but a team game |
| 20122 | We have no organ for knowledge or truth; we only 'know' what is useful to the human herd [Nietzsche] |
| Full Idea: We simply lack any organ for knowledge, for 'truth'; we 'know' [das Erkennen] (or believe or imagine) just as much as may be useful in the interests of the human herd, the species; and this 'utility' is ultimately also a mere belief. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
| A reaction: [Section §354 is fascinating!] An odd idea, that we can only have truth is we have an 'organ' for it. It seems plausible that the whole brain is a truth machine. This seems like pure pragmatism, with all its faults. Falsehoods can be useful. |
| 4423 | We assume causes, geometry, motion, bodies etc to live, but they haven't been proved [Nietzsche] |
| Full Idea: We have fixed up a world for ourselves in which we can live, with bodies, lines, planes, causes, motion and form; without these articles of faith nobody would endure life. But that does not mean they have been proved. Life is no argument. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §121) | |
| A reaction: It is hard to disagree. A lot of recent thought suggests that they are Hume's 'natural beliefs', like truth and induction, which simply can't be proved. 'Unprovable' does not mean 'incorrect', however. |
| 6579 | Nietzsche's perspectivism says our worldview depends on our personality [Nietzsche, by Fogelin] |
| Full Idea: Nietzsche recommends an extreme version of perspectivism in holding that a person's view of the world is a function of that person's life-affirming (Heraclitean) or life-denying (Parmenidean) personality. | |
| From: report of Friedrich Nietzsche (The Gay (Joyful) Science [1882]) by Robert Fogelin - Walking the Tightrope of Reason Ch.3 | |
| A reaction: Fogelin recommends Nehamas on this topic. I am not convinced Nietzsche takes such an individual view as is implied here. See Idea 4420, for example. This view is in tune with Charles Taylor's view that our values shape our understanding of our selves. |
| 24083 | It would be absurd to say we are only permitted our own single perspective [Nietzsche] |
| Full Idea: I think today we are at least far removed from the ridiculous immodesty of decreeing from our corner that one is permitted to have perspectives only from this corner. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §374) | |
| A reaction: He goes on to speculate about the possibility of infinite perspectives, most of them unknowable to us. But Nietzsche was not a simple relativism. The obvious concept needed to accompany a many-perspectives view is consensus. |
| 20115 | All of our normal mental life could be conducted without consciousness [Nietzsche] |
| Full Idea: We could think, feel, will and remember, and we could also 'act', and yet none of this would have to enter our consciousness. The whole of life would be possible without, as it were, seeing itself in a mirror. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
| A reaction: He credits Leibniz with this line of thought. Nowadays the unconscious aspects of thought are a commonplace, not just from Freud, but from neuroscience. We have no idea how conscious other animals are. Nietzsche attributes consciousness to communication. |
| 20117 | Only the need for communication has led to consciousness developing [Nietzsche] |
| Full Idea: I surmise that consciousness has developed only under the pressure of the need for communication; ...consciousness is really only a net of communication between human beings. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
| A reaction: An interesting speculation, well ahead of its time. Given that thought does not require consciousness, as he claims, it is not quite clear why communication needs it. Presumably two robots can communicate. But Idea 20118 is good. |
| 20118 | Only our conscious thought is verbal, and this shows the origin of consciousness [Nietzsche] |
| Full Idea: Only conscious thinking takes the form of words, which is to say signs of communication, and this fact uncovers the origin of consciousness. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
| A reaction: Chicken-and-egg question here. Persinally I take consciousnes to be associated with meta-thought, which bestows huge power, and I take language to arise from meta-thought. |
| 20116 | Most of our lives, even the important parts, take place outside of consciousness [Nietzsche] |
| Full Idea: By far the greatest proportion of our life takes place without this mirroring effect [of consciousness]; and this is true even of our thinking, feeling and willing life, however offensive this may sound to older philosophers. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
| A reaction: Nietzsche didn't just hint at the possibility of a (Freudian) sub-conscious - he was whole-heartedly committed to it, and Freud gave him credit for it. I think philosophers are only just beginning to digest this crucial idea. |
