78 ideas
| 6575 | Philosophy may never find foundations, and may undermine our lives in the process [Fogelin] |
| Full Idea: Not only is traditional philosophy incapable of discovering the foundations it seeks, but the philosophical enterprise may itself dislodge the contingent, de facto supports that our daily life depends upon. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.2) | |
| A reaction: In the end Fogelin is not so pessimistic, but he is worried by the concern of philosophers with paradox and contradiction. I don't remotely consider this a reason to reject philosophy, but it might be a reason to keep it sealed off from daily life. |
| 14456 | 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [Russell] |
| Full Idea: The is of 'Socrates is human' expresses the relation of subject and predicate; the is of 'Socrates is a man' expresses identity. It is a disgrace to the human race that it employs the same word 'is' for these entirely different ideas. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVI) | |
| A reaction: Does the second one express identity? It sounds more like membership to me. 'Socrates is the guy with the hemlock' is more like identity. |
| 6601 | Science rules the globe because of colonising power, not inherent rationality [Feyerabend] |
| Full Idea: Science now reigns supreme all over the globe; but the reason was not insight in its 'inherent rationality' but power play (the colonising nations imposed their way of living) and the need for weapons. | |
| From: Paul Feyerabend (Against Method [1975], 3), quoted by Robert Fogelin - Walking the Tightrope of Reason Ch.5 | |
| A reaction: A nice clear statement of ridiculous relativism about science. What gave the colonisers their power if it was not more accurate knowledge of how to manipulate nature? |
| 6585 | Rationality is threatened by fear of inconsistency, illusions of absolutes or relativism, and doubt [Fogelin] |
| Full Idea: The three main threats to our rational lives are fear of inconsistency, illusions (of absolutism and relativism) and doubt. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.4) | |
| A reaction: This is a very nice analysis of the forces that can destroy the philosopher's aspiration to the rational life. Personally I still suffer from a few illusions about the possibility of absolutes, but I may grow out of it. The other three don't bother me. |
| 6557 | Humans may never be able to attain a world view which is both rich and consistent [Fogelin] |
| Full Idea: It might be wholly unreasonable to suppose that human beings will ever be able to attain a view of the world that is both suitably rich and completely consistent. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Intro) | |
| A reaction: Fogelin's lectures develop this view very persuasively. I think all philosophers must believe that the gods could attain a 'rich and consistent' view. Our problem is that we are a badly organised team, whose members keep dying. |
| 6568 | A game can be played, despite having inconsistent rules [Fogelin] |
| Full Idea: The presence of an inconsistency in the rules that govern a game need not destroy the game. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.2) | |
| A reaction: He only defends this thesis if the inconsistency is away from the main centre of the action. You can't have an inconsistent definition of scoring a goal or a touchdown. |
| 6560 | The law of noncontradiction is traditionally the most basic principle of rationality [Fogelin] |
| Full Idea: Traditionally many philosophers (Aristotle among them) have considered the law of noncontradiction to be the deepest, most fundamental principle of rationality. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.1) | |
| A reaction: For Aristotle, see Idea 1601 (and 'Metaphysics' 1005b28). The only denier of the basic character of the law that I know of is Nietzsche (Idea 4531). Fogelin, despite many qualifications, endorses the law, and so do I. |
| 6565 | The law of noncontradiction makes the distinction between asserting something and denying it [Fogelin] |
| Full Idea: People who reject the law of noncontradiction obliterate any significant difference between asserting something and denying it; …this will not move anyone who genuinely opts either for silence or for madness. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.1) | |
| A reaction: This seems a sufficiently firm and clear assertion of the basic nature of this law. The only rival view seems to be that of Nietzsche (Idea 4531), but then you wonder how Nietzsche is in a position to assert the relativity of the law. |
| 14426 | A definition by 'extension' enumerates items, and one by 'intension' gives a defining property [Russell] |
| Full Idea: The definition of a class or collection which enumerates is called a definition by 'extension', and one which mentions a defining property is called a definition by 'intension'. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], II) | |
