24 ideas
| 2764 | Full coherence might involve consistency and mutual entailment of all propositions [Blanshard, by Dancy,J] |
| Full Idea: Blanshard says that in a fully coherent system there would not only be consistency, but every proposition would be entailed by the others, and no proposition would stand outside the system. | |
| From: report of Brand Blanshard (The Nature of Thought [1939], 2:265) by Jonathan Dancy - Intro to Contemporary Epistemology 8.1 | |
| A reaction: Hm. If a proposition is entailed by the others, then it is a necessary truth (given the others) which sounds deterministic. You could predict all the truths you had never encountered. See 1578:178 for quote. |
| 18543 | Do aesthetic reasons count as reasons, if they are rejectable without contradiction? [Scruton] |
| Full Idea: The judgement of beauty makes a claim about its object, and can be supported by reasons. But the reasons do not compel the judgement and can be rejected without contradiction. So are they reasons or aren't they? | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 1) | |
| A reaction: I suspect that what he is really referring to is evidence rather than reasons. |
| 18542 | Defining truth presupposes that there can be a true definition [Scruton] |
| Full Idea: How can you define truth, without already assuming the distinction between a true definition and a false one? | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 1) | |
| A reaction: Don't say we have to accept truth as yet another primitive! Philosophers are out of business if all the basic concepts are primitive. The axiomatic approach to truth is an alternative - by specifying how the primitive should be used. |
| 19080 | Coherence tests for truth without implying correspondence, so truth is not correspondence [Blanshard, by Young,JO] |
| Full Idea: Blanshard said that coherent justification leads to coherence truth. It might be said that coherence is a test for truth, but truth is correspondence. But coherence doesn't guarantee correspondence, and coherence is a test, so truth is not correspondence. | |
| From: report of Brand Blanshard (The Nature of Thought [1939], Ch.26) by James O. Young - The Coherence Theory of Truth §2.2 | |
| A reaction: [compression of Young's summary] Rescher (1973) says that Blanshard's argument depends on coherence being an infallible test for truth, which it isn't. |
| 10807 | Mathematics reduces to set theory, which reduces, with some mereology, to the singleton function [Lewis] |
| Full Idea: It is generally accepted that mathematics reduces to set theory, and I argue that set theory in turn reduces, with some aid of mereology, to the theory of the singleton function. | |
| From: David Lewis (Mathematics is Megethology [1993], p.03) |
| 10809 | We can accept the null set, but not a null class, a class lacking members [Lewis] |
| Full Idea: In my usage of 'class', there is no such things as the null class. I don't mind calling some memberless thing - some individual - the null set. But that doesn't make it a memberless class. Rather, that makes it a 'set' that is not a class. | |
| From: David Lewis (Mathematics is Megethology [1993], p.05) | |
| A reaction: Lewis calls this usage 'idiosyncratic', but it strikes me as excellent. Set theorists can have their vital null class, and sensible people can be left to say, with Lewis, that classes of things must have members. |
| 10811 | The null set plays the role of last resort, for class abstracts and for existence [Lewis] |
| Full Idea: The null set serves two useful purposes. It is a denotation of last resort for class abstracts that denote no nonempty class. And it is an individual of last resort: we can count on its existence, and fearlessly build the hierarchy of sets from it. | |
| From: David Lewis (Mathematics is Megethology [1993], p.09) | |
| A reaction: This passage assuages my major reservation about the existence of the null set, but at the expense of confirming that it must be taken as an entirely fictional entity. |
| 10812 | The null set is not a little speck of sheer nothingness, a black hole in Reality [Lewis] |
| Full Idea: Should we accept the null set as a most extraordinary individual, a little speck of sheer nothingness, a sort of black hole in the fabric of Reality itself? Not that either, I think. | |
| From: David Lewis (Mathematics is Megethology [1993], p.09) | |
| A reaction: Correct! |
| 10813 | What on earth is the relationship between a singleton and an element? [Lewis] |
| Full Idea: A new student of set theory has just one thing, the element, and he has another single thing, the singleton, and not the slightest guidance about what one thing has to do with the other. | |
| From: David Lewis (Mathematics is Megethology [1993], p.12) |
| 10814 | Are all singletons exact intrinsic duplicates? [Lewis] |
| Full Idea: Are all singletons exact intrinsic duplicates? | |
| From: David Lewis (Mathematics is Megethology [1993], p.13) |
| 10806 | Megethology is the result of adding plural quantification to mereology [Lewis] |
| Full Idea: Megethology is the result of adding plural quantification, as advocated by George Boolos, to the language of mereology. | |
| From: David Lewis (Mathematics is Megethology [1993], p.03) |
| 10816 | We can use mereology to simulate quantification over relations [Lewis] |
| Full Idea: We can simulate quantification over relations using megethology. Roughly, a quantifier over relations is a plural quantifier over things that encode ordered pairs by mereological means. | |
| From: David Lewis (Mathematics is Megethology [1993], p.18) | |
| A reaction: [He credits this idea to Burgess and Haven] The point is to avoid second-order logic, which quantifies over relations as ordered n-tuple sets. |
| 10808 | Mathematics is generalisations about singleton functions [Lewis] |
| Full Idea: We can take the theory of singleton functions, and hence set theory, and hence mathematics, to consist of generalisations about all singleton functions. | |
| From: David Lewis (Mathematics is Megethology [1993], p.03) | |
