47 ideas
| 23064 | So-called wisdom is just pondering things instead of acting [Cioran] |
| Full Idea: What is known as 'wisdom' is ultimately only a perpetual 'thinking it over', i.e. non-action as first impulse. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 01) | |
| A reaction: This may be how most people view wisdom. Wisdom is for the spectators, not the actors (perhaps). Wisdom needs a lot of thought, and I don't associate it with extremely active people. |
| 23072 | Systems are the worst despotism, in philosophy and in life [Cioran] |
| Full Idea: Aristotle, Aquinas, Hegel - three enslavers of the mind. The worst form of despotism is the system, in philosophy and in everything. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 07) | |
| A reaction: I'm not quite clear why intellectual 'despotism' is a dreadful crime. I revere Aristotle, partly because he is systematic, but I reject about 30% of what he says. Still, many people agree with this idea. |
| 23075 | A text explained ceases to be a text [Cioran] |
| Full Idea: Why embroider upon what excludes commentary? A text explained is not longer a text. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 09) | |
| A reaction: I like that. I'm not a great fan of explicating texts, especially if they are literary, where the whole point is the primary experience, of a novel, poem or play. Philosophy is different, because that is a dialogue between writer and reader. |
| 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 |
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
| A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
| 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. |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
| Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
| A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
| 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
| Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
| From: Ian Rumfitt ("Yes" and "No" [2000]) | |
| A reaction: This is the standard view which Rumfitt sets out to challenge. |
| 23066 | Negation doesn't arise from reasoning, but from deep instincts [Cioran] |
| Full Idea: Negation never proceeds from reasoning but from something much more obscure and old. Arguments come afterward, to justify and sustain it. Every no rises out of the blood. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 02) | |
| A reaction: Music to my ears. In the Fregean era no one is allowed to talk about the origins of logical relations in the universal facts of physical existence. You can watch dogs saying no. |
| 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 Michèle 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 Michèle 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 Michèle 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. |
| 23077 | The word 'being' is very tempting, but in fact means nothing at all [Cioran] |
| Full Idea: Whether it is spoken by a grocer or a philosopher, the word 'being', apparently so rich, so tempting, so charged with significance, in fact means nothing at all; incredible that a man in his right mind can use it on any occasion whatever. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 12) | |
| A reaction: I entirely agree. It resembles the redundancy view of 'true' (with which I do not agree). |
| 23068 | People who really believe anti-realism don't bother to prove it [Cioran] |
| Full Idea: When you know quite absolutely that everything is unreal, you then cannot see why you should take the trouble to prove it. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 02) | |
| A reaction: Does the same apply to realists? There are at least genuine arguments in both directions. Presumably the thought is that realists have something they care about, but true anti-realists don't. |
| 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. |
| 23078 | Opinions are fine, but having convictions means something has gone wrong [Cioran] |
| Full Idea: To have opinions is inevitable, is natural; to have convictions is less so. Each time I meet someone who has convictions, I wonder what intellectual vice, what flaw has caused him to acquire such a thing. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 12) | |
| A reaction: 'The best lack all conviction/ While the worst are full of passionate intensity' (Yeats). I agree with this. Convictions are so often accompanied by anger. |
| 23073 | Convictions are failures to study anything thoroughly [Cioran] |
| Full Idea: We have convictions only if we have studied nothing thoroughly. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 08) | |
| A reaction: Excellent! I cannot imagine studying anything at all in great depth without it resulting in a dwindling expectation of full understanding. Philosophy in spades, but also probably any topic in history. |
| 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. |
| 23076 | If people always acted without words we would take them for robots [Cioran] |
| Full Idea: It is because of speech that men give the illusion of being free. If they did - without a word - what they do, we would take them for robots. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 09) | |
| A reaction: Love this one. Though it might be said that the power of speech does add an extra dimension of freedom to an action, beyond what any animal could attain. I take the absolute idea of 'being free' to be nonsense. |
| 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. |
| 23065 | If only we could write like a reptile, of endless sensations and no concepts! [Cioran] |
| Full Idea: If only we could reach back before the concept, could write on a level with the senses, record the infinitesimal variations of what we touch, do what a reptile would do if it were to set about writing! | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 02) | |
| A reaction: A lovely thought. It is a huge effort for us to try to imagine a mental life without concepts. And then to express that mental life in words…..! |
| 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? |
| 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
| Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], IV) | |
| A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role). |
| 23071 | We could only be responsible if we had consented before birth to who we are [Cioran] |
| Full Idea: The problem of responsibility would have a meaning only if we had been consulted before our birth and had consented to be precisely who we are. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 06) | |
| A reaction: The question could still be asked retrospectively, like agreeing to be in an army into which you have been conscripted. People gripped by deeply anti-social desires would probably welcome the chance to become different. |
| 23070 | We morally dissolve if we spend time with excessive beauty [Cioran] |
| Full Idea: Moral disintegration when we spend time in a place that is too beautiful: the self dissolves upon contact with paradise. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 06) | |
| A reaction: I'm not sure whether that is true, but it is worth thinking about the value of experiences which are overwhelming. |
| 23074 | In anxiety people cling to what reinforces it, because it is a deep need [Cioran] |
| Full Idea: In anxiety, a man clings to whatever can reinforce, can stimulate his providential discomfort: to try to cure him of it is to destroy his equilibrium, anxiety being the basis of his existence and his prosperity. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 09) | |
| A reaction: A report from the front line of the age of anxiety, on which I am not qualified to comment. I assume that some anxiety can be a good thing, like nerves before a public performance. |
| 23062 | It is better to watch the hours pass, than trying to fill them [Cioran] |
| Full Idea: I do nothing, granted. But I see the hours pass - which is better than trying to fill them. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 01) | |
| A reaction: As Nietzsche would have pointed out, this came from a man who regularly wrote books. It is, though, certainly worth asking whether the way we fill our time is better than doing nothing. |
| 23069 | Fear cures boredom, because it is stronger [Cioran] |
| Full Idea: Fear is the antidote to boredom: the remedy must be stronger than the disease. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 05) | |
| A reaction: I suspect that this is the motivation of people who indulge in dangerous sports. Maybe all that is need is something daunting, rather than frightening. |
| 23067 | Suicide is pointless, because it always comes too late [Cioran] |
| Full Idea: It's not worth the bother of killing yourself, since you always kill yourself too late. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 02) | |
| A reaction: A neat thought, but unlikely to be true for those who commit suicide, which presumably results from a sustained and apparently incurable situation. |
| 23063 | The first man obviously found paradise unendurable [Cioran] |
| Full Idea: Paradise was unendurable, otherwise the first man would have adapted to it. | |
| From: E.M. Cioran (The Trouble with Being Born [1973], 01) | |
| A reaction: Seems a bit harsh. There was evidently one aspect that was missing (knowledge), and he was surprised to find himself ejected for wanting it. Like a holiday in a Mediterranean hotel, with good food. |