75 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. |
| 9955 | Contextual definitions replace a complete sentence containing the expression [George/Velleman] |
| Full Idea: A contextual definition shows how to analyse an expression in situ, by replacing a complete sentence (of a particular form) in which the expression occurs by another in which it does not. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2) | |
| A reaction: This is a controversial procedure, which (according to Dummett) Frege originally accepted, and later rejected. It might not be the perfect definition that replacing just the expression would give you, but it is a promising step. |
| 10031 | Impredicative definitions quantify over the thing being defined [George/Velleman] |
| Full Idea: When a definition contains a quantifier whose range includes the very entity being defined, the definition is said to be 'impredicative'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2) | |
| A reaction: Presumably they are 'impredicative' because they do not predicate a new quality in the definiens, but make use of the qualities already known. |
| 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. |
| 10098 | The 'power set' of A is all the subsets of A [George/Velleman] |
| Full Idea: The 'power set' of A is all the subsets of A. P(A) = {B : B ⊆ A}. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10099 | The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}} [George/Velleman] |
| Full Idea: The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}}. The existence of this set is guaranteed by three applications of the Axiom of Pairing. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: See Idea 10100 for the Axiom of Pairing. |
| 10101 |
Cartesian Product A x B: the set of all ordered pairs |
| Full Idea: The 'Cartesian Product' of any two sets A and B is the set of all ordered pairs <a, b> in which a ∈ A and b ∈ B, and it is denoted as A x B. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10103 | Grouping by property is common in mathematics, usually using equivalence [George/Velleman] |
| Full Idea: The idea of grouping together objects that share some property is a common one in mathematics, ...and the technique most often involves the use of equivalence relations. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10104 | 'Equivalence' is a reflexive, symmetric and transitive relation; 'same first letter' partitions English words [George/Velleman] |
| Full Idea: A relation is an equivalence relation if it is reflexive, symmetric and transitive. The 'same first letter' is an equivalence relation on the set of English words. Any relation that puts a partition into clusters will be equivalence - and vice versa. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This is a key concept in the Fregean strategy for defining numbers. |
| 10096 | Even the elements of sets in ZFC are sets, resting on the pure empty set [George/Velleman] |
| Full Idea: ZFC is a theory concerned only with sets. Even the elements of all of the sets studied in ZFC are also sets (whose elements are also sets, and so on). This rests on one clearly pure set, the empty set Φ. ..Mathematics only needs pure sets. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This makes ZFC a much more metaphysically comfortable way to think about sets, because it can be viewed entirely formally. It is rather hard to disentangle a chair from the singleton set of that chair. |
| 10097 | Axiom of Extensionality: for all sets x and y, if x and y have the same elements then x = y [George/Velleman] |
| Full Idea: The Axiom of Extensionality says that for all sets x and y, if x and y have the same elements then x = y. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This seems fine in pure set theory, but hits the problem of renates and cordates in the real world. The elements coincide, but the axiom can't tell you why they coincide. |
| 10100 | Axiom of Pairing: for all sets x and y, there is a set z containing just x and y [George/Velleman] |
| Full Idea: The Axiom of Pairing says that for all sets x and y, there is a set z containing x and y, and nothing else. In symbols: ∀x∀y∃z∀w(w ∈ z ↔ (w = x ∨ w = y)). | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: See Idea 10099 for an application of this axiom. |
| 17900 | The Axiom of Reducibility made impredicative definitions possible [George/Velleman] |
| Full Idea: The Axiom of Reducibility ...had the effect of making impredicative definitions possible. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10109 | ZFC can prove that there is no set corresponding to the concept 'set' [George/Velleman] |
| Full Idea: Sets, unlike extensions, fail to correspond to all concepts. We can prove in ZFC that there is no set corresponding to the concept 'set' - that is, there is no set of all sets. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) | |
| A reaction: This is rather an important point for Frege. However, all concepts have extensions, but they may be proper classes, rather than precisely defined sets. |
| 10108 | As a reduction of arithmetic, set theory is not fully general, and so not logical [George/Velleman] |
| Full Idea: The problem with reducing arithmetic to ZFC is not that this theory is inconsistent (as far as we know it is not), but rather that is not completely general, and for this reason not logical. For example, it asserts the existence of sets. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) | |
| A reaction: Note that ZFC has not been proved consistent. |
| 10111 | Asserting Excluded Middle is a hallmark of realism about the natural world [George/Velleman] |
| Full Idea: A hallmark of our realist stance towards the natural world is that we are prepared to assert the Law of Excluded Middle for all statements about it. For all statements S, either S is true, or not-S is true. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) | |
