44 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. |
| 10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
| Full Idea: For a set to be 'well-ordered' it is required that every subset of the set has a first element. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13) |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| Full Idea: Set theory made a closer study of infinity possible. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13) |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| Full Idea: The idea of the 'power set' means that it is always possible to generate a bigger one using only the elements of that set, namely the set of all its subsets. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.14) |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| Full Idea: Axiom of Extension: Two sets are equal if and only if they have the same elements. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
| Full Idea: Axiom of Pairing: For any two sets there exists a set to which they both belong. So you can make a set out of two other sets. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
| Full Idea: Axiom of Unions: For every collection of sets there exists a set that contains all the elements that belong to at least one of the sets in the collection. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| Full Idea: Axiom of Infinity: There exists a set containing the empty set and the successor of each of its elements. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) | |
| A reaction: This is rather different from the other axioms because it contains the notion of 'successor', though that can be generated by an ordering procedure. |
| 10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
| Full Idea: Axiom of Powers: For each set there exists a collection of sets that contains amongst its elements all the subsets of the given set. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) | |
| A reaction: Obviously this must include the whole of the base set (i.e. not just 'proper' subsets), otherwise the new set would just be a duplicate of the base set. |
| 10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
| Full Idea: Axiom of Choice: For every set we can provide a mechanism for choosing one member of any non-empty subset of the set. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) | |
| A reaction: This axiom is unusual because it makes the bold claim that such a 'mechanism' can always be found. Cohen showed that this axiom is separate. The tricky bit is choosing from an infinite subset. |
| 10871 | Axiom of Existence: there exists at least one set [Clegg] |
| Full Idea: Axiom of Existence: there exists at least one set. This may be the empty set, but you need to start with something. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
| Full Idea: Axiom of Specification: For every set and every condition, there corresponds a set whose elements are exactly the same as those elements of the original set for which the condition is true. So the concept 'number is even' produces a set from the integers. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) | |
| A reaction: What if the condition won't apply to the set? 'Number is even' presumably won't produce a set if it is applied to a set of non-numbers. |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| Full Idea: Three views of mathematics: 'pure' mathematics, where it doesn't matter if it could ever have any application; 'real' mathematics, where every concept must be physically grounded; and 'applied' mathematics, using the non-real if the results are real. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.17) | |
| A reaction: Very helpful. No one can deny the activities of 'pure' mathematics, but I think it is undeniable that the origins of the subject are 'real' (rather than platonic). We do economics by pretending there are concepts like the 'average family'. |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| Full Idea: With ordinary finite numbers ordinals and cardinals are in effect the same, but beyond infinity it is possible for two sets to have the same cardinality but different ordinals. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13) |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| Full Idea: You can think of an ordinal number as being defined by the set that comes before it, so, in the non-negative integers, ordinal 5 is defined as {0, 1, 2, 3, 4}. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13) |
| 10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
| Full Idea: The 'transcendental numbers' are those irrationals that can't be fitted to a suitable finite equation, of which π is far and away the best known. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch. 6) |
| 10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
| Full Idea: The realisation that brought 'i' into the toolkit of physicists and engineers was that you could extend the 'number line' into a new dimension, with an imaginary number axis at right angles to it. ...We now have a 'number plane'. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.12) |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
| Full Idea: It is a chicken-and-egg problem, whether the lack of zero forced forced classical mathematicians to rely mostly on a geometric approach to mathematics, or the geometric approach made 0 a meaningless concept, but the two remain strongly tied together. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch. 6) |
| 10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
| Full Idea: As far as Kronecker was concerned, Cantor had built a whole structure on the irrational numbers, and so that structure had no foundation at all. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
