42 ideas
| 7278 | Words of wisdom are precise and clear [Zhuangzi (Chuang Tzu)] |
| Full Idea: Words of wisdom are precise and clear. | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.2) | |
| A reaction: I can only approve of this. The issue of clarity is much discussed amongs philosophers, especially in the analytic v continental debate. Note, therefore, the additional requirement to be 'precise'. Should we be less clear in order to be precise? |
| 7281 | Don't even start, let's just stay put [Zhuangzi (Chuang Tzu)] |
| Full Idea: Don't even start, let's just stay put. | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.2) | |
| A reaction: What a remarkable proposal! He seems frightened to make an omelette, because he will have to break an egg, or he might burn himself. I can't relate to this idea, but it's existence must be noted, like other scepticisms. |
| 7282 | Disagreement means you do not understand at all [Zhuangzi (Chuang Tzu)] |
| Full Idea: The sage encompasses everything, while ordinary people just argue about things. Disagreement means you do not understand at all. | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.2) | |
| A reaction: This is why democracy and western analytical philosophy come as a package. We can't assume that our government is always right, and we can't assume that a 'sage' has managed to encompass everything. Criticism is essential! |
| 7284 | If you beat me in argument, does that mean you are right? [Zhuangzi (Chuang Tzu)] |
| Full Idea: If you get the better of me in a disagreement, rather than me getting the better of you, does this mean that you are automatically right and I am automatically wrong? | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.2) | |
| A reaction: Very nice. I don't, though, think that this invalidates the process of argument. What matters about such an exchange is the resulting reflection by the two parties. Only a fool thinks that he is right because he won, or wrong because he lost. |
| 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. |
| 7289 | Do not try to do things, or to master knowledge; just be empty [Zhuangzi (Chuang Tzu)] |
| Full Idea: Do not try to do things. Do not try to master knowledge. ...Just be empty. | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.7) | |
| A reaction: Stands as a nice challenge to the assumption that knowledge is a good thing. Aristotle's views make a nice contrast (Ideas 548 and 549). Personally I totally agree with Aristotle, and with the western tradition. |
| 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. |
| 23403 | You know you were dreaming when you wake, but there might then be a greater awakening from that [Zhuangzi (Chuang Tzu)] |
| Full Idea: Often after waking do you know that your dream was a dream. Still, there may be an even greater awakening after which you will know that this, too, was just a greater dream. | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], 02), quoted by Bryan van Norden - Intro to Classical Chinese Philosophy 9.2 | |
| A reaction: This is the key to the full horror of dream scepticism (as dramatised in the film 'The Matrix'). We can never know whether there is yet another awakening about to occur. |
| 7285 | Did Chuang Tzu dream he was a butterfly, or a butterfly dream he was Chuang Tzu? [Zhuangzi (Chuang Tzu)] |
| Full Idea: Once I, Chuang Tzu, dreamt that I was a butterfly, flitting around and enjoying myself. Suddenly I woke and was Chuang Tzu again. But had I been Chuang Tzu dreaming I was a butterfly, or a butterfly dreaming I was now Chuang Tzu? | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.2) | |
| A reaction: Plato (Idea 2047) also spotted this problem, later made famous by Descartes (Idea 2250). Given the size of a butterfly's brain, this suggests that Chuang Tzu was a dualist. What can't I take the idea seriously, when reason says I should? |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| Full Idea: There are six 'reductive levels' in science: social groups, (multicellular) living things, cells, molecules, atoms, and elementary particles. | |
| From: report of H.Putnam/P.Oppenheim (Unity of Science as a Working Hypothesis [1958]) by Peter Watson - Convergence 10 'Intro' | |
| A reaction: I have the impression that fields are seen as more fundamental that elementary particles. What is the status of the 'laws' that are supposed to govern these things? What is the status of space and time within this picture? |
| 7277 | The perfect man has no self [Zhuangzi (Chuang Tzu)] |
| Full Idea: As the saying goes, 'The perfect man has no self' | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.1) | |
| A reaction: This seems to be quoted with approval. This is interesting because it implies that lesser beings do have a self, and that having a self is a moral issue, and one which can be controlled. One could, I suppose, concentrate on externals. |
| 7286 | To see with true clarity, your self must be irrelevant [Zhuangzi (Chuang Tzu)] |
| Full Idea: When a man discerns his own self as irrelevant, he sees with true clarity. | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.6) | |
| A reaction: Seeing 'with clarity' is only one of the ways of seeing, and one mustn't unquestioningly assume that it is the best. Wisdom should contemplate vision with and without the self, and then rise higher and compare the two views. Compare Parfit (Idea 5518). |
| 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. |
| 7279 | If words can't be defined, they may just be the chirruping of chicks [Zhuangzi (Chuang Tzu)] |
| Full Idea: Our words are not just hot air. Words work because they are something, but the problem is that, if we cannot define a word's meaning, it doesn't really say anything. Can we make a case for it being anything different from the chirruping of chicks? | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.2) | |
| A reaction: This obviously points us towards Quine's challenge to analyticity, and hence the value of definitions (Ideas 1622 and 1624). Even for Chuang Tzu, it seems naďve to think that you cannot use a word well if you cannot define it. |
| 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? |
| 23404 | Words are for meaning, and once you have that you can forget the words [Zhuangzi (Chuang Tzu)] |
| Full Idea: Words are for meaning: when you've gotten the meaning, you can forget the words. | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], 26), quoted by Bryan van Norden - Intro to Classical Chinese Philosophy 9.VI | |
| A reaction: 'What exactly did this person say?' 'Don't know, but I've given you the accurate gist'. This is such an obvious phenomenon that I amazed by modern philosophers who deny propositions, or deny meaning entirely. |
| 7283 | Great courage is not violent [Zhuangzi (Chuang Tzu)] |
| Full Idea: Great courage is not violent. | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.2) | |
| A reaction: A very nice remark. This, I think, is what the Greeks were struggling to say about courage, but they never quite pinned it down as Chuang Tzu does. |
| 7280 | As all life is one, what need is there for words? [Zhuangzi (Chuang Tzu)] |
| Full Idea: As all life is one, what need is there for words? | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.2) | |
| A reaction: In a sense this is nonsense, but it has an appeal. I presume that God would not need words, any more than he would need arithmetic. Life is obviously a complex one, with parts which can be discussed. |
| 7288 | Go with the flow, and be one with the void of Heaven [Zhuangzi (Chuang Tzu)] |
| Full Idea: Don't struggle, go with the flow, and you will find yourself at one with the vastness of the void of Heaven. | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.6) | |
| A reaction: Ugh. I've got all eternity to do that. The underlying assumption of Taoism seems to be that it is better not to have been born, and if you are thus unfortunate, you should try to pretend that it never happened. Much too negative for my taste. |
| 7287 | Fish forget about each other in the pond and forget each other in the Tao [Zhuangzi (Chuang Tzu)] |
| Full Idea: Fish forget about each other in the pond and forget each other in the Tao. | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.6) | |
| A reaction: Strikingly different from Christianity. No wonder Europeans used to describe orientals as 'enigmatic'; the faces of Taoists presumably express indifference. Not for me, I'm afraid. I identify with my fellow humans, because of our shared predicaments. |