| A reaction: Personally I firmly subscribe to realism, so I suppose I must subscribe to Excluded Middle. ...Provided the statement is properly formulated. Or does liking excluded middle lead me to realism? |
| 10129 | A 'model' is a meaning-assignment which makes all the axioms true [George/Velleman] |
| Full Idea: A 'model' of a theory is an assignment of meanings to the symbols of its language which makes all of its axioms come out true. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: If the axioms are all true, and the theory is sound, then all of the theorems will also come out true. |
| 10105 | Differences between isomorphic structures seem unimportant [George/Velleman] |
| Full Idea: Mathematicians tend to regard the differences between isomorphic mathematical structures as unimportant. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This seems to be a pointer towards Structuralism as the underlying story in mathematics. The intrinsic character of so-called 'objects' seems unimportant. How theories map onto one another (and onto the world?) is all that matters? |
| 10119 | Consistency is a purely syntactic property, unlike the semantic property of soundness [George/Velleman] |
| Full Idea: Consistency is a purely syntactic property, unlike the semantic property of soundness. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10126 | A 'consistent' theory cannot contain both a sentence and its negation [George/Velleman] |
| Full Idea: If there is a sentence such that both the sentence and its negation are theorems of a theory, then the theory is 'inconsistent'. Otherwise it is 'consistent'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) |
| 10120 | Soundness is a semantic property, unlike the purely syntactic property of consistency [George/Velleman] |
| Full Idea: Soundness is a semantic property, unlike the purely syntactic property of consistency. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10127 | A 'complete' theory contains either any sentence or its negation [George/Velleman] |
| Full Idea: If there is a sentence such that neither the sentence nor its negation are theorems of a theory, then the theory is 'incomplete'. Otherwise it is 'complete'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: Interesting questions are raised about undecidable sentences, irrelevant sentences, unknown sentences.... |
| 10106 | Rational numbers give answers to division problems with integers [George/Velleman] |
| Full Idea: We can think of rational numbers as providing answers to division problems involving integers. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Cf. Idea 10102. |
| 10102 | The integers are answers to subtraction problems involving natural numbers [George/Velleman] |
| Full Idea: In defining the integers in set theory, our definition will be motivated by thinking of the integers as answers to subtraction problems involving natural numbers. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Typical of how all of the families of numbers came into existence; they are 'invented' so that we can have answers to problems, even if we can't interpret the answers. It it is money, we may say the minus-number is a 'debt', but is it? Cf Idea 10106. |
| 10107 | Real numbers provide answers to square root problems [George/Velleman] |
| Full Idea: One reason for introducing the real numbers is to provide answers to square root problems. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Presumably the other main reasons is to deal with problems of exact measurement. It is interesting that there seem to be two quite distinct reasons for introducing the reals. Cf. Ideas 10102 and 10106. |
| 9946 | Logicists say mathematics is applicable because it is totally general [George/Velleman] |
| Full Idea: The logicist idea is that if mathematics is logic, and logic is the most general of disciplines, one that applies to all rational thought regardless of its content, then it is not surprising that mathematics is widely applicable. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2) | |
| A reaction: Frege was keen to emphasise this. You are left wondering why pure logic is applicable to the physical world. The only account I can give is big-time Platonism, or Pythagoreanism. Logic reveals the engine-room of nature, where the design is done. |
| 10125 | The classical mathematician believes the real numbers form an actual set [George/Velleman] |
| Full Idea: Unlike the intuitionist, the classical mathematician believes in an actual set that contains all the real numbers. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 17899 | Second-order induction is stronger as it covers all concepts, not just first-order definable ones [George/Velleman] |
| Full Idea: The first-order version of the induction axiom is weaker than the second-order, because the latter applies to all concepts, but the first-order applies only to concepts definable by a formula in the first-order language of number theory. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7 n7) |
| 10128 | The Incompleteness proofs use arithmetic to talk about formal arithmetic [George/Velleman] |
| Full Idea: The idea behind the proofs of the Incompleteness Theorems is to use the language of Peano Arithmetic to talk about the formal system of Peano Arithmetic itself. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: The mechanism used is to assign a Gödel Number to every possible formula, so that all reasonings become instances of arithmetic. |
| 17902 | A successor is the union of a set with its singleton [George/Velleman] |
| Full Idea: For any set x, we define the 'successor' of x to be the set S(x) = x U {x}. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This is the Fregean approach to successor, where the Dedekind approach takes 'successor' to be a primitive. Frege 1884:§76. |
| 10133 | Frege's Theorem shows the Peano Postulates can be derived from Hume's Principle [George/Velleman] |