| A reaction: In ordinary usage we take intensional definitions for granted, so it is interesting to realise that you might define 'tiger' by just enumerating all the tigers. But all past tigers? All future tigers? All possible tigers which never exist? |
| 6574 | Legal reasoning is analogical, not deductive [Fogelin] |
| Full Idea: There is almost universal agreement that legal reasoning is fundamentally analogical, not deductive, in character. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.2) | |
| A reaction: This raises the question of whether analogy can be considered as 'reasoning' in itself. How do you compare the examples? Could you compare two examples if you lacked language, or rules, or a scale of values? |
| 8468 | The sentence 'procrastination drinks quadruplicity' is meaningless, rather than false [Russell, by Orenstein] |
| Full Idea: Russell proposed (in his theory of types) that sentences like 'The number two is fond of cream cheese' or 'Procrastination drinks quadruplicity' should be regarded as not false but meaningless. | |
| From: report of Bertrand Russell (Introduction to Mathematical Philosophy [1919]) by Alex Orenstein - W.V. Quine Ch.3 | |
| A reaction: This seems to be the origin of the notion of a 'category mistake', which Ryle made famous. The problem is always poetry, where abstractions can be reified, or personified, and meaning can be squeezed out of almost anything. |
| 14454 | An argument 'satisfies' a function φx if φa is true [Russell] |
| Full Idea: We say that an argument a 'satisfies' a function φx if φa is true. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XV) | |
| A reaction: We end up with Tarski defining truth in terms of satisfaction, so we shouldn't get too excited about what he achieved (any more than he got excited). |
| 14453 | The Darapti syllogism is fallacious: All M is S, all M is P, so some S is P' - but if there is no M? [Russell] |
| Full Idea: Some moods of the syllogism are fallacious, e.g. 'Darapti': 'All M is S, all M is P, therefore some S is P', which fails if there is no M. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XV) | |
| A reaction: This critique rests on the fact that the existential quantifier entails some existence, but the universal quantifier does not. |
| 14427 | We can enumerate finite classes, but an intensional definition is needed for infinite classes [Russell] |
| Full Idea: We know a great deal about a class without enumerating its members …so definition by extension is not necessary to knowledge about a class ..but enumeration of infinite classes is impossible for finite beings, so definition must be by intension. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], II) | |
| A reaction: Presumably mathematical induction (which keeps apply the rule to extend the class) will count as an intension here. |
| 14428 | Members define a unique class, whereas defining characteristics are numerous [Russell] |
| Full Idea: There is only one class having a given set of members, whereas there are always many different characteristics by which a given class may be defined. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], II) |
| 14447 | Infinity says 'for any inductive cardinal, there is a class having that many terms' [Russell] |
| Full Idea: The Axiom of Infinity may be enunciated as 'If n be any inductive cardinal number, there is at least one class of individuals having n terms'. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XIII) | |
| A reaction: So for every possible there exists a set of terms for it. Notice that they are 'terms', not 'objects'. We must decide whether we are allowed terms which don't refer to real objects. |
| 14440 | We may assume that there are infinite collections, as there is no logical reason against them [Russell] |
| Full Idea: There is no logical reason against infinite collections, and we are therefore justified, in logic, in investigating the hypothesis that there are such collections. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], VIII) |
| 14443 | The British parliament has one representative selected from each constituency [Russell] |
| Full Idea: We have a class of representatives, who make up our Parliament, one being selected out of each constituency. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XII) | |
| A reaction: You can rely on Russell for the clearest illustrations of these abstract ideas. He calls the Axiom of Choice the 'Multiplicative' Axiom. |
| 14445 | Choice shows that if any two cardinals are not equal, one must be the greater [Russell] |
| Full Idea: The [Axiom of Choice] is also equivalent to the assumption that of any two cardinals which are not equal, one must be the greater. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XII) | |
| A reaction: It is illuminating for the uninitiated to learn that this result can't be taken for granted (with infinite cardinals). |
| 14444 | Choice is equivalent to the proposition that every class is well-ordered [Russell] |
| Full Idea: Zermelo has shown that [the Axiom of Choice] is equivalent to the proposition that every class is well-ordered, i.e. can be arranged in a series in which every sub-class has a first term (except, of course, the null class). | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XII) | |
| A reaction: Russell calls Choice the 'Multiplicative' Axiom. |
| 14446 | We can pick all the right or left boots, but socks need Choice to insure the representative class [Russell] |
| Full Idea: Among boots we distinguish left and right, so we can choose all the right or left boots; with socks no such principle suggests itself, and we cannot be sure, without the [Axiom of Choice], that there is a class consisting of one sock from each pair. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XII) | |
| A reaction: A deservedly famous illustration of a rather tricky part of set theory. |
| 14459 | Reducibility: a family of functions is equivalent to a single type of function [Russell] |
| Full Idea: The Axiom of Reducibility says 'There is a type of a-functions such that, given any a-function, it is formally equivalent to some function of the type in question'. ..It involves all that is really essential in the theory of classes. But is it true? | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVII) | |
| A reaction: I take this to say that in the theory of types, it is possible to reduce each level of type down to one type. |
| 14461 | Propositions about classes can be reduced to propositions about their defining functions [Russell] |
| Full Idea: It is right (in its main lines) to say that there is a reduction of propositions nominally about classes to propositions about their defining functions. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVII) | |
| A reaction: The defining functions will involve the theory of types, in order to avoid the paradoxes of naïve set theory. This is Russell's strategy for rejecting the existence of sets. |
| 8469 | Russell's proposal was that only meaningful predicates have sets as their extensions [Russell, by Orenstein] |
| Full Idea: Russell's solution (in the theory of types) consists of restricting the principle that every predicate has a set as its extension so that only meaningful predicates have sets as their extensions. | |
| From: report of Bertrand Russell (Introduction to Mathematical Philosophy [1919]) by Alex Orenstein - W.V. Quine Ch.3 | |
| A reaction: There might be a chicken-and-egg problem here. How do you decide the members of a set (apart from ostensively) without deciding the predicate(s) that combine them? |
| 8745 | Classes are logical fictions, and are not part of the ultimate furniture of the world [Russell] |
| Full Idea: The symbols for classes are mere conveniences, not representing objects called 'classes'. Classes are in fact logical fictions; they cannot be regarded as part of the ultimate furniture of the world. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], Ch.18), quoted by Stewart Shapiro - Thinking About Mathematics 5.2 | |
| A reaction: I agree. For 'logical fictions' read 'abstractions'. To equate abstractions with fictions is to underline the fact that they are a human creation. They are either that or platonic objects - there is no middle way. |
| 14452 | All the propositions of logic are completely general [Russell] |
| Full Idea: It is part of the definition of logic that all its propositions are completely general. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XV) |
| 14462 | In modern times, logic has become mathematical, and mathematics has become logical [Russell] |
| Full Idea: Logic has become more mathematical, and mathematics has become more logical. The consequence is that it has now become wholly impossible to draw a line between the two; in fact, the two are one. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVIII) | |
| A reaction: This appears to be true even if you reject logicism about mathematics. Logicism is sometimes rejected because it always ends up with a sneaky ontological commitment, but maybe mathematics shares exactly the same commitment. |
| 10057 | Logic can only assert hypothetical existence [Russell] |
| Full Idea: No proposition of logic can assert 'existence' except under a hypothesis. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVIII) | |
| A reaction: I am prepared to accept this view fairly dogmatically, though Musgrave shows some of the difficulties of the if-thenist view (depending on which 'order' of logic is being used). |
| 12444 | Logic is concerned with the real world just as truly as zoology [Russell] |
| Full Idea: Logic is concerned with the real world just as truly as zoology, though with its more abstract and general features. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVI) | |
| A reaction: I love this idea and am very sympathetic to it. The rival view seems to be that logic is purely conventional, perhaps defined by truth tables etc. It is hard to see how a connective like 'tonk' could be self-evidently silly if it wasn't 'unnatural'. |
