48 ideas
2930 | The main aim of philosophy must be to determine the order of rank among values [Nietzsche] |
Full Idea: The future task of the philosophers is the solution of the problem of value, the determination of the order of rank among values. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], I.§17 note) | |
A reaction: 'Determine' is presumably either a power struggle, or needs criteria by which to do the judging. |
20143 | Scientific knowledge is nothing without a prior philosophical 'faith' [Nietzsche] |
Full Idea: Strictly speaking there is no knowledge [science] without presuppositions; a philosophy, a 'faith', must always be there first of all, for knowledge to win from it a direction, a meaning, a limit, a method, a right to exist. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], III.§24) | |
A reaction: He sees philosophers as the creators of this faith, and laughs at anyone who tries to set philosophy on a scientific basis. |
23722 | Objectivity is not disinterestedness (impossible), but the ability to switch perspectives [Nietzsche] |
Full Idea: 'Objectivity' should be understood not as 'contemplation without interest' (a non-concept and an absurdity), but as having in our power the ability to engage and disengage our 'pros' and 'cons'; we can use the difference in perspectives for knowledge. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], III.§12) | |
A reaction: Note that he will use perspectives to achieve knowledge. The idea that Perspectivalism is mere relativism is labelled as 'extreme' in Idea 4486. He is right that objectivity is a mental capacity and achievement of individuals. |
4417 | Only that which has no history is definable [Nietzsche] |
Full Idea: Only that which has no history is definable. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], II.§13) | |
A reaction: Too subtle to evaluate! It sounds as if it could be right, that some things are definable, but when the accretions of human history are interwoven into an identity, we can forget it. |
21697 | The Struthionic Fallacy is that of burying one's head in the sand [Quine] |
Full Idea: The Struthionic Fallacy is that of burying one's head in the sand [which I name from the Greek for 'ostrich'] | |
From: Willard Quine (Lecture on Nominalism [1946], §4) | |
A reaction: David Armstrong said this is the the fallacy involved in a denial of universals. Quine is accusing Carnap and co. of the fallacy. |
23715 | Psychologists should be brave and proud, and prefer truth to desires, even when it is ugly [Nietzsche] |
Full Idea: I hope [psychologists] are actually brave, generous, proud animals, who know how to control their own pleasure and pain and are taught to sacrifice desirability to truth, even a bitter, ugly, unchristian, immoral truth - Because there are such truths. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], I.§01) | |
A reaction: A nice expression of Nietzsche's values, which makes truth central, contrary to the widespread modern view that he was the high priest of relativism. If you think that, read him more carefully. |
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? |
21698 | All relations, apart from ancestrals, can be reduced to simpler logic [Quine] |
Full Idea: Much of the theory of relations can be developed as a virtual theory, in which we seem to talk of relations, but can explain our notation in terms {finally] of just the logic of truth-functions, quantification and identity. The exception is ancestrals. | |
From: Willard Quine (Lecture on Nominalism [1946], §8) | |
A reaction: The irreducibility of ancestrals is offered as a reason for treating sets as universals. |
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. |
21696 | Nominalism rejects both attributes and classes (where extensionalism accepts the classes) [Quine] |
Full Idea: 'Nominalism' is distinct from 'extensionalism'. The main point of the latter doctrine is rejection of properties or attributes in favour of classes. But class are universals equally with attributes, and nominalism in the defined sense rejects both. | |
From: Willard Quine (Lecture on Nominalism [1946], §3) | |
A reaction: Hence Quine soon settled on labelling himself as an 'extensionalist', leaving proper nominalism to Nelson Goodman. It is commonly observed that science massively refers to attributes, so they can't just be eliminated. |
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. |
4421 | Philosophers have never asked why there is a will to truth in the first place [Nietzsche] |
Full Idea: Both the earliest and most recent philosophers are all oblivious of how much the will to truth itself first requires justification: here there is a gap in every philosophy - how did this come about? | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], III.§24) | |
A reaction: This seems to me a meta-philosophical question which will lead off into (quite interesting) cultural studies and (trite) evolutionary theory. Truth isn't a value, it is the biological function of brains. |
23719 | Forgetfulness is a strong positive ability, not mental laziness [Nietzsche] |
Full Idea: Forgetfulness is not just a vis inertiae, as superficial people believe, but is rather an active ability to suppress, positive in the strongest sense of the word. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], II.§01) | |
A reaction: It is unimpressive when people remember small slights and grievances for a long time - and even being owed small sums - so the ability to forget such things is admirable. But wilfully forgetting some things is obviously shameful. |
