69 ideas
| 7846 | Nietzsche thinks philosophy makes us more profound, but not better [Nietzsche, by Ansell Pearson] |
| Full Idea: Nietzsche does not think philosopher exists to make us better human beings - but it can make us more profound ones. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by Keith Ansell Pearson - How to Read Nietzsche Intro | |
| A reaction: What is the point of being more 'profound' if that isn't 'better'? Are we sure that Kant is more 'profound' than a Yanomamo Indian? Personally I think philosophy tends to produce moral improvement, but I have seen a few striking counterexamples. |
| 20107 | How many mediocre thinkers are occupied with influential problems! [Nietzsche] |
| Full Idea: It is a terrible thought to contemplate that an immense number of mediocre thinkers are occupied with really influential matters. | |
| From: Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]), quoted by Rüdiger Safranski - Nietzsche: a philosophical biography 03 | |
| A reaction: [in a journal of 1867] What would he say now, with the plethora of academics and students aspiring to the highest levels of human thought? If I face up to the fact that I am 'mediocre', should I stop? And become mediocre at something else? |
| 20352 | Nietzsche has a metaphysics, as well as perspectives - the ontology is the perspectives [Nietzsche, by Richardson] |
| Full Idea: Nietzsche's thought includes both a metaphysics and a perspectivism, once these are more complexly grasped. But I argue that the metaphysics is basic: it's an ontology of perspectives. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by John Richardson - Nietzsche's System Intro | |
| A reaction: Very good. If it was just gormless relativism, which is what many people hope for in Nietzsche, why is it many perspectives? If they are just relative, having lots of them is no help. The point is they sum, and increase verisimilitude. |
| 20379 | Reason is just another organic drive, developing late, and fighting for equality [Nietzsche] |
| Full Idea: Reason is a support organ that slowly develops itself, ...and emancipates itself slowly to equal rights with the organic drives - so that reason (belief and knowledge) fights with the drives, as itself a new drive, very late come to preponderance. | |
| From: Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 9/11[243]), quoted by John Richardson - Nietzsche's System 4.3.2 n55 | |
| A reaction: A very powerful and fascinating idea. There is a silly post-modern tendency to think that Nietzsche denegrates and trivialises reason because of remarks like this, but he takes ranking the drives to be the supreme activity. I rank reason high. |
| 15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine] |
| Full Idea: The notion of a function evolved gradually from wanting to see what curves can be represented as trigonometric series. The study of arbitrary functions led Cantor to the ordinal numbers, which led to set theory. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite I |
| 18098 | Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock] |
| Full Idea: Cantor's diagonalisation argument generalises to show that any set has more subsets than it has members. | |
| From: report of George Cantor (works [1880]) by David Bostock - Philosophy of Mathematics 4.5 | |
| A reaction: Thus three members will generate seven subsets. This means that 'there is no end to the series of cardinal numbers' (Bostock p.106). |
| 13444 | Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD] |
| Full Idea: Cantor's Theorem says that for any set x, its power set P(x) has more members than x. | |
| From: report of George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 1 |
| 15505 | If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis] |
| Full Idea: Cantor taught that a set is 'a many, which can be thought of as one'. ...After a time the unfortunate beginner student is told that some classes - the singletons - have only a single member. Here is a just cause for student protest, if ever there was one. | |
| From: report of George Cantor (works [1880]) by David Lewis - Parts of Classes 2.1 | |
| A reaction: There is a parallel question, almost lost in the mists of time, of whether 'one' is a number. 'Zero' is obviously dubious, but if numbers are for counting, that needs units, so the unit is the precondition of counting, not part of it. |
| 10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter] |
| Full Idea: Cantor's theories exhibited the contradictions others had claimed to derive from the supposition of infinite sets as confusions resulting from the failure to mark the necessary distinctions with sufficient clarity. | |