| 14464 | Logic can be known a priori, without study of the actual world [Russell] |
| Full Idea: Logical propositions are such as can be known a priori, without study of the actual world. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVIII) | |
| A reaction: This remark constrasts strikingly with Idea 12444, which connects logic to the actual world. Is it therefore a priori synthetic? |
| 14458 | Asking 'Did Homer exist?' is employing an abbreviated description [Russell] |
| Full Idea: When we ask whether Homer existed, we are using the word 'Homer' as an abbreviated description. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVI) | |
| A reaction: It is hard to disagree with Russell over this rather unusual example. It doesn't seem so plausible when Ottiline refers to 'Bertie'. |
| 10450 | Russell admitted that even names could also be used as descriptions [Russell, by Bach] |
| Full Idea: Russell clearly anticipated Donnellan when he said proper names can also be used as descriptions, adding that 'there is nothing in the phraseology to show whether they are being used in this way or as names'. | |
| From: report of Bertrand Russell (Introduction to Mathematical Philosophy [1919], p.175) by Kent Bach - What Does It Take to Refer? 22.2 L1 | |
| A reaction: This seems also to anticipate Strawson's flexible and pragmatic approach to these things, which I am beginning to think is correct. |
| 14457 | Names are really descriptions, except for a few words like 'this' and 'that' [Russell] |
| Full Idea: We can even say that, in all such knowledge as can be expressed in words, with the exception of 'this' and 'that' and a few other words of which the meaning varies on different occasions - no names occur, but what seem like names are really descriptions. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVI) | |
| A reaction: I like the caveat about what is expressed in words. Russell is very good at keeping non-verbal thought in the picture. This is his famous final reduction of names to simple demonstratives. |
| 7311 | The only genuine proper names are 'this' and 'that' [Russell] |
| Full Idea: In all knowledge that can be expressed in words - with the exception of "this" and "that", and a few other such words - no genuine proper names occur, but what seem like genuine proper names are really descriptions | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVI) | |
| A reaction: This is the terminus of Russell's train of thought about descriptions. Suppose you point to something non-existent, like a ghost in a misty churchyard? You'd be back to the original problem of naming a non-existent! |
| 14455 | 'I met a unicorn' is meaningful, and so is 'unicorn', but 'a unicorn' is not [Russell] |
| Full Idea: In 'I met a unicorn' the four words together make a significant proposition, and the word 'unicorn' is significant, …but the two words 'a unicorn' do not form a group having a meaning of its own. It is an indefinite description describing nothing. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVI) |
| 14442 | If straight lines were like ratios they might intersect at a 'gap', and have no point in common [Russell] |
| Full Idea: We wish to say that when two straight lines cross each other they have a point in common, but if the series of points on a line were similar to the series of ratios, the two lines might cross in a 'gap' and have no point in common. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], X) | |
| A reaction: You can make a Dedekind Cut in the line of ratios (the rationals), so there must be gaps. I love this idea. We take for granted intersection at a point, but physical lines may not coincide. That abstract lines might fail also is lovely! |
| 14438 | New numbers solve problems: negatives for subtraction, fractions for division, complex for equations [Russell] |
| Full Idea: Every generalisation of number has presented itself as needed for some simple problem. Negative numbers are needed to make subtraction always possible; fractions to make division always possible; complex numbers to make solutions of equations possible. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], VII) | |
| A reaction: Doesn't this rather suggest that we made them up? If new problems turn up, we'll invent another lot. We already have added 'surreal' numbers. |
| 13510 | Could a number just be something which occurs in a progression? [Russell, by Hart,WD] |
| Full Idea: Russell toyed with the idea that there is nothing to being a natural number beyond occurring in a progression | |
| From: report of Bertrand Russell (Introduction to Mathematical Philosophy [1919], p.8) by William D. Hart - The Evolution of Logic 5 | |
| A reaction: How could you define a progression, without a prior access to numbers? - Arrange all the objects in the universe in ascending order of mass. Use scales to make the selection. Hence a finite progression, with no numbers! |
| 14436 | A series can be 'Cut' in two, where the lower class has no maximum, the upper no minimum [Russell] |
| Full Idea: There is no maximum to the ratios whose square is less than 2, and no minimum to those whose square is greater than 2. This division of a series into two classes is called a 'Dedekind Cut'. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], VII) |
| 14439 | A complex number is simply an ordered couple of real numbers [Russell] |
| Full Idea: A complex number may be regarded and defined as simply an ordered couple of real numbers | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], VII) |
| 14421 | Discovering that 1 is a number was difficult [Russell] |
| Full Idea: The discovery that 1 is a number must have been difficult. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], I) | |
| A reaction: Interesting that he calls it a 'discovery'. I am tempted to call it a 'decision'. |
| 14424 | Numbers are needed for counting, so they need a meaning, and not just formal properties [Russell] |
| Full Idea: We want our numbers to be such as can be used for counting common objects, and this requires that our numbers should have a definite meaning, not merely that they should have certain formal properties. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], I) | |
| A reaction: Why would just having certain formal properties be insufficient for counting? You just need an ordered series of unique items. It isn't just that we 'want' this. If you define something that we can't count with, you haven't defined numbers. |
| 14441 | The formal laws of arithmetic are the Commutative, the Associative and the Distributive [Russell] |
| Full Idea: The usual formal laws of arithmetic are the Commutative Law [a+b=b+a and axb=bxa], the Associative Law [(a+b)+c=a+(b+c) and (axb)xc=ax(bxc)], and the Distributive Law [a(b+c)=ab+ac)]. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], IX) |
| 14420 | Infinity and continuity used to be philosophy, but are now mathematics [Russell] |
| Full Idea: The nature of infinity and continuity belonged in former days to philosophy, but belongs now to mathematics. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], Pref) | |
| A reaction: It is hard to disagree, since mathematicians since Cantor have revealed so much about infinite numbers (through set theory), but I think it remains an open question whether philosophers have anything distinctive to contribute. |
| 14431 | The definition of order needs a transitive relation, to leap over infinite intermediate terms [Russell] |
| Full Idea: Order must be defined by means of a transitive relation, since only such a relation is able to leap over an infinite number of intermediate terms. ...Without it we would not be able to define the order of magnitude among fractions. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], IV) |
| 14422 | Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms [Russell] |
| Full Idea: Given any series which is endless, contains no repetitions, has a beginning, and has no terms that cannot be reached from the beginning in a finite number of steps, we have a set of terms verifying Peano's axioms. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], I) |
| 14423 | '0', 'number' and 'successor' cannot be defined by Peano's axioms [Russell] |
| Full Idea: That '0', 'number' and 'successor' cannot be defined by means of Peano's five axioms, but must be independently understood. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], I) |
| 14425 | A number is something which characterises collections of the same size [Russell] |
| Full Idea: The number 3 is something which all trios have in common, and which distinguishes them from other collections. A number is something that characterises certain collections, namely, those that have that number. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], II) | |
| A reaction: This is a verbal summary of the Fregean view of numbers, which marks the arrival of set theory as the way arithmetic will in future be characterised. The question is whether set theory captures all aspects of numbers. Does it give a tool for counting? |
| 14434 | What matters is the logical interrelation of mathematical terms, not their intrinsic nature [Russell] |
| Full Idea: What matters in mathematics is not the intrinsic nature of our terms, but the logical nature of their interrelations. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], VI) | |
| A reaction: If they have an instrinsic nature, that would matter far more, because that would dictate the interrelations. Structuralism seems to require that they don't actually have any intrinsic nature. |
| 14465 | Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men' [Russell] |
| Full Idea: 'Ten men' is grammatically the same form as 'white men', so that 10 might be thought to be an adjective qualifying 'men'. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVIII) | |
| A reaction: The immediate problem, as Frege spotted, is that such expressions can be rephrased to remove the adjective (by saying 'the number of men is ten'). |