| Full Idea: The derivability of Peano's Postulates from Hume's Principle in second-order logic has been dubbed 'Frege's Theorem', (though Frege would not have been interested, because he didn't think Hume's Principle gave an adequate definition of numebrs). | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8 n1) | |
| A reaction: Frege said the numbers were the sets which were the extensions of the sets created by Hume's Principle. |
| 10130 | Set theory can prove the Peano Postulates [George/Velleman] |
| Full Idea: The Peano Postulates can be proven in ZFC. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) |
| 10089 | Talk of 'abstract entities' is more a label for the problem than a solution to it [George/Velleman] |
| Full Idea: One might well wonder whether talk of abstract entities is less a solution to the empiricist's problem of how a priori knowledge is possible than it is a label for the problem. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Intro) | |
| A reaction: This pinpoints my view nicely. What the platonist postulates is remote, bewildering, implausible and useless! |
| 10131 | If mathematics is not about particulars, observing particulars must be irrelevant [George/Velleman] |
| Full Idea: As, in the logicist view, mathematics is about nothing particular, it is little wonder that nothing in particular needs to be observed in order to acquire mathematical knowledge. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002]) | |
| A reaction: At the very least we can say that no one would have even dreamt of the general system of arithmetic is they hadn't had experience of the particulars. Frege thought generality ensured applicability, but extreme generality might entail irrelevance. |
| 10092 | In the unramified theory of types, the types are objects, then sets of objects, sets of sets etc. [George/Velleman] |
| Full Idea: In the unramified theory of types, all objects are classified into a hierarchy of types. The lowest level has individual objects that are not sets. Next come sets whose elements are individuals, then sets of sets, etc. Variables are confined to types. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: The objects are Type 0, the basic sets Type 1, etc. |
| 10094 | The theory of types seems to rule out harmless sets as well as paradoxical ones. [George/Velleman] |
| Full Idea: The theory of types seems to rule out harmless sets as well as paradoxical ones. If a is an individual and b is a set of individuals, then in type theory we cannot talk about the set {a,b}. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Since we cheerfully talk about 'Cicero and other Romans', this sounds like a rather disasterous weakness. |
| 10095 | Type theory has only finitely many items at each level, which is a problem for mathematics [George/Velleman] |
| Full Idea: A problem with type theory is that there are only finitely many individuals, and finitely many sets of individuals, and so on. The hierarchy may be infinite, but each level is finite. Mathematics required an axiom asserting infinitely many individuals. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Most accounts of mathematics founder when it comes to infinities. Perhaps we should just reject them? |
| 17901 | Type theory prohibits (oddly) a set containing an individual and a set of individuals [George/Velleman] |
| Full Idea: If a is an individual and b is a set of individuals, then in the theory of types we cannot talk about the set {a,b}, since it is not an individual or a set of individuals, ...but it is hard to see what harm can come from it. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10114 | Bounded quantification is originally finitary, as conjunctions and disjunctions [George/Velleman] |
| Full Idea: In the first instance all bounded quantifications are finitary, for they can be viewed as abbreviations for conjunctions and disjunctions. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) | |
| A reaction: This strikes me as quite good support for finitism. The origin of a concept gives a good guide to what it really means (not a popular view, I admit). When Aristotle started quantifying, I suspect of he thought of lists, not totalities. |
| 10134 | Much infinite mathematics can still be justified finitely [George/Velleman] |
| Full Idea: It is possible to use finitary reasoning to justify a significant part of infinitary mathematics. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8) | |
| A reaction: This might save Hilbert's project, by gradually accepting into the fold all the parts which have been giving a finitist justification. |
| 10123 | The intuitionists are the idealists of mathematics [George/Velleman] |
| Full Idea: The intuitionists are the idealists of mathematics. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10124 | Gödel's First Theorem suggests there are truths which are independent of proof [George/Velleman] |
| Full Idea: For intuitionists, truth is not independent of proof, but this independence is precisely what seems to be suggested by Gödel's First Incompleteness Theorem. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8) | |
| A reaction: Thus Gödel was worse news for the Intuitionists than he was for Hilbert's Programme. Gödel himself responded by becoming a platonist about his unprovable truths. |
| 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. |
| 10110 | Corresponding to every concept there is a class (some of them sets) [George/Velleman] |
| Full Idea: Corresponding to every concept there is a class (some classes will be sets, the others proper classes). | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) |
| 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. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 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. |
| 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) |