| From: report of George Cantor (works [1880]) by Michael Potter - Set Theory and Its Philosophy Intro 1 |
| 10865 | The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg] |
| Full Idea: Cantor discovered that the continuum is the powerset of the integers. While adding or multiplying infinities didn't move up a level of complexity, multiplying a number by itself an infinite number of times did. | |
| From: report of George Cantor (works [1880]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.14 |
| 13016 | The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy] |
| Full Idea: Cantor first stated the Union Axiom in a letter to Dedekind in 1899. It is nearly too obvious to deserve comment from most commentators. Justifications usually rest on 'limitation of size' or on the 'iterative conception'. | |
| From: report of George Cantor (works [1880]) by Penelope Maddy - Believing the Axioms I §1.3 | |
| A reaction: Surely someone can think of some way to challenge it! An opportunity to become notorious, and get invited to conferences. |
| 14199 | Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley] |
| Full Idea: Cantor's definition of a set was a collection of its members into a whole, but within a few years Dedekind had the idea of a set as a container, enclosing its members like a sack. | |
| From: report of George Cantor (works [1880]) by Oliver,A/Smiley,T - What are Sets and What are they For? Intro | |
| A reaction: As the article goes on to show, these two view don't seem significantly different until you start to ask about the status of the null set and of singletons. I intuitively vote for Dedekind. Set theory is the study of brackets. |
| 13342 | Carnap defined consequence by contradiction, but this is unintuitive and changes with substitution [Tarski on Carnap] |
| Full Idea: Carnap proposed to define consequence as 'sentence X follows from the sentences K iff the sentences K and the negation of X are contradictory', but 1) this is intuitively impossible, and 2) consequence would be changed by substituting objects. | |
| From: comment on Rudolph Carnap (The Logical Syntax of Language [1934], p.88-) by Alfred Tarski - The Concept of Logical Consequence p.414 | |
| A reaction: This seems to be the first step in the ongoing explicit discussion of the nature of logical consequence, which is now seen by many as the central concept of logic. Tarski brings his new tool of 'satisfaction' to bear. |
| 13251 | Each person is free to build their own logic, just by specifying a syntax [Carnap] |
| Full Idea: In logic, there are no morals. Everyone is at liberty to build his own logic, i.e. his own form of language. All that is required is that he must state his methods clearly, and give syntactical rules instead of philosophical arguments. | |
| From: Rudolph Carnap (The Logical Syntax of Language [1934], §17), quoted by JC Beall / G Restall - Logical Pluralism 7.3 | |
| A reaction: This is understandable, but strikes me as close to daft relativism. If I specify a silly logic, I presume its silliness will be obvious. By what criteria? I say the world dictates the true logic, but this is a minority view. |
| 10082 | There are infinite sets that are not enumerable [Cantor, by Smith,P] |
| Full Idea: Cantor's Theorem (1874) says there are infinite sets that are not enumerable. This is proved by his 1891 'diagonal argument'. | |
| From: report of George Cantor (works [1880]) by Peter Smith - Intro to Gödel's Theorems 2.3 | |
| A reaction: [Smith summarises the diagonal argument] |
| 13483 | Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it [Cantor, by Hart,WD] |
| Full Idea: The problem of Cantor's Paradox is that the power set of the universe has to be both bigger than the universe (by Cantor's theorem) and not bigger (since it is a subset of the universe). | |
| From: report of George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 3 | |
| A reaction: Russell eliminates the 'universe' in his theory of types. I don't see why you can't just say that the members of the set are hypothetical rather than real, and that hypothetically the universe might contain more things than it does. |
| 8710 | The powerset of all the cardinal numbers is required to be greater than itself [Cantor, by Friend] |
| Full Idea: Cantor's Paradox says that the powerset of a set has a cardinal number strictly greater than the original set, but that means that the powerset of the set of all the cardinal numbers is greater than itself. | |
| From: report of George Cantor (works [1880]) by Michèle Friend - Introducing the Philosophy of Mathematics | |
