204 ideas
| 19693 | There is practical wisdom (for action), and theoretical wisdom (for deep understanding) [Aristotle, by Whitcomb] |
| Full Idea: Aristotle takes wisdom to come in two forms, the practical and the theoretical, the former of which is good judgement about how to act, and the latter of which is deep knowledge or understanding. | |
| From: report of Aristotle (works [c.330 BCE]) by Dennis Whitcomb - Wisdom Intro | |
| A reaction: The interesting question is then whether the two are connected. One might be thoroughly 'sensible' about action, without counting as 'wise', which seems to require a broader view of what is being done. Whitcomb endorses Aristotle on this idea. |
| 5361 | Philosophers must get used to absurdities [Russell] |
| Full Idea: Whoever wishes to become a philosopher must learn not to be frightened by absurdities. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 2) | |
| A reaction: He says this jokingly, but it is obviously true. Philosophy requires extreme imagination, and it also requires taking seriously possibilities that are dismissed by others. It would be a catastrophe if we all dismissed the truth as self-evidently false. |
| 5368 | Philosophy verifies that our hierarchy of instinctive beliefs is harmonious and consistent [Russell] |
| Full Idea: Philosophy should show us the hierarchy of our instinctive beliefs, ..and show that they do not clash, but form a harmonious system. There is no reason to reject an instinctive belief, except that it clashes with others. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 2) | |
| A reaction: This is open to the standard objections to the coherence theory of truth (as explained by Russell!), but I like this view of philosophy. Somewhere behind it is the rationalist dream that the final set of totally consistent beliefs will have to be true. |
| 5432 | Metaphysics cannot give knowledge of the universe as a whole [Russell] |
| Full Idea: It would seem that knowledge concerning the universe as a whole is not to be obtained by metaphysics. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.14) | |
| A reaction: Although Russell is strongly attracted to rationalism and platonism, this remark puts him firmly in the camp of Hume, and makes him godfather to the logical positivists. I regard metaphysics as extremely speculative attempts at explanation. |
| 14122 | Analysis gives us nothing but the truth - but never the whole truth [Russell] |
| Full Idea: Though analysis gives us the truth, and nothing but the truth, yet it can never give us the whole truth | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §138) |
| 14109 | The study of grammar is underestimated in philosophy [Russell] |
| Full Idea: The study of grammar, in my opinion, is capable of throwing far more light on philosophical questions than is commonly supposed by philosophers. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §046) | |
| A reaction: This is a dangerous tendency, which has led to some daft linguistic philosophy, but Russell himself was never guilty of losing the correct perspective on the matter. |
| 14165 | Analysis falsifies, if when the parts are broken down they are not equivalent to their sum [Russell] |
| Full Idea: It is said that analysis is falsification, that the complex is not equivalent to the sum of its constituents and is changed when analysed into these. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §439) | |
| A reaction: Not quite Moore's Paradox of Analysis, but close. Russell is articulating the view we now call 'holism' - that the whole is more than the sum of its parts - which I can never quite believe. |
| 5434 | Philosophy is similar to science, and has no special source of wisdom [Russell] |
| Full Idea: Philosophical knowledge does not differ essentially from scientific knowledge; there is no special source of wisdom which is open to philosophy but not to science. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.14) | |
| A reaction: I agree. I take Plato's Theory of Forms, for example, to be a scientific theory, for which no one can devise an empirical test (just like string theory). Personally I consider philosophy to be the senior partner, and regard scientists as servants. |
| 1575 | For Aristotle logos is essentially the ability to talk rationally about questions of value [Roochnik on Aristotle] |
| Full Idea: For Aristotle logos is the ability to speak rationally about, with the hope of attaining knowledge, questions of value. | |
| From: comment on Aristotle (works [c.330 BCE]) by David Roochnik - The Tragedy of Reason p.26 |
| 1589 | Aristotle is the supreme optimist about the ability of logos to explain nature [Roochnik on Aristotle] |
| Full Idea: Aristotle is the great theoretician who articulates a vision of a world in which natural and stable structures can be rationally discovered. His is the most optimistic and richest view of the possibilities of logos | |
| From: comment on Aristotle (works [c.330 BCE]) by David Roochnik - The Tragedy of Reason p.95 |
| 5405 | The law of contradiction is not a 'law of thought', but a belief about things [Russell] |
| Full Idea: The law of contradiction is not a 'law of thought' ..because it is a belief about things, not only about thoughts. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 9) | |
| A reaction: The principle is a commitment about things, but it is inconceivable that any experience, no matter how weird, could ever contradict it. It would be better to assume that we had gone insane, than that a contradiction had occurred in the world. |
| 5396 | Three Laws of Thought: identity, contradiction, and excluded middle [Russell] |
| Full Idea: For no very good reason, three principles have been singled out by tradition under the name of 'Laws of Thought': the laws of identity ('what is, is'), contradiction ('never be and not be'), and excluded middle ('always be or not be'). | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 7) | |
| A reaction: 'For no very good reason' seems a bit unfair, probably to medieval logicians, who deserve more respect. Russell suggests that the concept of implication deserves to be on the list. Presumably optimism about thinking is a presupposition of thought. |
| 8200 | Aristotelian definitions aim to give the essential properties of the thing defined [Aristotle, by Quine] |
| Full Idea: A real definition, according to the Aristotelian tradition, gives the essence of the kind of thing defined. Man is defined as a rational animal, and thus rationality and animality are of the essence of each of us. | |
| From: report of Aristotle (works [c.330 BCE]) by Willard Quine - Vagaries of Definition p.51 | |
| A reaction: Compare Idea 4385. Personally I prefer the Aristotelian approach, but we may have to say 'We cannot identify the essence of x, and so x cannot be defined'. Compare 'his mood was hard to define' with 'his mood was hostile'. |
| 4385 | Aristotelian definition involves first stating the genus, then the differentia of the thing [Aristotle, by Urmson] |
| Full Idea: For Aristotle, to give a definition one must first state the genus and then the differentia of the kind of thing to be defined. | |
| From: report of Aristotle (works [c.330 BCE]) by J.O. Urmson - Aristotle's Doctrine of the Mean p.157 | |
| A reaction: Presumably a modern definition would just be a list of properties, but Aristotle seeks the substance. How does he define a genus? - by placing it in a further genus? |
| 14115 | Definition by analysis into constituents is useless, because it neglects the whole [Russell] |
| Full Idea: A definition as an analysis of an idea into its constituents is inconvenient and, I think, useless; it overlooks the fact that wholes are not, as a rule, determinate when their constituents are given. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §108) | |
| A reaction: The influence of Leibniz seems rather strong here, since he was obsessed with explaining what creates true unities. |
| 14159 | In mathematics definitions are superfluous, as they name classes, and it all reduces to primitives [Russell] |
| Full Idea: The statement that a class is to be represented by a symbol is a definition in mathematics, and says nothing about mathematical entities. Any formula can be stated in terms of primitive ideas, so the definitions are superfluous. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §412) | |
| A reaction: [compressed wording] I'm not sure that everyone would agree with this (e.g. Kit Fine), as certain types of numbers seem to be introduced by stipulative definitions. |
| 14148 | Infinite regresses have propositions made of propositions etc, with the key term reappearing [Russell] |
| Full Idea: In the objectionable kind of infinite regress, some propositions join to constitute the meaning of some proposition, but one of them is similarly compounded, and so ad infinitum. This comes from circular definitions, where the term defined reappears. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §329) |
| 18002 | As well as a truth value, propositions have a range of significance for their variables [Russell] |
| Full Idea: Every proposition function …has, in addition to its range of truth, a range of significance, i.e. a range within which x must lie if φ(x) is to be a proposition at all, whether true or false. This is the first point of the theory of types. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], App B:523), quoted by Ofra Magidor - Category Mistakes 1.2 | |
| A reaction: Magidor quotes this as the origin of the idea of a 'category mistake'. It is the basis of the formal theory of types, but is highly influential in philosophy generally, especially as a criterion for ruling many propositions as 'meaningless'. |
| 5420 | Truth is a property of a belief, but dependent on its external relations, not its internal qualities [Russell] |
| Full Idea: Although truth and falsehood are properties of beliefs, they are properties dependent upon the relations of the beliefs to other things, not upon any internal quality of the beliefs. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: Beliefs can have an intrinsic property of subjective certainty, but Russell is right that that is not enough. So is truth a property or a relation? |
| 5419 | Truth and falsehood are properties of beliefs and statements [Russell] |
| Full Idea: Truth and falsehood are properties of beliefs and statements, so a world of mere matter would contain no truth or falsehood. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: Can it be beliefs AND statements? What about propositions? All that matters here is to establish that truth is a feature of certain mental states. This makes possible my slogan that "the brain is a truth-machine". Out there are the 'facts'. |
| 14102 | What is true or false is not mental, and is best called 'propositions' [Russell] |
| Full Idea: I hold that what is true or false is not in general mental, and requiring a name for the true or false as such, this name can scarcely be other than 'propositions'. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], Pref) | |
| A reaction: This is the Fregean and logicians' dream that that there is some fixed eternal realm of the true and the false. I think true and false concern the mental. We can talk about the 'facts' which are independent of minds, but not the 'truth'. |
| 5417 | A good theory of truth must make falsehood possible [Russell] |
| Full Idea: A good theory of truth must be such as to admit of its opposite, falsehood. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) |
| 7395 | Truth as congruence may work for complex beliefs, but not for simple beliefs about existence [Joslin on Russell] |
| Full Idea: If truth is congruence between a complex belief and a complex relation between objects in the world, this may work for Othello's belief about Desdemona, but it doesn't seem to work for the simple belief that an object exists. | |
| From: comment on Bertrand Russell (Problems of Philosophy [1912], Ch.12) by Jack Joslin - talk | |
| A reaction: Though Russell has an interesting and persuasive theory, this seems like a big problem. To have a complex belief about a complex of objects, you must first have beliefs about the objects (and that can't be acquaintance, because error is possible). |
| 5428 | Beliefs are true if they have corresponding facts, and false if they don't [Russell] |
| Full Idea: A belief is true when there is a corresponding fact, and is false when there is no corresponding fact. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: Russell tries to explain a 'fact' as a complex unity of constituents with a certain order among them. There is an obvious problem that some of the 'orders' in the world are imposed on it by the mind. But we don't invent 'D's love for C'. |
| 5421 | The coherence theory says falsehood is failure to cohere, and truth is fitting into a complete system of Truth [Russell] |
| Full Idea: The coherence theory of truth says falsehood is a failure to cohere in the body of our beliefs, and that it is the essence of a truth to form part of the completely rounded system which is The Truth. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: One could embrace the idea of coherence without accepting the extravagant ninenteenth century Idealists' dream of an ultimate complete Truth (or Absolute). The theory needs a decent account of coherence to get off the ground. |
| 5422 | More than one coherent body of beliefs seems possible [Russell] |
| Full Idea: There is no reason to suppose that only one coherent body of beliefs is possible. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: Presumably this possibility would not be accepted for the ultimate ideal body of beliefs, but it seems undeniable that limited humanity will be stuck with several coherent possibilities. Coherence, though, is within our grasp, unlike correspondence. |
