78 ideas
| 14888 | Wisdom prevents us from being ruled by the moment [Nietzsche] |
| Full Idea: The most important thing about wisdom is that it prevents human beings from being ruled by the moment. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 30 [25]) |
| 14863 | Unlike science, true wisdom involves good taste [Nietzsche] |
| Full Idea: Inherent in wisdom [sophia] is discrimination, the possession of good taste: whereas science, lacking such a refined sense of taste, gobbles up anything that is worth knowing. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [086]) | |
| A reaction: This is blatantly unfair to science, which may lack 'taste', but at least prefers deep theories with wide-ranging explanatory power to narrow local theories. Maybe the line across the philosophical community is the one picking out those with taste? |
| 14890 | Suffering is the meaning of existence [Nietzsche] |
| Full Idea: Suffering is the meaning of existence. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 32 [67]) | |
| A reaction: This doesn't mean that he is advocating suffering. The context of his remark is that the pursuit of truth involves suffering. |
| 14861 | Philosophy ennobles the world, by producing an artistic conception of our knowledge [Nietzsche] |
| Full Idea: Philosophy is indispensable for education because it draws knowledge into an artistic conception of the world, and thereby ennobles it. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [052]) | |
| A reaction: I take this to be an unusual way of saying that philosophy aims at the unification of knowledge, which is roughly my own view. It has hard for us to keep believing that life could be 'ennobled'. |
| 14885 | The first aim of a philosopher is a life, not some works [Nietzsche] |
| Full Idea: The philosopher's product is his life (first, before his works). It is his work of art. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 29 [205]) |
| 14887 | You should only develop a philosophy if you are willing to live by it [Nietzsche] |
| Full Idea: One should have a philosophy only to the extent that one is capable of living according to this philosophy: so that everything does not become mere words. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 30 [17]) |
| 14889 | Philosophy is pointless if it does not advocate, and live, a new way of life [Nietzsche] |
| Full Idea: As long as philosophers do not muster the courage to advocate a lifestyle structured in an entirely different way and demonstrate it by their own example, they will come to nothing. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 31 [10]) | |
| A reaction: This is a pretty tough requirement for the leading logicians and metaphysicians of our day, but they must face their marginality. The public will only be interested in philosophers who advocate new ways of living. |
| 14862 | Philosophy is more valuable than much of science, because of its beauty [Nietzsche] |
| Full Idea: The reason why unprovable philosophizing still has some value - more value, in fact, than many a scientific proposition - lies in the aesthetic value of such philosophizing, that is, in its beauty and sublimity. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [076]) | |
| A reaction: I am increasingly inclined to agree. I love wide-ranging and ambitious works of metaphysics, each of which is a unique creation of the human intellect (and with which no other individual will ever entirely agree). A great short paper is also beautiful. |
| 14878 | It would better if there was no thought [Nietzsche] |
| Full Idea: It would be better if thought did not exist at all. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 29 [004]) |
| 14881 | Why do people want philosophers? [Nietzsche] |
| Full Idea: Why do human beings even want philosophers? | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 29 [019]) | |
| A reaction: It is not clear, of course, that they do want philosophers. The standard attitude to them seems to be a mixture of contempt and fear. |
| 14876 | Philosophy is always secondary, because it cannot support a popular culture [Nietzsche] |
| Full Idea: It is not possible to base a popular culture on philosophy. Thus, with regard to culture, philosophy never can have primary, but always only secondary, significance. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 23 [14]) | |
| A reaction: It is the brilliance of Christianity as a set of ideas that it is simple enough to found a popular culture. A complex theology would make that impossible. Luther brought it back to its roots, when the priesthood lost touch with the people. |
| 14860 | Kant has undermined our belief in metaphysics [Nietzsche] |
| Full Idea: In a certain sense, Kant's influence was detrimental; for the belief in metaphysics has been lost. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [028]) | |
| A reaction: As I understand it, there are two interpretations of Kant, one of which is fairly thoroughly anti-metaphysical, and another which is less so. Also one path leads to idealism and the other doesn't, but I need to research that. |
| 14859 | If philosophy controls science, then it has to determine its scope, and its value [Nietzsche] |
| Full Idea: The philosophy that is in control of science must also consider the extent to which science should be allowed to develop; it must determine its value! | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [024]) |
| 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 |
| 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 |
| 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). |
| 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. |
| 14880 | Logic is just slavery to language [Nietzsche] |