| A reaction: Friend cites this with the Burali-Forti paradox and the Russell paradox as the best examples of the problems of set theory in the early twentieth century. Did this mean that sets misdescribe reality, or that we had constructed them wrongly? |
| 15910 | Cantor named the third realm between the finite and the Absolute the 'transfinite' [Cantor, by Lavine] |
| Full Idea: Cantor believed he had discovered that between the finite and the 'Absolute', which is 'incomprehensible to the human understanding', there is a third category, which he called 'the transfinite'. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite III.4 |
| 15905 | Cantor proved the points on a plane are in one-to-one correspondence to the points on a line [Cantor, by Lavine] |
| Full Idea: In 1878 Cantor published the unexpected result that one can put the points on a plane, or indeed any n-dimensional space, into one-to-one correspondence with the points on a line. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite III.1 |
| 9983 | Cantor took the ordinal numbers to be primary [Cantor, by Tait] |
| Full Idea: Cantor took the ordinal numbers to be primary: in his generalization of the cardinals and ordinals into the transfinite, it is the ordinals that he calls 'numbers'. | |
| From: report of George Cantor (works [1880]) by William W. Tait - Frege versus Cantor and Dedekind VI | |
| A reaction: [Tait says Dedekind also favours the ordinals] It is unclear how the matter might be settled. Humans cannot give the cardinality of large groups without counting up through the ordinals. A cardinal gets its meaning from its place in the ordinals? |
| 17798 | Cantor presented the totality of natural numbers as finite, not infinite [Cantor, by Mayberry] |
| Full Idea: Cantor taught us to regard the totality of natural numbers, which was formerly thought to be infinite, as really finite after all. | |
| From: report of George Cantor (works [1880]) by John Mayberry - What Required for Foundation for Maths? p.414-2 | |
| A reaction: I presume this is because they are (by definition) countable. |
| 9971 | Cantor introduced the distinction between cardinals and ordinals [Cantor, by Tait] |
| Full Idea: Cantor introduced the distinction between cardinal and ordinal numbers. | |
| From: report of George Cantor (works [1880]) by William W. Tait - Frege versus Cantor and Dedekind Intro | |
| A reaction: This seems remarkably late for what looks like a very significant clarification. The two concepts coincide in finite cases, but come apart in infinite cases (Tait p.58). |
| 9892 | Cantor showed that ordinals are more basic than cardinals [Cantor, by Dummett] |
| Full Idea: Cantor's work revealed that the notion of an ordinal number is more fundamental than that of a cardinal number. | |
| From: report of George Cantor (works [1880]) by Michael Dummett - Frege philosophy of mathematics Ch.23 | |
| A reaction: Dummett makes it sound like a proof, which I find hard to believe. Is the notion that I have 'more' sheep than you logically prior to how many sheep we have? If I have one more, that implies the next number, whatever that number may be. Hm. |
| 14136 | A cardinal is an abstraction, from the nature of a set's elements, and from their order [Cantor] |
| Full Idea: The cardinal number of M is the general idea which, by means of our active faculty of thought, is deduced from the collection M, by abstracting from the nature of its diverse elements and from the order in which they are given. | |
| From: George Cantor (works [1880]), quoted by Bertrand Russell - The Principles of Mathematics §284 | |
| A reaction: [Russell cites 'Math. Annalen, XLVI, §1'] See Fine 1998 on this. |
| 11015 | Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 [Cantor, by Read] |
| Full Idea: Cantor's diagonal argument showed that all the infinite decimals between 0 and 1 cannot be written down even in a single never-ending list. | |
| From: report of George Cantor (works [1880]) by Stephen Read - Thinking About Logic Ch.6 |
| 15906 | Cantor tried to prove points on a line matched naturals or reals - but nothing in between [Cantor, by Lavine] |
| Full Idea: Cantor said he could show that every infinite set of points on the line could be placed into one-to-one correspondence with either the natural numbers or the real numbers - with no intermediate possibilies (the Continuum hypothesis). His proof failed. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite III.1 |
| 15903 | A real is associated with an infinite set of infinite Cauchy sequences of rationals [Cantor, by Lavine] |
