42 ideas
| 19695 | The devil was wise as an angel, and lost no knowledge when he rebelled [Whitcomb] |
| Full Idea: The devil is evil but nonetheless wise; he was a wise angel, and through no loss of knowledge, but, rather, through some sort of affective restructuring tried and failed to take over the throne. | |
| From: Dennis Whitcomb (Wisdom [2011], 'Argument') | |
| A reaction: ['affective restructuring' indeed! philosophers- don't you love 'em?] To fail at something you try to do suggests a flaw in the wisdom. And the new regime the devil wished to introduce doesn't look like a wise regime. Not convinced. |
| 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. |
| 9542 | The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell] |
| Full Idea: The best known axiomatization of PL is Whitehead/Russell. There are four axioms: (p∨p)→p, q→(p∨q), (p→q)→(q∨p), and (q→r)→((p∨q)→(p∨r)), plus Substitution and Modus Ponens rules. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by GE Hughes/M Cresswell - An Introduction to Modal Logic Ch.1 |
| 21720 | Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead] |
| Full Idea: The axiom of Reducibility ...is crucial in the reduction of classes to logic, ...and seems to be a quite legitimate logical notion for Russell. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 6.4 | |
| A reaction: This is an unusual defence of the axiom, which is usually presumed to have been kicked into the long grass by Quine. If one could reduce classes to logic, that would destroy the opposition to logicism in a single neat coup. |
| 10044 | Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro] |
| Full Idea: Russell adduces two reasons against the extensional view of classes, namely the existence of the null class (which cannot very well be a collection), and the unit classes (which would have to be identical with their single elements). | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Structure and Ontology p.459 | |
| A reaction: Gödel believes in the reality of classes. I have great sympathy with Russell, when people start to claim that sets are not just conveniences to help us think about things, but actual abstract entities. Is the singleton of my pencil is on this table? |
| 18208 | We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead] |
| Full Idea: Classes, so far as we introduce them, are merely symbolic or linguistic conveniences, not genuine objects. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.72), quoted by Penelope Maddy - Naturalism in Mathematics III.2 |
| 8204 | Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead] |
| Full Idea: Russell call 'if...then' implication, when the material conditional is a much better account; C.I.Lewis (in founding modern modal logic) preserved Russell's confusion by creating 'strict implication', and called that implication. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Willard Quine - Reply to Professor Marcus p.177 | |
| A reaction: [A compession of Quine's paragraph]. All of this assumes that logicians can give an accurate account of what if...then means, when ordinary usage is broad and vague. Strict implication seems to drain all the normal meaning out of 'if...then'. |
| 9359 | Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead] |
| Full Idea: In Mr Russell's idea of implication, if twenty random sentences from a newspaper were put in a hat, and two of them drawn at random, one will certainly imply the other, and it is an even bet the implication will be mutual. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by C.I. Lewis - A Pragmatic Conception of the A Priori p.366 | |
| A reaction: This sort of lament leads modern logicians to suggest 'relevance' as an important criterion. It certainly seems odd that so-called 'classical logic' should contain a principle so at variance with everyday reasoning. |
| 21707 | Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B] |
| Full Idea: Russell did not view logic as an uninterpreted calculus awaiting interpretations [the modern view]. Rather, logic is a single 'interpreted' body of a priori truths, of propositions rather than sentence forms - but maximally general and topic neutral. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 1 | |
| A reaction: This is the view which Wittgenstein challenged, saying logic is just conventional. Linsky claims that Russell's logicism is much more plausible, once you understand his view of logic. |
| 10036 | In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel] |
| Full Idea: In 'Principia' a young science was enriched with a new abstract theory of relations, ..and not only Cantor's set theory but also ordinary arithmetic and the theory of measurement are treated from this abstract relational standpoint. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.448 | |
| A reaction: I presume this is accounting for relations in terms of ordered sets. |
| 18248 | A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro] |
| Full Idea: For Russell the real number 2 is the class of rationals less than 2 (i.e. 2/1). ...Notice that on this definition, real numbers are classes of rational numbers. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Thinking About Mathematics 5.2 |
| 18152 | Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock] |
| Full Idea: Although Russell takes numbers to be certain classes, his 'no-class' theory then eliminates all mention of classes in favour of the 'propositional functions' that define them; and in the case of the numbers these just are the numerical quantifiers. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by David Bostock - Philosophy of Mathematics 9.B.4 |
| 10025 | Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes] |
| Full Idea: Russell and Whitehead took arithmetic to be higher-order logic, ..and came close to identifying numbers with numerical quantifiers. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.148 | |
| A reaction: The point here is 'higher-order'. |
| 8683 | Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend] |
| Full Idea: Unlike Frege, Russell and Whitehead were not realists about mathematical objects, and whereas Frege thought that only arithmetic and analysis are branches of logic, they think the vast majority of mathematics (including geometry) is essentially logical. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Michčle Friend - Introducing the Philosophy of Mathematics 3.1 | |
| A reaction: If, in essence, Descartes reduced geometry to algebra (by inventing co-ordinates), then geometry ought to be included. It is characteristic of Russell's hubris to want to embrace everything. |
| 10037 | 'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead] |
| Full Idea: What is missing, above all, in 'Principia', is a precise statement of the syntax of the formalism. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.448 |
| 10093 | The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman] |
| Full Idea: Russell and Whitehead's ramified theory of types worked not with sets, but with propositional functions (similar to Frege's concepts), with a more restrictive assignment of variables, insisting that bound, as well as free, variables be of lower type. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.3 | |