| Full Idea: Logic is merely slavery in the fetters of language. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 29 [008]) | |
| A reaction: I don't think I agree with this, but I still like it. |
| 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. |
| 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 |
| 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 |
| 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 |
| 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. |
| 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. |
| 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. |
| 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 |
| 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. |
| 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? |
| 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 |
| 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'. |
| 14869 | If some sort of experience is at the root of matter, then human knowledge is close to its essence [Nietzsche] |
| Full Idea: If pleasure, displeasure, sensation, memory, reflex movements are all part of the essence of matter, then human knowledge penetrates far more deeply into the essence of things. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [161]) | |
| A reaction: I don't think Nietzsche is thinking of monads at this point, but his idea certainly applies to them. Leibniz rested his whole theory on the close analogy between how minds work and how matter must also work. |
| 14875 | Belief matters more than knowledge, and only begins when knowledge ceases [Nietzsche] |
| Full Idea: The human being starts to believe when he ceases to know. …Knowledge is not as important for the welfare of human beings as is belief. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 21 [13]) | |
| A reaction: The first idea is now associated with Williamson (and Hossack). The second is something like the pragmatic view of belief espoused by Ramsey. |
| 14866 | It always remains possible that the world just is the way it appears [Nietzsche] |
| Full Idea: Against Kant we can still object, even if we accept all his propositions, that it is still possible that the world is as it appears to us. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [125]) | |
| A reaction: This little thought at least seems to be enough to block the slide from phenomenalism into total idealism. The idea that direct realism can never be ruled out, even if it is false, is very striking. |
| 14872 | Our knowledge is illogical, because it rests on false identities between things [Nietzsche] |
| Full Idea: Every piece of knowledge that is beneficial to us involves an identification of nonidentical things, of things that are similar, which means that it is essentially illogical. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [236]) | |
| A reaction: I take the thought to be that no two tigers are alike, but we call them all 'tigers' and merge them into a type, and then all our knowledge is based on this distortion. A wonderful idea. I love particulars You should love particulars. |
| 14879 | The most extreme scepticism is when you even give up logic [Nietzsche] |
| Full Idea: Even skepticism contains a belief: the belief in logic. The most extreme position is hence the abandoning of logic. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 29 [008]) | |
| A reaction: Some might say that flirting with non-classical logic (as in Graham Priest) is precisely travelling down this road. You could also be sceptical about meaning in language, so you couldn't articulate your abandonment of logic. |
| 14873 | If we find a hypothesis that explains many things, we conclude that it explains everything [Nietzsche] |
| Full Idea: The feeling of certainty is the most difficult to develop. Initially one seeks explanation: if a hypothesis explains many things, we draw the conclusion that it explains everything. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [238]) | |
| A reaction: As so often, a wonderful warning from Nietzsche to other philosophers. They love to latch onto a Big Idea, and offer it as the answer to everything (especially, dare I say it, continental philosophers). |
| 14868 | Our primary faculty is perception of structure, as when looking in a mirror [Nietzsche] |
| Full Idea: The primary faculty seems to me to be the perception of structure, that is, based upon the mirror. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [153]) | |
| A reaction: The point about the mirror makes this such an intriguingly original idea. Personally I like very much the idea that structure is our prime perception. See Sider 2011 on structure. |
| 14870 | We experience causation between willing and acting, and thereby explain conjunctions of changes [Nietzsche] |
| Full Idea: The only form of causality of which we are aware is that between willing and acting - we transfer this to all things, and thereby explain the relationship between two changes that always occur together. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [209]) | |
| A reaction: This is a rather Humean view, of projecting our experience onto the world, but it may be that we really are experiencing real causation, just as it occurs between insentiate things. |
| 3444 | If actions are not caused by other events, and are not causeless, they must be caused by the person [Chisholm] |
| Full Idea: If the action is not caused by some other event, and it is not causeless, this leaves the possibility that it is caused by something else instead, and this something can only be the agent, the man. | |
| From: Roderick Chisholm (Human Freedom and the Self [1964], p.28) |
| 3446 | For Hobbes (but not for Kant) a person's actions can be deduced from their desires and beliefs [Chisholm] |