| Full Idea: Cantor's theory of Cauchy sequences defines a real number to be associated with an infinite set of infinite sequences of rational numbers. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite II.6 | |
| A reaction: This sounds remarkably like the endless decimals we use when we try to write down an actual real number. |
| 18251 | Irrational numbers are the limits of Cauchy sequences of rational numbers [Cantor, by Lavine] |
| Full Idea: Cantor introduced irrationals to play the role of limits of Cauchy sequences of rational numbers. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite 4.2 |
| 15902 | Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties [Cantor, by Lavine] |
| Full Idea: From the very nature of an irrational number, it seems necessary to understand the mathematical infinite thoroughly before an adequate theory of irrationals is possible. Infinite classes are obvious in the Dedekind Cut, but have logical difficulties | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite II Intro | |
| A reaction: Almost the whole theory of analysis (calculus) rested on the irrationals, so a theory of the infinite was suddenly (in the 1870s) vital for mathematics. Cantor wasn't just being eccentric or mystical. |
| 15908 | It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers [Cantor, by Lavine] |
| Full Idea: Cantor's 1891 diagonal argument revealed there are infinitely many infinite powers. Indeed, it showed more: it shows that given any set there is another of greater power. Hence there is an infinite power strictly greater than that of the set of the reals. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite III.2 |
| 13464 | Cantor proposes that there won't be a potential infinity if there is no actual infinity [Cantor, by Hart,WD] |
| Full Idea: What we might call 'Cantor's Thesis' is that there won't be a potential infinity of any sort unless there is an actual infinity of some sort. | |
| From: report of George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 1 | |
| A reaction: This idea is nicely calculated to stop Aristotle in his tracks. |
| 10112 | The naturals won't map onto the reals, so there are different sizes of infinity [Cantor, by George/Velleman] |
| Full Idea: Cantor showed that the complete totality of natural numbers cannot be mapped 1-1 onto the complete totality of the real numbers - so there are different sizes of infinity. | |
| From: report of George Cantor (works [1880]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.4 |
| 17889 | CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner] |
| Full Idea: Cantor's Continuum Hypothesis (CH) says that for every infinite set X of reals there is either a one-to-one correspondence between X and the natural numbers, or between X and the real numbers. | |
| From: report of George Cantor (works [1880]) by Peter Koellner - On the Question of Absolute Undecidability 1.2 | |
| A reaction: Every single writer I read defines this differently, which drives me crazy, but is also helpfully illuminating. There is a moral there somewhere. |
| 10883 | Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers [Cantor, by Horsten] |
| Full Idea: Cantor's Continuum Hypothesis states that there are no sets which are too large for there to be a one-to-one correspondence between the set and the natural numbers, but too small for there to exist a one-to-one correspondence with the real numbers. | |
| From: report of George Cantor (works [1880]) by Leon Horsten - Philosophy of Mathematics §5.1 |
| 8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
| Full Idea: Cantor's 'continuum hypothesis' is the assertion that there are no infinite cardinalities strictly between the size of the natural numbers and the size of the real numbers. | |
| From: report of George Cantor (works [1880]) by Stewart Shapiro - Thinking About Mathematics 2.4 | |
| A reaction: The tricky question is whether this hypothesis can be proved. |
| 13528 | Continuum Hypothesis: there are no sets between N and P(N) [Cantor, by Wolf,RS] |
| Full Idea: Cantor's conjecture (the Continuum Hypothesis) is that there are no sets between N and P(N). The 'generalized' version replaces N with an arbitrary infinite set. | |
| From: report of George Cantor (works [1880]) by Robert S. Wolf - A Tour through Mathematical Logic 2.2 | |
| A reaction: The initial impression is that there is a single gap in the numbers, like a hole in ozone layer, but the generalised version implies an infinity of gaps. How can there be gaps in the numbers? Weird. |
| 9555 | Continuum Hypothesis: no cardinal greater than aleph-null but less than cardinality of the continuum [Cantor, by Chihara] |
| Full Idea: Cantor's Continuum Hypothesis was that there is no cardinal number greater than aleph-null but less than the cardinality of the continuum. | |
| From: report of George Cantor (works [1880]) by Charles Chihara - A Structural Account of Mathematics 05.1 | |
| A reaction: I have no view on this (have you?), but the proposal that there are gaps in the number sequences has to excite all philosophers. |
| 13447 | Cantor: there is no size between naturals and reals, or between a set and its power set [Cantor, by Hart,WD] |
| Full Idea: Cantor conjectured that there is no size between those of the naturals and the reals - called the 'continuum hypothesis'. The generalized version says that for no infinite set A is there a set larger than A but smaller than P(A). | |
| From: report of George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 1 | |
| A reaction: Thus there are gaps between infinite numbers, and the power set is the next size up from any infinity. Much discussion as ensued about whether these two can be proved. |
| 15893 | Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine] |
| Full Idea: Cantor's set theory was not of collections in some familiar sense, but of collections that can be counted using the indexes - the finite and transfinite ordinal numbers. ..He treated infinite collections as if they were finite. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite I |
| 18174 | Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy] |
| Full Idea: Cantor's second innovation was to extend the sequence of ordinal numbers into the transfinite, forming a handy scale for measuring infinite cardinalities. | |
| From: report of George Cantor (works [1880]) by Penelope Maddy - Naturalism in Mathematics I.1 | |
| A reaction: Struggling with this. The ordinals seem to locate the cardinals, but in what sense do they 'measure' them? |
| 18173 | Cardinality strictly concerns one-one correspondence, to test infinite sameness of size [Cantor, by Maddy] |
| Full Idea: Cantor's first innovation was to treat cardinality as strictly a matter of one-to-one correspondence, so that the question of whether two infinite sets are or aren't of the same size suddenly makes sense. | |
| From: report of George Cantor (works [1880]) by Penelope Maddy - Naturalism in Mathematics I.1 | |
| A reaction: It makes sense, except that all sets which are infinite but countable can be put into one-to-one correspondence with one another. What's that all about, then? |
| 10232 | Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro] |
| Full Idea: Cantor's theorem entails that there are more property extensions than objects. So there are not enough objects in any domain to serve as extensions for that domain. So Frege's view that numbers are objects led to the Caesar problem. | |
| From: report of George Cantor (works [1880]) by Stewart Shapiro - Philosophy of Mathematics 4.6 | |
| A reaction: So the possibility that Caesar might have to be a number arises because otherwise we are threatening to run out of numbers? Is that really the problem? |
| 18176 | Pure mathematics is pure set theory [Cantor] |
| Full Idea: Pure mathematics ...according to my conception is nothing other than pure set theory. | |
| From: George Cantor (works [1880], I.1), quoted by Penelope Maddy - Naturalism in Mathematics I.1 | |
| A reaction: [an unpublished paper of 1884] So right at the beginning of set theory this claim was being made, before it was axiomatised, and so on. Zermelo endorsed the view, and it flourished unchallenged until Benacerraf (1965). |
| 8631 | Cantor says that maths originates only by abstraction from objects [Cantor, by Frege] |
| Full Idea: Cantor calls mathematics an empirical science in so far as it begins with consideration of things in the external world; on his view, number originates only by abstraction from objects. | |
| From: report of George Cantor (works [1880]) by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §21 | |
| A reaction: Frege utterly opposed this view, and he seems to have won the day, but I am rather thrilled to find the great Cantor endorsing my own intuitions on the subject. The difficulty is to explain 'abstraction'. |
| 20123 | First see nature as non-human, then fit ourselves into this view of nature [Nietzsche] |
| Full Idea: My task is the dehumanisation of nature, and then the naturalisation of humanity once it has attained the pure concept of 'nature'. | |
| From: Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 9.525), quoted by Rüdiger Safranski - Nietzsche: a philosophical biography 10 | |
| A reaction: Safranski sees this as summarising Nietzsche's project, and it could be a mission statement for naturalism. This idea pinpoints why I take Nietzsche to be important - as a pioneer of the naturalistic view of people. |
