29 ideas
| 14085 | 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo] |
| Full Idea: The 'deductivist' version of eliminativist structuralism avoids ontological commitments to mathematical objects, and to modal vocabulary. Mathematics is formulations of various (mostly categorical) theories to describe kinds of concrete structures. | |
| From: Øystein Linnebo (Structuralism and the Notion of Dependence [2008], 1) | |
| A reaction: 'Concrete' is ambiguous here, as mathematicians use it for the actual working maths, as opposed to the metamathematics. Presumably the structures are postulated rather than described. He cites Russell 1903 and Putnam. It is nominalist. |
| 14084 | Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo] |
| Full Idea: The 'non-eliminative' version of mathematical structuralism takes it to be a fundamental insight that mathematical objects are really just positions in abstract mathematical structures. | |
| From: Øystein Linnebo (Structuralism and the Notion of Dependence [2008], I) | |
| A reaction: The point here is that it is non-eliminativist because it is committed to the existence of mathematical structures. I oppose this view, since once you are committed to the structures, you may as well admit a vast implausible menagerie of abstracta. |
| 14086 | 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo] |
| Full Idea: The 'modal' version of eliminativist structuralism lifts the deductivist ban on modal notions. It studies what necessarily holds in all concrete models which are possible for various theories. | |
| From: Øystein Linnebo (Structuralism and the Notion of Dependence [2008], I) | |
| A reaction: [He cites Putnam 1967, and Hellman 1989] If mathematical truths are held to be necessary (which seems to be right), then it seems reasonable to include modal notions, about what is possible, in its study. |
| 14087 | 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo] |
| Full Idea: 'Set-theoretic' structuralism rejects deductive nominalism in favour of a background theory of sets, and mathematics as the various structures realized among the sets. This is often what mathematicians have in mind when they talk about structuralism. | |
| From: Øystein Linnebo (Structuralism and the Notion of Dependence [2008], I) | |
| A reaction: This is the big shift from 'mathematics can largely be described in set theory' to 'mathematics just is set theory'. If it just is set theory, then which version of set theory? Which axioms? The safe iterative conception, or something bolder? |
| 14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo] |
| Full Idea: Structuralism can be distinguished from traditional Platonism in that it denies that mathematical objects from the same structure are ontologically independent of one another | |
| From: Øystein Linnebo (Structuralism and the Notion of Dependence [2008], III) | |
| A reaction: My instincts strongly cry out against all versions of this. If you are going to be a platonist (rather as if you are going to be religious) you might as well go for it big time and have independent objects, which will then dictate a structure. |
| 14083 | Structuralism is right about algebra, but wrong about sets [Linnebo] |
| Full Idea: Against extreme views that all mathematical objects depend on the structures to which they belong, or that none do, I defend a compromise view, that structuralists are right about algebraic objects (roughly), but anti-structuralists are right about sets. | |
| From: Øystein Linnebo (Structuralism and the Notion of Dependence [2008], Intro) |
| 14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo] |
| Full Idea: If objects depend on the other objects, this would mean an 'upward' dependence, in that they depend on the structure to which they belong, where the physical realm has a 'downward' dependence, with structures depending on their constituents. | |
| From: Øystein Linnebo (Structuralism and the Notion of Dependence [2008], III) | |
| A reaction: This nicely captures an intuition I have that there is something wrong with a commitment primarily to 'structures'. Our only conception of such things is as built up out of components. Not that I am committing to mathematical 'components'! |
| 14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
| Full Idea: We can give an exhaustive account of the identity of the empty set and its singleton without mentioning infinite sets, and it might be possible to defend the view that one natural number depends on its predecessor but not vice versa. | |
| From: Øystein Linnebo (Structuralism and the Notion of Dependence [2008], V) | |
| A reaction: Linnebo uses this as one argument against mathematical structuralism, where the small seems to depend on the large. The view of sets rests on the iterative conception, where each level is derived from a lower level. He dismisses structuralism of sets. |
| 14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
| Full Idea: There are two main ways of spelling out an 'intrinsic' property: if and only if it is shared by every duplicate of an object, ...and if and only if the object would have this property even if the rest of the universe were removed or disregarded. | |
| From: Øystein Linnebo (Structuralism and the Notion of Dependence [2008], II) | |