| Full Idea: According to Hobbes, if we fully know what a man desires and believes, and we know the state of his physical stimuli, we may logically deduce what he will try to do. But Kant says no such statements can ever imply what a man will do. | |
| From: Roderick Chisholm (Human Freedom and the Self [1964], p.32) |
| 9268 | If free will miraculously interrupts causation, animals might do that; why would we want to do it? [Frankfurt on Chisholm] |
| Full Idea: Chisholm holds the quaint doctrine that human freedom entails an absence of causal determination; a free action is a miracle. This gives no basis for doubting that animals have such freedom; and why would we care whether we can interrupt the causal order? | |
| From: comment on Roderick Chisholm (Human Freedom and the Self [1964]) by Harry G. Frankfurt - Freedom of the Will and concept of a person §IV | |
| A reaction: [compressed] Chisholm is the spokesman for 'agent causation', Frankfurt for freedom as second-level volitions. I'm with Frankfurt. The belief in 'agents' and 'free will' may sound plausible, until the proposal is spelled out in causal terms. |
| 14867 | It is just madness to think that the mind is supernatural (or even divine!) [Nietzsche] |
| Full Idea: To view 'spirit', the product of the brain, as supernatural. Even to deify it. What madness! | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [127]) | |
| A reaction: When I started philolosophy I was obliged to take mind-body dualism very seriously, but I have finally managed to drag myself to the shores of this lake of madness, where Nietzsche awaited with a helping hand. |
| 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. |
| 3442 | Responsibility seems to conflict with events being either caused or not caused [Chisholm] |
| Full Idea: The free will problem is that humans seem to be responsible, but this seems to conflict with the idea that every event is caused by some other event, and it also conflicts with the view that the action is not caused at all. | |
| From: Roderick Chisholm (Human Freedom and the Self [1964], p.24) |
| 3443 | Desires may rule us, but are we responsible for our desires? [Chisholm] |
| Full Idea: If a flood of desires causes a weak-willed man to give in to temptation, …the question now becomes, is he responsible for the beliefs and desires he happens to have? | |
| From: Roderick Chisholm (Human Freedom and the Self [1964], p.25) |
| 14884 | The shortest path to happiness is forgetfulness, the path of animals (but of little value) [Nietzsche] |
| Full Idea: If happiness were the goal, then animals would be the highest creatures. Their cynicism is grounded in forgetfulness: that is the shortest path to happiness, even if it is a happiness with little value. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 29 [143]) | |
| A reaction: I would be reluctant to describe an apparently contented cow as 'happy'. Is a comatose person happy? Maybe happiness is fulfilling one's nature, like a monkey swinging through trees? |
| 14886 | Education is contrary to human nature [Nietzsche] |
| Full Idea: Education runs contrary to the nature of a human being. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 30 [06]) | |
| A reaction: Tell me about it! |
| 14883 | We should evaluate the past morally [Nietzsche] |
| Full Idea: For the past I desire above all a moral evaluation. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 29 [096]) | |
| A reaction: There is a bit of a contradiction with Idea 14819, of only a few years later. He was always interested in a historical approach to morality, but I'm not sure if his ethics gives a decent basis for moral assessments of remote historical eras. |
| 14882 | Protest against vivisection - living things should not become objects of scientific investigation [Nietzsche] |
| Full Idea: Protest against vivisection of living things, that is, those things that are not yet dead should be allowed to live and not immediately be treated as an object for scientific investigation. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 29 [027]) | |
| A reaction: Wow. How many other people had come up with this idea in 1873? |
| 14865 | We do not know the nature of one single causality [Nietzsche] |
| Full Idea: We do not know the nature of one single causality. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [121]) |
| 3445 | Causation among objects relates either events or states [Chisholm] |
| Full Idea: Between natural objects we may say that causation is a relation between events or states of affairs. | |
| From: Roderick Chisholm (Human Freedom and the Self [1964], p.28) |
| 14871 | Laws of nature are merely complex networks of relations [Nietzsche] |
| Full Idea: All laws of nature are only relations between x, y and z. We define laws of nature as relations to an x, y, and z, each of which in turn, is known to us only in relation to other x's, y's and z's. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [235]) | |
| A reaction: This could be interpreted in Armstrong's terms, as only identifying the x's, y's and z's by their universals, and then seeing laws as how those universal relate. I suspect, though, that Nietzsche has a Humean regularity pattern in mind. |
| 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'. |
| 14864 | The Greeks lack a normative theology: each person has their own poetic view of things [Nietzsche] |
| Full Idea: The Greeks lack a normative theology: everyone has the right to deal with it in a poetic manner and he can believe whatever he wants. | |
| From: Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 19 [110]) | |
| A reaction: There is quite a lot of record of harshness towards atheists, and the trial of Socrates seems to have been partly over theology. However, no proper theological texts have come down, or records of the teachings of the priests. |