| 20105 | Storms are wonderful expressions of free powers! [Nietzsche] |
| Full Idea: How different the lightning, the storm, the hail, free powers, without ethics! How happy, how powerful they are, pure will, untarnished by intellect! | |
| From: Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 2.122), quoted by Rüdiger Safranski - Nietzsche: a philosophical biography 02 | |
| A reaction: Nietzsche was a perfect embodiment of the Romantic Movement! I take this to be a deep observation, since I think raw powers are the most fundamental aspect of nature. Schopenhauer is behind this idea. |
| 20376 | We begin with concepts of kinds, from individuals; but that is not the essence of individuals [Nietzsche] |
| Full Idea: The overlooking of individuals gives us the concept and with this our knowledge begins: in categorising, in the setting up of kinds. But the essence of things does not correspond to this. | |
| From: Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], p.51) | |
| A reaction: [dated c1873] Aha! So Nietzsche agrees with me in my defence of individual essences, against kind essences (which seem to me to obviously derive from the nature of individuals). Deep in my heart I knew I would find this quotation one day. |
| 8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
| Full Idea: Cantor (in his exploration of infinities) pushed the bounds of conceivability further than anyone before him. To discover what is conceivable, we have to enquire into the concept. | |
| From: report of George Cantor (works [1880]) by Michèle Friend - Introducing the Philosophy of Mathematics 6.5 | |
| A reaction: This remark comes during a discussion of Husserl's phenomenology. Intuitionists challenge Cantor's claim, and restrict what is conceivable to what is provable. Does possibility depend on conceivability? |
| 13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
| Full Idea: Cantor thought that we abstract a number as something common to all and only those sets any one of which has as many members as any other. ...However one wants to see the logic of the inference. The irony is that set theory lays out this logic. | |
| From: comment on George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 1 | |
| A reaction: The logic Hart has in mind is the notion of an equivalence relation between sets. This idea sums up the older and more modern concepts of abstraction, the first as psychological, the second as logical (or trying very hard to be!). Cf Idea 9145. |
| 22501 | Nietzsche classified actions by the nature of the agent, not the nature of the act [Nietzsche, by Foot] |
| Full Idea: Nietzsche thought profoundly mistaken a taxonomy that classified actions as the doing of this or that, insisting that the true nature of an action depended rather on the nature of the individual who did it. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 7) by Philippa Foot - Natural Goodness 7 | |
| A reaction: This is more in the spirit of Aristotle than in the modern legalistic style. It seems to totally ignore consequences, which would puzzle victims or beneficiaries of the action. |
| 22500 | Nietzsche failed to see that moral actions can be voluntary without free will [Foot on Nietzsche] |
| Full Idea: To threaten morality Nietzsche needed to show not only that free will was an illusion, but also that no other distinction between voluntary and involuntary action (Aristotle's, for instance) would do instead. He seems to be wrong about this. | |
| From: comment on Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 7) by Philippa Foot - Natural Goodness | |
| A reaction: Just the idea I have been seeking! There is no free will, so in what way are we responsible? Simple: we are responsible for any act which can be shown to be voluntary. It can't just be any action we fully caused, because of accidents. |
| 20128 | Each person has a fixed constitution, which makes them a particular type of person [Nietzsche, by Leiter] |
| Full Idea: Nietzsche's view (which we may call the 'Doctrine of Types') is that each person has a fixed psycho-physical constitution, which defines him as a particular type of person. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by Brian Leiter - Nietzsche On Morality 1 'What kind' | |
| A reaction: An interestesting variant, standing between the Aristotelian picture of one shared human nature, and the existentialist picture of our endlessly malleable nature. So what type am I, and what type are you? How many types are there? |
