36 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? |
| 13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
| Full Idea: In current set theory, the search is on for new axioms to determine the size of the continuum. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §0) | |
| A reaction: This sounds the wrong way round. Presumably we seek axioms that fix everything else about set theory, and then check to see what continuum results. Otherwise we could just pick our continuum, by picking our axioms. |
| 13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
| Full Idea: Most writers agree that if any sense can be made of the distinction between analytic and synthetic, then the Axiom of Extensionality should be counted as analytic. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.1) | |
| A reaction: [Boolos is the source of the idea] In other words Extensionality is not worth discussing, because it simply tells you what the world 'set' means, and there is no room for discussion about that. The set/class called 'humans' varies in size. |
| 13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
| Full Idea: The extensional view of sets is preferable because it is simpler, clearer, and more convenient, because it individuates uniquely, and because it can simulate intensional notions when the need arises. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.1) | |
| A reaction: [She cites Fraenkel, Bar-Hillet and Levy for this] The difficulty seems to be whether the extensional notion captures our ordinary intuitive notion of what constitutes a group of things, since that needs flexible size and some sort of unity. |
| 13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
| Full Idea: The Axiom of Infinity is a simple statement of Cantor's great breakthrough. His bold hypothesis that a collection of elements that had lurked in the background of mathematics could be infinite launched modern mathematics. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.5) | |
| A reaction: It also embodies one of those many points where mathematics seems to depart from common sense - but then most subjects depart from common sense when they get more sophisticated. Look what happened to art. |
| 13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
| Full Idea: If one is interested in analysis then infinite sets are indispensable since even the notion of a real number cannot be developed by means of finite sets alone. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.5) | |
| A reaction: [Maddy is citing Fraenkel, Bar-Hillel and Levy] So Cantor's great breakthrough (Idea 13021) actually follows from the earlier acceptance of the real numbers, so that's where the departure from common sense started. |
| 13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
| Full Idea: The Power Set Axiom is indispensable for a set-theoretic account of the continuum, ...and in so far as those attempts are successful, then the power-set principle gains some confirmatory support. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.6) | |
| A reaction: The continuum is, of course, notoriously problematic. Have we created an extra problem in our attempts at solving the first one? |
| 13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
| Full Idea: Jordain made consistent and ill-starred efforts to prove the Axiom of Choice. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.7) | |
| A reaction: This would appear to be the fate of most axioms. You would presumably have to use a different system from the one you are engaged with to achieve your proof. |
| 13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
| Full Idea: Resistance to the Axiom of Choice centred on opposition between existence and construction. Modern set theory thrives on a realistic approach which says the choice set exists, regardless of whether it can be defined, constructed, or given by a rule. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.7) | |
| A reaction: This seems to be a key case for the ontology that lies at the heart of theory. Choice seems to be an invaluable tool for proofs, so it won't go away, so admit it to the ontology. Hm. So the tools of thought have existence? |
| 13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
| Full Idea: Many theorems depend on the Axiom of Choice, including that a countable union of sets is countable, and results in analysis, topology, abstract algebra and mathematical logic. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.7) | |
| A reaction: The modern attitude seems to be to admit anything if it leads to interesting results. It makes you wonder about the modern approach of using mathematics and logic as the cutting edges of ontological thinking. |
| 13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
| Full Idea: The Iterative Conception (Zermelo 1930) says everything appears at some stage. Given two objects a and b, let A and B be the stages at which they first appear. Suppose B is after A. Then the pair set of a and b appears at the immediate stage after B. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.3) | |
| A reaction: Presumably this all happens in 'logical time' (a nice phrase I have just invented!). I suppose we might say that the existence of the paired set is 'forced' by the preceding sets. No transcendental inferences in this story? |
| 13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
| Full Idea: The 'limitation of size' is a vague intuition, based on the idea that being too large may generate the paradoxes. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.3) | |
| A reaction: This is an intriguing idea to be found right at the centre of what is supposed to be an incredibly rigorous system. |
| 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. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |