40 ideas
| 21584 | A sense of timelessness is essential to wisdom [Russell] |
| Full Idea: Both in thought and in feeling, to realize the unimportance of time is the gate of wisdom. | |
| From: Bertrand Russell (Our Knowledge of the External World [1914], 6) | |
| A reaction: A very rationalist and un-Heraclitean view of wisdom. This picture may give wisdom a bad name, if wise people are (at a minimum) at least expected to give good advice about real life. |
| 21572 | Philosophical disputes are mostly hopeless, because philosophers don't understand each other [Russell] |
| Full Idea: Explicit controversy is almost always fruitless in philosophy, owing to the fact that no two philosophers ever understand one another. | |
| From: Bertrand Russell (Our Knowledge of the External World [1914], 1) | |
| A reaction: Contemporaries don't even seem to read one another very much, especially these days, when there are thousands of professional philosophers. (If you are a professional, have you read all the works written by your colleagues and friends?) |
| 21571 | Philosophical systems are interesting, but we now need a more objective scientific philosophy [Russell] |
| Full Idea: The great systems of the past serve a very useful purpose, and are abundantly worthy of study. But something different is required if philosophy is to become a science, and to aim at results independent of the tastes of the philosophers who advocate them. | |
| From: Bertrand Russell (Our Knowledge of the External World [1914], Pref) | |
| A reaction: An interesting product of this move in philosophy is (about sixty years later) the work of David Lewis, who set out to be precise and scientific, and ended up creating a very personal system. Why not a collaborative system? |
| 21574 | Hegel's confusions over 'is' show how vast systems can be built on simple errors [Russell] |
| Full Idea: Hegel's confusion of the 'is' of predication with the 'is' of identity ...is an example of how, for want of care at the start, vast and imposing systems of philosophy are built upon stupid and trivial confusions. | |
| From: Bertrand Russell (Our Knowledge of the External World [1914], 2 n1) | |
| A reaction: [He explains the confusion in more detail in the note] Russell cites an English translation, and I am wondering how this occurs in the German. Plato has been accused of similar elementary blunders about properties. Russell treats Berkeley similarly. |
| 21587 | Philosophers sometimes neglect truth and distort facts to attain a nice system [Russell] |
| Full Idea: The desire for unadulterated truth is often obscured, in professional philosophers, by love of system: the one little fact which will not come inside the philosophical edifice has to be pushed and tortured until it seems to consent. | |
| From: Bertrand Russell (Our Knowledge of the External World [1914], 8) | |
| A reaction: Bit of hypocrisy here. Russell was continually trying to find a system, grounded in physics and logic. Presumably his shifting views are indications of integrity, because he changes the system rather than the facts. |
| 21582 | Physicists accept particles, points and instants, while pretending they don't do metaphysics [Russell] |
| Full Idea: Physicists, ignorant and contemptuous of philosophy, have been content to assume their particles, points and instants in practice, while contending, with ironical politeness, that their concepts laid no claim to metaphysical validity. | |
| From: Bertrand Russell (Our Knowledge of the External World [1914], 4) | |
| A reaction: Presumably physicists are allowed to wave their hands and utter the word 'instrumentalism', and then get on with the job. They just have to ensure they never speculate about what is being measured. |
| 21573 | When problems are analysed properly, they are either logical, or not philosophical at all [Russell] |
| Full Idea: Every philosophical problem, when it is subjected to the necessary analysis and purification, is found either to be not really philosophical at all, or else to be, in the sense in which we are using the word, logical. | |
| From: Bertrand Russell (Our Knowledge of the External World [1914], 2) | |
| A reaction: [All Lecture 2 discusses 'logical'] I think Bertie was getting carried away here. In his life's corpus he barely acknowledges the existence of ethics, or political philosophy, or aesthetics. He never even engages with 'objects' the way Aristotle does. |
| 9572 | Realists about sets say there exists a null set in the real world, with no members [Chihara] |
| Full Idea: In the Gödelian realistic view of set theory the statement that there is a null set as the assertion of the existence in the real world of a set that has no members. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 11.6) | |
| A reaction: It seems to me obvious that such a claim is nonsense on stilts. 'In the beginning there was the null set'? |
| 9550 | We only know relational facts about the empty set, but nothing intrinsic [Chihara] |
| Full Idea: Everything we know about the empty set is relational; we know that nothing is the membership relation to it. But what do we know about its 'intrinsic properties'? | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.5) | |
| A reaction: Set theory seems to depend on the concept of the empty set. Modern theorists seem over-influenced by the Quine-Putnam view, that if science needs it, we must commit ourselves to its existence. |
| 9562 | In simple type theory there is a hierarchy of null sets [Chihara] |
| Full Idea: In simple type theory, there is a null set of type 1, a null set of type 2, a null set of type 3..... (Quine has expressed his distaste for this). | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 07.4) | |
