24 ideas
| 13451 | The two best understood conceptions of set are the Iterative and the Limitation of Size [Rayo/Uzquiano] |
| Full Idea: The two best understood conceptions of set are the Iterative Conception and the Limitation of Size Conception. | |
| From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.2) |
| 13452 | Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano] |
| Full Idea: There are set theories that countenance exceptions to the Principle of Separation in exchange for a universal set. | |
| From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.2) |
| 17807 | To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry] |
| Full Idea: In the study of formal systems we do not confine ourselves to the derivation of elementary propositions step by step. Rather we take the system, defined by its primitive frame, as datum, and then study it by any means at our command. | |
| From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The formalist') | |
| A reaction: This is what may potentially lead to an essentialist view of such things. Focusing on bricks gives formalism, focusing on buildings gives essentialism. |
| 13449 | We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano] |
| Full Idea: The possibility of unrestricted quantification does not immediately presuppose the existence of an all-inclusive domain. One could deny an all-inclusive domain but grant that some quantifications are sometimes unrestricted. | |
| From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.1) | |
| A reaction: Thus you can quantify over anything you like, but only from what is available. Eat what you like (in this restaurant). |
| 13450 | Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano] |
| Full Idea: There are doubts about whether absolute generality is possible, if there are certain concepts which are indefinitely extensible, lacking definite extensions, and yielding an ever more inclusive hierarchy. Sets and ordinals are paradigm cases. | |
| From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.1) |
| 13453 | Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano] |
| Full Idea: If one thought of second-order quantification as quantification over first-level Fregean concepts [note: one under which only objects fall], talk of domains might be regimented as talk of first-level concepts, which are not objects. | |
| From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.2) | |
| A reaction: That is (I take it), don't quantify over objects, but quantify over concepts, but only those under which known objects fall. One might thus achieve naïve comprehension without paradoxes. Sound like fun. |
| 17806 | It is untenable that mathematics is general physical truths, because it needs infinity [Curry] |
| Full Idea: According to realism, mathematical propositions express the most general properties of our physical environment. This is the primitive view of mathematics, yet on account of the essential role played by infinity in mathematics, it is untenable today. | |
| From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The problem') | |
| A reaction: I resist this view, because Curry's view seems to imply a mad metaphysics. Hilbert resisted the role of the infinite in essential mathematics. If the physical world includes its possibilities, that might do the job. Hellman on structuralism? |
| 17808 | Saying mathematics is logic is merely replacing one undefined term by another [Curry] |
| Full Idea: To say that mathematics is logic is merely to replace one undefined term by another. | |
| From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'Mathematics') |
| 13448 | The domain of an assertion is restricted by context, either semantically or pragmatically [Rayo/Uzquiano] |
| Full Idea: We generally take an assertion's domain of discourse to be implicitly restricted by context. [Note: the standard approach is that this restriction is a semantic phenomenon, but Kent Bach (2000) argues that it is a pragmatic phenomenon] | |
| From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.1) | |
| A reaction: I think Kent Bach is very very right about this. Follow any conversation, and ask what the domain is at any moment. The reference of a word like 'they' can drift across things, with no semantics to guide us, but only clues from context and common sense. |
| 12157 | Kant gave form and status to aesthetics, and Hegel gave it content [Kant, by Scruton] |
| Full Idea: Kant gave form and status to aesthetics, and Hegel endowed it with content. | |
| From: report of Immanuel Kant (Critique of Judgement I: Aesthetic [1790]) by Roger Scruton - Recent Aesthetics in England and America p.3 |