| 13414 | For Russell, numbers are sets of equivalent sets [Russell, by Benacerraf] |
| Full Idea: Russell's own stand was that numbers are really only sets of equivalent sets. | |
| From: report of Bertrand Russell (Introduction to Mathematical Philosophy [1919]) by Paul Benacerraf - Logicism, Some Considerations (PhD) p.168 | |
| A reaction: Benacerraf is launching a nice attack on this view, based on our inability to grasp huge numbers on this basis, or to see their natural order. |
| 14449 | There is always something psychological about inference [Russell] |
| Full Idea: There is always unavoidably something psychological about inference. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XIV) | |
| A reaction: Glad to find Russell saying that. Only pure Fregeans dream of a logic that rises totally above the minds that think it. See Robert Hanna on the subject. |
| 14463 | Existence can only be asserted of something described, not of something named [Russell] |
| Full Idea: Existence can only be asserted of something described, not of something named. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVIII) | |
| A reaction: This is the motivation behind Russell's theory of definite descriptions, and epitomises the approach to ontology through language. Sounds wrong to me! |
| 14429 | Classes are logical fictions, made from defining characteristics [Russell] |
| Full Idea: Classes may be regarded as logical fictions, manufactured out of defining characteristics. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], II n1) | |
| A reaction: I agree with this. The idea that in addition to the members there is a further object, the set containing them, is absurd. Sets are a tool for thinking about the world. |
| 14430 | If a relation is symmetrical and transitive, it has to be reflexive [Russell] |
| Full Idea: It is obvious that a relation which is symmetrical and transitive must be reflexive throughout its domain. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], II) | |
| A reaction: Compare Idea 13543! The relation will return to its originator via its neighbours, rather than being directly reflexive? |
| 14432 | 'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a [Russell] |
| Full Idea: The relation of 'asymmetry' is incompatible with the converse. …The relation 'husband' is asymmetrical, so that if a is the husband of b, b cannot be the husband of a. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], V) | |
| A reaction: This is to be contrasted with 'non-symmetrical', where there just happens to be no symmetry. |
| 14435 | The essence of individuality is beyond description, and hence irrelevant to science [Russell] |
| Full Idea: The essence of individuality always eludes words and baffles description, and is for that very reason irrelevant to science. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], VI) | |
| A reaction: [context needed for a full grasp of this idea] Russell seems to refer to essence as much as to individuality. The modern essentialist view is that essences are not beyond description after all. Fundamental physics is clearer now than in 1919. |
| 12197 | Inferring q from p only needs p to be true, and 'not-p or q' to be true [Russell] |
| Full Idea: In order that it be valid to infer q from p, it is only necessary that p should be true and that the proposition 'not-p or q' should be true. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XIV) | |
| A reaction: Rumfitt points out that this approach to logical consequences is a denial of any modal aspect, such as 'logical necessity'. Russell observes that for a good inference you must know the disjunction as a whole. Could disjunction be modal?... |
| 14450 | All forms of implication are expressible as truth-functions [Russell] |
| Full Idea: There is no need to admit as a fundamental notion any form of implication not expressible as a truth-function. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XIV) | |
| A reaction: Note that this is from a book about 'mathematical' philosophy. Nevertheless, it seems to have the form of a universal credo for Russell. He wasn't talking about conditionals here. Maybe conditionals are not implications (in isolation, that is). |
| 6582 | Conventions can only work if they are based on something non-conventional [Fogelin] |
| Full Idea: Convention, to exist at all, must have a basis in something that is not conventional; conventions, to work, need something nonconventional to build upon and shape. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.3) | |
| A reaction: Fogelin attributes his point to Hume. I agree entirely. No convention could ever possibly catch on in a society unless there were some point to it. If you can't see a point to a convention (like wearing ties) then start looking, because it's there. |
| 14460 | If something is true in all possible worlds then it is logically necessary [Russell] |
