87 ideas
| 7950 | Philosophy tries to explain how the actual is possible, given that it seems impossible [Macdonald,C] |
| Full Idea: Philosophical problems are problems about how what is actual is possible, given that what is actual appears, because of some faulty argument, to be impossible. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: [She is discussing universals when she makes this comment] A very appealing remark, given that most people come into philosophy because of a mixture of wonder and puzzlement. It is a rather Wittgensteinian view, though, that we must cure our own ills. |
| 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. |
| 7923 | 'Did it for the sake of x' doesn't involve a sake, so how can ontological commitments be inferred? [Macdonald,C] |
| Full Idea: In 'She did it for the sake of her country' no one thinks that the expression 'the sake' refers to an individual thing, a sake. But given that, how can we work out what the ontological commitments of a theory actually are? | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.1) | |
| A reaction: For these sorts of reasons it rapidly became obvious that ordinary language analysis wasn't going to reveal much, but it is also a problem for a project like Quine's, which infers an ontology from the terms of a scientific theory. |
| 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? |
| 7933 | Don't assume that a thing has all the properties of its parts [Macdonald,C] |
| Full Idea: The fallacy of composition makes the erroneous assumption that every property of the things that constitute a thing is a property of the thing as well. But every large object is constituted by small parts, and every red object by colourless parts. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.5) | |
| A reaction: There are nice questions here like 'If you add lots of smallness together, why don't you get extreme smallness?' Colours always make bad examples in such cases (see Idea 5456). Distinctions are needed here (e.g. Idea 7007). |
| 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! |
| 7944 | Reduce by bridge laws (plus property identities?), by elimination, or by reducing talk [Macdonald,C] |
| Full Idea: There are four kinds of reduction: the identifying of entities of two theories by means of bridge or correlation laws; the elimination of entities in favour of the other theory; reducing by bridge laws and property identities; and merely reducing talk. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3 n5) | |
| A reaction: [She gives references] The idea of 'bridge laws' I regard with caution. If bridge laws are ceteris paribus, they are not much help, and if they are strict, or necessary, then there must be an underlying reason for that, which is probably elimination. |
| 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. |
| 7938 | Relational properties are clearly not essential to substances [Macdonald,C] |
| Full Idea: In statements attributing relational properties ('Felix is my favourite cat'), it seems clear that the property truly attributed to the substance is not essential to it. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: A fairly obvious point, but an important one when mapping out (cautiously) what we actually mean by 'property'. However, maybe the relational property is essential: the ceiling is ('is' of predication!) above the room. |
| 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. |
| 7967 | Being taller is an external relation, but properties and substances have internal relations [Macdonald,C] |
| Full Idea: The relation of being taller than is an external relation, since it relates two independent material substances, but the relation of instantiation or exemplification is internal, in that it relates a substance with a property. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: An interesting revival of internal relations. To be plausible it would need clear notions of 'property' and 'substance'. We are getting a long way from physics, and I sense Ockham stropping his Razor. How do you individuate a 'relation'? |
| 7965 | Does the knowledge of each property require an infinity of accompanying knowledge? [Macdonald,C] |
| Full Idea: An object's being two inches long seems to guarantee an infinite number of other properties, such as being less than three inches long. If we must understand the second property to understand the first, then there seems to be a vicious infinite regress. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.2) | |
| A reaction: She dismisses this by saying that we don't need to know an infinity of numbers in order to count. I would say that we just need to distinguish between intrinsic and relational properties. You needn't know all a thing's relations to know the thing. |
| 7934 | Tropes are abstract (two can occupy the same place), but not universals (they have locations) [Macdonald,C] |
| Full Idea: Tropes are abstract entities, at least in the sense that more than one can be in the same place at the same time (e.g. redness and roundness). But they are not universals, because they have unique and particular locations. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: I'm uneasy about the reification involved in this kind of talk. Does a coin possess a thing called 'roundness', which then has to be individuated, identified and located? I am drawn to the two extreme views, and suspicious of compromise. |
| 7958 | Properties are sets of exactly resembling property-particulars [Macdonald,C] |
| Full Idea: Trope Nominalism says properties are classes or sets of exactly similar or resembling tropes, where tropes are what we might called 'property-tokens' or 'particularized properties'. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: We still seem to have the problem of 'resembling' here, and we certainly have the perennial problem of why any given particular should be placed in any particular set. See Idea 7959. |
| 7972 | Tropes are abstract particulars, not concrete particulars, so the theory is not nominalist [Macdonald,C] |
| Full Idea: Trope 'Nominalism' is not a version of nominalism, because tropes are abstract particulars, rather than concrete particulars. Of course, a trope account of the relations between particulars and their properties has ramifications for concrete particulars. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6 n16) | |
| A reaction: Cf. Idea 7971. At this point the boundary between nominalist and realist theories seems to blur. Possibly that is bad news for tropes. Not many dilemmas can be solved by simply blurring the boundary. |
| 7959 | How do a group of resembling tropes all resemble one another in the same way? [Macdonald,C] |
| Full Idea: The problem is how a group of resembling tropes can be of the same type, that is, that they can resemble one another in the same way. This problem is not settled simply by positing tropes. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: There seems to be a fundamental fact that there is no resemblance unless the respect of resemblance is specified. Two identical objects could still said to be different because of their locations. Is resemblance natural or conventional? Consider atoms. |
| 7960 | Trope Nominalism is the only nominalism to introduce new entities, inviting Ockham's Razor [Macdonald,C] |