| A reaction: At first glance this sounds like a fancy version of the somewhat discredited Greek idea that mathematics is built on the concept of a 'unit'. |
| 10815 | We don't need 'abstract structures' to have structural truths about successor functions [Lewis] |
| Full Idea: We needn't believe in 'abstract structures' to have general structural truths about all successor functions. | |
| From: David Lewis (Mathematics is Megethology [1993], p.16) |
| 10810 | I say that absolutely any things can have a mereological fusion [Lewis] |
| Full Idea: I accept the principle of Unrestricted Composition: whenever there are some things, no matter how many or how unrelated or how disparate in character they may be, they have a mereological fusion. ...The trout-turkey is part fish and part fowl. | |
| From: David Lewis (Mathematics is Megethology [1993], p.07) | |
| A reaction: This nicely ducks the question of when things form natural wholes and when they don't, but I would have thought that that might be one of the central issues of metaphysicals, so I think I'll give Lewis's principle a miss. |
| 18546 | The pleasure taken in beauty also aims at understanding and valuing [Scruton] |
| Full Idea: Like the pleasure in friendship, the pleasure in beauty is curious: it aims to understand its object, and to value what it finds. | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 1) | |
| A reaction: At least he is trying to pin down the way in which aesthetic pleasure is phenomenologically different from other kinds of pleasure. |
| 18550 | Art gives us imaginary worlds which we can view impartially [Scruton] |
| Full Idea: One aim of art is to present imaginary worlds, towards which we can adopt, as part of the integral aesthetic attitude, a posture of impartial concern. | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 5) | |
| A reaction: It connects to the pleasure of watching people when they don't know they are being watched (such as watching the street from a restaurant window). Scruton's suggestion makes art resemble examples in philosophy. Cf the Frege-Geach problem in ethics. |
| 18544 | Maybe 'beauty' is too loaded, and we should talk of fittingness or harmony [Scruton] |
| Full Idea: Maybe we can understand the 'beauty' of a building better if we describe it in another and less loaded way, as a form of fittingness or harmony. | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 1) | |
| A reaction: Almost everyone accepts the word 'beauty' for some things, such as a beautiful face, or goal, or steak. I remember a female interviewer writing that, reluctantly, the only appropriate word she could find for Nureyev's face was 'beautiful'. |
| 18553 | Beauty shows us what we should want in order to achieve human fulfilment [Scruton] |
| Full Idea: Beauty speaks to us of human fulfilment: not of things that we want, but of things that we ought to want, because human nature requires them. Such, at least, is my belief. | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 7) | |
| A reaction: I'm not sure how this works with a beautiful natural landscape. And what should I see that I ought to desire after viewing a great Rembrandt self-portrait? That I don't want to end up looking as bleak as that? Hm. Lofty words. |
| 18556 | Beauty is rationally founded, inviting meaning, comparison and self-reflection [Scruton] |
| Full Idea: Beauty is rationally founded; it challenges us to find meaning in its object, to make critical comparisons, and to examine our own lives and emotions in the light of what we find. | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 9) | |
| A reaction: This is the Kantian tradition, and I'm not finding it very persuasive. It seems to place the value of beauty in what we do with it afterwards, and he seems to make beauty a necessary stepping stone to virtue. I see beauty as more sui generis. |
| 18548 | Natural beauty reassures us that the world is where we belong [Scruton] |
| Full Idea: The experience of natural beauty is not a sense of 'how nice!' or 'how pleasant!' It contains a reassurance that this world is a right and fitting place to be - a home in which our human powers and prospects find confirmation. | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 2) | |
| A reaction: To call it a 'reassurance' and 'confirmation' sounds like theism, anthropomorphism, or the pathetic fallacy. That said, this is certainly a heart-warming idea, and hence must contain a grain of truth. |
| 18551 | Croce says art makes inarticulate intuitions conscious; rival views say the audience is the main concern [Scruton] |
| Full Idea: The Croce model is of an inarticulate inner state (an 'intuition') becoming articulate and conscious through artistic expression. The rival model is fitting thing together so as to create links which resonate in the audience's feelings. | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 5) | |
| A reaction: The first model tells you nothing about how the artist imagines the audience reacting. The second model tells you nothing about what matters personally to the artist. A good theory must do both! |
| 18541 | Beauty (unlike truth and goodness) is questionable as an ultimate value [Scruton] |
| Full Idea: The status of beauty as an ultimate value is questionable, in the way that the status of truth and goodness are not. | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 1) | |
| A reaction: We suspect that a love of beauty may be a bit parochial, where it is hard to conceive of living creatures anywhere in the cosmos who don't value the other two. |
| 18554 | Prostitution is wrong because it hardens the soul, since soul and body are one [Scruton] |
| Full Idea: The condemnation of prostitution was not just puritan bigotry; it was a recognition of a profound truth, that you and your body are not two things but one, and by selling the body you harden your soul. | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 7) | |
| A reaction: No one, I imagine, who condones or even enthuses about prostitution would hope that their own daughter followed the profession, so there is something wrong with it. But must an enthusiastic and cheerful prostitute necessarily have a hard soul? |