39 ideas
| 6420 | Only by analysing is progress possible in philosophy [Russell] |
| Full Idea: I remain firmly persuaded, in spite of some modern tendencies to the contrary, that only by analysing is progress possible, …for example, by analysing physics and perception, the problem of mind and matter can be completely solved. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.1) | |
| A reaction: I don't share his confidence in the second part of this, but I subscribe to the maxim that 'analsis is the path to wisdom'. It is a very western view, and lots of people (mostly of a mystical disposition) hate it, but I see no better path. |
| 6432 | Analysis gives new knowledge, without destroying what we already have [Russell] |
| Full Idea: It seems to me evident that, as in the case of impure water, analysis gives new knowledge without destroying any of the previously existing knowledge. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.11) | |
| A reaction: I agree. On the whole, opponents of analysis are sentimental mystics who are reluctant to think carefully about life. I'm not sure what careful and concentrated thought is capable of, apart from analysis. |
| 6437 | The theory of types makes 'Socrates and killing are two' illegitimate [Russell] |
| Full Idea: 'Socrates and killing are two' would be an illegitimate sentence according to the doctrine of types. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.14) | |
| A reaction: This nicely shows how Ryle's notion of a 'category mistake', although it is a commonsense observation of bogus reasoning, arises out of Russell's logical analysis of sets. Of course, the theory of types has its critics. |
| 6442 | Truth belongs to beliefs, not to propositions and sentences [Russell] |
| Full Idea: Truth and falsehood both belong primarily to beliefs, and only derivatively to propositions and sentences. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.15) | |
| A reaction: I'm not sure why a proposition which is date/place stamped ('it is raining, here and now') could not be considered a truth, even if no one believed it. Is not the proposition 'squares have four sides' true? |
| 13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
| Full Idea: A 'linear ordering' (or 'total ordering') on A is a binary relation R meeting two conditions: R is transitive (of xRy and yRz, the xRz), and R satisfies trichotomy (either xRy or x=y or yRx). | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:62) |
| 13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
| Full Idea: To know if A ∈ B, we look at the set A as a single object, and check if it is among B's members. But if we want to know whether A ⊆ B then we must open up set A and check whether its various members are among the members of B. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:04) | |
| A reaction: This idea is one of the key ideas to grasp if you are going to get the hang of set theory. John ∈ USA ∈ UN, but John is not a member of the UN, because he isn't a country. See Idea 12337 for a special case. |
| 13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
| Full Idea: The 'ordered pair' <x,y> is defined to be {{x}, {x,y}}; hence it can be proved that <u,v> = <x,y> iff u = x and v = y (given by Kuratowski in 1921). ...The definition is somewhat arbitrary, and others could be used. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:36) | |
| A reaction: This looks to me like one of those regular cases where the formal definitions capture all the logical behaviour of the concept that are required for inference, while failing to fully capture the concept for ordinary conversation. |
| 13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
| Full Idea: Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ. A man with an empty container is better off than a man with nothing. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1.03) |
| 13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
| Full Idea: It might be thought at first that the empty set would be a rather useless or even frivolous set to mention, but from the empty set by various set-theoretic operations a surprising array of sets will be constructed. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:02) | |
| A reaction: This nicely sums up the ontological commitments of mathematics - that we will accept absolutely anything, as long as we can have some fun with it. Sets are an abstraction from reality, and the empty set is the very idea of that abstraction. |
| 13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
| Full Idea: Given any x we have the singleton {x}, which is defined by the pairing axiom to be {x,x}. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 2:19) | |
| A reaction: An interesting contrivance which is obviously aimed at keeping the axioms to a minimum. If you can do it intuitively with a new axiom, or unintuitively with an existing axiom - prefer the latter! |
| 13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
| Full Idea: It was observed by several people that for a satisfactory theory of ordinal numbers, Zermelo's axioms required strengthening. The Axiom of Replacement was proposed by Fraenkel and others, giving rise to the Zermelo-Fraenkel (ZF) axioms. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:15) |
| 13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