| Full Idea: Saying that the axiom of reducibility is logically necessary is what would be meant by saying that it is true in all possible worlds. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVII) | |
| A reaction: This striking remark is a nice bridge between Leibniz (about whom Russell wrote a book) and Kripke. |
| 6576 | My view is 'circumspect rationalism' - that only our intellect can comprehend the world [Fogelin] |
| Full Idea: My own view might be called 'circumspect rationalism' - the view that our intellectual faculties provide our only means for comprehending the world in which we find oruselves. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.3) | |
| A reaction: He needs to say more than that to offer a theory, but I like the label, and it fits the modern revival of rationalism, with which I sympathise, and which rests, I think, on Russell's point that self-evidence comes in degrees, not as all-or-nothing truth. |
| 6589 | Knowledge is legitimate only if all relevant defeaters have been eliminated [Fogelin] |
| Full Idea: In general a knowledge claim is legitimate only if all relevant defeaters have been eliminated. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.4) | |
| A reaction: The problem here is what is 'relevant'. Fogelin's example is 'Are you sure the suspect doesn't have a twin brother?' If virtual reality is relevant, most knowledge is defeated. Certainly, imaginative people feel that they know less than others. |
| 6596 | For coherentists, circularity is acceptable if the circle is large, rich and coherent [Fogelin] |
| Full Idea: Coherentists argue that if the circle of justifications is big enough, rich enough, coherent enough, and so on, then there is nothing wrong circularity. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.4) | |
| A reaction: There must always be something wrong with circularity, and no god would put up with it, but we might have to. Of course, two pieces of evidence might be unconnected, such as an equation and an observation. |
| 6597 | A rule of justification might be: don't raise the level of scrutiny without a good reason [Fogelin] |
| Full Idea: One rule for the justification of knowledge might be: Do not raise the level of scrutiny in the absence of a particular reason that triggers it. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.4) | |
| A reaction: That won't decide the appropriate level of scrutiny from which to start. One of my maxims is 'don't set the bar too high', but it seems tough that one should have to justify moving it. The early scientists tried raising it, and were amazed by the results. |
| 6588 | Scepticism is cartesian (sceptical scenarios), or Humean (future), or Pyrrhonian (suspend belief) [Fogelin] |
| Full Idea: The three forms of scepticism are cartesian, Humean and Pyrrhonian. The first challenges belief by inventing sceptical scenarios; the second doubts the future; the third aims to suspend belief. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.4) | |
| A reaction: A standard distinction is made between methodological and global scepticism. The former seems to be Cartesian, and the latter Pyrrhonian. The interest here is see Hume placed in a distinctive category, because of his views on induction. |
| 6590 | Scepticism deals in remote possibilities that are ineliminable and set the standard very high [Fogelin] |
| Full Idea: Sceptical scenarios deal in wildly remote defeating possibilities, so that the level of scrutiny becomes unrestrictedly high, and they also usually deal with defeators that are in principle ineliminable. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.4) | |
| A reaction: The question of how high we 'set the bar' seems to me central to epistemology. There is clearly an element of social negotiation involved, centring on what is appropriate. If, though, scepticism is 'ineliminable', we must face up to that. |
| 6583 | Radical perspectivism replaces Kant's necessary scheme with many different schemes [Fogelin] |
| Full Idea: We reach radical perspectivism by replacing Kant's single, necessary categorial scheme with a plurality of competing categorial schemes. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.3) | |
| A reaction: It certainly looks as if Kant sent us down a slippery slope into the dafter aspects of twentieth century relativism. The best antidote I know of is Davidson's (e.g. Idea 6398). But then it seems unimaginative to say that only one scheme is possible. |
| 14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
| Full Idea: We know that certain scientific propositions - often expressed in mathematical symbols - are more or less true of the world, but we are very much at sea as to the interpretation to be put upon the terms which occur in these propositions. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], VI) | |
| A reaction: Enter essentialism, say I! Russell's remark is pretty understandable in 1919, but I don't think the situation has changed much. The problem of interpretation may be of more interest to philosophers than to physicists. |
