61 ideas
| 23755 | Genius and love of truth are always accompanied by great humility [Weil] |
| Full Idea: Love of truth is always accompanied by humility, and real genius is nothing else but the supernatural virtue of humility in the domain of thought. | |
| From: Simone Weil (Human Personality [1943], p.87) | |
| A reaction: A striking and attractive thought, true of all the lovers of truth I have ever encountered. Socrates is the role model. She likens truth to an inarticulate plaintiff stammering before a judge who fluently manipulates opinions. |
| 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. |
| 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'. |
| 18278 | Kant showed that our perceptions are partly constructed from our concepts [Reichenbach] |
| Full Idea: It was Kant's great discovery that the object of knowledge is not simply given but constructed, and that it contains conceptual elements not contained in pure perception. | |
| From: Hans Reichenbach (The Theory of Relativity and A Priori Knowledge [1965], p.49), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap |
| 23747 | What is sacred is not a person, but the whole physical human being [Weil] |
| Full Idea: There is something sacred in every man, but it is not his person. Nor yet is it the human personality. It is this man; no more and no less. …It is he. The whole of him. The arms, they eyes, the thoughts, everything. | |
| From: Simone Weil (Human Personality [1943], p,70) | |
| A reaction: I take her to be referring to exactly the concept of a 'person' which Locke introduced. It is important to remember that his concept is mainly forensic - as a concept of ownership and contracts. A person is an abstraction. Even a corpse is a human. |
| 23756 | The mind is imprisoned and limited by language, restricting our awareness of wider thoughts [Weil] |
| Full Idea: At the very best, a mind is enclosed in language is in a prison. It is limited to the number of relations which words can make simultaneously present to it; and remains in ignorance of thoughts which involve the combination of a greater number. | |
| From: Simone Weil (Human Personality [1943], p.89) | |
| A reaction: This seems to be a germ of the type of view of language which blossoms in Derrida. But she is on to something. None of us grasp fully, I think, the non-linguistic nature of good thinking. |
| 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. |
| 23758 | Beauty is an attractive mystery, leaving nothing to be desired [Weil] |
| Full Idea: Beauty is the supreme mystery of the world. It is a gleam which attracts the attention and yet does nothing to sustain it. …While exciting desire, it makes clear that there is nothing in it to be desired, because what we want is that it should not change. | |
| From: Simone Weil (Human Personality [1943], p.92) | |
| A reaction: She attributes beauty to a supernatural source. I catalogue this idea under 'the sublime', rather than 'beauty'. It may be better to say that beauty inspires love, rather than desire. |
| 23760 | All we need are the unity of justice, truth and beauty [Weil] |
| Full Idea: Justice, truth, and beauty are sisters and comrades. With three such beautiful words we have no need to look for any others. | |
| From: Simone Weil (Human Personality [1943], p.93) | |
| A reaction: The embodiment of platonist values. Without the platonist ontology, I like the identification of a few core values, and have always thought that Beauty, Goodness and Truth were a well chosen trio. Swapping 'justice' for 'goodness' is interesting. |
| 23748 | The sacred in every human is their expectation of good rather than evil [Weil] |
| Full Idea: At the bottom of every human heart …there is something that goes on indomitably expecting, in the teeth of all crimes committed, suffered and witnessed, that good and not evil will be done to him. It is this above all that is sacred in every human being. | |
| From: Simone Weil (Human Personality [1943], p.71) | |
| A reaction: I'm thinking that this expectation may come from having at least one loving parent, and failing that there are people who have no such expectation as adults. Simone obviously thinks the hope runs deeper than that. |
| 23759 | Everything which originates in love is beautiful [Weil] |
| Full Idea: Everything which originates from pure love is lit with the radiance of beauty. | |
| From: Simone Weil (Human Personality [1943], p.93) | |
| A reaction: I suppose if I found a counterexample, she would say that is not 'pure' love. This sentence leaves open the possibility of beauty in the absence of love (such as a beautiful face noticed in the street). In her case, can beauty and love be separated? |
| 23762 | Evil is transmitted by comforts and pleasures, but mostly by doing harm to people [Weil] |
| Full Idea: One may transmit evil to a human being by flattering him or giving him comforts and pleasures; but most often men transmit evil to other men by doing them harm. | |
| From: Simone Weil (Human Personality [1943], p.94) | |
| A reaction: Some people receive harm very passively, especially if it is normal. What of tough love, which is erroneously seen as harm? |
| 23750 | It is not more money which the wretched members of society need [Weil] |
| Full Idea: Suppose the devil were bargaining for the soul of some wretch, and some pitying person said to the devil 'Shame on you, that commodity is worth twice as much'. Such is the sinister farce played by the working class unions, parties and intellectuals. | |