| Full Idea: For functions, we know that for any y there exists an appropriate x, but we can't yet form a function H, as we have no way of defining one particular choice of x. Hence we need the axiom of choice. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:48) |
| 6436 | I gradually replaced classes with properties, and they ended as a symbolic convenience [Russell] |
| Full Idea: My original use of classes was gradually more and more replaced by properties, and in the end disappeared except as a symbolic convenience. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.14) | |
| A reaction: I wish I knew what properties are. On the whole, though, I agree with this, because it is more naturalistic. We may place things in classes because of their properties, and this means there are natural classes, but classes can't have a life of their own. |
| 7528 | Leibniz bases everything on subject/predicate and substance/property propositions [Russell] |
| Full Idea: The metaphysics of Leibniz was explicitly based upon the doctrine that every proposition attributes a predicate to a subject and (what seemed to him almost the same thing) that every fact consists of a substance having a property. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.5) | |
| A reaction: I think it is realised now that although predicates tend to attribute properties to things, they are far from being the same thing. See Idea 4587, for example. Russell gives us an interesting foot in the door of Leibniz's complex system. |
| 6439 | Names are meaningless unless there is an object which they designate [Russell] |
| Full Idea: Unlike descriptions, names are meaningless unless there is an object which they designate. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.14) | |
| A reaction: This interests Russell because of its ontological implications. If we reduce language to names, we can have a pure ontology of 'objects'. We need a system for saying whether a description names something - which is his theory of definite descriptions. |
| 6423 | We tried to define all of pure maths using logical premisses and concepts [Russell] |
| Full Idea: The primary aim of our 'Principia Mathematica' was to show that all pure mathematics follows from purely logical premisses and uses only concepts definable in logical terms. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.7) | |
| A reaction: This spells out the main programme of logicism, by its great hero, Russell. The big question now is whether Gödel's Incompleteness Theorems have succeeded in disproving logicism. |
| 6425 | Formalism can't apply numbers to reality, so it is an evasion [Russell] |
| Full Idea: Formalism is perfectly adequate for doing sums, but not for the application of number, such as the simple statement 'there are three men in this room', so it must be regarded as an unsatisfactory evasion. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.10) | |
| A reaction: This seems to me a powerful and simple objection. The foundation of arithmetic is that there are three men in the room, not that one plus two is three. Three men and three ties make a pattern, which we call 'three'. |
| 6424 | Formalists say maths is merely conventional marks on paper, like the arbitrary rules of chess [Russell] |
| Full Idea: The Formalists, led by Hilbert, maintain that arithmetic symbols are merely marks on paper, devoid of meaning, and that arithmetic consists of certain arbitrary rules, like the rules of chess, by which these marks can be manipulated. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.10) | |
| A reaction: I just don't believe that maths is arbitrary, and this view pushes me into the arms of the empiricists, who say maths is far more likely to arise from experience than from arbitrary convention. The key to maths is patterns. |
| 6426 | Intuitionism says propositions are only true or false if there is a method of showing it [Russell] |
| Full Idea: The nerve of the Intuitionist theory, led by Brouwer, is the denial of the law of excluded middle; it holds that a proposition can only be accounted true or false when there is some method of ascertaining which of these it is. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.2) | |
| A reaction: He cites 'there are three successive sevens in the expansion of pi' as a case in point. This seems to me an example of the verificationism and anti-realism which is typical of that period. It strikes me as nonsense, but Russell takes it seriously. |
| 6419 | In 1899-1900 I adopted the philosophy of logical atomism [Russell] |
| Full Idea: In the years 1899-1900 I adopted the philosophy of logical atomism. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.1) | |
| A reaction: This is interesting (about Russell) because he only labelled it as 'logical atomism' in about 1912, and only wrote about it as such in 1918. It is helpful to understand that the theory of definite descriptions was part of his logical atomism. |
| 6438 | Complex things can be known, but not simple things [Russell] |
| Full Idea: I have come to think that, although many things can be known to be complex, nothing can be known to be simple. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.14) | |
| A reaction: This appears to be a rejection of his logical atomism. It goes with a general rebellion against foundationalist epistemology, because the empiricists foundations (e.g. Hume's impressions) seem devoid of all content. |