| 2561 | For Feyerabend the meaning of a term depends on a whole theory [Feyerabend, by Rorty] |
| Full Idea: For Feyerabend the meaning of a term depends on a whole theory containing the term. | |
| From: report of Paul Feyerabend (Against Method [1975]) by Richard Rorty - Philosophy and the Mirror of Nature 6.3 |
| 6555 | We are also irrational, with a unique ability to believe in bizarre self-created fictions [Fogelin] |
| Full Idea: We as human beings are also irrational animals, unique among animals in our capacity to place faith in bizarre fictions of our own construction. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Intro) | |
| A reaction: This is glaringly true, and a very nice corrective to the talk of Greeks and others about man as the 'rational animal'. From a distance we might be described by Martians as the 'mad animal'. Is the irrational current too strong to swim against? |
| 14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
| Full Idea: We mean by 'proposition' primarily a form of words which expresses what is either true or false. I say 'primarily' because I do not wish to exclude other than verbal symbols, or even mere thoughts if they have a symbolic character. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XV) | |
| A reaction: I like the last bit, as I think of propositions as pre-verbal thoughts, and I am sympathetic to Fodor's 'language of thought' thesis, that there is a system of representations within the brain. |
| 6605 | Critics must be causally entangled with their subject matter [Fogelin] |
| Full Idea: Critics must become causally entangled with their subject matter. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.6) | |
| A reaction: This remark is built on Hume's views. You may have a strong view about a singer, but it may be hard to maintain when someone plays you six rival versions of the same piece. I agree entirely with the remark. It means there are aesthetic experts. |
| 6607 | The word 'beautiful', when deprived of context, is nearly contentless [Fogelin] |
| Full Idea: Like the word 'good', the word 'beautiful', when deprived of contextual support, is nearly contentless. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.6) | |
| A reaction: If I say with, for example, Oscar Wilde that beauty is the highest ideal in life, this doesn't strike me as contentless, but I still sympathise with Fogelin's notion that beauty is rooted in particulars. |
| 6604 | Saying 'It's all a matter to taste' ignores the properties of the object discussed [Fogelin] |
| Full Idea: "It is all a matter of taste" may be an all-purpose stopper of discussions of aesthetic values, but it also completely severs the connection with the actual properties of the object under consideration. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.6) | |
| A reaction: This remark grows out of his discussion of Hume. I like this remark, which ties in with Particularism in morality, and with the central role of experiments in science. The world forces beliefs on us. |
| 6586 | Cynics are committed to morality, but disappointed or disgusted by human failings [Fogelin] |
| Full Idea: Cynics are usually unswerving in their commitment to a moral ideal, but disappointed or disgusted by humanity's failure to meet it. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.3) | |
| A reaction: I felt quite suicidal the other day when I saw someone park diagonally across two parking spaces. They can't seem to grasp the elementary Kantian slogan 'What if everybody did that?' It's all hopeless. I wonder if I am becoming a bit of a Cynic? |
| 6572 | Deterrence, prevention, rehabilitation and retribution can come into conflict in punishments [Fogelin] |
| Full Idea: The purposes of punishment include deterrence, prevention, rehabilitation, and retribution, but they don't always sit well together. Deterrence is best served by making prisons miserable places, but this may run counter to rehabilitation. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.2) | |
| A reaction: It seems to most educated people that retribution should be pushed far down the list if we are to be civilised (see Idea 1659), and yet personal revenge for a small act of aggression seems basic, normal and acceptable. We dream of rehabilitation. |
| 6573 | Retributivists say a crime can be 'paid for'; deterrentists still worry about potential victims [Fogelin] |
| Full Idea: A strict retributivist is likely to say that once a crime is paid for, that's that; a deterrence theorist is likely to say that the protection of potential victims overrides the released convict's right to a free and fresh start. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.2) | |
| A reaction: Interesting since the retributivist here has the more liberal attitude. Reformists will also have a dilemma when years in prison have failed to reform the convict. Virtue theorists like balance, and sensitively consider our relations with the criminals. |