| 20346 | The aesthetic attitude is a matter of disinterestedness [Kant, by Wollheim] |
| Full Idea: The aesthetic attitude is defined by Kant in terms of disinterestedness. | |
| From: report of Immanuel Kant (Critique of Judgement I: Aesthetic [1790]) by Richard Wollheim - Art and Its Objects 54 | |
| A reaction: This is presumably, mainly, to explain our enjoyment of the miseries of tragedy. We just give ourselves up to a merry jig by Haydn. |
| 18547 | Only rational beings can experience beauty [Kant, by Scruton] |
| Full Idea: Kant is surely right that the experience of beauty, like the judgements in which it issues, is the prerogative of rational beings. | |
| From: report of Immanuel Kant (Critique of Judgement I: Aesthetic [1790]) by Roger Scruton - Beauty: a very short introduction 1 | |
| A reaction: I'm not sure how Scruton can say that Kant is 'surely right'. It is an interesting speculation. Are we to dogmatically affirm that bees get no aesthetic thrill when they spot a promising flower? Something in their little brains attracts them. |
| 24172 | It is hard to see why we would have developed Kant's 'disinterested' aesthetic attitude [Cochrane on Kant] |
| Full Idea: The Kantian notion of disinterest isolated aesthetic value from the rest of our lives. It is hard to understand why we should have developed a tendency that is detached from our everyday practical purposes. | |
| From: comment on Immanuel Kant (Critique of Judgement I: Aesthetic [1790], §2) by Tom Cochrane - The Aesthetic Value of the World 1.4 | |
| A reaction: Cochrane always seeks an evolutionary framework for accounts of aesthetics, and I agree with him. That doesn't devalue them. The best things in life, like piano music, are obviously offshoots of things which evolved for other reasons. |
| 20408 | With respect to the senses, taste is an entirely personal matter [Kant] |
| Full Idea: With regard to the agreeable, the principle Everyone has his own taste (of the senses) is valid. | |
| From: Immanuel Kant (Critique of Judgement I: Aesthetic [1790], CUP 7 5:212), quoted by Elizabeth Schellekens - Immanuel Kant (aesthetics) 1 | |
| A reaction: This is a preliminary concession, and he goes on to defend more objective views of taste. |
| 20409 | When we judge beauty, it isn't just personal; we judge on behalf of everybody [Kant] |
| Full Idea: It is ridiculous if someone justifies his tast by saying 'this object is beautiful for me'. . .If he pronounces that something is beautiful, then he expects the very same satisfaction of others: he judges not merely for himself, but for everyone. | |
| From: Immanuel Kant (Critique of Judgement I: Aesthetic [1790], CUP 7 5:213), quoted by Elizabeth Schellekens - Immanuel Kant (aesthetics) 1 | |
| A reaction: For Kant this would also be the hallmark of rationality - that we expect, or hope for, a consensus when we express a rational judgement. But this expectation is far less in cases of beauty. We do not expect total agreement from very tasteful people. |
| 20411 | Saying everyone has their own taste destroys the very idea of taste [Kant] |
| Full Idea: To say thast 'Everyone has his special taste' would be to dismiss the very possibility of aesthetic taste, and to deny that there could be aesthetic judgement 'that could make a rightful claim to the assent of everyone'. | |
| From: Immanuel Kant (Critique of Judgement I: Aesthetic [1790], CUP 7 5:213), quoted by Elizabeth Schellekens - Immanuel Kant (aesthetics) 2.2 | |
| A reaction: I am a great believer in the objectivity of taste (within sensible reason). But the great evidence against it is the shifting standards of taste over the centuries. Nineteenth century collectors wasted fortunes on inferior works, it seems to us. |
| 24170 | Kant thinks beauty ignores its objects, because it is only 'form' engaging with mind [Cochrane on Kant] |
| Full Idea: Kant thinks that the ideal of beauty requires no concept of what the object is. Universality demands that appreciation be purely a matter of the way the form of the object fits one's cognitive machinery. | |
| From: comment on Immanuel Kant (Critique of Judgement I: Aesthetic [1790]) by Tom Cochrane - The Aesthetic Value of the World 1.3 | |
| A reaction: This confirms further my increasingly negative view of Kant. Everything in him points to idealism (despite denials by his fans), and via Hegel we arrive at the idea that our values are all 'cultural constructs', rather than responses to reality. |
| 22711 | The beautiful is not conceptualised as moral, but it symbolises or resembles goodness [Kant, by Murdoch] |