| 5423 | If we suspend the law of contradiction, nothing will appear to be incoherent [Russell] |
| Full Idea: If the law of contradiction itself were subjected to the test of coherence, we should find that, if we choose to suppose it false, nothing will any longer be incoherent with anything else. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: Russell is in error in treating coherence as if it was merely non-contradiction. If I see you as four feet tall today and six feet tall tomorrow, that is incoherent (to me) but not an actual contradiction. All accounts of truth need presuppositions. |
| 5424 | Coherence is not the meaning of truth, but an important test for truth [Russell] |
| Full Idea: Coherence cannot be accepted as the meaning of truth, though it is often a most important test of truth after a certain amount of truth has become known. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: The coherence theory is in fact a confusion of epistemology and ontology. Compare Idea 1364, where Reid charges Locke with confusing the test for personal identity with the thing itself. I wonder if refusal to accept essences causes this problem? |
| 14176 | "The death of Caesar is true" is not the same proposition as "Caesar died" [Russell] |
| Full Idea: "The death of Caesar is true" is not, I think, the same proposition as "Caesar died". | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §478) | |
| A reaction: I suspect that it was this remark which provoked Ramsey into rebellion, because he couldn't see the difference. Nowadays we must talk first of conversational implicature, and then of language and metalanguage. |
| 5401 | The mortality of Socrates is more certain from induction than it is from deduction [Russell] |
| Full Idea: We would do better to go straight from the evidence that some men have died to the mortality of Socrates, than to go via 'all men are mortal', for the probability that Socrates is mortal is greater than the probability that all men are mortal. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 7) | |
| A reaction: Russell claims that deduction should stick to a priori truth, and induction is best for the real world. Interesting. To show that something is a member of a set (e.g. planets) you need an awful lot of knowledge of the set. |
| 14113 | The null class is a fiction [Russell] |
| Full Idea: The null class is a fiction. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §079) | |
| A reaction: This does not commit him to regarding all classes as fictions - though he seems to have eventually come to believe that. The null class seems to have a role something like 'Once upon a time...' in story-telling. You can then tell truth or fiction. |
| 15894 | Russell invented the naïve set theory usually attributed to Cantor [Russell, by Lavine] |
| Full Idea: Russell was the inventor of the naïve set theory so often attributed to Cantor. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903]) by Shaughan Lavine - Understanding the Infinite I |
| 14126 | Order rests on 'between' and 'separation' [Russell] |
| Full Idea: The two sources of order are 'between' and 'separation'. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §204) |
| 14127 | Order depends on transitive asymmetrical relations [Russell] |
| Full Idea: All order depends upon transitive asymmetrical relations. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §208) |
| 14121 | The part-whole relation is ultimate and indefinable [Russell] |
| Full Idea: The relation of whole and part is, it would seem, an indefinable and ultimate relation, or rather several relations, often confounded, of which one at least is indefinable. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §135) | |
| A reaction: This is before anyone had produced a mathematical account of mereology (qv). |
| 13282 | Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki] |
| Full Idea: Aristotle proposes to relativise unity and plurality, so that a single object can be both one (indivisible) and many (divisible) simultaneously, without contradiction, relative to different measures. Wholeness has degrees, with the strength of the unity. | |
| From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 7.2.12 | |
| A reaction: [see Koslicki's account of Aristotle for details] As always, the Aristotelian approach looks by far the most promising. Simplistic mechanical accounts of how parts make wholes aren't going to work. We must include the conventional and conceptual bit. |
| 5395 | Demonstration always relies on the rule that anything implied by a truth is true [Russell] |
| Full Idea: All demonstrations involve the principle that 'anything implied by a true proposition is true', or 'whatever follows from a true proposition is true'. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 7) | |
| A reaction: This is modus ponens, a broad principle of rationality, rather than of strict logicality, because it covers practical inferences and vague propositions. Presumably truth is a prior concept to implication, and therefore more metaphysically basic. |
| 14106 | Implication cannot be defined [Russell] |
| Full Idea: A definition of implication is quite impossible. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §016) |
| 14108 | It would be circular to use 'if' and 'then' to define material implication [Russell] |
| Full Idea: It would be a vicious circle to define material implication as meaning that if one proposition is true, then another is true, for 'if' and 'then' already involve implication. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §037) | |
| A reaction: Hence the preference for defining it by the truth table, or as 'not-p or q'. |
| 14167 | The only classes are things, predicates and relations [Russell] |
| Full Idea: The only classes appear to be things, predicates and relations. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §440) | |
| A reaction: This is the first-order logic view of reality, which has begun to look incredibly impoverished in modern times. Processes certainly demand a hearing, as do modal facts. |
| 4730 | For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady] |
| Full Idea: Aristotle apparently believed that the subject-predicate structure of Greek reflected the substance-accident nature of reality. | |
| From: report of Aristotle (works [c.330 BCE]) by Paul O'Grady - Relativism Ch.4 | |
| A reaction: We need not assume that Aristotle is wrong. It is a chicken-and-egg. There is something obvious about subject-predicate language, if one assumes that unified objects are part of nature, and not just conventional. |
| 14105 | There seem to be eight or nine logical constants [Russell] |
| Full Idea: The number of logical constants is not great: it appears, in fact, to be eight or nine. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §012) | |
| A reaction: There is, of course, lots of scope for interdefinability. No one is going to disagree greatly with his claim, so it is an interesting fact, which invites some sort of (non-platonic) explanation. |
| 18722 | Negations are not just reversals of truth-value, since that can happen without negation [Wittgenstein on Russell] |
| Full Idea: Russell explained ¬p by saying that ¬p is true if p is false and false if p is true. But this is not an explanation of negation, for it might apply to propositions other than the negative. | |
| From: comment on Bertrand Russell (The Principles of Mathematics [1903]) by Ludwig Wittgenstein - Lectures 1930-32 (student notes) B XI.3 | |
| A reaction: Presumably he is thinking of 'the light is on' and 'the light is off'. A very astute criticism, which seems to be correct. What would Russell say? Perhaps we add that negation is an 'operation' which achieves flipping of the truth-value? |
| 14104 | Constants are absolutely definite and unambiguous [Russell] |
| Full Idea: A constant is something absolutely definite, concerning which there is no ambiguity whatever. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §006) |
| 14114 | Variables don't stand alone, but exist as parts of propositional functions [Russell] |
| Full Idea: A variable is not any term simply, but any term as entering into a propositional function. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §093) | |
| A reaction: So we should think of variables entirely by their role, rather than as having a semantics of their own (pace Kit Fine? - though see Russell §106, p.107). |
| 5386 | Proper names are really descriptions, and can be replaced by a description in a person's mind [Russell] |
| Full Idea: Common words, even proper names, are usually really descriptions; that is, the thought in the mind of a person using a proper name correctly can generally only be expressed explicitly if we replace the proper name by a description. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: This is open to challenge, and the modern idea is that they are more like baptisms, but it all comes down to the debate about internal and external content. Russell would appear to be voicing the internalist theory of names. |
| 5385 | The phrase 'a so-and-so' is an 'ambiguous' description'; 'the so-and-so' (singular) is a 'definite' description [Russell] |
| Full Idea: A phrase of the form 'a so-and-so' I shall call an 'ambiguous' description, and a phrase of the form 'the so-and-so' (in the singular) I shall call a 'definite' description. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: This leaves the problem of those definite descriptions which succeed in referring ('the present Prime Minister'), those which haven't succeeded yet ('the person who will get the most votes'), and those which won't refer ('the present King of France'). |
| 14137 | 'Any' is better than 'all' where infinite classes are concerned [Russell] |
| Full Idea: The word 'any' is preferable to the word 'all' where infinite classes are concerned. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §284) | |
| A reaction: The reason must be that it is hard to quantify over 'all' of the infinite members, but it is easier to say what is true of any one of them. |
| 14149 | The Achilles Paradox concerns the one-one correlation of infinite classes [Russell] |
| Full Idea: When the Achilles Paradox is translated into arithmetical language, it is seen to be concerned with the one-one correlation of two infinite classes. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §321) | |
| A reaction: Dedekind's view of infinity (Idea 9826) shows why this results in a horrible tangle. |
| 15895 | Russell discovered the paradox suggested by Burali-Forti's work [Russell, by Lavine] |
| Full Idea: Burali-Forti didn't discover any paradoxes, though his work suggested a paradox to Russell. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903]) by Shaughan Lavine - Understanding the Infinite I |
| 14152 | In geometry, Kant and idealists aimed at the certainty of the premisses [Russell] |
| Full Idea: The approach to practical geometry of the idealists, and especially of Kant, was that we must be certain of the premisses on their own account. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §353) |
| 14154 | Geometry throws no light on the nature of actual space [Russell] |
| Full Idea: Geometry no longer throws any direct light on the nature of actual space. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §353) | |
| A reaction: This was 1903. Minkowski then contributed a geometry of space which was used in Einstein's General Theory. It looks to me as if geometry reveals the possibilities for actual space. |
| 14151 | Pure geometry is deductive, and neutral over what exists [Russell] |
| Full Idea: As a branch of pure mathematics, geometry is strictly deductive, indifferent to the choice of its premises, and to the question of whether there strictly exist such entities. It just deals with series of more than one dimension. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §352) | |
| A reaction: This seems to be the culmination of the seventeenth century reduction of geometry to algebra. Russell admits that there is also the 'study of actual space'. |
| 14153 | In geometry, empiricists aimed at premisses consistent with experience [Russell] |
| Full Idea: The approach to practical geometry of the empiricists, notably Mill, was to show that no other set of premisses would give results consistent with experience. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §353) | |
| A reaction: The modern phrase might be that geometry just needs to be 'empirically adequate'. The empiricists are faced with the possibility of more than one successful set of premisses, and the idealist don't know how to demonstrate truth. |
| 14155 | Two points have a line joining them (descriptive), a distance (metrical), and a whole line (projective) [Russell, by PG] |
| Full Idea: Two points will define the line that joins them ('descriptive' geometry), the distance between them ('metrical' geometry), and the whole of the extended line ('projective' geometry). | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903], §362) by PG - Db (ideas) | |
| A reaction: [a summary of Russell's §362] Projective Geometry clearly has the highest generality, and the modern view seems to make it the master subject of geometry. |
| 18254 | Russell's approach had to treat real 5/8 as different from rational 5/8 [Russell, by Dummett] |
| Full Idea: Russell defined the rationals as ratios of integers, and was therefore forced to treat the real number 5/8 as an object distinct from the rational 5/8. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903]) by Michael Dummett - Frege philosophy of mathematics 21 'Frege's' |
| 14144 | Ordinals result from likeness among relations, as cardinals from similarity among classes [Russell] |
| Full Idea: Ordinal numbers result from likeness among relations, as cardinals from similarity among classes. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §293) |
| 14128 | Some claim priority for the ordinals over cardinals, but there is no logical priority between them [Russell] |
| Full Idea: It is claimed that ordinals are prior to cardinals, because they form the progression which is relevant to mathematics, but they both form progressions and have the same ordinal properties. There is nothing to choose in logical priority between them. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §230) | |
| A reaction: We have an intuitive notion of the size of a set without number, but you can't actually start counting without number, so the ordering seems to be the key to the business, which (I would have thought) points to ordinals as prior. |
| 14129 | Ordinals presuppose two relations, where cardinals only presuppose one [Russell] |
| Full Idea: Ordinals presuppose serial and one-one relations, whereas cardinals only presuppose one-one relations. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §232) | |
| A reaction: This seems to award the palm to the cardinals, for their greater logical simplicity, but I have already given the award to the ordinals in the previous idea, and I am not going back on that. |
| 14132 | Properties of numbers don't rely on progressions, so cardinals may be more basic [Russell] |
| Full Idea: The properties of number must be capable of proof without appeal to the general properties of progressions, since cardinals can be independently defined, and must be seen in a progression before theories of progression are applied to them. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §243) | |
| A reaction: Russell says there is no logical priority between ordinals and cardinals, but it is simpler to start an account with cardinals. |
| 14141 | Ordinals are defined through mathematical induction [Russell] |
| Full Idea: The ordinal numbers are defined by some relation to mathematical induction. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §290) |
| 14142 | Ordinals are types of series of terms in a row, rather than the 'nth' instance [Russell] |
| Full Idea: The finite ordinals may be conceived as types of series; ..the ordinal number may be taken as 'n terms in a row'; this is distinct from the 'nth', and logically prior to it. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §290) | |
| A reaction: Worth nothing, because the popular and traditional use of 'ordinal' (as in learning a foreign language) is to mean the nth instance of something, rather than a whole series. |
| 14139 | Transfinite ordinals don't obey commutativity, so their arithmetic is quite different from basic arithmetic [Russell] |
| Full Idea: Unlike the transfinite cardinals, the transfinite ordinals do not obey the commutative law, and their arithmetic is therefore quite different from elementary arithmetic. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §290) |
| 14145 | For Cantor ordinals are types of order, not numbers [Russell] |
| Full Idea: In his most recent article Cantor speaks of ordinals as types of order, not as numbers. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §298) | |
| A reaction: Russell likes this because it supports his own view of ordinals as classes of serial relations. It has become orthodoxy to refer to heaps of things as 'numbers' when the people who introduced them may not have seen them that way. |
| 14146 | We aren't sure if one cardinal number is always bigger than another [Russell] |
| Full Idea: We do not know that of any two different cardinal numbers one must be the greater. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §300) | |
| A reaction: This was 1903, and I don't know whether the situation has changed. I find this thought extremely mind-boggling, given that cardinals are supposed to answer the question 'how many?' Presumably they can't be identical either. See Burali-Forti. |
| 14135 | Real numbers are a class of rational numbers (and so not really numbers at all) [Russell] |
| Full Idea: Real numbers are not really numbers at all, but something quite different; ...a real number, so I shall contend, is nothing but a certain class of rational numbers. ...A segment of rationals is a real number. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §258) |
| 14123 | Some quantities can't be measured, and some non-quantities are measurable [Russell] |
| Full Idea: Some quantities cannot be measured (such as pain), and some things which are not quantities can be measured (such as certain series). | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §150) |
| 14158 | Quantity is not part of mathematics, where it is replaced by order [Russell] |
| Full Idea: Quantity, though philosophers seem to think it essential to mathematics, does not occur in pure mathematics, and does occur in many cases not amenable to mathematical treatment. The place of quantity is taken by order. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §405) | |
| A reaction: He gives pain as an example of a quantity which cannot be treated mathematically. |
| 14120 | Counting explains none of the real problems about the foundations of arithmetic [Russell] |
| Full Idea: The process of counting gives us no indication as to what the numbers are, as to why they form a series, or as to how it is to be proved that there are n numbers from 1 to n. Hence counting is irrelevant to the foundations of arithmetic. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §129) | |
| A reaction: I take it to be the first truth in the philosophy of mathematics that if there is a system of numbers which won't do the job of counting, then that system is irrelevant. Counting always comes first. |
| 14118 | We can define one-to-one without mentioning unity [Russell] |
| Full Idea: It is possible, without the notion of unity, to define what is meant by one-to-one. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §109) | |
| A reaction: This is the trick which enables the Greek account of numbers, based on units, to be abandoned. But when you have arranged the boys and the girls one-to-one, you have not yet got a concept of number. |
| 14119 | We do not currently know whether, of two infinite numbers, one must be greater than the other [Russell] |
| Full Idea: It is not at present known whether, of two different infinite numbers, one must be greater and the other less. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §118) | |
| A reaction: This must refer to cardinal numbers, as ordinal numbers have an order. The point is that the proper subset is equal to the set (according to Dedekind). |
| 14133 | There are cardinal and ordinal theories of infinity (while continuity is entirely ordinal) [Russell] |
| Full Idea: The theory of infinity has two forms, cardinal and ordinal, of which the former springs from the logical theory of numbers; the theory of continuity is purely ordinal. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §249) |
| 14134 | Infinite numbers are distinguished by disobeying induction, and the part equalling the whole [Russell] |
| Full Idea: There are two differences of infinite numbers from finite: that they do not obey mathematical induction (both cardinals and ordinals), and that the whole contains a part consisting of the same number of terms (applying only to ordinals). | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §250) |
| 14143 | ω names the whole series, or the generating relation of the series of ordinal numbers [Russell] |
| Full Idea: The ordinal representing the whole series must be different from what represents a segment of itself, with no immediate predecessor, since the series has no last term. ω names the class progression, or generating relation of series of this class. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §291) | |
| A reaction: He is paraphrasing Cantor's original account of ω. |
| 14138 | You can't get a new transfinite cardinal from an old one just by adding finite numbers to it [Russell] |
| Full Idea: It must not be supposed that we can obtain a new transfinite cardinal by merely adding one to it, or even by adding any finite number, or aleph-0. On the contrary, such puny weapons cannot disturb the transfinite cardinals. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §288) | |
| A reaction: If you add one, the original cardinal would be a subset of the new one, and infinite numbers have their subsets equal to the whole, so you have gone nowhere. You begin to wonder whether transfinite cardinals are numbers at all. |
| 14140 | For every transfinite cardinal there is an infinite collection of transfinite ordinals [Russell] |
| Full Idea: For every transfinite cardinal there is an infinite collection of transfinite ordinals, although the cardinal number of all ordinals is the same as or less than that of all cardinals. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §290) | |
| A reaction: Sort that one out, and you are beginning to get to grips with the world of the transfinite! Sounds like there are more ordinals than cardinals, and more cardinals than ordinals. |
| 14124 | Axiom of Archimedes: a finite multiple of a lesser magnitude can always exceed a greater [Russell] |
| Full Idea: The Axiom of Archimedes asserts that, given any two magnitudes of a kind, some finite multiple of the lesser exceeds the greater. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §168 n*) |
| 7530 | Russell tried to replace Peano's Postulates with the simple idea of 'class' [Russell, by Monk] |
| Full Idea: What Russell tried to show [at this time] was that Peano's Postulates (based on 'zero', 'number' and 'successor') could in turn be dispensed with, and the whole edifice built upon nothing more than the notion of 'class'. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.4 | |
| A reaction: (See Idea 5897 for Peano) Presumably you can't afford to lose the notion of 'successor' in the account. If you build any theory on the idea of classes, you are still required to explain why a particular is a member of that class, and not another. |
| 18246 | Dedekind failed to distinguish the numbers from other progressions [Shapiro on Russell] |
| Full Idea: Dedekind's demonstrations nowhere - not even where he comes to cardinals - involve any property distinguishing numbers from other progressions. | |
| From: comment on Bertrand Russell (The Principles of Mathematics [1903], p.249) by Stewart Shapiro - Philosophy of Mathematics 5.4 | |
| A reaction: Shapiro notes that his sounds like Frege's Julius Caesar problem, of ensuring that your definition really does capture a number. Russell is objecting to mathematical structuralism. |
| 14147 | Denying mathematical induction gave us the transfinite [Russell] |
| Full Idea: The transfinite was obtained by denying mathematical induction. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §310) | |
| A reaction: This refers to the work of Dedekind and Cantor. This raises the question (about which thinkers have ceased to care, it seems), of whether it is rational to deny mathematical induction. |
| 14125 | Finite numbers, unlike infinite numbers, obey mathematical induction [Russell] |
| Full Idea: Finite numbers obey the law of mathematical induction: infinite numbers do not. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §183) |
| 14116 | Numbers were once defined on the basis of 1, but neglected infinities and + [Russell] |
| Full Idea: It used to be common to define numbers by means of 1, with 2 being 1+1 and so on. But this method was only applicable to finite numbers, made a tiresome different between 1 and the other numbers, and left + unexplained. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §109) | |
| A reaction: Am I alone in hankering after the old approach? The idea of a 'unit' is what connected numbers to the patterns of the world. Russell's approach invites unneeded platonism. + is just 'and', and infinities are fictional extrapolations. Sounds fine to me. |
| 14117 | Numbers are properties of classes [Russell] |
| Full Idea: Numbers are to be regarded as properties of classes. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §109) | |
| A reaction: If properties are then defined extensionally as classes, you end up with numbers as classes of classes. |
| 9977 | Ordinals can't be defined just by progression; they have intrinsic qualities [Russell] |
| Full Idea: It is impossible that the ordinals should be, as Dedekind suggests, nothing but the terms of such relations as constitute a progression. If they are anything at all, they must be intrinsically something. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §242) | |
| A reaction: This is the obvious platonist response to the incipient doctrine of structuralism. We have a chicken-and-egg problem. Bricks need intrinsic properties to make a structure. A structure isomorphic to numbers is not thereby the numbers. |
| 14162 | Mathematics doesn't care whether its entities exist [Russell] |
| Full Idea: Mathematics is throughout indifferent to the question whether its entities exist. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §434) | |
| A reaction: There is an 'if-thenist' attitude in this book, since he is trying to reduce mathematics to logic. Total indifference leaves the problem of why mathematics is applicable to the real world. |
| 5399 | Maths is not known by induction, because further instances are not needed to support it [Russell] |
| Full Idea: If induction was the source of our mathematical knowledge, we should proceed differently. In fact, a certain number of instances make us think of two abstractly, and we then see the general principle, and further instances become unnecessary. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 7) | |