| Full Idea: Paul Cohen showed that the Continuum Hypothesis is independent of the axioms of set theory. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
| Full Idea: The 'continuum hypothesis' says that aleph-one is the cardinality of the rational and irrational numbers. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.14) |
| 8836 | Must all justification be inferential? [Ginet] |
| Full Idea: The infinitist view of justification holds that every justification must be inferential: no other kind of justification is possible. | |
| From: Carl Ginet (Infinitism not solution to regress problem [2005], p.141) | |
| A reaction: This is the key question in discussing whether justification is foundational. I'm not sure whether 'inference' is the best word when something is evidence for something else. I am inclined to think that only propositions can be reasons. |
| 8837 | Inference cannot originate justification, it can only transfer it from premises to conclusion [Ginet] |
| Full Idea: Inference cannot originate justification, it can only transfer it from premises to conclusion. And so it cannot be that, if there actually occurs justification, it is all inferential. | |
| From: Carl Ginet (Infinitism not solution to regress problem [2005], p.148) | |
| A reaction: The idea that justification must have an 'origin' seems to beg the question. I take Klein's inifinitism to be a version of coherence, where the accumulation of good reasons adds up to justification. It is not purely inferential. |
| 22591 | We know perfection when we see what is imperfect [Murdoch] |
| Full Idea: We know of perfection as we look upon what is imperfect. | |
| From: Iris Murdoch (Metaphysics as a Guide to Morals [1992], 13) | |
| A reaction: This is in the context of a discussion of the ontological argument for God's existence, but I seize on it as a nice expression of the idealisation capacity of our minds. The alternative is that perfection is innate idea, since we aren't seeing it. |
| 22709 | We should first decide what are the great works of art, with aesthetic theory following from that [Murdoch] |
| Full Idea: Our aesthetic must stand to be judged by great works of art which we know to be such independently. …So let us start by saying that Shakespeare is the greatest of all artists, and let our aesthetic be the philosophical justification of this judgement. | |
| From: Iris Murdoch (The Sublime and the Good [1959], p.205) | |
| A reaction: She offers this view in specific contradiction of Tolstoy, which says we should first have a theory, and then judge accordingly. I take Murdoch to be entirely right, but it means that our aesthetic theory will shift over time. |
| 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. |
| 22715 | Great art proves the absurdity of art for art's sake [Murdoch] |
| Full Idea: The work of the great artists shows up 'art-for-art's-sake' as a flimsy frivolous doctrine. | |
| From: Iris Murdoch (The Sublime and the Good [1959], p.218) | |
| A reaction: She keeps referring to tragedy (as the greatest art), but it is hard to see how we learn love and morality from a great pot or a great abstract painting. Wilde makes the doctrine frivolous, but I think it contains a degree of truth. Music. |
| 22714 | Because art is love, it improves us morally [Murdoch] |
| Full Idea: It is of course a fact that if art is love then art improves us morally, but this is, as it were, accidental. | |
| From: Iris Murdoch (The Sublime and the Good [1959], p.218) | |
| A reaction: Is an enhancement of one's love necessarily a moral improvement? Love is a fine feeling, but how does it motivate? Has no wickedness ever been perpetrated in the name of love? 'All's fair in love and war'. |
| 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. |
| 22712 | Art and morals are essentially the same, and are both identical with love [Murdoch] |
| Full Idea: Art and morals are (with certain provisos) one. Their essence is the same. The essence of both of them is love. Love is the perception of individuals. | |
| From: Iris Murdoch (The Sublime and the Good [1959], p.215) | |
| A reaction: The idea that art, morals and love are all just a single thing seems unhelpful. What about satire? What about duty without love? What about pure abstract painting? What about Stravinsky's highly formal view of his music? |
| 22713 | Love is realising something other than oneself is real [Murdoch] |
| Full Idea: Love is the extremely difficult realisation that something other than oneself is real. | |
| From: Iris Murdoch (The Sublime and the Good [1959], p.215) | |
| A reaction: I suspect that this is a necessary condition for love, but not the thing itself. The realisation she describes may not be love. You would attain her realisation if you shared a prison cell with a terrifying psychopath. |
| 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). |
| 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? |
| 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. |
| 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. |
| 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. |
| 20765 | Man is a brave naked will, separate from a background of values and realities [Murdoch] |
| Full Idea: Existentialists no longer see man against a background of values, of realities, which transcend him. We picture man as a brave naked will. | |
| From: Iris Murdoch (Against Dryness: a polemical sketch [1983], p.46), quoted by Kevin Aho - Existentialism: an introduction 7 'Subjectivism' | |
| A reaction: It is one thing to deny the values, and another to deny the realities. This piece is a 'polemic', and reads more like an exhortation than a truth. Many of us are, at best, cowardly naked wills. |
| 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. |
| 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. |
| 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. |