| A reaction: It is bad enough trying to individuate the unique null set, without whole gangs of them drifting indistinguishably through the logical fog. All rational beings should share Quine's distaste, even if Quine is wrong. |
| 9573 | The null set is a structural position which has no other position in membership relation [Chihara] |
| Full Idea: In the structuralist view of sets, in structures of a certain sort the null set is taken to be a position (or point) that will be such that no other position (or point) will be in the membership relation to it. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 11.6) | |
| A reaction: It would be hard to conceive of something having a place in a structure if nothing had a relation to it, so is the null set related to singeton sets but not there members. It will be hard to avoid Platonism here. Set theory needs the null set. |
| 9551 | What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara] |
| Full Idea: What is it about the intrinsic properties of just that one unit set in virtue of which Bill Clinton is related to just it and not to any other unit sets in the set-theoretical universe? | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.5) | |
| A reaction: If we all kept pet woodlice, we had better not hold a wood louse rally, or we might go home with the wrong one. My singleton seems seems remarkably like yours. Could we, perhaps, swap, just for a change? |
| 9549 | The set theorist cannot tell us what 'membership' is [Chihara] |
| Full Idea: The set theorist cannot tell us anything about the true relationship of membership. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.5) | |
| A reaction: If three unrelated objects suddenly became members of a set, it is hard to see how the world would have changed, except in the minds of those thinking about it. |
| 9571 | ZFU refers to the physical world, when it talks of 'urelements' [Chihara] |
| Full Idea: ZFU set theory talks about physical objects (the urelements), and hence is in some way about the physical world. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 11.5) | |
| A reaction: This sounds a bit surprising, given that the whole theory would appear to be quite unaffected if God announced that idealism is true and there are no physical objects. |
| 9563 | A pack of wolves doesn't cease when one member dies [Chihara] |
| Full Idea: A pack of wolves is not thought to go out of existence just because some member of the pack is killed. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 07.5) | |
| A reaction: The point is that the formal extensional notion of a set doesn't correspond to our common sense notion of a group or class. Even a highly scientific theory about wolves needs a loose notion of a wolf pack. |
| 21588 | Logic gives the method of research in philosophy [Russell] |
| Full Idea: Logic gives the method of research in philosophy, just as mathematics gives the method in physics. | |
| From: Bertrand Russell (Our Knowledge of the External World [1914], 8) | |
| A reaction: I'm struck by how rarely philosophers actually prove anything. Mostly they just use the language of logic as a tool for disambiguation. Only a tiny handful of philosophers can actually create sustained and novel proofs. |
| 21586 | The logical connectives are not objects, but are formal, and need a context [Russell] |
| Full Idea: Such words as 'or' and 'not' are not names of definite objects, but are words that require a context in order to have a meaning. All of them are formal. | |
| From: Bertrand Russell (Our Knowledge of the External World [1914], 7) | |
| A reaction: [He cites Wittgenstein's 1922 Tractatus in a footnote - presumably in a later edition than 1914] This is the most famous idea which Russell acquired from Wittgenstein. It was yet another step in his scaling down of ontology. |
| 9561 | The mathematics of relations is entirely covered by ordered pairs [Chihara] |
| Full Idea: Everything one needs to do with relations in mathematics can be done by taking a relation to be a set of ordered pairs. (Ordered triples etc. can be defined as order pairs, so that <x,y,z> is <x,<y,z>>). | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 07.2) | |
| A reaction: How do we distinguish 'I own my cat' from 'I love my cat'? Or 'I quite like my cat' from 'I adore my cat'? Nevertheless, this is an interesting starting point for a discussion of relations. |
| 9552 | Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara] |
| Full Idea: In first-order logic a set of sentences is 'consistent' iff there is an interpretation (or structure) in which the set of sentences is true. ..For Frege, though, a set of sentences is consistent if it is not possible to deduce a contradiction from it. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 02.1) | |
| A reaction: The first approach seems positive, the second negative. Frege seems to have a higher standard, which is appealing, but the first one seems intuitively right. There is a possible world where this could work. |
| 21585 | The tortoise won't win, because infinite instants don't compose an infinitely long time [Russell] |
| Full Idea: The idea that an infinite number of instants make up an infinitely long time is not true, and therefore the conclusion that Achilles will never overtake the tortoise does not follow. | |
| From: Bertrand Russell (Our Knowledge of the External World [1914], 6) | |
| A reaction: Aristotle spotted this, but didn't express it as clearly as Russell. |
| 9553 | Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara] |