| 22503 | Nietzsche could only revalue human values for a different species [Nietzsche, by Foot] |
| Full Idea: It is only for a different species that Nietzsche's most radical revaluation of values could be valid. It is not valid for us as we are, or are ever likely to be. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by Philippa Foot - Natural Goodness 7 | |
| A reaction: This is the Aristotelian view, that our values and virtues arise out of our human nature, with which I largely agree, though we should resist its rather conservative tendencies. |
| 8041 | The superman is a monstrous oddity, not a serious idea [MacIntyre on Nietzsche] |
| Full Idea: The Übermensch belongs in the pages of a philosophical bestiary rather than in serious discussion. | |
| From: comment on Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by Alasdair MacIntyre - After Virtue: a Study in Moral Theory Ch.2 | |
| A reaction: It may just be an empirical and historical fact that the value-systems of a culture arise from the characters of a few strong-willed and charismatic individuals, rather than from collective need - let along collective philosophising. |
| 20135 | Nietzsche's higher type of man is much more important than the idealised 'superman' [Nietzsche, by Leiter] |
| Full Idea: The 'superman' has received far more attention from commentators than it warrants: the higher type of human being (a Goethe or a Nietzsche) is much more important than the hyperbolic, and often obscure, Zarathustrian rhetoric about the über-mensch. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by Brian Leiter - Nietzsche On Morality 4 'Higher' n2 | |
| A reaction: Leiter says the über-mensch idea almost entirely drops out of Nietzsche's mature work. |
| 20353 | The 'will to power' is basically applied to drives and forces, not to people [Nietzsche, by Richardson] |
| Full Idea: 'Will to power' is most basically applied not to people but to 'drives' or 'forces', simpler units which Nietzsche sometimes calls 'points' and 'power quanta'. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 1) by John Richardson - Nietzsche's System 1 | |
| A reaction: This strikes as a correct account of Nietzsche, and a hugely important interpretative point. He wasn't saying that all human beings would conquer the world if they could. The point is there are many conflicting and combining wills to power. |
| 20113 | Friendly chats undermine my philosophy; wanting to be right at the expense of love is folly [Nietzsche] |
| Full Idea: My entire philosophy wavers after just an hour of friendly conversation with complete strangers. It strikes me as so foolish to insist on being right at the expense of love. | |
| From: Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 6.37), quoted by Rüdiger Safranski - Nietzsche: a philosophical biography 09 | |
| A reaction: [Letter to Gast, 1880] Strangers who met Nietzsche on walks reported how kind and friendly he was. Most people want to be right most of the time, but a few people have this vice in rather excessive form. Especially philosophers! |
| 22475 | Moral generalisation is wrong, because we should evaluate individual acts [Nietzsche, by Foot] |
| Full Idea: Nietzsche believed that moral generalisation was impossible because the proper subject of evaluation was, instead, a person's individual act. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by Philippa Foot - Nietzsche's Immoralism p.155 | |
| A reaction: This suggests a different type of particularism, focusing on the particular decision, rather than on the details of the situation. Presumable no two moral decisions are ever sufficiently the same to be compared. But a lie is a lie. |
| 22476 | Nietzsche thought our psychology means there can't be universal human virtues [Nietzsche, by Foot] |
| Full Idea: Nietzsche believed, in effect, that as the facts of human psychology really were, there could be no such thing as human virtues, dispositions good in any man. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by Philippa Foot - Nietzsche's Immoralism p.157 | |
| A reaction: Presumably each individual can only have virtues appropriate to their individual nature, which is something like channelling their personal psychological drives. Can't we each have our individual version of courage or honesty? |
| 20104 | Nietzsche tried to lead a thought-provoking life [Safranski on Nietzsche] |
| Full Idea: All of us ponder our existences, but Nietzsche strove to lead the kind of life that would yield food for thought. | |
| From: comment on Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 01) by Rüdiger Safranski - Nietzsche: a philosophical biography 01 | |
