73 ideas
| 21887 | Derrida focuses on other philosophers, rather than on science [Derrida] |
| Full Idea: We should focus on other philosophers, and not on science. | |
| From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction |
| 21888 | Philosophy is just a linguistic display [Derrida] |
| Full Idea: Philosophy is entirely linguistic, and is a display. | |
| From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction |
| 21896 | Philosophy aims to build foundations for thought [Derrida, by May] |
| Full Idea: Derrida points out that the project of philosophy consists largely in attempting to build foundations for thought. | |
| From: report of Jacques Derrida (works [1990]) by Todd May - Gilles Deleuze 1.04 | |
| A reaction: You would first need to be convinced that there could be such a thing as foundations for thinking. Derrida thinks the project is hopeless. I think of it more as building an ideal framework for thought. |
| 21893 | Philosophy is necessarily metaphorical, and its writing is aesthetic [Derrida] |
| Full Idea: All of philosophy is necessarily metaphorical, and hence aesthetic. | |
| From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction |
| 21892 | Interpretations can be interpreted, so there is no original 'meaning' available [Derrida] |
| Full Idea: Because interpretations of texts can be interpreted, they can therefore have no 'original meaning'. | |
| From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction |
| 20925 | Hermeneutics blunts truth, by conforming it to the interpreter [Derrida, by Zimmermann,J] |
| Full Idea: Derrida worried that hermeneutics blunts the disruptive power of truth by forcing it conform to the interpreter's mental horizon. | |
| From: report of Jacques Derrida (works [1990]) by Jens Zimmermann - Hermeneutics: a very short introduction 3 'The heart' | |
| A reaction: Good heavens - I agree with Derrida. Very French, though, to see the value of truth in its disruptiveness. I tend to find the truth reassuring, but then I'm English. |
| 20934 | Hermeneutics is hostile, trying to overcome the other person's difference [Derrida, by Zimmermann,J] |
| Full Idea: Derrida described the hermeneutic impulse to understand another as a form of violence that seeks to overcome the other's particularity and unique difference. | |
| From: report of Jacques Derrida (works [1990]) by Jens Zimmermann - Hermeneutics: a very short introduction App 'Derrida' | |
| A reaction: I'm not sure about 'violence', but Derrida was on to somethng here. The 'hermeneutic circle' sounds like a creepy process of absorption, where the original writer disappears in a whirlpool of interpretation. |
| 21895 | Structuralism destroys awareness of dynamic meaning [Derrida] |
| Full Idea: Structuralism destroys awareness of dynamic meaning. | |
| From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction |
| 21934 | The idea of being as persistent presence, and meaning as conscious intelligibility, are self-destructive [Derrida, by Glendinning] |
| Full Idea: The tradition of conceiving being in terms of persisting presence, and meaning in terms of pure intelligibility or logos potentially present to the mind, finds itself dismantled by resources internal to its own construction. | |
| From: report of Jacques Derrida (works [1990]) by Simon Glendinning - Derrida: A Very Short Introduction 6 | |
| A reaction: [compressed] Glendinning says this is the basic meaning of de-construction. My personal reading of this is that Aristotle is right, and grand talk of Being is hopeless, so we should just aim to understand objects. I also believe in propositions. |
| 21883 | Sincerity can't be verified, so fiction infuses speech, and hence reality also [Derrida] |
| Full Idea: Sincerity can never be verified, so fiction infuses all speech, which means that reality is also fictional. | |
| From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction |
| 21882 | Sentences are contradictory, as they have opposite meanings in some contexts [Derrida] |
| Full Idea: Sentences are implicitly contradictory, because they can be used differently in different contexts (most obviously in 'I am ill'). | |
| From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction |
| 21881 | We aim to explore the limits of expression (as in Mallarmé's poetry) [Derrida] |
| Full Idea: The aim is to explore the limits of expression (which is what makes the poetry of Mallarmé so important). | |
| From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction |
| 4756 | Derrida says that all truth-talk is merely metaphor [Derrida, by Engel] |
| Full Idea: Derrida's view is that every discourse is metaphorical, and there is no difference between truth-talk and metaphor. | |
| From: report of Jacques Derrida (works [1990]) by Pascal Engel - Truth §2.5 | |
| A reaction: Right. Note that this is a Frenchman's summary. How would one define metaphor, without mentioning that it is parasitic on truth? Certainly some language tries to be metaphor, and other language tries not to be. |
| 21877 | True thoughts are inaccessible, in the subconscious, prior to speech or writing [Derrida] |
| Full Idea: 'True' thoughts are inaccessible, buried in the subconscious, long before they get to speech or writing. | |
| From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction | |
| A reaction: [My reading of some Derrida produced no quotations. I've read two commentaries, which were obscure. The Derrida ideas in this db are my simplistic tertiary summaries. Experts can chuckle over my failure] |
| 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. |
| 21889 | 'I' is the perfect name, because it denotes without description [Derrida] |
| Full Idea: 'I' is the perfect name, because it denotes without description. | |
| From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction |
| 21878 | Names have a subjective aspect, especially the role of our own name [Derrida] |
| Full Idea: We can give a subjective account of names, by considering our own name. | |
| From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction |
| 21879 | Even Kripke can't explain names; the word is the thing, and the thing is the word [Derrida] |