| A reaction: [He cites B.Weatherson's Stanford Encyclopaedia article] How about an intrinsic property being one which explains its identity, or behaviour, or persistence conditions? |
| 23928 | Good art produces exaltation and detachment [Bell,C] |
| Full Idea: The contemplation of pure form leads to a state of extraordinary exaltation and complete detachment from the concerns of life. | |
| From: Clive Bell (Art [1913], I.III) | |
| A reaction: The last part is what gets the arts a bad name with the people who do deal with the concerns of life (which won't go away, even for an artist!). However, being totally trapped in the concerns of life is probably a recipe for misery. |
| 23922 | The word 'beauty' leads to confusion, because it denotes distinct emotions [Bell,C] |
| Full Idea: The word 'beauty' connotes objects of quite distinguishable emotions, and the term would land me in confusions and misunderstandings. | |
| From: Clive Bell (Art [1913], I.I) | |
| A reaction: His main example is a comparison of beautiful women with beautiful art. Personally I don't think the word aspires to be precise, so there is no problem. Maths has beautiful solutions, golf has beautiful shots, cooking has beautiful results. Wow! |
| 23921 | Our feeling for natural beauty is different from the aesthetic emotion of art [Bell,C] |
| Full Idea: It is not what I call an aesthetic emotion that most of us feel, generally, for natural beauty. …Most people feel a very different kind of emotion for birds, flowers and butterfly wings from that we feel for pictures, pots, temples and statues. | |
| From: Clive Bell (Art [1913], I.I) | |
| A reaction: Not convinced. I think the main difference is our awareness that art is a human production, the result of choice, whereas nature is a given. Beethoven 9 and a good sunset don't seem to me far apart in our responses. |
| 23929 | We only see landscapes as artistic if we ignore their instrumental value [Bell,C] |
| Full Idea: It is only when we cease to regard the objects in a landscape as means to anything that we can feel the landscape artistically. | |
| From: Clive Bell (Art [1913], II.I) | |
| A reaction: This sounds as if only the exploitative attitude blocks the artistic view, but I would expect the scientific view (of an ecologist, for example) to do the same. |
| 23923 | Visual form can create a sublime mental state [Bell,C] |
| Full Idea: Pure visual form transports me to an infinitely sublime state of mind. | |
| From: Clive Bell (Art [1913], I.I) | |
| A reaction: Unusual for anyone to use to term 'sublime' for works of art, and I suspect that Bell was the last to do so. Bell offers a quasi-religious role for art. I accept that being struck by something exceptionally good in art is a very distinctive experience. |
| 23932 | Art is the expression of an emotion for ultimate reality [Bell,C] |
| Full Idea: My hypothesis is that art is the expression of an emotion for ultimate reality. | |
| From: Clive Bell (Art [1913], II.II) | |
| A reaction: So later in his discussion the word 'ultimate' has crept in, after a chapter about the close relation between religious and artistic attitudes. He also sees good art as deeply 'spiritual'. It seems that religious belief is essential to his theory of art. |
| 23927 | Aestheticism invites artist to create beauty, but with no indication of how to do it [Bell,C] |
| Full Idea: The danger of aestheticism is that the artist who has got nothing to do but make something beautiful hardly knows where to begin or where to end | |
| From: Clive Bell (Art [1913], I.III) | |
| A reaction: Aestheticism strikes me as the main motivation for art nouveau artifacts, which I love. You start with beautiful lines, and then find ways to implement them. Bell has a point, though! |
| 8115 | Only artists can discern significant form; other people must look to art to find it [Bell,C, by Gardner] |
| Full Idea: Bell thinks that only artists can discern significant form directly in the natural world, and that all others must look to art for significant form. | |
| From: report of Clive Bell (Art [1913]) by Sebastian Gardner - Aesthetics 3.3 | |
| A reaction: I have a horrible feeling that 'significant' form will turn out to be the sort of form that artists can see. Presumably the form spotted by geologists won't be quite so 'significant'. Not a promising theory. |
| 23924 | Maybe significant form gives us a feeling for ultimate reality [Bell,C] |
| Full Idea: When we strip things of all associations and significance, what is left is 'the thing in itself', or 'ultimate reality'. …Artists can express an emotion felt for reality through line and colour. …So through 'significant form' we sense ultimate reality. | |
| From: Clive Bell (Art [1913], I.III) | |
| A reaction: [compressed] The thing in itself is a Kantian idea. He offers this as a speculation, rather than a fact. Maybe quantum physics gets us closer to the thing in itself? Bell knows that his faith in significant form needs more justification than an emotion. |
| 23931 | Significant form is the essence of art, which I believe expresses an emotion about reality [Bell,C] |
| Full Idea: My view that the essential quality in work of art is significant form was based on experience I am sure about. Of my view that significant form is the expression of a peculiar emotion felt for reality I am far from confident. | |