| A reaction: In practice, of course, we stop checking whether the sun has come up yet again this morning. Russell's point is better expressed as: if contradictory evidence were observed, we would believe the arithmetic and doubt the experience. |
| 14103 | Pure mathematics is the class of propositions of the form 'p implies q' [Russell] |
| Full Idea: Pure mathematics is the class of all propositions of the form 'p implies q', where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §001) | |
| A reaction: Linnebo calls Russell's view here 'deductive structuralism'. Russell gives (§5) as an example that Euclid is just whatever is deduced from his axioms. |
| 21555 | For 'x is a u' to be meaningful, u must be one range of individuals (or 'type') higher than x [Russell] |
| Full Idea: In his 1903 theory of types he distinguished between individuals, ranges of individuals, ranges of ranges of individuals, and so on. Each level was a type, and it was stipulated that for 'x is a u' to be meaningful, u must be one type higher than x. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], App) | |
| A reaction: Russell was dissatisfied because this theory could not deal with Cantor's Paradox. Is this the first time in modern philosophy that someone has offered a criterion for whether a proposition is 'meaningful'? |
| 18003 | In 'x is a u', x and u must be of different types, so 'x is an x' is generally meaningless [Russell, by Magidor] |
| Full Idea: Russell argues that in a statement of the form 'x is a u' (and correspondingly, 'x is a not-u'), 'x must be of different types', and hence that ''x is an x' must in general be meaningless'. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903], App B:524) by Ofra Magidor - Category Mistakes 1.2 | |
| A reaction: " 'Word' is a word " comes to mind, but this would be the sort of ascent to a metalanguage (to distinguish the types) which Tarski exploited. It is the simple point that a classification can't be the same as a member of the classification. |
| 11010 | Being is what belongs to every possible object of thought [Russell] |
| Full Idea: Being is that which belongs to every conceivable, to every possible object of thought. | |
| From: Bertrand Russell (The Principles of Mathematics [1903]), quoted by Stephen Read - Thinking About Logic Ch.5 | |
| A reaction: I take Russell's (or anyone's) attempt to distinguish two different senses of the word 'being' or 'exist' to be an umitigated metaphysical disaster. |
| 14161 | Many things have being (as topics of propositions), but may not have actual existence [Russell] |
| Full Idea: Numbers, the Homeric gods, relations, chimeras and four-dimensional space all have being, for if they were not entities of a kind, we could not make propositions about them. Existence, on the contrary, is the prerogative of some only amongst the beings. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §427) | |
| A reaction: This is the analytic philosophy account of being (a long way from Heidegger). Contemporary philosophy seems to be full of confusions on this, with many writers claiming existence for things which should only be awarded 'being' status. |
| 14173 | What exists has causal relations, but non-existent things may also have them [Russell] |
| Full Idea: It would seem that whatever exists at any part of time has causal relations. This is not a distinguishing characteristic of what exists, since we have seen that two non-existent terms may be cause and effect. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §449) | |
| A reaction: Presumably he means that the non-existence of something (such as a safety rail) might the cause of an event. This is a problem for Alexander's Principle, in Idea 3534. I think we could redescribe his problem cases, to save Alexander. |
| 5370 | Space is neutral between touch and sight, so it cannot really be either of them [Russell] |
| Full Idea: The space of science is neutral as between touch and sight; thus it cannot be either the space of touch or the space of sight. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 3) | |
| A reaction: I find this persuasive, although it is hardly a knock-down argument. It is a very simple problem for anti-realists, that if you say reality IS sensations (à la Berkeley), then you have conflicting sensations of what seems to be one reality. |
| 5418 | In a world of mere matter there might be 'facts', but no truths [Russell] |
| Full Idea: If we imagine a world of mere matter, there would be no room for falsehood, and although it would contain what may be called 'facts', it would not contain any truths. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: Only a realist will buy a concept of mind-independent 'facts', but I am with Russell all the way here. We should not say "the truth is out there", but "the facts are out there". Facts are the target of thought, and truth is a relationship to the facts. |
| 14163 | Four classes of terms: instants, points, terms at instants only, and terms at instants and points [Russell] |
| Full Idea: Among terms which appear to exist, there are, we may say, four great classes: 1) instants, 2) points, 3) terms which occupy instants but not points, 4) terms which occupy both points and instants. Analysis cannot explain 'occupy'. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §437) | |
| A reaction: This is a massively reductive scientific approach to categorising existence. Note that it homes in on 'terms', which seems a rather linguistic approach, although Russell is cautious about such things. |
| 21341 | Philosophers of logic and maths insisted that a vocabulary of relations was essential [Russell, by Heil] |
| Full Idea: Relations were regarded with suspicion, until philosophers working in logic and mathematics advanced reasons to doubt that we could provide anything like an adequate description of the world without developing a relational vocabulary. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903], Ch.26) by John Heil - Relations | |
| A reaction: [Heil cites Russell as the only reference] A little warning light, that philosophers describing the world managed to do without real relations, and it was only for the abstraction of logic and maths that they became essential. |
| 5371 | Because we depend on correspondence, we know relations better than we know the items that relate [Russell] |
| Full Idea: We can know the properties of the relations required to preserve the correspondence between sense-data and reality, but we cannot know the nature of the terms between which the relations hold. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 3) | |
| A reaction: Thus Russell always puts great emphasis on relations in his metaphysics. I would say that he is right, and that what he calls the 'nature of the terms' are essences, and that these are knowable, by inference and explanation. |
| 5407 | That Edinburgh is north of London is a non-mental fact, so relations are independent universals [Russell] |
| Full Idea: Nothing mental is presupposed in the fact that Edinburgh is north of London, but this involves the universal 'north of', so we must admit that relations are not dependent upon thought, but belong to the independent world which thought apprehends. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 9) | |
| A reaction: We cannot deny that Edinburgh being north of London is independent of our minds, but we might deny that 'north of' is a universal. 'North' is clearly a human convention, but 'nearer a pole' isn't. Distances exist in space, rather than as relations. |
| 10586 | 'Reflexiveness' holds between a term and itself, and cannot be inferred from symmetry and transitiveness [Russell] |
| Full Idea: The property of a relation which insures that it holds between a term and itself is called by Peano 'reflexiveness', and he has shown, contrary to what was previously believed, that this property cannot be inferred from symmetry and transitiveness. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §209) | |
| A reaction: So we might say 'this is a sentence' has a reflexive relation, and 'this is a wasp' does not. While there are plenty of examples of mental properties with this property, I'm not sure that it makes much sense of a physical object. Indexicality... |
| 10585 | Symmetrical and transitive relations are formally like equality [Russell] |
| Full Idea: Relations which are both symmetrical and transitive are formally of the nature of equality. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §209) | |
| A reaction: This is the key to the whole equivalence approach to abstraction and Frege's definition of numbers. Establish equality conditions is the nearest you can get to saying what such things are. Personally I think we can say more, by revisiting older views. |
| 5383 | Every complete sentence must contain at least one word (a verb) which stands for a universal [Russell] |
| Full Idea: Every complete sentence must contain at least one word which stands for a universal, since all verbs have a meaning which is universal. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: Not all meaningful statements are sentences. One could try a programme of eliminating from discourse all words which imply universals. Daily physical life would survive all right, but universities would close down. |
| 4428 | Propositions express relations (prepositions and verbs) as well as properties (nouns and adjectives) [Russell] |
| Full Idea: In general, adjectives and nouns express properties of things, whereas prepositions and verbs express relations between things, so neglect of the latter led to the belief that every proposition attributes properties rather than relations. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 9) | |
| A reaction: A simple point on which Russell was very keen to insist, and which seems right. It invites the question whether there are further universals, beyond properties and relations. |
| 5406 | Confused views of reality result from thinking that only nouns and adjectives represent universals [Russell] |
| Full Idea: The monism of Spinoza and Bradley, and the monadism of Leibniz, result, in my opinion, from an undue attention to one sort of universals, namely the sort represented by adjectives and substantives rather than by verbs and prepositions. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 9) | |
| A reaction: The 'linguistic turn' of 20th century philosophy, which should be treated with caution, but I agree that if we are going to accept universals, we need a wide vision of what categories they might fall into. I would prefer an ontology without 'relations'. |
| 4479 | All universals are like the relation "is north of", in having no physical location at all [Russell, by Loux] |
| Full Idea: Russell denies that universals have any location at all. ..He is generalising from the case of "is north of", which does not exist any more in Edinburgh than in London. | |
| From: report of Bertrand Russell (Problems of Philosophy [1912], Ch. 9) by Michael J. Loux - Metaphysics: contemporary introduction p.55 | |
| A reaction: Russell may claim that the relation "is north of" is natural, but I suspect that it is a convention, mapped onto a physical situation. Reifying relations invite charges of a regress (as Bradley noted). |
| 4427 | Every sentence contains at least one word denoting a universal, so we need universals to know truth [Russell] |
| Full Idea: No sentence can be made up without at least one word which denotes a universal. ..Thus all truths involve universals, and all knowledge of truths involves acquaintance with universals. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 9) | |
| A reaction: Sounds right, and is a beautifully neat way of showing the connection between metaphysics and life. |
| 4030 | Russell claims that universals are needed to explain a priori knowledge (as their relations) [Russell, by Mellor/Oliver] |
| Full Idea: Russell's positive argument for universals is that they explain how we can have a priori knowledge, which 'deals exclusively with the relations of universals'. | |
| From: report of Bertrand Russell (Problems of Philosophy [1912], Ch. 9) by DH Mellor / A Oliver - Introduction to 'Properties' §3 | |
| A reaction: Unfortunately we can invent the universals, and then delude ourselves that we have a priori knowledge |
| 5409 | Normal existence is in time, so we must say that universals 'subsist' [Russell] |
| Full Idea: We think of things existing when they are in time (though possibly at all times), but universals do not exist in this sense, so we shall say that they 'subsist' or 'have being'. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 9) | |
| A reaction: Russell picked up the word 'subsist' from medieval philosophy. This idea brings the full Platonic metaphysics with it, which is tricky, to say the least. But what can you do? Admitting the content of thought brings baggage with it. |
| 5408 | If we identify whiteness with a thought, we can never think of it twice; whiteness is the object of a thought [Russell] |
| Full Idea: If whiteness were the thought as opposed to its object no two different men could think of it, and no one man could think of it twice. What many different thoughts of whiteness have in common is their object, and this object is different from all of them. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 9) | |
| A reaction: This seems to me a powerful argument in favour of thinking of universals as in some sense real - but in what sense? The crux is that Russell shows that we must find a place in our ontology for the content of thoughts, as well as of thoughts. |
| 4441 | 'Resemblance Nominalism' won't work, because the theory treats resemblance itself as a universal [Russell] |