4420 | There is only 'perspective' seeing and knowing, and so the best objectivity is multiple points of view [Nietzsche] |
Full Idea: There is only a perspective seeing, only a perspective "knowing", and the more different eyes we can use to observe one thing, the more complete will our "concept" of this thing, our "objectivity", be. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], III.§12) | |
A reaction: A very perceptive statement of the most plausible and sophisticated version of relativism. It is hard to see how we could distinguish multiple viewpoints from pure objectivity. |
4414 | Philosophers invented "free will" so that our virtues would be permanently interesting to the gods [Nietzsche] |
Full Idea: The philosophers invented "free will" - absolute human spontaneity in good and evil - to furnish a right to the idea that the interest of the gods in man, in human virtue, could never be exhausted. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], II.§07) | |
A reaction: Wonderfully outrageous suggestion! If we had true metaphysical 'absolute' free will, we would be much more interesting, and have a much higher status in the cosmos. Nietzsche is probably right. |
4419 | People who think in words are orators rather than thinkers, and think about facts instead of thinking facts [Nietzsche] |
Full Idea: Whoever thinks in words thinks as an orator and not as a thinker (it shows that he does not think facts, but only in relation to facts). | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], III.§08) | |
A reaction: Good. It is certainly not true that we have to think in words, or else animals wouldn't think. Good thinking should focus on reality, and be too fast for words to keep up. |
4411 | It is a delusion to separate the man from the deed, like the flash from the lightning [Nietzsche] |
Full Idea: Just as the popular mind separates the lightning from its flash and takes the latter for a 'action', so they separate strength from expressions of strength, but there is no such substratum; the deed is everything. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], I.§13) | |
A reaction: Of course, there is no reason why an analysis should not separate the doer and the deed (to explain, for example, a well-meaning fool), but it is a blunder to think of a human action as a merely physical event. |
3793 | We must question the very value of moral values [Nietzsche] |
Full Idea: We need a critique of moral values; the value of these values themselves must just be called in question. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], Pre f§3) | |
A reaction: But we must start somewhere with values, to avoid an infinite regress. |
4408 | The concept of 'good' was created by aristocrats to describe their own actions [Nietzsche] |
Full Idea: The judgement 'good' did not first originate with those to whom goodness was shown! Rather it was the 'good' themselves, that is to say the noble, powerful, high-stationed and high-minded who established themselves and their action as good. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], I.§02) | |
A reaction: This may be right, but not very profound. Virtually all concepts are created by the most educated classes. The first recipient of charity may not have had the concept, but they would have been gobsmacked by the novelty. |
23716 | A strong rounded person soon forgets enemies, misfortunes, and even misdeeds [Nietzsche] |
Full Idea: To be unable to take his enemies, his misfortunes and even his misdeeds seriously for long - that is the sign of strong, rounded natures with a superabundance of power. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], I.§10) | |
A reaction: An aspect of the 'higher man' that I don't recall being mentioned elsewhere. I basically approve of this, if it means not holding grudges, and living for the future rather than for the past. |
20129 | All animals strive for the ideal conditions to express their power, and hate any hindrances [Nietzsche] |
Full Idea: Every animal instinctively strives for an optimum of favourable conditions under which it can expend all its strength and achieve its maximal feeling of power; every animal abhors ...every hindrance that obstructs this path to the optimum. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], III.§07) | |
A reaction: This became the lynchpin of Nietzsche's account of the source of values. It is a highly naturalistic view, fitting it into evolutionary theory (thought running deeper than that), so I have a lot of sympathy with the view. |
4409 | Only the decline of aristocratic morality led to concerns about "egoism" [Nietzsche] |
Full Idea: It was only when aristocratic value judgements declined that the whole antithesis of "egoistic" and "unegoistic" obtruded itself more and more on the human conscience. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], I.§02) | |
A reaction: But Aristotle, who is no aristocrat, has a balanced and sensible view of 'egoism', where it isn't the patronising arrogance that Nietzsche seems to like, but a proper concern with one's own character. |
3259 | Nietzsche rejects impersonal morality, and asserts the idea of living well [Nietzsche, by Nagel] |
Full Idea: Nietzsche's rejection of impersonal morality is an assertion of the dominance of the ideal of living well. | |
From: report of Friedrich Nietzsche (On the Genealogy of Morals [1887], I) by Thomas Nagel - The View from Nowhere X.2 |
4416 | Basic justice is the negotiation of agreement among equals, and the imposition of agreement [Nietzsche] |
Full Idea: Justice on the elementary level is good will among parties of approximately equal power to come to terms with one another, and to compel parties of lesser power to reach a settlement among themselves. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], II.§08) | |
A reaction: This pinpoints a key problem with the social contract as a moral theory - that it requires equals, and recognises only terror of superiors, and indifference to useless inferiors who have nothing to offer (paraplegics and animals). |
4418 | A masterful and violent person need have nothing to do with contracts [Nietzsche] |
Full Idea: He who can command, he who is "master", he who is violent in act and bearing - what has he to do with contracts! | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], II.§17) | |
A reaction: The persistent problem with social contract theory is that those much stronger or much weaker seem to have no interest in morality at all, and yet they can all have standards of behaviour. |
4407 | Plato, Spinoza and Kant are very different, but united in their low estimation of pity [Nietzsche] |
Full Idea: Plato, Spinoza, La Rochefoucauld, and Kant are four spirits very different from one another, but united in one thing: their low estimation of pity. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], Pref §5) | |
A reaction: Plato is no surprise, as virtually no Greeks value pity. Spinoza and Kant are interesting. Presumably Kant's 'contractualism' places respect far above pity, and is theoretical neglect of animals would fit. Remember Nietzsche embraced a horse in Turin. |
4415 | Guilt and obligation originated in the relationship of buying and selling, credit and debt [Nietzsche] |
Full Idea: The feeling of guilt, of personal obligation, had its origin in the oldest and most primitive personal relationship, that between buyer and seller, between creditor and debtor. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], II.§08) | |
A reaction: In other words, lofty Kantian ideals started life in the grubby world of the Hobbesian social contract, and self-seeking has been disguised by idealism. Too harsh on Kant, who explains why contracts have force, not just convenience. |
23718 | If we say birds of prey could become lambs, that makes them responsible for being birds of prey [Nietzsche] |
Full Idea: Scientists …do not defend any belief more strongly than that the strong are free to be weak, and the birds of prey are free to be lambs: - in this way, they gain the right to make the birds of prey responsible for being birds of prey. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], I.§13) | |
A reaction: This is a flat rejection of the Sartrean idea that we can what sort of person we want to be. He cares about birds of prey, but also lambs can't become eagles. I would say that adolescents have a reasonable degree of choice about what they will become. |
23717 | Modern nihilism is now feeling tired of mankind [Nietzsche] |
Full Idea: The sight of man now makes us tired - what is nihilism today if it is not that? …We are tired of man… | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], I.§12) | |
A reaction: That is close to Hume's nihilist, who would destroy the world to protect his own finger from a scratch. The actor George Sanders committed suicide because he was bored. Don't ever think that Nietzsche was a nihilist, just because he mentions it a lot! |
23721 | Old tribes always felt an obligation to the earlier generations, and the founders [Nietzsche] |
Full Idea: Within the original tribal association the living generation always acknowledged a legal obligation towards the earlier generation, and in particular towards the earliest. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], II.§19) | |
A reaction: This is still a factor in modern politics, though the people remember are either military heroes or the great figures of a particular political movement. We remember the big artists and personalities, but don't feel obligated to them. |
20142 | The state begins with brutal conquest of a disorganised people, not with a 'contract' [Nietzsche] |
Full Idea: Some pack of blond beasts of prey, on a war footing, unscrupulously lays its dreadful paws on a populace which is shapeless. In this way the 'state' began on earth. I think I have dispensed with the fantasy which has it begin with a 'contract'. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], II.§17) | |
A reaction: [compressed] It is certainly likely that a tribe which got itself well organised and focused on some end would achieve total dominance over other tribes that just focus on food. |
23720 | Punishment makes people harder, more alienated, and hostile [Nietzsche] |
Full Idea: On the whole, punishment makes men harder and colder, it concentrates, it sharpens the feeling of alienation; it strengthens the power to resist. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], II.§14) | |
A reaction: If the school system involves routine harsh punishments, that means that the whole population ends up in that state. I would have thought that this was an obvious truth about punishment, but no one seems to want to face up to it. |
4410 | The truly great haters in world history have always been priests [Nietzsche] |
Full Idea: The truly great haters in world history have always been priests. | |
From: Friedrich Nietzsche (On the Genealogy of Morals [1887], I.§07) | |
A reaction: Wicked, but it has a lot of truth. Priests have a lot to defend, and a lot of reasons for feeling threatened. |