| 20120 | Whatever moves into consciousness becomes thereby much more superficial [Nietzsche] |
| Full Idea: Whatever becomes conscious becomes by the same token shallow, thin, relatively stupid, general, sign, herd signal; all becoming conscious involves a great and thorough corruption, falsification, reduction to superficialities, and generalisation. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
| A reaction: Nietzsche would have made a great speech writer for someone. This vision is increasingly how I see people. It is a view reinforced by modern neuroscience, which suggests that we greatly overestimate the conscious part of ourselves. |
| 2932 | 'Know thyself' is impossible and ridiculous [Nietzsche] |
| Full Idea: "Everybody is farthest away - from himself"; and the maxim "know thyself" addressed to human beings by a god, is almost malicious. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §335) | |
| A reaction: Expressed with characteristcally Nietzschean brio, but I couldn't agree more, and it is a very important truth. You can only require full self-knowledge if the whole mind is available to be known, and that isn't even remotely the case. |
| 24078 | Thoughts cannot be fully reproduced in words [Nietzsche] |
| Full Idea: Even one's thoughts one cannot reproduce entirely in words. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §244) | |
| A reaction: I suppose this is the germ of Derrida, who seems to see little connection between thought and speech. I take this idea to be entirely correct. Our simplistic view of language reduces the fluidity and many dimensions of thought to a pile of lego bricks. |
| 24081 | Most of our intellectual activity is unconscious [Nietzsche] |
| Full Idea: Only now is the truth dawning on us that the biggest part by far of our intellectual activity takes place unconsciously, and unfelt by us. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §333) | |
| A reaction: Note that this is 'intellectual activity', and just the hidden rumblings of instincts and emotions. I think he is right. Philosophers want to verbalise everything, but I don't think the main insights of philosophical thinking are verbal. |
| 2933 | Why do you listen to the voice of your conscience? [Nietzsche] |
| Full Idea: Why do you listen to the voice of your conscience? | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §335) | |
| A reaction: Nice question. It is perfectly plausible to say that I seem to feel guilty about doing something, but can't see any reason why I should. |
| 20141 | Higher human beings see and hear far more than others, and do it more thoughtfully [Nietzsche] |
| Full Idea: What distinguishes the higher human being from the lower is that the former see and hear immeasurably more, and see and hear thoughtfully - and precisely this distinguishes human beings from animals, and the higher animals from the lower. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §301) | |
| A reaction: Since most people are well equipped with eyes and ears, I take it that this phenomenon, if true, arises from the 'higher' type of person having more interest in what they experience. |
| 24076 | A morality ranks human drives and actions, for the sake of the herd, and subordinating individuals [Nietzsche] |
| Full Idea: Whenever we encounter a morality we find an estimation and order of rank of human drives and actions. These are always the expression of the needs of a community and herd. The individual is valued only as a function of the herd. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §116) | |
| A reaction: A particularly clear summary of Nietzsche's understanding of modern morality (which he rejects). I tend to see values as what is important, but Nietzsche sees them as a ranking. Could be both. I see the individualism here as existentialist. |
| 22471 | Nietzsche thought it 'childish' to say morality isn't binding because it varies between cultures [Nietzsche, by Foot] |
| Full Idea: Nietzsche was not simply a run-of-the-mill moral relativist. He branded as 'childish' the idea that no morality can be binding because moral valuations are necessarily different among different nations. | |
| From: report of Friedrich Nietzsche (The Gay (Joyful) Science [1882], §345) by Philippa Foot - Nietzsche's Immoralism p.146 | |
| A reaction: Relativists about knowledge and morality are inclined to take quotations from Nietzsche out of context. The existence of this database probably exacerbates such intellectual wickedness. Get a feeling for the whole thinker! |
| 2935 | No two actions are the same [Nietzsche] |
| Full Idea: There neither are nor can be actions which are the same. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §335) |
| 20198 | Many virtues are harmful traps, but that is why other people praise them [Nietzsche] |
| Full Idea: Virtues like industriousness, obedience, chastity, filial piety and justice are usually harmful to those who possess them. When you have a real, whole virtue you are its victim. But your neighbour praises your virtue precisely on that account. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §021) | |
