33 ideas
| 12452 | Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer] |
| Full Idea: Not to the mathematician, but to the psychologist, belongs the task of explaining why ...we are averse to so-called contradictory systems in which the negative as well as the positive of certain propositions are valid. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.79) | |
| A reaction: Was the turning point of Graham Priest's life the day he read this sentence? I don't agree. I take the principle of non-contradiction to be a highly generalised observation of how the world works (and Russell agrees with me). |
| 15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |
| Full Idea: From the intuitionist standpoint the dogma of the universal validity of the principle of excluded third in mathematics can only be considered as a phenomenon of history of civilization, like the rationality of pi or rotation of the sky about the earth. | |
| From: Luitzen E.J. Brouwer (works [1930]), quoted by Shaughan Lavine - Understanding the Infinite VI.2 | |
| A reaction: [Brouwer 1952:510-11] |
| 18119 | Mathematics is a mental activity which does not use language [Brouwer, by Bostock] |
| Full Idea: Brouwer made the rather extraordinary claim that mathematics is a mental activity which uses no language. | |
| From: report of Luitzen E.J. Brouwer (Mathematics, Science and Language [1928]) by David Bostock - Philosophy of Mathematics 7.1 | |
| A reaction: Since I take language to have far less of a role in thought than is commonly believed, I don't think this idea is absurd. I would say that we don't use language much when we are talking! |
| 18247 | Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro] |
| Full Idea: In his early writing, Brouwer took a real number to be a Cauchy sequence determined by a rule. Later he augmented rule-governed sequences with free-choice sequences, but even then the attitude is that Cauchy sequences are potential, not actual infinities. | |
| From: report of Luitzen E.J. Brouwer (works [1930]) by Stewart Shapiro - Philosophy of Mathematics 6.6 | |
| A reaction: This is the 'constructivist' view of numbers, as espoused by intuitionists like Brouwer. |
| 12451 | Scientific laws largely rest on the results of counting and measuring [Brouwer] |
| Full Idea: A large part of the natural laws introduced by science treat only of the mutual relations between the results of counting and measuring. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.77) | |
| A reaction: His point, I take it, is that the higher reaches of numbers have lost touch with the original point of the system. I now see the whole issue as just depending on conventions about the agreed extension of the word 'number'. |
| 18118 | Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock] |
| Full Idea: Brouwer regards as somehow 'wicked' the idea that mathematics can be applied to a non-mental subject matter, the physical world, and that it might develop in response to the needs which that application reveals. | |
| From: report of Luitzen E.J. Brouwer (Mathematics, Science and Language [1928]) by David Bostock - Philosophy of Mathematics 7.1 | |
| A reaction: The idea is that mathematics only concerns creations of the human mind. It presumably has no more application than, say, noughts-and-crosses. |
| 12454 | Intuitionists only accept denumerable sets [Brouwer] |
| Full Idea: The intuitionist recognises only the existence of denumerable sets. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80) | |
| A reaction: That takes you up to omega, but not beyond, presumably because it then loses sight of the original intuition of 'bare two-oneness' (Idea 12453). I sympathise, but the word 'number' has shifted its meaning a lot these days. |
| 12453 | Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer] |
| Full Idea: Neo-intuitionism sees the falling apart of moments, reunited while remaining separated in time, as the fundamental phenomenon of human intellect, passing by abstracting to mathematical thinking, the intuition of bare two-oneness. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80) | |
| A reaction: [compressed] A famous and somewhat obscure idea. He goes on to say that this creates one and two, and all the finite ordinals. |
| 8728 | Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer] |
| Full Idea: Mathematics rigorously treated from the point of view of deducing theorems exclusively by means of introspective construction, is called intuitionistic mathematics. It deviates from classical mathematics, which believes in unknown truths. | |
| From: Luitzen E.J. Brouwer (Consciousness, Philosophy and Mathematics [1948]), quoted by Stewart Shapiro - Thinking About Mathematics 1.2 | |
| A reaction: Clearly intuitionist mathematics is a close cousin of logical positivism and the verification principle. This view would be anathema to Frege, because it is psychological. Personally I believe in the existence of unknown truths, big time! |
| 1457 | Morality requires a minimum commitment to the self [Rashdall] |
| Full Idea: A bare minimum of metaphysical belief about the self is found to be absolutely presupposed in the very idea of morality. | |
| From: Hastings Rashdall (Theory of Good and Evil [1907], II.III.I.4) | |
| A reaction: This may not be true of virtue theory, where we could have a whole creature which lacked any sense of personhood, but yet had clear virtues and vices in its social functioning. Even if choices are central to morality, that might not need a self. |
| 10117 | Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman] |
| Full Idea: The concern of mathematical intuitionists was that the use of certain forms of inference generates, not contradiction, but unjustified assertions. | |
| From: report of Luitzen E.J. Brouwer (Intuitionism and Formalism [1912]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: This seems to be the real origin of the verificationist idea in the theory of meaning. It is a hugely revolutionary idea - that ideas are not only ruled out of court by contradiction, but that there are other criteria which should also be met. |
| 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. |
| 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! |
| 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. |
| 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. |
| 6674 | All moral judgements ultimately concern the value of ends [Rashdall] |
| Full Idea: All moral judgements are ultimately judgements as to the value of ends. | |
| From: Hastings Rashdall (Theory of Good and Evil [1907], VII.I) | |
| A reaction: I am increasingly struck by this, especially when observing that it is the great gap in Kant's theory. For some odd reason, he gives being rational the highest possible value. Why? Nietzsche is good on this. 'Eudaimonia' seems a good start, to me. |
| 6673 | Ideal Utilitarianism is teleological but non-hedonistic; the aim is an ideal end, which includes pleasure [Rashdall] |
| Full Idea: My view, called Ideal Utilitarianism, combines the utilitarian principle that Ethics must be teleological with a non-hedonistic view of ethical ends; actions are right or wrong as they produce an ideal end, which includes, but is not limited to, pleasure. | |
| From: Hastings Rashdall (Theory of Good and Evil [1907], VII.I) | |
| A reaction: I certainly think that if you are going to be a consequentialist, then it is ridiculous to limit the end to pleasure, as it is an 'open question' as to whether we judge pleasures or pains to be good or bad. I am fond of beauty, goodness and truth, myself. |
| 1458 | Conduct is only reasonable or unreasonable if the world is governed by reason [Rashdall] |
| Full Idea: Absolutely reasonable or unreasonable conduct could not exist in a world which was not itself the product of reason or governed by its dictates. | |
| From: Hastings Rashdall (Theory of Good and Evil [1907], II.III.I.4) |
| 1459 | Absolute moral ideals can't exist in human minds or material things, so their acceptance implies a greater Mind [Rashdall, by PG] |
| Full Idea: An absolute moral ideal cannot exist in material things, or in the minds of individual people, so belief in it requires belief in a Mind which contains the ideal and is its source. | |
| From: report of Hastings Rashdall (Theory of Good and Evil [1907], II.III.I.4) by PG - Db (ideas) |
| 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? |