| A reaction: I don't fully understand this (and no one seems much interested any more), but I think variables are a key notion, and there is something interesting going on here. I am intrigued by ordinary language which behaves like variables. |
| 8691 | The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead] |
| Full Idea: The Russell/Whitehead type theory reduces mathematics to a consistent founding discipline, but is criticised for not really being logic. They could not prove the existence of infinite sets, and introduced a non-logical 'axiom of reducibility'. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Michčle Friend - Introducing the Philosophy of Mathematics 3.6 | |
| A reaction: To have reduced most of mathematics to a founding discipline sounds like quite an achievement, and its failure to be based in pure logic doesn't sound too bad. However, it seems to reduce some maths to just other maths. |
| 10305 | In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead] |
| Full Idea: In the system of 'Principia Mathematica', it is not only the axioms of infinity and reducibility which go beyond pure logic, but also the initial conception of a universal domain of individuals and of a domain of predicates. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913], p.267) by Paul Bernays - On Platonism in Mathematics p.267 | |
| A reaction: This sort of criticism seems to be the real collapse of the logicist programme, rather than Russell's paradox, or Gödel's Incompleteness Theorems. It just became impossible to stick strictly to logic in the reduction of arithmetic. |
| 8684 | Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend] |
| Full Idea: Russell and Whitehead are particularly careful to avoid paradox, and consider the paradoxes to indicate that we create mathematical reality. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Michčle Friend - Introducing the Philosophy of Mathematics 3.1 | |
| A reaction: This strikes me as quite a good argument. It is certainly counterintuitive that reality, and abstractions from reality, would contain contradictions. The realist view would be that we have paradoxes because we have misdescribed the facts. |
| 8746 | To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro] |
| Full Idea: Russell insisted on the vicious circle principle, and thus rejected impredicative definitions, which resulted in an unwieldy ramified type theory, with the ad hoc axiom of reducibility. Ramsey's simpler theory was impredicative and avoided the axiom. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Thinking About Mathematics 5.2 | |
| A reaction: Nowadays the theory of types seems to have been given up, possibly because it has no real attraction if it lacks the strict character which Russell aspired to. |
| 12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
| Full Idea: Trivially, the Identity of Indiscernibles says that two individuals, Castor and Pollux, cannot have all properties in common. For Castor must have the properties of being identical with Castor and not being identical with Pollux, which Pollux can't share. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913], I p.57) by Robert Merrihew Adams - Primitive Thisness and Primitive Identity 2 | |
| A reaction: I suspect that either the property of being identical with itself is quite vacuous, or it is parasytic on primitive identity, or it is the criterion which is actually used to define identity. Either way, I don't find this claim very illuminating. |
| 10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
| Full Idea: By analyzing the paradoxes to which Cantor's set theory had led, ..Russell brought to light the amazing fact that our logical intuitions (concerning such notions as truth, concept, being, class) are self-contradictory. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.452 | |
| A reaction: The main intuition that failed was, I take it, that every concept has an extension, that is, there are always objects which will or could fall under the concept. |
| 21725 | The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B] |
| Full Idea: The multiple relations theory of judgement proposes that assertions about propositions are dependent upon genuine facts involving belief and other attitude relations, subjects of those attitudes, and the constituents of the belief. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 7.2 | |
| A reaction: This seems to require a commitment to universals (especially relations) with which we can be directly acquainted. I prefer propositions, but as mental entities, not platonic entities. |
| 23474 | A judgement is a complex entity, of mind and various objects [Russell/Whitehead] |
| Full Idea: When a judgement occurs, there is a certain complex entity, composed of the mind and the various objects of the judgement. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44) | |
| A reaction: This is Russell's multiple-relation theory of judgement, which replaced his earlier belief in unified propositions (now 'false abstractions'). He seems to have accepted Locke's view, that the act of judgement produces the unity. |
| 23455 | The meaning of 'Socrates is human' is completed by a judgement [Russell/Whitehead] |
| Full Idea: When I judge 'Socrates is human', the meaning is completed by the act of judging. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by Michael Morris - Guidebook to Wittgenstein's Tractatus | |
| A reaction: Morris says this is Russell's multiple-relations theory of judgement. The theory accompanies the rejection of the concept of the unified proposition. When I hear 'Socrates had a mole on his shoulder' I get the meaning without judging. |
| 23480 | The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M on Russell/Whitehead] |
| Full Idea: When Russell moved to his multiple relation theory of judgement …he then faced difficulties making sense of the unity of sentences. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913], p.44) by Michael Morris - Guidebook to Wittgenstein's Tractatus 3A | |
| A reaction: Roughly, he seems committed to saying that there is only unity if you think there is unity; there is no unity in a sentence prior to the act of judgement. |
| 18275 | Only the act of judging completes the meaning of a statement [Russell/Whitehead] |
| Full Idea: When I judge 'Socrates is human', the meaning is completed by the act of judging, and we no longer have an incomplete symbol. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap | |
| A reaction: Personally I would have thought that you needed to know the meaning properly before you could make the judgement, but then he is Bertrand Russell and I'm not. |
| 23453 | Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead] |
| Full Idea: A 'proposition', in the sense in which a proposition is supposed to be the object of a judgement, is a false abstraction, because a judgement has several objects, not one. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by Michael Morris - Guidebook to Wittgenstein's Tractatus 2E | |
| A reaction: This is the rejection of the 'Russellian' theory of propositions, in favour of his multiple-relations theory of judgement. But why don't the related objects add up to a proposition about a state of affairs? |
| 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. |
| 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. |
| 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. |