| Full Idea: With the invention of analytic geometry (by Fermat and then Descartes) physical space could be represented as having a mathematical structure, which could eventually lead to its axiomatization (by Hilbert). | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 02.3) | |
| A reaction: The idea that space might have axioms seems to be pythagoreanism run riot. I wonder if there is some flaw at the heart of Einstein's General Theory because of this? |
| 10192 | We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride] |
| Full Idea: Chihara's 'constructability theory' is nominalist - mathematics is reducible to a simple theory of types. Instead of talk of sets {x:x is F}, we talk of open sentences Fx defining them. Existence claims become constructability of sentence tokens. | |
| From: report of Charles Chihara (A Structural Account of Mathematics [2004]) by Fraser MacBride - Review of Chihara's 'Structural Acc of Maths' p.81 | |
| A reaction: This seems to be approaching the problem in a Fregean way, by giving an account of the semantics. Chihara is trying to evade the Quinean idea that assertion is ontological commitment. But has Chihara retreated too far? How does he assert existence? |
| 21684 | Atomic facts may be inferrable from others, but never from non-atomic facts [Russell] |
| Full Idea: Perhaps one atomic fact may sometimes be capable of being inferred from another, though I do not believe this to be the case; but in any case it cannot be inferred from premises no one of which is an atomic fact. | |
| From: Bertrand Russell (Our Knowledge of the External World [1914], p.48) | |
| A reaction: I prefer Russell's caution to Wittgenstein's dogmatism. I presume utterly simple facts give you nothing to work with. Hegel thought that you could infer new concepts from given concepts. |
| 22316 | A positive and negative fact have the same constituents; their difference is primitive [Russell] |
| Full Idea: It must not be supposed that a negative fact contains a constituent corresponding to the word 'not'. It contains no more constituents than a positive fact of the correlative positive form. The differenece between the two forms is ultimate and irreducible. | |
| From: Bertrand Russell (Our Knowledge of the External World [1914], VIII.279), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 41 'Neg' | |
| A reaction: ['Harvard Lectures'] The audience disliked this. How does one fact exclude the other fact? Potter asks whether absence is a fact, and whether an absence can be a truthmaker. |
| 9559 | If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara] |
| Full Idea: If mathematics shares whatever confirmation accrues to the theories using it, would it not be reasonable to suppose that mathematics shares whatever disconfirmation accrues to the theories using it? | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 05.8) | |
| A reaction: Presumably Quine would bite the bullet here, although maths is much closer to the centre of his web of belief, and so far less likely to require adjustment. In practice, though, mathematics is not challenged whenever an experiment fails. |
| 9566 | No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara] |
| Full Idea: Evidently, no scientific explanations of specific phenomena would collapse as a result of any hypothetical discovery that no mathematical objects exist. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 09.1) | |
| A reaction: It is inconceivable that anyone would challenge this claim. A good model seems to be drama; a play needs commitment from actors and audience, even when we know it is fiction. The point is that mathematics doesn't collapse either. |
| 21576 | With asymmetrical relations (before/after) the reduction to properties is impossible [Russell] |
| Full Idea: When we come to asymmetrical relations, such as before and after, greater and less etc., the attempt to reduce them to properties becomes obviously impossible. | |
| From: Bertrand Russell (Our Knowledge of the External World [1914], 2) | |
| A reaction: The traditional Aristotelian reduction to properties is attributed by Russell to logic based on subject-predicate. As an example he cites being greater than as depending on more than the mere magnitudes of the entities. Direction of the relation. |
| 21575 | When we attribute a common quality to a group, we can forget the quality and just talk of the group [Russell] |
| Full Idea: When a group of objects have the similarity we are inclined to attribute to possession of a common quality, the membership of the group will serve all the purposes of the supposed common quality ...which need not be assumed to exist. | |
| From: Bertrand Russell (Our Knowledge of the External World [1914], 2) | |
| A reaction: This is the earliest account I have found of properties being treated as sets of objects. It more or less coincides with the invention of set theory. I am reminded of Idea 9208. What is the bazzing property? It's what those three things have in common. |
| 21580 | Science condemns sense-data and accepts matter, but a logical construction must link them [Russell] |
| Full Idea: Men of science condemn immediate data as 'merely subjective', while maintaining the truths of physics from those data. ...The only justification possible for this must be one which exhibits matter as a logical construction from sense-data. | |
| From: Bertrand Russell (Our Knowledge of the External World [1914], 4) | |
| A reaction: Since we blatantly aren't doing logic when we stare out of the window, this aspires to finding something like the 'logical form' of perception. |
| 21583 | When sense-data change, there must be indistinguishable sense-data in the process [Russell] |
| Full Idea: In all cases of sense-data capable of gradual change, we may find one sense-datum indistinguishable from another, and that indistinguishable from a third, while yet the first and third are quite easily distinguishable. | |