| Full Idea: Even Kripke can't explain names, because the word is the thing, and also the thing is the word. | |
| From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction |
| 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'. |
| 3644 | Two things being joined together doesn't prove they are the same [Descartes] |
| Full Idea: The fact that we often see two things joined together does not license the inference that they are one and the same. | |
| From: René Descartes (Reply to Sixth Objections [1641], 444) | |
| A reaction: Correct. The problem comes when they are never ever apart, and you begin to suspect that they are conjoined in all possible worlds. Why might this be so? It can only be identity or a causal link. |
| 3621 | Only judgement decides which of our senses are reliable [Descartes] |
| Full Idea: Sense alone does not suffice to correct visual error: we also need a degree of reason to tell us that we should believe the judgement based on touch rather than vision. Since we don't have this power in infancy, it must be attributed to the intellect. | |
| From: René Descartes (Reply to Sixth Objections [1641], 439) |
| 21890 | Heidegger showed that passing time is the key to consciousness [Derrida] |
| Full Idea: Heidegger showed us the importance of transient time for consciousness. | |
| From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction |
| 21880 | 'Tacit theory' controls our thinking (which is why Freud is important) [Derrida] |
| Full Idea: All thought is controlled by tacit theory (which is why Freud is so important). | |
| From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction | |
| A reaction: This idea is said to be the essential thought of Derrida's Deconstruction. The aim is liberation of thought, by identifying and bypassing these tacit metaphysical schemas. |
| 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. |
| 21886 | Meanings depend on differences and contrasts [Derrida] |
| Full Idea: Meaning depends on 'differences' (contrasts). | |
| From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction |
| 21930 | For Aristotle all proper nouns must have a single sense, which is the purpose of language [Derrida] |
| Full Idea: A noun [for Aristotle] is proper when it has but a single sense. Better, it is only in this case that it is properly a noun. Univocity is the essence, or better, the telos of language. | |
| From: Jacques Derrida (works [1990]), quoted by Simon Glendinning - Derrida: A Very Short Introduction 5 | |
| A reaction: [no ref given] His target seem to be Aristotelian definition, and also formal logic, which usually needs unambiguous meanings. {I'm puzzled that he thinks 'telos' is simply better than 'essence', since it is quite different]. |
| 21884 | Capacity for repetitions is the hallmark of language [Derrida] |
| Full Idea: The capacity for repetitions is the hallmark of language. | |
| From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction |
| 21935 | The sign is only conceivable as a movement between elusive presences [Derrida] |
| Full Idea: The sign is conceivable only on the basis of the presence that it defers, and moving toward the deferred presence that it aims to reappropriate. | |
| From: Jacques Derrida (works [1990]), quoted by Simon Glendinning - Derrida: A Very Short Introduction 6 | |
| A reaction: [Glendinning gives no source for this] I take the fundamental idea to be that meanings are dynamic, when they are traditionally understood as static (and specifiable in dictionaries). |
| 21933 | Writing functions even if the sender or the receiver are absent [Derrida, by Glendinning] |
| Full Idea: Writing can and must be able to do without the presence of the sender. ...Also writing can and must he able to do without the presence of the receiver. | |
| From: report of Jacques Derrida (works [1990]) by Simon Glendinning - Derrida: A Very Short Introduction 6 | |
| A reaction: In simple terms, one of them could die during the transmission. This is the grounds for the assertion of the primacy of writing. It opposes orthodox views which define language in terms of sender and receiver. |
| 21894 | Madness and instability ('the demonic hyperbole') lurks in all language [Derrida] |
| Full Idea: Madness and instability ('the demonic hyperbole') lurks behind all language. | |
| From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction |
| 21931 | 'Dissemination' is opposed to polysemia, since that is irreducible, because of multiple understandings [Derrida, by Glendinning] |
| Full Idea: The intention to oppose polysemia with dissemination does not aim to affirm that everything we say is ambiguous, but that polysemia is irreducible in the sense that each and every 'meaning' is itself subject to more than one understanding. | |
| From: report of Jacques Derrida (works [1990]) by Simon Glendinning - Derrida: A Very Short Introduction 5 | |
| A reaction: The key point, I think, is that ambiguity and polysemia are not failures of language (which is the way most logicians see it), but part of the essential and irreducible nature of language. Nietzsche started this line of thought. |
| 21885 | Words exist in 'spacing', so meanings are never synchronic except in writing [Derrida] |
| Full Idea: Words only exist is 'spacings' (of time and space), so there are no synchronic meanings (except perhaps in writing). | |
| From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction |
| 21891 | The good is implicitly violent (against evil), so there is no pure good [Derrida] |
| Full Idea: Even the good is implicitly violent (against evil), so there can be no 'pure' good. | |
| From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction |
| 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'. |
| 3637 | Ideas in God's mind only have value if he makes it so [Descartes] |
| Full Idea: It is impossible to imagine that anything is thought of in the divine intellect as good or true, or worthy of belief or action or omission, prior to the decision of the divine will to make it so. | |
| From: René Descartes (Reply to Sixth Objections [1641], 432) |