| 6434 | Facts are everything, except simples; they are either relations or qualities [Russell] |
| Full Idea: Facts, as I am using the word, consist always of relations between parts of a whole or qualities of single things; facts, in a word, are whatever there is except what (if anything) is completely simple. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.13) | |
| A reaction: This is the view that goes with Russell's 'logical atomism', where the 'completely simple' is used to build up the 'facts'. If World War One was a fact, was it a 'relation' or a 'quality'. Must events then be defined in terms of those two? |
| 6440 | Universals can't just be words, because words themselves are universals [Russell] |
| Full Idea: Those who dislike universals have thought that they could be merely words; the trouble with this view is that a word itself is a universal. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.14) | |
| A reaction: Russell gradually lost his faith in most things, but never in universals. I find it unconvincing that we might dismiss nominalism so easily. I'm not sure why the application of the word 'cat' could not just be conventional. |
| 6430 | In epistemology we should emphasis the continuity between animal and human minds [Russell] |
| Full Idea: It seems to me desirable in the theory of knowledge to emphasise the continuity between animal and human minds. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.11) | |
| A reaction: I strongly agree with this, mainly because it avoids overemphasis on language in epistemology. It doesn't follow that animals know a lot, and there is a good case for saying that they don't actually 'know' anything, despite having true beliefs. |
| 6441 | Pragmatism judges by effects, but I judge truth by causes [Russell] |
| Full Idea: Pragmatism holds that a belief is to be judged if it has certain effects, whereas I hold that an empirical belief is to be judged true if it has certain kinds of causes. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.15) | |
| A reaction: I'm with Russell here, and this seems to me a convincing objection to pragmatism. The simple problem is that falsehoods can occasionally have very beneficial effects. Beliefs are made true by the facts, not by their consequences. |
| 6431 | Empiricists seem unclear what they mean by 'experience' [Russell] |
| Full Idea: When I began to think about theory of knowledge, I found that none of the philosophers who emphasise 'experience' tells us what they mean by the word. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.11) | |
| A reaction: A very significant comment about empiricism. Hume does not seem very clear about what an 'impression' is. Russell's problem has been dealt with intensively by modern empiricists, who discuss 'the given', and conceptualised perception. |
| 6444 | True belief about the time is not knowledge if I luckily observe a stopped clock at the right moment [Russell] |
| Full Idea: Not all true beliefs are knowledge; the stock example to the contrary is that of a clock which has stopped by which I believe to be going and which I happen to look at when, by chance, it shows the right time. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.15) | |
| A reaction: [in his 1948:112] Russell had spotted Gettier-type problems long before Gettier. The problem of lucky true beliefs dates back to Plato (Idea 2140). This example is also a problem for reliabilism, if the clock is usually working fine. |
| 6433 | Behaviourists struggle to explain memory and imagination, because they won't admit images [Russell] |
| Full Idea: Behaviourists refuse to admit images because they cannot be observed from without, but this causes them difficulties when they attempt to explain either memory or imagination. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.13) | |
| A reaction: This is a striking objection to behaviourism, and it is rarely mentioned in modern discussions of the topic. They might try denying the existence of private 'images', but that wouldn't be very plausible. |
| 6443 | Surprise is a criterion of error [Russell] |
| Full Idea: Surprise is a criterion of error. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.15) | |
| A reaction: Russell is not too precise about this, but it is a nice point. Surprise is thwarted expectation, which implies prior misjudgement. |
| 6427 | Unverifiable propositions about the remote past are still either true or false [Russell] |
| Full Idea: There is no conceivable method by which we can discover whether the proposition 'It snowed on Manhattan Island on the 1st January in the year 1 A.D.' is true or false, but it seems preposterous to maintain that it is neither. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.10) | |
| A reaction: I love this example, which seems so simple and so clear-cut. It criticises verificationism, and gives strong intuitive support for realism, and supports the law of excluded middle. |
| 6435 | You can believe the meaning of a sentence without thinking of the words [Russell] |
| Full Idea: If you have just heard a loud clap of thunder, you believe what is expressed by 'there has just been a loud clap of thunder' even if no words come into your mind. | |