| Full Idea: To be a universal, a resemblance must hold between many pairs of white things. We can't say there is a different resemblance between each pair, since the resemblances must resemble each other, so we are forced to admit that resemblance is a universal. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 9) | |
| A reaction: Apparently this objection is much discussed and controversial. It looks like a threat to any theory of universals (involving 'sets', or 'concepts', or 'predicates'). We seem to need 'basic' and 'derivative' universals. Cf Idea 7956. |
| 4429 | If we consider whiteness to be merely a mental 'idea', we rob it of its universality [Russell] |
| Full Idea: If we come to regard an 'idea' like whiteness as an act of thought, then we come to think of whiteness as mental, but in doing so we rob it of its essential quality of universality. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 9) | |
| A reaction: Presumably we need an ontological commitment to the existence of universals, which is very Platonic. Fatherhood might be a better example, since whiteness is a quale. |
| 7781 | I call an object of thought a 'term'. This is a wide concept implying unity and existence. [Russell] |
| Full Idea: Whatever may be an object of thought, or occur in a true or false proposition, or be counted as one, I call a term. This is the widest word in the philosophical vocabulary, which I use synonymously with unit, individual, entity (being one, and existing). | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §047) | |
| A reaction: The claim of existence begs many questions, such as whether the non-existence of the Loch Ness Monster is an 'object' of thought. |
| 14166 | Unities are only in propositions or concepts, and nothing that exists has unity [Russell] |
| Full Idea: It is sufficient to observe that all unities are propositions or propositional concepts, and that consequently nothing that exists is a unity. If, therefore, it is maintained that things are unities, we must reply that no things exist. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §439) | |
| A reaction: The point, I presume, is that you end up as a nihilist about identities (like van Inwagen and Merricks) by mistakenly thinking (as Aristotle and Leibniz did) that everything that exists needs to have something called 'unity'. |
| 14164 | The only unities are simples, or wholes composed of parts [Russell] |
| Full Idea: The only kind of unity to which I can attach any precise sense - apart from the unity of the absolutely simple - is that of a whole composed of parts. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §439) | |
| A reaction: This comes from a keen student of Leibniz, who was obsessed with unity. Russell leaves unaddressed the question of what turns some parts into a whole. |
| 14112 | A set has some sort of unity, but not enough to be a 'whole' [Russell] |
| Full Idea: In a class as many, the component terms, though they have some kind of unity, have less than is required for a whole. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §070) | |
| A reaction: This is interesting because (among many other things), sets are used to stand for numbers, but numbers are usually reqarded as wholes. |
| 13276 | The unmoved mover and the soul show Aristotelian form as the ultimate mereological atom [Aristotle, by Koslicki] |
| Full Idea: Aristotle's discussion of the unmoved mover and of the soul confirms the suspicion that form, when it is not thought of as the object represented in a definition, plays the role of the ultimate mereological atom within his system. | |
| From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 6.6 | |
| A reaction: Aristotle is concerned with which things are 'divisible', and he cites these two examples as indivisible, but they may be too unusual to offer an actual theory of how Aristotle builds up wholes from atoms. He denies atoms in matter. |
| 13277 | The 'form' is the recipe for building wholes of a particular kind [Aristotle, by Koslicki] |
| Full Idea: Thus in Aristotle we may think of an object's formal components as a sort of recipe for how to build wholes of that particular kind. | |
| From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 7.2.5 | |
| A reaction: In the elusive business of pinning down what Aristotle means by the crucial idea of 'form', this analogy strikes me as being quite illuminating. It would fit DNA in living things, and the design of an artifact. |
| 14170 | Change is obscured by substance, a thing's nature, subject-predicate form, and by essences [Russell] |
| Full Idea: The notion of change is obscured by the doctrine of substance, by a thing's nature versus its external relations, and by subject-predicate form, so that things can be different and the same. Hence the useless distinction between essential and accidental. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §443) | |
| A reaction: He goes on to object to vague unconscious usage of 'essence' by modern thinkers, but allows (teasingly) that medieval thinkers may have been precise about it. It is a fact, in common life, that things can change and be the same. Explain it! |
| 14107 | Terms are identical if they belong to all the same classes [Russell] |
| Full Idea: Two terms are identical when the second belongs to every class to which the first belongs. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §026) |
| 11849 | It at least makes sense to say two objects have all their properties in common [Wittgenstein on Russell] |
| Full Idea: Russell's definition of '=' is inadequate, because according to it we cannot say that two objects have all their properties in common. (Even if this proposition is never correct, it still has a sense). | |
| From: comment on Bertrand Russell (The Principles of Mathematics [1903]) by Ludwig Wittgenstein - Tractatus Logico-Philosophicus 5.5302 | |
| A reaction: This is what now seems to be a standard denial of the bizarre Leibniz claim that there never could be two things with identical properties, even, it seems, in principle. What would Leibniz made of two electrons? |
| 22303 | It makes no sense to say that a true proposition could have been false [Russell] |
| Full Idea: There seems to be no true proposition of which it makes sense to say that it might have been false. One might as well say that redness might have been a taste and not a colour. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §430), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 29 'Analy' | |
| A reaction: Few thinkers agree with this rejection of counterfactuals. It seems to rely on Moore's idea that true propositions are facts. It also sounds deterministic. Does 'he is standing' mean he couldn't have been sitting (at t)? |
| 5400 | In any possible world we feel that two and two would be four [Russell] |
| Full Idea: In any possible world we feel that two and two would be four. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 7) | |
| A reaction: Thinking of necessity in terms of possible worlds is not a new invention, but then Russell was a keen fan of Leibniz. Suppose there were no world at all, and only one truth, namely that two and two make five? (No, I can't make sense of that!) |
| 5991 | For Aristotle, knowledge is of causes, and is theoretical, practical or productive [Aristotle, by Code] |
| Full Idea: Aristotle thinks that in general we have knowledge or understanding when we grasp causes, and he distinguishes three fundamental types of knowledge - theoretical, practical and productive. | |
| From: report of Aristotle (works [c.330 BCE]) by Alan D. Code - Aristotle | |
| A reaction: Productive knowledge we tend to label as 'knowing how'. The centrality of causes for knowledge would get Aristotle nowadays labelled as a 'naturalist'. It is hard to disagree with his three types, though they may overlap. |
| 5431 | Knowledge cannot be precisely defined, as it merges into 'probable opinion' [Russell] |
| Full Idea: 'Knowledge' is not a precise conception: it merges into 'probable opinion', and so a very precise definition should not be sought. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.13) | |
| A reaction: This announcement comes as a relief, after endless attempts (mainly by American academics) to give watertight, carefully worded definitions. It seems to me undeniable that what we will accept as knowledge is partly a matter of social negotiation. |
| 5426 | Belief relates a mind to several things other than itself [Russell] |
| Full Idea: A belief or judgement relates a mind to several things other than itself. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: Presumably we must say that if I believe that (say) 'x exists', this is relating x to the universal 'exists'. If so, Russell's point becomes a bit of a tautology. We believe propositions, which are combinations of concepts, so are multiple. |
| 5366 | We have an 'instinctive' belief in the external world, prior to all reflection [Russell] |
| Full Idea: We find a belief in an independent external world ready in ourselves as soon as we begin to reflect: it is what may be called an 'instinctive' belief. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 2) | |
| A reaction: Somewhere Hume calls this a 'natural belief', and it is fairly central to his idea that most of our beliefs are built up fairly mechanically by associations. I am tempted to ask whether such things even count as beliefs, if they are so uncritical. |
| 5359 | Descartes showed that subjective things are the most certain [Russell] |
| Full Idea: By showing that subjective things are the most certain, Descartes performed a great service to philosophy. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 2) | |
| A reaction: This praise comes from an empiricist, who has just said that 'sense-data' are the most certain things. I presume that animals are more certain of the world than they are of subjective things. In fact, probably on philosophers agree with Russell. |
| 5377 | 'Acquaintance' is direct awareness, without inferences or judgements [Russell] |
| Full Idea: We shall say we have 'acquaintance' with anything of which we are directly aware, without the intermediary of any process of inference or any knowledge of truths. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: Although Russell understands the difficulty of precise distinctions here, he implies that some knowledge is directly knowable, although truth only enters at the stage of judgement. Personally I would suggest that pure acquaintance is not knowledge. |
| 6510 | Russell (1912) said phenomena only resemble reality in abstract structure [Russell, by Robinson,H] |
| Full Idea: Russell held in 'Problems of Philosophy' that the physical world resembles the phenomenal only in abstract structure. | |
| From: report of Bertrand Russell (Problems of Philosophy [1912]) by Howard Robinson - Perception VII.5 | |
| A reaction: Russell's problem is that he then requires full-blown and elaborate 'inferences' to get from the abstract structure to some sort of 'theory' of reality, but our experience seems much more direct, even if it isn't actually 'naïve'. |
| 5372 | There is no reason to think that objects have colours [Russell] |
| Full Idea: It is quite gratuitous to suppose that physical objects have colours. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 3) | |
| A reaction: This has always seemed to me self-evident, from the day I started to study philosophy. I cannot make sense of serious attempts to defend direct (naïve) realism. Colour is a brilliant trick of natural selection for extracting environmental information. |
| 5373 | 'Idealism' says that everything which exists is in some sense mental [Russell] |
| Full Idea: We shall understand 'idealism' to be the doctrine that whatever exists, or at any rate whatever can be known to exist, must be in some sense mental. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 4) | |
| A reaction: The interesting thing here is the phrase 'in some sense', which takes on a new light when we begin once against to take seriously ideas such as panpsychism. If the boundary between mind and brain is blurred, so is that between realism and idealism. |
| 5362 | It is not illogical to think that only myself and my mental events exist [Russell] |
| Full Idea: No logical absurdity results from the hypothesis that the world consists of myself and my thoughts and feelings and sensations, and that everything else is mere fancy. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 2) | |
| A reaction: The only real attempt to meet this challenge is Wittgenstein's Private Language Argument, which tried to show that it would be a logical impossibility to speak a language if there were no other minds. Personally, I am with Russell. |
| 11239 | The notion of a priori truth is absent in Aristotle [Aristotle, by Politis] |
| Full Idea: The notion of a priori truth is conspicuously absent in Aristotle. | |
| From: report of Aristotle (works [c.330 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.5 | |
| A reaction: Cf. Idea 11240. |
| 5412 | Some propositions are self-evident, but their implications may also be self-evident [Russell] |
| Full Idea: When a certain number of logical principles have been admitted as self-evident, the rest can be deduced from them; but the propositions deduced are often just as self-evident as those that were assumed without proof. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.11) | |
| A reaction: This seems an important corrective to the traditional rationalist dream, based on Euclid, that all knowledge is self-evident axioms followed by proofs of the rest. But Russell here endorses a more sensible sort of rationalism. |
| 5413 | Particular instances are more clearly self-evident than any general principles [Russell] |
| Full Idea: Particular instances are more self-evident than general principles; for example, the law of contradiction is evident as soon as it is understood, but it is not as evident as that a particular rose cannot be both red and not red. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.11) | |
