26 ideas
| 22338 | An unexamined life can be virtuous [Murdoch] |
| Full Idea: An unexamined life can be virtuous. | |
| From: Iris Murdoch (The Sovereignty of Good [1970], I) | |
| A reaction: Nice. A firm rejection of the intellectualist view of virtue, to which most Greeks subscribed. Jesus would have liked this one. |
| 22337 | Philosophy must keep returning to the beginning [Murdoch] |
| Full Idea: Philosophy has in a sense to keep trying to return to the beginning. | |
| From: Iris Murdoch (The Sovereignty of Good [1970], I) | |
| A reaction: This is a sign that philosophy is not like other subjects, and indicates that although the puzzles are not solved, they won't go away. Also that, unlike most other subjects, the pre-suppositions are not part of the subject. |
| 23563 | Philosophy moves continually between elaborate theories and the obvious facts [Murdoch] |
| Full Idea: There is a two-way movement in philosophy, a movement towards the building of elaborate theories, and a move back again towards the consideration of simple and obvious facts. | |
| From: Iris Murdoch (The Sovereignty of Good [1970], I) | |
| A reaction: Nice. Without the theories there is no philosophy, but without continual reference back to the obvious facts the theories are worthless. |
| 12461 | We believe all mathematical problems are solvable [Hilbert] |
| Full Idea: The thesis that every mathematical problem is solvable - we are all convinced that it really is so. | |
| From: David Hilbert (On the Infinite [1925], p.200) | |
| A reaction: This will include, for example, Goldbach's Conjecture (every even is the sum of two primes), which is utterly simple but with no proof anywhere in sight. |
| 12456 | I aim to establish certainty for mathematical methods [Hilbert] |
| Full Idea: The goal of my theory is to establish once and for all the certitude of mathematical methods. | |
| From: David Hilbert (On the Infinite [1925], p.184) | |
| A reaction: This is the clearest statement of the famous Hilbert Programme, which is said to have been brought to an abrupt end by Gödel's Incompleteness Theorems. |
| 9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
| Full Idea: No one shall drive us out of the paradise the Cantor has created for us. | |
| From: David Hilbert (On the Infinite [1925], p.191), quoted by James Robert Brown - Philosophy of Mathematics | |
| A reaction: This is Hilbert's famous refusal to accept any account of mathematics, such as Kant's, which excludes actual infinities. Cantor had laid out a whole glorious hierarchy of different infinities. |
| 12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
| Full Idea: To preserve the simple formal rules of ordinary Aristotelian logic, we must supplement the finitary statements with ideal statements. | |
| From: David Hilbert (On the Infinite [1925], p.195) | |
| A reaction: I find very appealing the picture of mathematics as rooted in the physical world, and then gradually extended by a series of 'idealisations', which should perhaps be thought of as fictions. |
| 12462 | Only the finite can bring certainty to the infinite [Hilbert] |
| Full Idea: Operating with the infinite can be made certain only by the finitary. | |
| From: David Hilbert (On the Infinite [1925], p.201) | |
| A reaction: See 'Compactness' for one aspect of this claim. I think Hilbert was fighting a rearguard action, and his idea now has few followers. |
| 12455 | The idea of an infinite totality is an illusion [Hilbert] |
| Full Idea: Just as in the limit processes of the infinitesimal calculus, the infinitely large and small proved to be a mere figure of speech, so too we must realise that the infinite in the sense of an infinite totality, used in deductive methods, is an illusion. | |
| From: David Hilbert (On the Infinite [1925], p.184) | |
| A reaction: This is a very authoritative rearguard action. I no longer think the dispute matters much, it being just a dispute over a proposed new meaning for the word 'number'. |
| 12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
| Full Idea: A homogeneous continuum which admits of the sort of divisibility needed to realise the infinitely small is nowhere to be found in reality. | |
| From: David Hilbert (On the Infinite [1925], p.186) | |
| A reaction: He makes this remark as a response to Planck's new quantum theory (the year before the big works of Heisenberg and Schrödinger). Personally I don't see why infinities should depend on the physical world, since they are imaginary. |
| 12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
| Full Idea: The subject matter of mathematics is the concrete symbols themselves whose structure is immediately clear and recognisable. | |
| From: David Hilbert (On the Infinite [1925], p.192) | |
| A reaction: I don't think many people will agree with Hilbert here. Does he mean token-symbols or type-symbols? You can do maths in your head, or with different symbols. If type-symbols, you have to explain what a type is. |
| 18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
| Full Idea: We can conceive mathematics to be a stock of two kinds of formulas: first, those to which the meaningful communications of finitary statements correspond; and secondly, other formulas which signify nothing and which are ideal structures of our theory. | |
| From: David Hilbert (On the Infinite [1925], p.196), quoted by David Bostock - Philosophy of Mathematics 6.1 |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| Full Idea: The goal of my theory is to establish once and for all the certitude of mathematical methods. | |
| From: David Hilbert (On the Infinite [1925], p.184), quoted by James Robert Brown - Philosophy of Mathematics Ch.5 | |
| A reaction: This dream is famous for being shattered by Gödel's Incompleteness Theorem a mere six years later. Neverless there seem to be more limited certainties which are accepted in mathematics. The certainty of the whole of arithmetic is beyond us. |
| 22341 | Literature is the most important aspect of culture, because it teaches understanding of living [Murdoch] |
| Full Idea: The most essential and fundamental aspect of culture is the study of literature, since this is an education in how to picture and understand human situations. | |