| From: Bertrand Russell (My Philosophical Development [1959], Ch.13) | |
| A reaction: This seems to me important, and accurate. We should not be too mesmerised by language. Animals have beliefs, and this is a nice example of an undeniable non-linguistic human belief. |
| 7590 | Consequentialism emphasises value rather than obligation in morality [Scruton] |
| Full Idea: According to consequentialism, the fundamental concept of morality is not obligation (deontological ethics) but value (axiological ethics). | |
| From: Roger Scruton (A Dictionary of Political Thought [1982], 'consequentialism') | |
| A reaction: These two views could come dramatically apart, in wartime, or in big ecological crises, or in a family breakup, or in religious disputes. Having identified the pair so clearly, why can we not aim for a civilised (virtuous) balance between the two? |
| 7589 | Altruism is either emotional (where your interests are mine) or moral (where they are reasons for me) [Scruton] |
| Full Idea: Two distinct motives go by the name of altruism: the emotions of liking, love and friendship, making another's interest automatically mine; and the moral motive of respect or considerateness, where another's interests become reasons for me, but not mine. | |
| From: Roger Scruton (A Dictionary of Political Thought [1982], 'altruism') | |
| A reaction: The second one has a strongly Kantian flavour, with its notion of impersonal duty. Virtue theorists will aspire to achieve the first state rather than the second, because good actions are then actively desired, and give pleasure to the doer. |
| 7595 | The idea of a right seems fairly basic; justice may be the disposition to accord rights to people [Scruton] |
| Full Idea: The idea of a right seems to be as basic as any other; we might even define justice in terms of it, as the disposition to accord to every person his rights. | |
| From: Roger Scruton (A Dictionary of Political Thought [1982], 'rights') | |
| A reaction: I am inclined to think that a set of fairly pure values (such as equality, kindness, sympathy, respect) must be in place before the idea of a right would occur to anyone. Aristotle has a powerful moral sense, but rights for slaves don't cross his mind. |
| 7588 | Allegiance is fundamental to the conservative view of society [Scruton] |
| Full Idea: Conservatives have made the concept of allegiance, conceived as a power, fundamental to their description of the experience of society | |
| From: Roger Scruton (A Dictionary of Political Thought [1982], 'allegiance') | |
| A reaction: This provokes the famous slogan of "My country - right or wrong!" However, the issue here is not going to be decided by a consequentialist analysis, but by a view a of human nature. I think I would want to carefully prise allegiance apart from loyalty. |
| 7594 | Democrats are committed to a belief and to its opposite, if the majority prefer the latter [Scruton] |
| Full Idea: The paradox of democracy (emphasised by Rousseau) is that I am compelled by my belief in democracy to embrace conflicting - perhaps even contradictory - opinions. If I believe A, and the majority vote for B, I am committed to enacting them both. | |
| From: Roger Scruton (A Dictionary of Political Thought [1982], 'paradox of democracy') | |
| A reaction: The paradox would have to be resolved by qualifying what exactly one is committed to by being a democrat. I would say I am committed to the right of my opponents to enact a policy with which I disagree. |
| 7593 | Liberals focus on universal human freedom, natural rights, and tolerance [Scruton, by PG] |
| Full Idea: Liberalism believes (roughly) in the supremacy of the individual, who has freedom and natural rights; it focuses on human, not divine affairs; it claims rights and duties are universal; and it advocates tolerance in religion and morality. | |
| From: report of Roger Scruton (A Dictionary of Political Thought [1982], 'liberalism') by PG - Db (ideas) | |
| A reaction: I find it hard to disagree with these principles, but the upshot in practice is often an excessive commitment to freedom and tolerance, because people fail to realise the subtle long-term erosions of society that can result. |
| 7592 | For positivists law is a matter of form, for naturalists it is a matter of content [Scruton] |
| Full Idea: For the positivist, law is law by virtue of its form; for the naturalist, by virtue of its content. | |
| From: Roger Scruton (A Dictionary of Political Thought [1982], 'law') | |
| A reaction: Clearly a perverse and 'unnatural' social rule (backed by government and implied force) is a 'law' in some sense of the word. It is hard to see how you could gain social consensus for a law if it didn't appear in some way to be 'natural justice'. |
| 7587 | The issue of abortion seems insoluble, because there is nothing with which to compare it [Scruton] |
| Full Idea: The issue of abortion is intractable, partly because of the absence of any other case to which it can be assimilated. | |
| From: Roger Scruton (A Dictionary of Political Thought [1982], 'abortion') | |
| A reaction: This is the legalistic approach to the problem, which always looks for precedents and comparisons. All problems must hav solutions, though (mustn't they?). The problem, though, is not the value of the foetus, but the unique form of 'ownership'. |