| From: Simone Weil (Human Personality [1943], p.80) | |
| A reaction: A striking thought. It is paradoxical when the working classes despise the middle classes, and yet aspire to be like them. It's hard to know what a mystic like Weil has in mind. An obvious thought is that the aspiration should be freedom, not money. |
| 23749 | The problem of the collective is not suppression of persons, but persons erasing themselves [Weil] |
| Full Idea: The chief danger does not lie in the collectivity's tendency to circumscribe the person, but in the person's tendency to immolate himself in the collective. | |
| From: Simone Weil (Human Personality [1943], p.78) | |
| A reaction: I'm guessing that in 1943 she had in mind both Nazis and Communists. She seems to articulate a strong form of liberalism in an interesting way. It sounds like a form of Bad Faith. |
| 23753 | People absurdly claim an equal share of things which are essentially privileged [Weil] |
| Full Idea: To the dimmed understanding of our age there seems nothing odd in claiming an equal share of privilege for everybody - an equal share in things whose essence is privilege. | |
| From: Simone Weil (Human Personality [1943], p.84) | |
| A reaction: Not sure what she has in mind. Probably not the finest food and drink. I suppose she is attacking the modern egalitarian view of democratic society. What things have privilege as their 'essence'? Being a 'winner'? Interesting, though. |
| 23751 | Rights are asserted contentiously, and need the backing of force [Weil] |
| Full Idea: Rights are always asserted in a tone of contention; and when this tone is adopted, it must rely upon force in the background, or else it will be laughed at. | |
| From: Simone Weil (Human Personality [1943], p.81) | |
| A reaction: This is the sort of observation which leads on to Foucault's account of all-pervasive power. Her observation may not be so sinister. It is obvious that introductions of new rights go against the grain of a conservative society - and so need a push. |
| 23752 | Giving centrality to rights stifles all impulses of charity [Weil] |
| Full Idea: To place the notion of rights at the centre of social conflicts is to inhibit any possible impulse of charity on both sides. | |
| From: Simone Weil (Human Personality [1943], p.83) | |
| A reaction: I think she exaggerates. To place personal charity at the centre of social conflicts strikes me as extremely conservative, and unlikely to improve the situation very much. I'm unsure how to reconcile this with Idea 23750. What sort of charity? |
| 23757 | The spirit of justice needs the full attention of truth, and that attention is love [Weil] |
| Full Idea: Because affliction and truth need the same kind of attention …the spirit of justice and the spirit of truth are one. The spirit of justice and truth is nothing else be a certain kind of attention, which is pure love. | |
| From: Simone Weil (Human Personality [1943], p.92) | |
| A reaction: I'm not sure about this as an observation, but as an inspiration it is very appealing, and (as so often with Weil) strikingly and attractively independent. I prefer love to arise naturally, rather than be a product of exhortation. |
| 23761 | Justice (concerning harm) is distinct from rights (concerning inequality) [Weil] |
| Full Idea: Justice is seeing that no harm is done to men. When a man cries inwardly 'Why am I being hurt?' he is being harmed. The other cry of 'Why have others got more than me?' refers to rights. We must distinguish them, and hush the second with law. | |
| From: Simone Weil (Human Personality [1943], p.93) | |
| A reaction: Her great passion is for justice, and so she downplays rights. The simple 'why am I being hurt?' has a horrible resonance in 1943. What of the hurts of disease? Are they unjust? |
| 23764 | The only thing in society worse than crime is repressive justice [Weil] |
| Full Idea: There is one, and only one, thing in society more hideous than crime - namely, repressive justice. | |
| From: Simone Weil (Human Personality [1943], p.95) | |
| A reaction: Presumably fans of 'repressive' justice would describe it as 'reformative' justice. In general, one of the most hideous parts of historical human societies has been the punishments they dished out (simply because they had the power to do it). |
| 23763 | Punishment aims at the good for men who don't desire it [Weil] |
| Full Idea: Punishment is solely a method of procuring pure good for men who do not desire it. The art of punishing is the art of awakening in a criminal, by pain or even death, the desire for pure good. | |
| From: Simone Weil (Human Personality [1943], p.95) | |
| A reaction: I know Weil is seen as some sort of saint, but this remark could have come from the Inquisition. I'm always alarmed by talk of 'pure' good and 'pure' evil, which seem to need a superior insight the rest of us lack. But see Idea 23764. |
| 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'. |
| 23754 | The only choice is between supernatural good, or evil [Weil] |
| Full Idea: In all the crucial problems of human existence the only choice is between supernatural good on the one hand and evil on the other. | |
| From: Simone Weil (Human Personality [1943], p.86) | |
| A reaction: This idea strikes me as absurd, but I include it for a fuller picture of Simone Weil. Aristotle (my hero) is referred to, and labelled as more stupid than a village idiot. |