| From: Bertrand Russell (Our Knowledge of the External World [1914], 5) | |
| A reaction: This point is key to the sense-data theory, because it gives them independent existence, standing between reality and subjective experience. It is also the reason why they look increasingly implausible, if they may not be experienced. |
| 21577 | Empirical truths are particular, so general truths need an a priori input of generality [Russell] |
| Full Idea: All empirical evidence is of particular truths. Hence, if there is any knowledge of general truths at all, there must be some knowledge of general truths which is independent of empirical evidence. | |
| From: Bertrand Russell (Our Knowledge of the External World [1914], 2) | |
| A reaction: Humean empiricists respond by being a sceptical of general truths. At this stage of his career Russell looks like a thoroughgoing rationalist, and he believes in the reality of universals, relations and propositions. He became more empirical later. |
| 21579 | Objects are treated as real when they connect with other experiences in a normal way [Russell] |
| Full Idea: Objects of sense are called 'real' when they have the kind of connection with other objects of sense which experience has led us to regard as normal; when they fail this, they are called 'illusions'. | |
| From: Bertrand Russell (Our Knowledge of the External World [1914], 3) | |
| A reaction: This rests rather too much on the concept of 'normal', but offers an attractive coherence account of perception. Direct perceptions are often invoked by anti-coherentists, but I think coherence is just as much needed in that realm. |
| 21578 | Global scepticism is irrefutable, but can't replace our other beliefs, and just makes us hesitate [Russell] |
| Full Idea: Universal scepticism, though logically irrefutable, is practically barren; it can only, therefore, give a certain flavour of hesitancy to our beliefs, and cannot be used to substitute other beliefs for them. | |
| From: Bertrand Russell (Our Knowledge of the External World [1914], 3) | |
| A reaction: Spot on. There is no positive evidence for scepticism, so must just register it as the faintest of possibilities, like the existence of secretive fairies. |
| 6416 | Other minds seem to exist, because their testimony supports realism about the world [Russell, by Grayling] |
| Full Idea: Russell gives an argument that other minds exist, because if one is entitled to believe this, then one can rely on the testimony of others, which, jointly with one's own experience, will give powerful support to the view that there a real spatial world. | |
| From: report of Bertrand Russell (Our Knowledge of the External World [1914], 3) by A.C. Grayling - Russell Ch.2 | |
| A reaction: I rather like this argument. It is quite close to Wittgenstein's Private Language Argument, which also seems to refute scepticism about other minds. I think Russell's line, using testimony, knowledge and realism, may be better than Wittgenstein's. |
| 9568 | I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara] |
| Full Idea: What I refer to as an 'equivalence class' (of line segments of a particular length) is an open sentence in my Constructibility Theory. I just use this terminology of the Platonist for didactic purposes. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 09.10) | |
| A reaction: This is because 'equivalence classes' is committed to the existence of classes, which is Quinean Platonism. I am with Chihara in wanting a story that avoids such things. Kit Fine is investigating similar notions of rules of construction. |
| 9547 | Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara] |
| Full Idea: Causal theories of reference seem doomed to failure for the case of reference to mathematical entities, since such entities are evidently causally inert. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.3) | |
| A reaction: Presumably you could baptise a fictional entity such as 'Polonius', and initiate a social causal chain, with a tradition of reference. You could baptise a baby in absentia. |
| 9574 | 'Gunk' is an individual possessing no parts that are atoms [Chihara] |
| Full Idea: An 'atomless gunk' is defined to be an individual possessing no parts that are atoms. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], App A) | |
| A reaction: [Lewis coined it] If you ask what are a-toms made of and what are ideas made of, the only answer we can offer is that the a-toms are made of gunk, and the ideas aren't made of anything, which is still bad news for the existence of ideas. |
| 21581 | We never experience times, but only succession of events [Russell] |
| Full Idea: There is no reason in experience to suppose that there are times as opposed to events: the events, ordered by the relations of simultaneity and succession, are all that experience provides. | |
| From: Bertrand Russell (Our Knowledge of the External World [1914], 4) | |
| A reaction: We experience events, but also have quite an accurate sense of how much time has passed during the occurrence of events. If asked how much time has lapsed, why don't we say '32 events'? How do we distinguish long events from short ones? |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| Full Idea: Philosophers are the forefathers of heretics. | |
| From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2 |
| 6610 | I believe because it is absurd [Tertullian] |
| Full Idea: I believe because it is absurd ('Credo quia absurdum est'). | |
| From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2 | |
| A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though. |