| Full Idea: Kant insists that the beautiful must not be tainted with the good (that is, not conceptualised in any way which would bring it into the sphere of moral judgement) yet he says that the beautiful symbolises the good, it is an analogy of the good. | |
| From: report of Immanuel Kant (Critique of Judgement I: Aesthetic [1790]) by Iris Murdoch - The Sublime and the Good p.209 | |
| A reaction: Kant evidently wanted a very pure view of the aesthetic experience, drained of any overlapping feelings or beliefs. I'm not sure I understand how the beautiful can symbolise or be analogous to the good, while being devoid of it. |
| 4025 | Kant saw beauty as a sort of disinterested pleasure, which has become separate from the good [Kant, by Taylor,C] |
| Full Idea: Kant, in his third critique, defined beauty in terms of a certain kind of disinterested pleasure;….this is the basis for a declaration of independence of the beautiful relative to the good. | |
| From: report of Immanuel Kant (Critique of Judgement I: Aesthetic [1790]) by Charles Taylor - Sources of the Self §23.1 | |
| A reaction: This is a rebellion against the Greeks, especially Plato, and prepares the ground for the idea of 'art for art's sake'. Personally, I'm with Plato. |
| 20412 | Beauty is only judged in pure contemplation, and not with something else at stake [Kant] |
| Full Idea: If the question is whether something is beautiful, one does not want to know whether there is something that is or that could be at stake, for us or for someone else, in the existence of the thing, but rather how we judge it in mere contemplation. | |
| From: Immanuel Kant (Critique of Judgement I: Aesthetic [1790], CUP 2 5:204), quoted by Elizabeth Schellekens - Immanuel Kant (aesthetics) 2.3 | |
| A reaction: This evidently denies that function has anything to do with beauty, and seems to be a prelude to 'art for art's sake'. But a running cheetah cannot be separated from the sheer efficiencey and focus of the performance. |
| 22046 | The mathematical sublime is immeasurable greatness; the dynamical sublime is overpowering [Kant, by Pinkard] |
| Full Idea: Kant distinguished the 'mathematical' and 'dynamical' sublime. The former involves immeasurable greatness (or smallness) such that we cannot even present them to ourselves. The latter is of something large and overpowering, which we can morally resist. | |
| From: report of Immanuel Kant (Critique of Judgement I: Aesthetic [1790]) by Terry Pinkard - German Philosophy 1760-1860 13 | |
| A reaction: Presumably Cantor revealed the full extent of the mathematical sublime ('heaven', according to Hilbert). We await the comet that destroys the Earth to fully experience the other one. |
| 21458 | The sublime is a moral experience [Kant, by Gardner] |
| Full Idea: The sublime is understood by Kant as a moral experience. | |
| From: report of Immanuel Kant (Critique of Judgement I: Aesthetic [1790], 28-9) by Sebastian Gardner - Kant and the Critique of Pure Reason 09 'Judgment' | |
| A reaction: Gardner give the source in Kant. I can't accept that the initial experience of the sublime is moral in character. It could easily acquire a moral character after contemplation by someone who had such inclinations. |
| 5643 | Aesthetic values are not objectively valid, but we must treat them as if they are [Kant, by Scruton] |
| Full Idea: The 'Critique of Judgement' argues, then, not for the objective validity of aesthetic values, but for the fact that we must think of them as objectively valid. | |
| From: report of Immanuel Kant (Critique of Judgement I: Aesthetic [1790]) by Roger Scruton - Short History of Modern Philosophy §11.7 | |
| A reaction: The trouble with these transcendental arguments of Kant is that they render you powerless to discuss the question of whether values are actually objective. We are all trapped in presuppositions, instead of testing suppositions. |
| 20410 | The judgement of beauty is not cognitive, but relates, via imagination, to pleasurable feelings [Kant] |
| Full Idea: In order to understand whether or not something is beautiful, we do not relate the representation by means of understanding to the object for cognition, but relate it by means of the imagination ..to the subject and its feeling of pleasure or displeasure. | |
| From: Immanuel Kant (Critique of Judgement I: Aesthetic [1790], CUP 1 5:203), quoted by Elizabeth Schellekens - Immanuel Kant (aesthetics) 2.1 | |
| A reaction: This is to distinguish the particular type of judgement which counts as 'aesthetic' - the point being that it is not cognitive - it is not a matter of knowledge and facts, but a cool judgement made about a warm feeling of pleasure. I think. |