| From: Iris Murdoch (The Sovereignty of Good [1970], i) | |
| A reaction: It is significant that literature belongs more clearly to a nation or community than does most music or painting. You learn about Russians from their literature, but not much from their music. |
| 22347 | Appreciating beauty in art or nature opens up the good life, by restricting selfishness [Murdoch] |
| Full Idea: The appreciation of beauty in art or nature is not only the easiest available spiritual exercise; it is also a completely adequate entry into (and not just analogy of) the good life, since it checks selfishness in the interest of seeing the real. | |
| From: Iris Murdoch (The Sovereignty of Good [1970], II) | |
| A reaction: Not keen on 'spiritual' exercises, but I very much like 'seeing the real' as a promotion of the good life. The hard bit is to know what reality you are seeing in a work of art. [p.84] Her example is the sudden sight of a hovering kestrel. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 22339 | Love is a central concept in morals [Murdoch] |
| Full Idea: Love is a central concept in morals. ....[p.30] The central concept of morality is 'the individual' thought of as knowable by love, thought of in the light of the command 'Be ye therefore perfect'. | |
| From: Iris Murdoch (The Sovereignty of Good [1970], I) | |
| A reaction: This seems to be a critique of the chillier aspects of utilitarianism and Kantian duty. Love doesn't seem essential to Aristotle's concept of virtue either, and Murdoch's tradition seems to be Christian. I'm undecided about this idea. |
| 22348 | Ordinary human love is good evidence of transcendent goodness [Murdoch] |
| Full Idea: Is not ordinary human love ...striking evidence of a transcendental principle of good? | |
| From: Iris Murdoch (The Sovereignty of Good [1970], II) | |
| A reaction: Sorry to be mean, but I would say not. Love is tied up with sexual desire, and with family and tribal loyalty, and can be observed in quite humble animals. (Love, I should quickly add, is a very good thing indeed. Really). |
| 22343 | If I attend properly I will have no choices [Murdoch] |
| Full Idea: If I attend properly I will have no choices, and this is the ultimate condition to be aimed at. | |
| From: Iris Murdoch (The Sovereignty of Good [1970], I) | |
| A reaction: I take it this is an expression of what we now call Particularism. It is not just that every moral situation is subtly morally different, but that the particulars of the situation will lead directly to moral choices (in a 'healthy' agent). |
| 22340 | It is hard to learn goodness from others, because their virtues are part of their personal history [Murdoch] |
| Full Idea: It is the historical, individual, nature of the virtues as actually exemplified which makes it difficult to learn goodness from another person. | |
| From: Iris Murdoch (The Sovereignty of Good [1970], I) | |
| A reaction: A penetrating remark, which strikes me as true. When confronted with a virtuous person you might want to acquire their virtue, just as you might want them to teach you algebra, but their virtues are too bound up with their individuality. |
| 22349 | Art trains us in the love of virtue [Murdoch] |
| Full Idea: The enjoyment of art is a training in the love of virtue. | |
| From: Iris Murdoch (The Sovereignty of Good [1970], III) | |
| A reaction: Very Aristotelian to talk of 'training'. Unfortunately it is children who have the greatest need for training, but most art is aimed at mature adults. Can you be too old to be trained by art, even if you enjoy it? |
| 22346 | Moral reflection and experience gradually reveals unity in the moral world [Murdoch] |
| Full Idea: Reflection rightly tends to unify the moral world, and increasing moral sophistication reveals increasing unity. | |
| From: Iris Murdoch (The Sovereignty of Good [1970], II) | |
| A reaction: As an example she suggests asking what is the best type of courage. Connections to other virtues will emerge. That is a persuasive example. We all have strong views on what type of courage is the most admirable. |
| 22350 | Only trivial virtues can be possessed on their own [Murdoch] |
| Full Idea: It would be impossible to have only one virtue, unless it were a very trivial one such as thrift. | |
| From: Iris Murdoch (The Sovereignty of Good [1970], III) | |
| A reaction: A nicely nuanced commitment to the unity of virtue. You might exhibit courage alone in a brute animal way, but the sort of courage we all admire is part of more extended virtues. |
| 22351 | Only a philosopher might think choices create values [Murdoch] |
| Full Idea: The ordinary person does not, unless corrupted by philosophy, believe that he creates values by his choices. | |
| From: Iris Murdoch (The Sovereignty of Good [1970], III) | |
| A reaction: This looks like a swipe at Nietzsche, more than anyone. Sartre and co talk less about values, other than authenticity. Philosophy can definitely be corrupting. |
| 22342 | Kantian existentialists care greatly for reasons for action, whereas Surrealists care nothing [Murdoch] |
| Full Idea: What may be called the Kantian wing and the Surrealist wing of existentialism may be distinguished by the degree of their interest in reasons for action, which diminishes to nothing at the Surrealist end. | |
| From: Iris Murdoch (The Sovereignty of Good [1970], I) | |
| A reaction: Presumably for all existentialists moral decisions are the most important aspect of life, since they define what you are, but the Surrealist wing seem to be nihilists about that, so they barely count as existentialists. For them life is sleepwalking. |
| 22345 | Moral philosophy needs a central concept with all the traditional attributes of God [Murdoch] |
| Full Idea: God was (or is) a single perfect transcendent non-representable and necessarily real object of attention. ....Moral philosophy should attempt to retain a central concept which has all these characteristics. | |
| From: Iris Murdoch (The Sovereignty of Good [1970], II) | |
| A reaction: This is a combination of middle Platonism (which sees the Form of the Good as the mind of God) and G.E. Moore's indefinable ideal of goodness. Murdoch connects this suggestion with the centrality of love in moral philosophy. I disagree. |