| A reaction: This seems to true about nearly all reasoning, because whenever we are faced with a general principle for assessment, we check it by testing it against a series of particular instances, and try to think of contradictory particular counterexamples. |
| 5415 | As shown by memory, self-evidence comes in degrees [Russell] |
| Full Idea: It is clear from the case of memory that self-evidence has degrees, and is present in gradations ranging from absolute certainty down to an almost imperceptible faintness. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.11) | |
| A reaction: I am beginning to see Russell as the 'father of modern rationalism'. His relaxation of notions of an all-or-nothing a priori, and of a sharp distinction between axioms and proofs, lead to a sensible rationalism which even a Humean sceptic might buy. |
| 5416 | If self-evidence has degrees, we should accept the more self-evident as correct [Russell] |
| Full Idea: If propositions can have some degree of self-evidence without being true, we must say, where there is a conflict, that the more self-evident proposition is to be retained and the less self-evident rejected. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.11) | |
| A reaction: This is a key part of Russell's 'moderate rationalism'. Presumably the rejected propositions were therefore not self-evident, and can be used as training for intuitions, by seeing why we got it wrong. Fools find absurd falsehoods self-evidently true. |
| 5397 | The rationalists were right, because we know logical principles without experience [Russell] |
| Full Idea: In the most important point of the controversy between empiricists and rationalist, the rationalists were right, since logical principles are known to us, but cannot be proved by experience, since all proof presupposes them | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 7) | |
| A reaction: Russell initially presents this as the answer to 'innate ideas'. I would prefer to say, in the style of Descartes, that logic is self-evident to the natural light of reason. The debate isn't over. A Turing machine may be able to do logic. |
| 4430 | All a priori knowledge deals with the relations of universals [Russell] |
| Full Idea: All a priori knowledge deals with the relations of universals. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.10) | |
| A reaction: A nice bold proposition, and remarkably Platonic for a famous empiricist. But then a priori knowledge of particulars sounds unlikely. |
| 5411 | We can know some general propositions by universals, when no instance can be given [Russell] |
| Full Idea: The general proposition 'All products of two integers, which never have been and never will be thought of by any human being, are over 100' is undeniably true, and yet we can never give an instance of it; ..only a knowledge of the universals is required. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.10) | |
| A reaction: A nice example which it seems to be impossible to contradict. But maybe we can explain our knowledge of it in terms of rules, instead of mentioning universals. Can a rule be stated without recourse to universals? Sounds unlikely. |
| 6514 | Russell's representationalism says primary qualities only show the structure of reality [Russell, by Robinson,H] |
| Full Idea: The weakest version of representationalism, found in Russell, asserts that there is no resemblance to reality on the level of secondary qualities, and also that primary qualities exhibit only a structural isomorphism. | |
| From: report of Bertrand Russell (Problems of Philosophy [1912]) by Howard Robinson - Perception IX.2 | |
| A reaction: This seems a plausible thing to say about, say, shape, but it is not clear how the idea works for hardness or mass. The sense of touch seems to be much more directly in contact with actual primary qualities than visions does (let alone smell or hearing). |
| 6415 | After 1912, Russell said sense-data are last in analysis, not first in experience [Russell, by Grayling] |
| Full Idea: During the decade after 'Problems of Philosophy' Russell points our repeatedly that specifications of sense-data come last in analysis, not first in experience. | |
| From: report of Bertrand Russell (Problems of Philosophy [1912]) by A.C. Grayling - Russell Ch.2 | |
| A reaction: This was a symptom of Russell losing faith in sense-data, and he eventually abandoned them. There is a possible position where we deny any such item as sense-data in a scientific account, but allow them in our metaphysics. |
| 5358 | 'Sense-data' are what are immediately known in sensation, such as colours or roughnesses [Russell] |
| Full Idea: Let us give the name 'sense-data' to the things that are immediately known in sensation: such things as colours, sounds, smells, hardnesses, roughnesses, and so on. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 1) | |
| A reaction: This idea gradually became notorious, because it seems to create a new ontological category unnecessarily, and it creates problems, such as how the intermediary interacts with us and with things. Are sense-data totally non-conceptual? |
| 23312 | Aristotle is a rationalist, but reason is slowly acquired through perception and experience [Aristotle, by Frede,M] |
| Full Idea: Aristotle is a rationalist …but reason for him is a disposition which we only acquire over time. Its acquisition is made possible primarily by perception and experience. | |
| From: report of Aristotle (works [c.330 BCE]) by Michael Frede - Aristotle's Rationalism p.173 | |
| A reaction: I would describe this process as the gradual acquisition of the skill of objectivity, which needs the right knowledge and concepts to evaluate new experiences. |
| 7290 | If Russell rejects innate ideas and direct a priori knowledge, he is left with a tabula rasa [Russell, by Thompson] |
| Full Idea: If Russell rejects innate ideas, and he even thinks the laws of thought must by triggered by experiences (e.g. of a beech tree), and he doesn't embrace associations, this implies that he thinks the mind begins as a tabula rasa. | |
| From: report of Bertrand Russell (Problems of Philosophy [1912]) by George Thompson - talk | |
| A reaction: This nice observation places Russell as (in my view) a rather old-fashioned empiricist, who ignores Hume and Kant, and is not willing to speculate about how the mind can turn acquaintances with sense-data into knowledge |
| 5357 | It is natural to begin from experience, and presumably that is the basis of knowledge [Russell] |
| Full Idea: In the search for certainty, it is natural to begin with our present experiences, and in some sense, no doubt, knowledge is to be derived from them. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 1) | |
| A reaction: Is experience the 'natural' place to begin? It didn't seem to strike Descartes that way. It seems better to say that philosophy begins when we are not quite satisfied with experience, and the natural place to begin is 'dissatisfaction'. |
| 5382 | We are acquainted with outer and inner sensation, memory, Self, and universals [Russell, by PG] |
| Full Idea: We have acquaintance with outer senses, with inner sense (by introspection), with memory (of outer or inner sensations), with a Self (probably), and also with universals (general ideas). | |
| From: report of Bertrand Russell (Problems of Philosophy [1912], Ch. 5) by PG - Db (ideas) | |
| A reaction: The spectacular odd one out in a basic empiricist theory is, of course, universals, when one expects some sort of nominalist reduction of those into sense-data. I am very sympathetic to the Russell line, though it spells big ontological trouble. |
| 5389 | Knowledge by descriptions enables us to transcend private experience [Russell] |
| Full Idea: The chief importance of knowledge by descriptions is that it enables us to pass beyond the limits of our private experience. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: The most basic question for empiricism concerns how we can know things beyond immediate experience. Russell is right, though this doesn't tell us much. We need to know the rules for valid descriptions, explanation, speculations etc. |
| 5376 | I can know the existence of something with which nobody is acquainted [Russell] |
| Full Idea: There is no reason why I should not know of the existence of something with which nobody is acquainted. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 4) | |
| A reaction: This sort of realist claim (which he goes on to say results from inferences from descriptions) is needed to save empiricism from the absurdities of Berkeley and (dare I say it?) Quine. The Kantian Ego is a candidate. |
| 16111 | Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML] |
| Full Idea: Since Aristotle generally prefers a metaphysical theory that accords with common intuitions, he frequently relies on facts about language to guide his metaphysical claims. | |
| From: report of Aristotle (works [c.330 BCE]) by Mary Louise Gill - Aristotle on Substance Ch.5 | |
| A reaction: I approve of his procedure. I take intuition to be largely rational justifications too complex for us to enunciate fully, and language embodies folk intuitions in its concepts (especially if the concepts occur in many languages). |
| 5414 | Images are not memory, because they are present, and memories are of the past [Russell] |
| Full Idea: An image cannot constitute a memory, because we notice that the image is in the present, whereas what is remembered is known to be in the past. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.11) | |
| A reaction: This sounds a bit glib, and maybe makes the mistake for which he criticises Berkeley, of confusing a thought and its content. The puzzle is how we know that some images represent the past, others the present, others predictions, and others fantasy. |
| 5430 | A true belief is not knowledge if it is reached by bad reasoning [Russell] |
| Full Idea: A true belief cannot be called knowledge when it is deduced by a fallacious process of reasoning. If I know all Greeks are men, and Socrates was a man, I cannot know that Socrates was a Greek, even if I falsely infer it. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.13) | |
| A reaction: Another very nice 'Gettier' example, fifty years before Gettier. There is a danger of circularity here, between knowledge, fallacy and truth. Giving them three independent definitions does not look promising. |
| 5429 | True belief is not knowledge when it is deduced from false belief [Russell] |
| Full Idea: A true belief is not knowledge when it is deduced from a false belief (as when deducing that the late Prime Minister's name began with B, believing it was Balfour, when actually it was Bannerman). | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.13) | |
| A reaction: Correct me if I am wrong, but isn't this the 'Gettier Problem'? It raises the central question of modern epistemology, which is what will be counted as adequate justification to make a true belief qualify as knowledge. How high do we set the bar? |
| 5378 | All knowledge (of things and of truths) rests on the foundations of acquaintance [Russell] |
| Full Idea: All our knowledge, both knowledge of things and knowledge of truths, rests upon acquaintance as its foundations. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: Russell here allies himself with Hume, and with the empiricist version of foundationalism. 'Acquaintance' plays the role which 'impressions' played for Hume. He is eliminating any possible cognitive content from the Hume idea, implying pure sense-data. |
| 5365 | Dreams can be explained fairly scientifically if we assume a physical world [Russell] |
| Full Idea: Dreams are more or less suggested by what we call waking life, and are capable of being more or less accounted for on scientific principles if we assume that there really is a physical world. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 2) | |
| A reaction: This sounds a bit circular, since scientific principles depend entirely on the assumption that there is a physical world. No doubt if we assume fairies, 'fairy lore' will explain everything. 'Explanation' is the basic concept here. |
| 16971 | Plato says sciences are unified around Forms; Aristotle says they're unified around substance [Aristotle, by Moravcsik] |
| Full Idea: Plato's unity of science principle states that all - legitimate - sciences are ultimately about the Forms. Aristotle's principle states that all sciences must be, ultimately, about substances, or aspects of substances. | |
| From: report of Aristotle (works [c.330 BCE], 1) by Julius Moravcsik - Aristotle on Adequate Explanations 1 |
| 5391 | Science aims to find uniformities to which (within the limits of experience) there are no exceptions [Russell] |
| Full Idea: The business of science is to find uniformities, such as the laws of motion and the law of gravitation, to which, so far as our experience extends, there are no exceptions. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 6) | |
| A reaction: This seems nicely stated, based on the Humean 'regularity' view of scientific laws. When we discover such uniformities (such as the gravitational equation), we are still faced with the metaphysical question of their status. Necessity, or pattern? |
| 5394 | We can't prove induction from experience without begging the question [Russell] |
| Full Idea: We can never use experience to prove the inductive principle without begging the question. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 6) | |
| A reaction: This highlights why induction is such a big problem for hard-line empiricists, who are reduced to saying that it is a 'dogma', or an unsupported 'natural belief'. And that seems right. All creatures which evolve in a stable universe will do induction. |