| From: Clive Bell (Art [1913], II.II) | |
| A reaction: It is hard to understand the idea of 'significant' form without a clear proposal for the nature of the significance. A detective doesn't stop at the point where evidence is seen as significant. Why should a 'peculiar' emotion matter? |
| 20434 | 'Form' is visual relations, and it is 'significant' if it moves us aesthetically; art needs both [Bell,C, by Feagin] |
| Full Idea: By 'form' Bell means the relations of lines, colours and shapes. Forms are 'significant' when the relationships of lines and so on move us aesthetically. If something is art it must have, to at least a minimum extent, significant form. | |
| From: report of Clive Bell (Art [1913], p.17) by Susan Feagin - Roger Fry and Clive Bell 3 | |
| A reaction: So art has two necessary conditions - that it move us aesthetically, and that it does so by means of its form. The obvious problem is to explain which forms are 'significant' without mentioning the aesthetic feeling they have to invoke. |
| 23934 | The only expression art could have is the emotion resulting from pure form [Bell,C] |
| Full Idea: If art expresses anything, it expresses an emotion felt for pure form and that which gives pure form its extraordinary significance. | |
| From: Clive Bell (Art [1913], III.I) | |
| A reaction: I don't think 'expresses' is the right word here. Artists express, but works just transmit. I personally doubt whether anything can have 'extraordinary significance' simply because it expresses one particular emotion. Why art, but not geometry? |
| 23925 | Mere copies of pictures are not significant - unless the copies are very exact [Bell,C] |
| Full Idea: A literal copy is seldom reckoned even by its owner a work of art. Its forms are not significant. Yet if it were an absolutely exact copy, clearly it would be as moving as the original, and a photographic reproduction of a drawing often is. | |
| From: Clive Bell (Art [1913], I.III) | |
| A reaction: What if the original artist made the copy? In 1913, Bell begins to spot this modern problem. He undermines his own theory of significant form here, if the form only becomes significant once we have checked it is an original. |
| 23926 | Art is distinguished by its aesthetic emotion, which produces appropriate form [Bell,C] |
| Full Idea: The characteristic of a work of art is its power of provoking aesthetic emotion; the expression of emotion is what gives it its power. ...Rightness of form is invariably a consequence of rightness of emotion. | |
| From: Clive Bell (Art [1913], I.III) | |
| A reaction: Bell doesn't dig very deep, because the obvious next question, not really addressed, is what makes the emotion 'right'. He suggests that significant form reveals reality, but why would an emotion do that? Does each work have a distinct emotion? |
| 23933 | Aesthetic contemplation is the best and most intense mental state [Bell,C] |
| Full Idea: Art is not only a means to good states of mind, but, perhaps, the best and most potent that we possess; …there is no state of mind more excellent or more intense than the state of aesthetic contemplation. | |
| From: Clive Bell (Art [1913], II.III) | |
| A reaction: Why does intensity make it good? It is pretty intense being involved in a road accident, but that doesn't make it good. There are many states of mind we enjoy or value highly, but we need more than that to prove them objectively 'excellent'. |
| 23935 | Aesthetic experience is an exaltation which increases the possibilities of life [Bell,C] |
| Full Idea: Those who have been thrilled by the pure aesthetic significance of a work of art …carry a state of excitement and exaltation making them more sensitive to all that is going forward about them. Thus they realise …the significance and possibility of life. | |
| From: Clive Bell (Art [1913], IV.III) | |
| A reaction: This seems like a bit of an afterthought, because he struggles to explain why his 'significant form' is so important. He shifts between it being an end - an intrinsic value - or a moral state, or now an increaser of life potential. |
| 22691 | Only artistic qualities matter in art, because they also have the highest moral value [Bell,C] |
| Full Idea: The only relevant qualities in art are artistic qualities: judged as a means to good, no other qualities are worth considering; for there are no qualities of greater moral value than artistic qualities, since there is no greater means to good than art. | |
| From: Clive Bell (Art [1913], II.III) | |
| A reaction: Wishful thinking, I suspect. I can't see anyone acquiring a moral education just by looking a Cezannes. This seems to be a late manifesto for the aesthetic movement. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |
| 23930 | Religion sees infinite value in some things, and irrelevance in the rest [Bell,C] |
| Full Idea: The essence of religion is a conviction that because some things are of infinite value most are profoundly unimportant. | |
| From: Clive Bell (Art [1913], II.I) | |
| A reaction: The aspect of religion which most worries atheists like Nietzsche. You can end up with a rather cool and detached view of genocide, if you really believe that worldly matters are unimportant. Do souls in heaven worry about the next life after that? |