19 ideas
| 18085 | Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy] |
| Full Idea: When the successive absolute values of a variable decrease indefinitely in such a way as to become less than any given quantity, that variable becomes what is called an 'infinitesimal'. Such a variable has zero as its limit. | |
| From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4 | |
| A reaction: The creator of the important idea of the limit still talked in terms of infinitesimals. In the next generation the limit took over completely. |
| 18084 | When successive variable values approach a fixed value, that is its 'limit' [Cauchy] |
| Full Idea: When the values successively attributed to the same variable approach indefinitely a fixed value, eventually differing from it by as little as one could wish, that fixed value is called the 'limit' of all the others. | |
| From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4 | |
| A reaction: This seems to be a highly significan proposal, because you can now treat that limit as a number, and adds things to it. It opens the door to Cantor's infinities. Is the 'limit' just a fiction? |
| 20339 | Classes rarely share properties with their members - unlike universals and types [Wollheim] |
| Full Idea: Classes can share properties with their members (e.g. the class of big things is big), but this is very rare. ....In the case of both universals and types, there will be shared properties. Red things can be exhilarating, and so can redness. | |
| From: Richard Wollheim (Art and Its Objects [1968], 92) | |
| A reaction: 'Exhilarating' is an extrinsic property, so not the best illustration. This is interesting, but would need checking with a wide range of examples. (Too busy for that right now) |
| 20338 | We often treat a type as if it were a sort of token [Wollheim] |
| Full Idea: Much of the time we think and talk of a type as though it were itself a kind of token. | |
| From: Richard Wollheim (Art and Its Objects [1968], 35) | |
| A reaction: A helpful way of connecting what I call 'objectification' to the more conventional modern philosophical vocabulary. Thus I might claim that beauty is superior to truth, as if they were two tokens. |
| 20342 | Interpretation is performance for some arts, and critical for all arts [Wollheim] |
| Full Idea: Performative interpretation occurs only with certain arts, but critical intepretation pertains to all. | |
| From: Richard Wollheim (Art and Its Objects [1968], 38) | |
| A reaction: Fairly obvious, but this is the first point to make about the concept of 'interpretation'. Does the word in fact have two meanings? Or do I perform a painting when I look carefully at it? |
| 20343 | A love of nature must precede a love of art [Wollheim] |
| Full Idea: We could not have a feeling for the beauties of art unless we had been correspondingly moved in front of nature. | |
| From: Richard Wollheim (Art and Its Objects [1968], 43) | |
| A reaction: Wollheim offers this in defence of Kant's view, without necessarily agreeing. Similarly one could hardly care for fictional characters, but not for real people. So the aesthetic attitude may arise from life, rather than from art. Is art hence unimportant? |
| 20348 | A criterion of identity for works of art would be easier than a definition [Wollheim] |
| Full Idea: Maybe, rather than defining art, it would be more fruitful, and more realistic, to seek a general method of identifying works of art. | |
| From: Richard Wollheim (Art and Its Objects [1968], 60) | |
| A reaction: The whole enterprise is ruined by Marcel Duchamp! I'm more interested in identifying or defining good art. |
| 20347 | If beauty needs organisation, then totally simple things can't be beautiful [Wollheim] |
| Full Idea: It is said that beauty cannot consist in organisation because, if it did, we would not be able to predicate beauty of totally simple objects. | |
| From: Richard Wollheim (Art and Its Objects [1968], 59) | |
| A reaction: [He says this idea originates in Plotinus] I'm struggling to think of an example of something which is 'totally' simple and beautiful. Maybe a patch of colour like the breast of a bullfinch? |
| 20345 | Some say art must have verbalisable expression, and others say the opposite! [Wollheim] |
| Full Idea: The view that a work of art expresses nothing if it can't be put into other words ...is reduced by the view that a work of art has no value if what it expresses or says can be put into (other) words. | |
| From: Richard Wollheim (Art and Its Objects [1968], 49) | |
| A reaction: I prefer the second view. Poetry is what is lost in translation. Good art actually seems to evoke emotions which one virtually never feels in ordinary life. But how could that be possible? What are those emotions doing there? |
| 20331 | It is claimed that the expressive properties of artworks are non-physical [Wollheim] |
| Full Idea: The argument that works of art have properties that physical objects could not have characteristically concentrates on the expressive properties of works of art. | |
| From: Richard Wollheim (Art and Its Objects [1968], 10) | |