| 5390 | Chickens are not very good at induction, and are surprised when their feeder wrings their neck [Russell] |
| Full Idea: The man who has fed his chicken every day throughout its life at last wrings its neck instead, showing that more refined views as to the uniformity of nature would have been useful to the chicken. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 6) | |
| A reaction: A justly famous illustration of Hume's problem of induction, that a vast amount of evidence could still support a false conclusion. If we say 'the future will be like the past', this depends on understanding what was happening in the past. |
| 5392 | It doesn't follow that because the future has always resembled the past, that it always will [Russell] |
| Full Idea: We have experience of past futures, but not of future futures, and the question is: Will future futures resemble past futures? This question is not to be answered by an argument which starts from past futures alone. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 6) | |
| A reaction: This nicely makes the problem of induction unavoidable, for anyone who preferred not to face the problem. The simple solution is to recognise that the future may NOT resemble the past, for all we know. Actually I think it will, but what was the past like? |
| 11243 | Aristotelian explanations are facts, while modern explanations depend on human conceptions [Aristotle, by Politis] |
| Full Idea: For Aristotle things which explain (the explanantia) are facts, which should not be associated with the modern view that says explanations are dependent on how we conceive and describe the world (where causes are independent of us). | |
| From: report of Aristotle (works [c.330 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 2.1 | |
| A reaction: There must be some room in modern thought for the Aristotelian view, if some sort of robust scientific realism is being maintained against the highly linguistic view of philosophy found in the twentieth century. |
| 3320 | Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA] |
| Full Idea: The standard Aristotelian doctrine of species and genus in the theory of anything whatever involves specifying what the thing is in terms of something more general. | |
| From: report of Aristotle (works [c.330 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.10 |
| 12000 | Aristotle regularly says that essential properties explain other significant properties [Aristotle, by Kung] |
| Full Idea: The view that essential properties are those in virtue of which other significant properties of the subjects under investigation can be explained is encountered repeatedly in Aristotle's work. | |
| From: report of Aristotle (works [c.330 BCE]) by Joan Kung - Aristotle on Essence and Explanation IV | |
| A reaction: What does 'significant' mean here? I take it that the significant properties are the ones which explain the role, function and powers of the object. |
| 5363 | If the cat reappears in a new position, presumably it has passed through the intermediate positions [Russell] |
| Full Idea: If the cat appears at one moment in one part of the room, and at another in another part, it is natural to suppose that it has moved from the one to the other, passing over a series of intermediate positions. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 2) | |
| A reaction: This example seems perfect as an illustration of inference to the best explanation (now called 'abduction'), and that seems to me the absolute key to human knowledge. The cat example is what made me a devotee of Bertrand Russell. |
| 5367 | Belief in real objects makes our account of experience simpler and more systematic [Russell] |
| Full Idea: The belief that there are objects corresponding to our sense-data tends to simplify and systematize our account of our experiences, so there seems no good reason for rejecting it. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 2) | |
| A reaction: This hardly counts as a good argument against the logical possibility of global scepticism, but it is a nice statement of the concept of 'best explanation', which obviously requires some sort of rational criteria if it is to provide a theory of knowledge. |
| 5364 | It is hard not to believe that speaking humans are expressing thoughts, just as we do ourselves [Russell] |
| Full Idea: When human beings speak, it is very difficult to suppose that what we hear is not the expression of a thought, as we know it would be if we emitted the same sounds. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 2) | |
| A reaction: This is partly the 'argument from analogy', which seems a bit suspect (induction from a single instance), but it is also the rather undeniable Humean idea that we have a 'natural belief' in other minds, which we could never disbelieve. |
| 5379 | If we didn't know our own minds by introspection, we couldn't know that other people have minds [Russell] |
| Full Idea: But for our acquaintance with the contents of our own minds, we should be unable to imagine the minds of others, and therefore we could never arrive at the knowledge that they have minds. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: Not only does this depend on the notorious 'argument from analogy', but it actually strikes me as false. If a robot observed a human to be writhing in pain, it would be mystified, until it inferred that we have minds in which we actually 'feel' damage. |
| 5410 | I learn the universal 'resemblance' by seeing two shades of green, and their contrast with red [Russell] |
| Full Idea: If I see simultaneously two shades of green, I can see that they resemble each other, and I see that they resemble each other more than they resemble a shade of red; in this way I become acquainted with the universal 'resemblance'. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.10) | |
| A reaction: This is strikingly different from the account of Hume, who seemed to regard resemblance as a fairly mechanical, computer-like activity of the brain, whereas Russell (an empiricist) responds by inclining towards Platonism. Hume sounds better here. |
| 5381 | In seeing the sun, we are acquainted with our self, but not as a permanent person [Russell] |
| Full Idea: When I see the sun, it does not seem necessary to suppose that we are acquainted with a more or less permanent person, but we must be acquainted with that thing which sees the sun and has acquaintance with sense-data. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: I think this is exactly right. I personally believe that I have a very clear personal identity as I write this, but I do not believe that there is a strict identity with the person who wrote similar comments three years ago. So how do I change 'my' mind? |
| 5380 | In perceiving the sun, I am aware of sun sense-data, and of the perceiver of the data [Russell] |
| Full Idea: When I am acquainted with 'my seeing the sun', it seems plain that on the one hand there is the sense-datum which represents the sun to me, on the other hand there is that which sees this sense-datum. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: This appears to flatly contradict Hume's scepticism about seeing his 'self', but maybe Russell is only aware of his body, and then fictionalises a 'self' as the controller of this body. But I agree with Russell. I am the thing that cares about the sun. |
| 5369 | It is rational to believe in reality, despite the lack of demonstrative reasons for it [Russell] |
| Full Idea: In the preceding chapter we agreed, though without being able to find demonstrative reasons, that it is rational to believe that our sense-data are signs of an independent reality. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 3) | |
| A reaction: I wonder if Russell was the first to grasp this essential distinction. I suspect that three hundred years (1600-1900) were wasted in philosophy because they thought that everything rational had to be demonstrable. E.g. Hume on induction. |
| 23300 | Aristotle and the Stoics denied rationality to animals, while Platonists affirmed it [Aristotle, by Sorabji] |
| Full Idea: Aristotle, and also the Stoics, denied rationality to animals. …The Platonists, the Pythagoreans, and some more independent Aristotelians, did grant reason and intellect to animals. | |
| From: report of Aristotle (works [c.330 BCE]) by Richard Sorabji - Rationality 'Denial' | |
| A reaction: This is not the same as affirming or denying their consciousness. The debate depends on how rationality is conceived. |
| 5375 | Knowledge of truths applies to judgements; knowledge by acquaintance applies to sensations and things [Russell] |
| Full Idea: The word 'know' has two senses: the first is 'knowledge of truths', which is opposed to error, applies to judgements, and is knowing that something; the second is 'acquaintance', and is knowledge of things, particularly of sense-data. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 4) | |
| A reaction: We can also add procedural knowledge ('knowing how'). The question for Russell is whether his 'knowledge by acquaintance' can ever qualify as knowledge on its own, without the intrusion of judgements. Does perception necessarily have content? |
| 21711 | Russell's 'multiple relations' theory says beliefs attach to ingredients, not to propositions [Russell, by Linsky,B] |
| Full Idea: The basic idea of Russell's new 'multiple relations' theory of belief was that belief does not relate an individual to a proposition composed of various individuals and universals, but rather relates the believer directly to those constituents. | |
| From: report of Bertrand Russell (Problems of Philosophy [1912], Ch.12) by Bernard Linsky - Russell's Metaphysical Logic 3.1 | |
| A reaction: Russell abandoned his commitment to propositions in 1908, and retained this new view until 1918. Wittgenstein gave Russell hell over this theory. This view made his 'congruence' account of the correspondence theory of truth possible. |
| 5427 | Truth is when a mental state corresponds to a complex unity of external constituents [Russell] |
| Full Idea: Judging or believing is a certain complex unity of which a mind is a constituent; if the remaining constituents, taken in the order which they have in the belief, form a complex unity, then the belief is true. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: The modern label of 'congruence' for this view of truth makes it clearer. We aim to get a complex unity of constituents in our minds which are in the same 'order' as the constituents in the world. It is a good proposal, but leaves 'facts' as a problem. |
| 5425 | In order to explain falsehood, a belief must involve several terms, not two [Russell] |
| Full Idea: The relation involved in judging or believing must, if falsehood is to be duly allowed for, be taken to be a relation between several terms, not between two. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: His point is that if a belief relates to one object ('D's love for C') it will always be true. Russell is trying to explain what goes wrong when we believe a falsehood. It is not clear how the judgement 'x exists' involves several terms. |
| 5384 | A universal of which we are aware is called a 'concept' [Russell] |
| Full Idea: A universal of which we are aware is called a 'concept'. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: I am doubtful about this. Do children, and even animals, have a concept of 'my mother', without ever grasping the generalisation to 'his mother'? Is the word 'this' a non-universal concept? |
| 10583 | Abstraction principles identify a common property, which is some third term with the right relation [Russell] |
| Full Idea: The relations in an abstraction principle are always constituted by possession of a common property (which is imprecise as it relies on 'predicate'), ..so we say a common property of two terms is any third term to which both have the same relation. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §157) | |
| A reaction: This brings out clearly the linguistic approach of the modern account of abstraction, where the older abstractionism was torn between the ontology and the epistemology (that is, the parts of objects, or the appearances of them in the mind). |
| 10582 | The principle of Abstraction says a symmetrical, transitive relation analyses into an identity [Russell] |
| Full Idea: The principle of Abstraction says that whenever a relation with instances is symmetrical and transitive, then the relation is not primitive, but is analyzable into sameness of relation to some other term. ..This is provable and states a common assumption. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §157) | |
| A reaction: At last I have found someone who explains the whole thing clearly! Bertrand Russell was wonderful. See other ideas on the subject from this text, for a proper understanding of abstraction by equivalence. |
| 10584 | A certain type of property occurs if and only if there is an equivalence relation [Russell] |
| Full Idea: The possession of a common property of a certain type always leads to a symmetrical transitive relation. The principle of Abstraction asserts the converse, that such relations only spring from common properties of the above type. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §157) | |
| A reaction: The type of property is where only one term is applicable to it, such as the magnitude of a quantity, or the time of an event. So symmetrical and transitive relations occur if and only if there is a property of that type. |
| 13468 | Russell started philosophy of language, by declaring some plausible sentences to be meaningless [Russell, by Hart,WD] |