| A reaction: This is the conspiracy theory of virtue. We want people to do menial or undesirable jobs, so we dress them up as wonderful virtues, and make people feel good for possessing them. There must be some truth in this. |
| 4275 | You cannot advocate joyful wisdom while rejecting pity, because the two are complementary [Scruton on Nietzsche] |
| Full Idea: Pity and good cheer are complementary, ..so there is something contradictory in a philosophy that advocates joyful wisdom, while slandering pity as the enemy of the higher life. | |
| From: comment on Friedrich Nietzsche (The Gay (Joyful) Science [1882]) by Roger Scruton - Animal Rights and Wrongs p.35 | |
| A reaction: A good objection to Nietzsche. He has a rather solipsistic view of joyful exuberance etc., and fails to realise how social such things must be. In that, Nietzsche was caught in the romantic tradition of Wordsworth and co. |
| 2934 | To see one's own judgement as a universal law is selfish [Nietzsche] |
| Full Idea: It is selfish to experience one's own judgement as a universal law. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §335) |
| 24080 | We should give style to our character - by applying an artistic plan to its strengths and weaknesses [Nietzsche] |
| Full Idea: One thing is essential - 'giving style' to one's character. It is practised by the one who surveys everything that his nature offers in strengths and weaknesses, and subjects it to an artistic plan until each thing appears as art and reason. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §290) | |
| A reaction: Clearly existentialist, in its proposal to change one's own character. I invite the reader to consider applying this to themselves - and I submit that it is an impossible project. Nice thought, though. |
| 20125 | The ethical teacher exists to give purpose to what happens necessarily and without purpose [Nietzsche] |
| Full Idea: That what happens necessarily, spontaneously and without any purpose, may henceforth appear to be done for some purpose, and strike man as rational and an ultimate commandment, the ethical teacher comes on stage, as teacher of the purpose of existence. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §001) | |
| A reaction: This doesn't look like much of a solution to the problem of nihilism, unless the teacher plants an idea in us which endures and grows. Nietzsche's 'eternal recurrence' was supposed to be just such an idea. |
| 9306 | To ward off boredom at any cost is vulgar [Nietzsche] |
| Full Idea: To ward off boredom at any cost is vulgar. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §042) | |
| A reaction: Ignoring 'vulgar', this is a nice thought. Do affluent retired people now travel so much because they are terrified of boredom? What would they end up doing if they stayed at home and lived through the boredom to something else? |
| 24079 | The best life is the dangerous life [Nietzsche] |
| Full Idea: The secret of harvesting the greatest fruitfulness and the greatest enjoyment from existence is: live dangerously! | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §283) | |
| A reaction: I treasured this quotation when I was 17, but failed to live up to it. |
| 2936 | Imagine if before each of your actions you had to accept repeating the action over and over again [Nietzsche] |
| Full Idea: Suppose a demon were to say to you, "This life as you have lived it, you will have to live once more and innumerable times more". …Then the question in each thing, "Do you desire this once more and innumerable times more?" would lie across your actions. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §341) | |
| A reaction: If you were stuck in nihilistic indifference, this thought might not be enough to rouse you from your torpor. If all possibilities in life are boring, repetition cannot pep it up, or make it any worse. But I still love this idea! |
| 6842 | Nietzsche says facing up to the eternal return of meaninglessness is the response to nihilism [Nietzsche, by Critchley] |
| Full Idea: Nietzsche is overwhelmingly concerned with how to respond to nihilism, and he offers the concept of eternal return; the Overman is one who can affirm over and over that one is equal to meaninglessness, without turning to despair or idols. | |
| From: report of Friedrich Nietzsche (The Gay (Joyful) Science [1882], §342) by Simon Critchley - Interview with Baggini and Stangroom p.192 | |
| A reaction: I agree with Critchley that this is not much of a recipe for ordinary people's lives, and I don't even find it very congenial for a tough-minded philosopher. We should make the best of the cards we are dealt, however feeble they may appear. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |
| 2931 | God is dead, and we have killed him [Nietzsche] |
| Full Idea: God is dead. God remains dead. And we have killed him. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §125) |