| A reaction: Could Nietzsche possibly be a role model for us in this respect? If I were starting afresh, guided by this thought, I'm not sure how I would go about it. It is Nietzsche's astonishing independence of thought that hits you. |
| 7847 | Initially nihilism was cosmic, but later Nietzsche saw it as a cultural matter [Nietzsche, by Ansell Pearson] |
| Full Idea: Nietzsche's first presentation of nihilism is an existential affair arising from cosmic problems, but he later stressed nihilism as a historical and cultural problem of values, where mankind's highest values reach a point of devaluation. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by Keith Ansell Pearson - How to Read Nietzsche Ch.1 | |
| A reaction: The second version seems to imply a quasi-Marxist determinism about social progress. Then you would have to ask, what is the point of fighting against it? I wonder if Nietzsche's values are anti-nihilist, but his metaethics makes nihilism unavoidable? |
| 9782 | Nietzsche urges that nihilism be active, and will nothing itself [Nietzsche, by Zizek] |
| Full Idea: Nietzsche opposes active to passive nihilism - it is better to actively will nothing itself than not to will anything. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by Slavoj Zizek - Conversations, with Glyn Daly §3 | |
| A reaction: To 'actively will nothing' sounds to me indistinguishable from suicide, which I don't believe was ever on Nietzsche's agenda. It is hard, though, to disentangle Nietzsche's attitude to nihilism. |
| 20102 | Flight from boredom leads to art [Nietzsche] |
| Full Idea: Flight from boredom is the mother of all art. | |
| From: Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 8.432), quoted by Rüdiger Safranski - Nietzsche: a philosophical biography Intro | |
| A reaction: I might even say that all human achievement comes from boredom. |
| 20106 | Nietzsche was fascinated by a will that can turn against itself [Nietzsche, by Safranski] |
| Full Idea: Nietzsche was fascinated by the idea of a will that turns against itself, against its usual impulses. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by Rüdiger Safranski - Nietzsche: a philosophical biography 03 | |
| A reaction: This strikes me as very existentialist - a case of existence before essence. |
| 20367 | Individual development is more important than the state, but a community is necessary [Nietzsche] |
| Full Idea: All states and communities are something lower than the individual, but necessary kinds for his higher development. | |
| From: Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 10/7[98]), quoted by John Richardson - Nietzsche's System 2.4 n104 | |
| A reaction: This indicates why Nietzsche should not really be taken as a political thinker, though I would say there is a sort of communitarianism implied in this, just as for Aristotle virtue is supreme, which needs social expression. |
| 20371 | Nietzsche thinks we should join a society, in order to criticise, heal and renew it [Nietzsche, by Richardson] |
| Full Idea: Nietzsche thinks the best way of both joining and opposing a society is to find where it's sick, to be its merciless critic and exposer, and to help heal and renew it. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by John Richardson - Nietzsche's System 3.3 | |
| A reaction: This sounds like the great Victorian sages, such as Ruskin and Arnold. Christopher Hitchens was a nice recent example. Maybe these have been the finest British citizens? |
| 20108 | Every culture loses its identity and power if it lacks a major myth [Nietzsche] |
| Full Idea: Without myth every culture loses its natural healthy creating power: only a horizon encircled with myths can mark off a cultural movement as a discrete unit. | |
| From: Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 1.145) | |
| A reaction: In the early part of his career this was a big idea for Nietzsche, especially associated with Wagner's Ring, but he moved away from the idea later. |
| 10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
| Full Idea: Cantor proved that one-dimensional space has exactly the same number of points as does two dimensions, or our familiar three-dimensional space. | |
| From: report of George Cantor (works [1880]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.14 |
| 13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |
| Full Idea: Cantor said that only God is absolutely infinite. | |
| From: report of George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 1 | |
| A reaction: We are used to the austere 'God of the philosophers', but this gives us an even more austere 'God of the mathematicians'. |