| Full Idea: Russell inadvertently started the philosophy of language by declaring that some sentences (like "Everything is identical with itself") that seem utterly in order are meaningless and express no proposition. | |
| From: report of Bertrand Russell (Problems of Philosophy [1912]) by William D. Hart - The Evolution of Logic 2 | |
| A reaction: The normal candidate for this honour would be Frege, with the sense/reference distinction, but this idea sounds right to me. Declaring that some sentences are 'meaningless' really gets people excited and interested. I like the example! |
| 5388 | Every understood proposition is composed of constituents with which we are acquainted [Russell] |
| Full Idea: Every proposition which we can understand must be composed wholly of constituents with which we are acquainted. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 6) | |
| A reaction: This is somewhere between Hume and logical positivism, but it concerns understanding (not meaning) of propositions (not sentences), and its acquaintance can be of universals as well as of sense experience. I like Russell's version more than Ayer's. |
| 5387 | It is pure chance which descriptions in a person's mind make a name apply to an individual [Russell] |
| Full Idea: It is a matter of chance which characteristics of a man's appearance will come into a friend's mind when he thinks of Bismarck; thus the description in the friend's mind is accidental; he knows the various descriptions all apply to the same entity. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: This seems to be an internalist account of reference, later called the 'bundle' theory of reference and associated with John Searle. It was attacked by Kripke. Personally I side, unfashionably, with Russell. |
| 14110 | Proposition contain entities indicated by words, rather than the words themselves [Russell] |
| Full Idea: A proposition, unless it happens to be linguistic, does not itself contain words: it contains the entities indicated by words. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §051) | |
| A reaction: Russell says in his Preface that he took over this view of propositions from G.E. Moore. They are now known as 'Russellian' propositions, which are mainly distinguished by not being mental event, but by being complexes out in the world. |
| 19164 | If propositions are facts, then false and true propositions are indistinguishable [Davidson on Russell] |
| Full Idea: Russell often treated propositions as facts, but discovered that correspondence then became useless for explaining truth, since every meaningful expression, true or false, expresses a proposition. | |
| From: comment on Bertrand Russell (The Principles of Mathematics [1903]) by Donald Davidson - Truth and Predication 6 | |
| A reaction: So 'pigs fly' would have to mean pigs actually flying (which they don't). They might correspond to possible situations, but only if pigs might fly. What do you make of 'circles are square'? Russell had many a sleepless night over that. |
| 14111 | A proposition is a unity, and analysis destroys it [Russell] |
| Full Idea: A proposition is essentially a unity, and when analysis has destroyed the unity, no enumeration of constituents will restore the proposition. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §054) | |
| A reaction: The question of the 'unity of the proposition' led to a prolonged debate. |
| 19157 | Russell said the proposition must explain its own unity - or else objective truth is impossible [Russell, by Davidson] |
| Full Idea: Moore and Russell reacted strongly against the idea that the unity of the proposition depended on human acts of judgement. ...Russell decided that unless the unity is explained in terms of the proposition itself, there can be no objective truth. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903], p.42) by Donald Davidson - Truth and Predication 5 | |
| A reaction: Put like this, the Russellian view strikes me as false. Effectively he is saying that a unified proposition is the same as a fact. I take a proposition to be a brain event, best labelled by Frege as a 'thought'. Thoughts may not even have parts. |
| 21724 | The main aim of the multiple relations theory of judgement was to dispense with propositions [Russell, by Linsky,B] |
| Full Idea: While the multiple relation theory (of belief, or of judgement) is nominally an account of belief and judgement, the emphasis in the account is on eliminating the need for propositions as objects of rational belief or judgement. | |
| From: report of Bertrand Russell (Problems of Philosophy [1912]) by Bernard Linsky - Russell's Metaphysical Logic 7.2 | |
| A reaction: The idea is that the mind relates directly with the ingredients of the proposition, and with the universals (such as relations) which connect them. He cuts out the middle man, just as he cut out sense-data, for similar reasons of economy. |
| 11240 | The notion of analytic truth is absent in Aristotle [Aristotle, by Politis] |
| Full Idea: The notion of analytic truth is conspicuously absent in Aristotle. | |
| From: report of Aristotle (works [c.330 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.5 | |
| A reaction: Cf. Idea 11239. |
| 6559 | Aristotle never actually says that man is a rational animal [Aristotle, by Fogelin] |
| Full Idea: To the best of my knowledge (and somewhat to my surprise), Aristotle never actually says that man is a rational animal; however, he all but says it. | |
| From: report of Aristotle (works [c.330 BCE]) by Robert Fogelin - Walking the Tightrope of Reason Ch.1 | |
| A reaction: When I read this I thought that this database would prove Fogelin wrong, but it actually supports him, as I can't find it in Aristotle either. Descartes refers to it in Med.Two. In Idea 5133 Aristotle does say that man is a 'social being'. But 22586! |
| 5398 | Judgements of usefulness depend on judgements of value [Russell] |
| Full Idea: All judgements as to what is useful depend upon some judgement as to what has value on its own account. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 7) | |
| A reaction: This is a beautifully simple point to be made about utilitarianism. The notion that pleasure is the sole good is prior, and the first two sentences in Bentham totally beg that question. What is the value of pleasure? Is it wicked to turn down a pleasure? |
| 11150 | It is the mark of an educated mind to be able to entertain an idea without accepting it [Aristotle] |
| Full Idea: It is the mark of an educated mind to be able to entertain an idea without accepting it. | |
| From: Aristotle (works [c.330 BCE]) | |
| A reaction: The epigraph on a David Chalmers website. A wonderful remark, and it should be on the wall of every beginners' philosophy class. However, while it is in the spirit of Aristotle, it appears to be a misattribution with no ancient provenance. |
| 3037 | Aristotle said the educated were superior to the uneducated as the living are to the dead [Aristotle, by Diog. Laertius] |
| Full Idea: Aristotle was asked how much educated men were superior to those uneducated; "As much," he said, "as the living are to the dead." | |
| From: report of Aristotle (works [c.330 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 05.1.11 |
| 8660 | There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend] |
| Full Idea: Aristotle developed his own distinction between potential infinity (never running out) and actual infinity (there being a collection of an actual infinite number of things, such as places, times, objects). He decided that actual infinity was incoherent. | |
| From: report of Aristotle (works [c.330 BCE]) by Michèle Friend - Introducing the Philosophy of Mathematics 1.3 | |
| A reaction: Friend argues, plausibly, that this won't do, since potential infinity doesn't make much sense if there is not an actual infinity of things to supply the demand. It seems to just illustrate how boggling and uncongenial infinity was to Aristotle. |
| 12058 | Aristotle's matter can become any other kind of matter [Aristotle, by Wiggins] |
| Full Idea: Aristotle's conception of matter permits any kind of matter to become any other kind of matter. | |
| From: report of Aristotle (works [c.330 BCE]) by David Wiggins - Substance 4.11.2 | |
| A reaction: This is obviously crucial background information when we read Aristotle on matter. Our 92+ elements, and fixed fundamental particles, gives a quite different picture. Aristotle would discuss form and matter quite differently now. |
| 14175 | We can drop 'cause', and just make inferences between facts [Russell] |
| Full Idea: On the whole it is not worthwhile preserving the word 'cause': it is enough to say, what is far less misleading, that any two configurations allow us to infer any other. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §460) | |
| A reaction: Russell spelled this out fully in a 1912 paper. This sounds like David Hume, but he prefers to talk of 'habit' rather than 'inference', which might contain a sneaky necessity. |
| 14172 | Moments and points seem to imply other moments and points, but don't cause them [Russell] |
| Full Idea: Some people would hold that two moments of time, or two points of space, imply each other's existence; yet the relation between these cannot be said to be causal. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §449) | |
| A reaction: Famously, Russell utterly rejected causation a few years after this. The example seems clearer if you say that two points or moments can imply at least one point or instant between them, without causing them. |
| 14174 | The laws of motion and gravitation are just parts of the definition of a kind of matter [Russell] |
| Full Idea: For us, as pure mathematicians, the laws of motion and the law of gravitation are not properly laws at all, but parts of the definition of a certain kind of matter. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §459) | |
| A reaction: The 'certain kind of matter' is that which has 'mass'. Since these are paradigm cases of supposed laws, this is the beginning of the end for real laws of nature, and good riddance say I. See Mumford on this. |
| 5393 | We can't know that our laws are exceptionless, or even that there are any laws [Russell] |
| Full Idea: If some law which has no exceptions applies to a case, we can never be sure that we have discovered that law and not one to which there are exceptions; also the reign of law would seem to be itself only probable. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 6) | |
| A reaction: None of this can be denied. In modern physics, several supposed laws have come up for question. Is the proton stable? Are the gravitational constant or the speed of light necessarily fixed? Russell is doing epistemology. How do we conceive the laws? |
| 14168 | Occupying a place and change are prior to motion, so motion is just occupying places at continuous times [Russell] |
| Full Idea: The concept of motion is logically subsequent to that of occupying as place at a time, and also to that of change. Motion is the occupation, by one entity, of a continuous series of places at a continuous series of times. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §442) | |
| A reaction: This is Russell's famous theory of motion, which came to be called the 'At-At' theory (at some place at some time). It seems to mathematically pin down motion all right, but seems a bit short on the poetry of the thing. |
| 14171 | Force is supposed to cause acceleration, but acceleration is a mathematical fiction [Russell] |
| Full Idea: A force is the supposed cause of acceleration, ...but an acceleration is a mere mathematical fiction, a number, not a physical fact. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §448) | |
| A reaction: This rests on his at-at theory of motion, in Idea 14168. I'm not sure that if I fell off a cliff I could be reassured on the way down that my acceleration was just a mathematical fiction. |
| 14160 | Space is the extension of 'point', and aggregates of points seem necessary for geometry [Russell] |
| Full Idea: I won't discuss whether points are unities or simple terms, but whether space is an aggregate of them. ..There is no geometry without points, nothing against them, and logical reasons in their favour. Space is the extension of the concept 'point'. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §423) |
| 14156 | Mathematicians don't distinguish between instants of time and points on a line [Russell] |
| Full Idea: To the mathematician as such there is no relevant distinction between the instants of time and the points on a line. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §387) | |
| A reaction: This is the germ of the modern view of space time, which is dictated by the mathematics, rather than by our intuitions or insights into what is actually going on. |
| 14169 | The 'universe' can mean what exists now, what always has or will exist [Russell] |
| Full Idea: The universe is a somewhat ambiguous term: it may mean all the things that exist at a single moment, or all things that ever have existed or will exist, or the common quality of whatever exists. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §442) |
| 22729 | The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus] |
| Full Idea: Aristotle said that the conception of gods arose among mankind from two originating causes, namely from events which concern the soul and from celestial phenomena. | |
| From: report of Aristotle (works [c.330 BCE], Frag 10) by Sextus Empiricus - Against the Physicists (two books) I.20 | |
| A reaction: The cosmos suggests order, and possible creation. What do events of the soul suggest? It doesn't seem to be its non-physical nature, because Aristotle is more of a functionalist. Puzzling. (It says later that gods are like the soul). |