| A reaction: Since the idea of an object having non-physical properties strikes me as ridiculous, this gets off to a bad start. If artworks are abstract objects, then all of their properties are non-physical. |
| 20336 | Style can't be seen directly within a work, but appreciation needs a grasp of style [Wollheim] |
| Full Idea: 'Style' would seem to be a concept that cannot be applied to a work solely on the basis of what is represented and yet it is also essential to a proper understanding or appreciation of a work. | |
| From: Richard Wollheim (Art and Its Objects [1968], 32) | |
| A reaction: Sounds right. One long held musical note creates an expectation which depends on the presumed style of the piece of music. A single bar from a piece may well not exhibit its characteristic style. |
| 20337 | The traditional view is that knowledge of its genre to essential to appreciating literature [Wollheim] |
| Full Idea: From Aristotle onwards it has been a tenet of the traditional rhetoric that the proper understanding of a literary work involves the location of it in the correct genre, that is, as drama, epic or lyric. | |
| From: Richard Wollheim (Art and Its Objects [1968], 32) | |
| A reaction: Walton argues this persuasively. I've seen the climax of a Jacobean tragedy ruined by laughter from the audience. Genre dictates appropriate responses, so it is a communal concept. |
| 20333 | If artworks are not physical objects, they are either ideal entities, or collections of phenomena [Wollheim] |
| Full Idea: In denying that works of art are physical objects, one theory (the 'ideal') withdraws them altogether from experience, and a second theory ('phenomenal') pins them too it inescapably and at all points. | |
| From: Richard Wollheim (Art and Its Objects [1968], 21) | |
| A reaction: I incline towards them being transient ideals, created by human minds. As with so much, we idealise and objectify them as 'works', and abstract their image from the instance(s) we encounter. |
| 20334 | The ideal theory says art is an intuition, shaped by a particular process, and presented in public [Wollheim] |
| Full Idea: The ideal theory of Croce and Collingwood says art is first an inner intuition or expression of the artist, resulting from a particular process of organisation and unification, which can be externalised in public form. | |
| From: Richard Wollheim (Art and Its Objects [1968], 22) | |
| A reaction: [compressed] As stated this doesn't sound very controversial or 'ideal'. I take it the theory is intended to be more platonist than this expression of it suggests. I think the idea that it is an 'expression' of the artist is wrong. |
| 20335 | The ideal theory of art neglects both the audience and the medium employed [Wollheim] |
| Full Idea: Because the ideal theory makes a work of art inner or mental, the link between the artist and the audience has been severed .....and it also totally ignores the significance of the medium. | |
| From: Richard Wollheim (Art and Its Objects [1968], 23) | |
| A reaction: Emily Dickinson had virtually no audience for her poetry. The medium used to perform Bach's 'Art of Fugue' seems unimportant. For paintings of painterly painters paint matters. For some visual art many different media will suffice. |
| 20340 | A musical performance has virtually the same features as the piece of music [Wollheim] |
| Full Idea: With the usual reservations, there is nothing that can be predicated of a performance of a piece of music that could not also be predicated of that piece of music itself. | |
| From: Richard Wollheim (Art and Its Objects [1968], 37) | |
| A reaction: He offers this as evidence that it fits the performance being a token, and music (and all other art) being a type. There are quite a few 'reservations'. Music too difficult to perform. Great music always badly performed. |
| 20341 | An interpretation adds further properties to the generic piece of music [Wollheim] |
| Full Idea: Interpretation may be regarded as the production of a token that has properties in excess of those of the type. | |
| From: Richard Wollheim (Art and Its Objects [1968], 37) | |
| A reaction: I suppose so. If you play accurately everything that is written in the score, then anything else has to be an addition. If you play less than the score, you aren't quite playing that piece of music. |
| 20332 | A drawing only represents Napoleon if the artist intended it to [Wollheim] |
| Full Idea: It is necessary, if a drawing is to represent Napoleon, that the draughtsman should intend it to be Napoleon. | |
| From: Richard Wollheim (Art and Its Objects [1968], 13) | |
| A reaction: Does a perfect and intended representation of a person also count as a representation of the person's identical twin? The families of both might well order copies. |
| 6017 | Nomos is king [Pindar] |
| Full Idea: Nomos is king. | |
| From: Pindar (poems [c.478 BCE], S 169), quoted by Thomas Nagel - The Philosophical Culture | |
| A reaction: This seems to be the earliest recorded shot in the nomos-physis wars (the debate among sophists about moral relativism). It sounds as if it carries the full relativist burden - that all that matters is what has been locally decreed. |