| Full Idea: Of all the nominalist solutions, Trope Nominalism is the only one that tries to solve the problem at issue by introducing entities; all the others try to get by with concrete particulars and sets of them. This might invite Ockham's Razor. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: We could reply that tropes are necessities. The issue seems to be a key one, which is whether our fundamental onotology should include properties (in some form or other). I am inclined to exclude them (Ideas 3322, 3906, 4029). |
| 7951 | Numerical sameness is explained by theories of identity, but what explains qualitative identity? [Macdonald,C] |
| Full Idea: We can distinguish between numerical identity and qualitative identity. Numerical sameness is explained by a theory of identity, but what explains qualitative sameness? | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: The distinction is between type and token identity. Tokens are particulars, and types are sets, so her question comes down to the one of what entitles something to be a member of a set? Nothing, if sets are totally conventional, but they aren't. |
| 7964 | How can universals connect instances, if they are nothing like them? [Macdonald,C] |
| Full Idea: The 'one over many' problem is to explain how universals can unify their instances if they are wholly other than them. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: If universals are self-predicating (beauty is beautiful) then they have a massive amount in common, despite one being general. You then have the regress problem of explaining the beauty of the beautiful. Baffling regress, or baffling participation. |
| 7971 | Real Nominalism is only committed to concrete particulars, word-tokens, and (possibly) sets [Macdonald,C] |
| Full Idea: All real forms of Nominalism should hold that the only objects relevant to the explanation of generality are concrete particulars, words (i.e. word-tokens, not word-types), and perhaps sets. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6 n16) | |
| A reaction: The addition of sets seems controversial (see Idea 7970). The context is her rejection of the use of tropes in nominalist theories. I would doubt whether a theory still counted as nominalist if it admitted sets (e.g. Quine). |
| 7955 | Resemblance Nominalism cannot explain either new resemblances, or absence of resemblances [Macdonald,C] |
| Full Idea: Resemblance Nominalism cannot explain the fact that we know when and in what way new objects resemble old ones, and that we know when and in what ways new objects do not resemble old ones. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: It is not clear what sort of theory would be needed to 'explain' such a thing. Unless there is an explanation of resemblance waiting in the wings (beyond asserting that resemblance is a universal), then this is not a strong objection. |
| 7961 | A 'thing' cannot be in two places at once, and two things cannot be in the same place at once [Macdonald,C] |
| Full Idea: The so-called 'laws of thinghood' govern particulars, saying that one thing cannot be wholly present at different places at the same time, and two things cannot occupy the same place at the same time. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: Is this an empirical observation, or a tautology? Or might it even be a priori synthetic? What happens when two water drops or clouds merge? Or an amoeba fissions? In what sense is an image in two places at once? Se also Idea 2351. |
| 7926 | We 'individuate' kinds of object, and 'identify' particular specimens [Macdonald,C] |
| Full Idea: We can usefully refer to 'individuation conditions', to distinguish objects of that kind from objects not of that kind, and to 'identity conditions', to distinguish objects within that kind from one another. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.2) | |
| A reaction: So we individuate types or sets, and identify tokens or particulars. Sounds good. Should be in every philosopher's toolkit, and on every introductory philosophy course. |
| 7936 | Unlike bundles of properties, substances have an intrinsic unity [Macdonald,C] |
| Full Idea: Substances have a kind of unity that mere collocations of properties do not have, namely an instrinsic unity. So substances cannot be collocations - bundles - of properties. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: A team is a unity. Compare a similar thought, Idea 1395, about personal identity. How can something which is a pure unity have more than one property? What distinguishes substances? Why can't a substance have a certain property? |
| 7930 | The bundle theory of substance implies the identity of indiscernibles [Macdonald,C] |
| Full Idea: The bundle theory of substance requires unconditional commitment to the truth of the Principle of the Identity of Indiscernibles: that things that are alike with respect to all of their properties are identical. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: Since the identity of indiscernibles is very dubious (see Ideas 1365, 4476, 5746, 7928), this is bad news for the bundle theory. I suspect that all of these problems arise because no one seems to have a clear concept of a property. |
| 7932 | A phenomenalist cannot distinguish substance from attribute, so must accept the bundle view [Macdonald,C] |
| Full Idea: Commitment to the view that only what can be an object of possible sensory experience can exist eliminates the possibility of distinguishing between substance and attribute, leaving only one alternative, namely the bundle view. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: Phenomenalism strikes me as a paradigm case of confusing ontology with epistemology. Presumably physicists (even empiricist ones) are committed to the 'interior' of quarks and electrons, but no one expects to experience them. |
| 7937 | When we ascribe a property to a substance, the bundle theory will make that a tautology [Macdonald,C] |
| Full Idea: The bundle theory makes all true statements ascribing properties to substances uninformative, by making them logical truths. The property of being a feline animal is literally a constituent of a cat. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: The solution would seem to a distinction between accidental and essential properties. Compare 'that plane is red' with 'that plane has wings'. 'Of course it does - it's a plane'. We might still survive without a plane-substance. |
| 7939 | Substances persist through change, but the bundle theory says they can't [Macdonald,C] |
| Full Idea: Substances are capable of persisting through change, where this involves change in properties; but the bundle theory has the consequence that substances cannot survive change. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: Her example is an apple remaining an apple when it turns brown. It doesn't look, though, as if there is a precise moment when the apple-substance ceases. The end of an apple seems to be more a matter of a loss of crucial properties. |
| 7940 | A substance might be a sequence of bundles, rather than a single bundle [Macdonald,C] |
| Full Idea: Maybe a substance is not itself a bundle of properties, but a sum or sequence of bundles of properties, a bundle of bundles of properties (which 'perdures' rather than 'endures'). | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: There remains the problem of deciding when the bundle has drifted too far away from the original to perdure correctly. A caterpillar can turn into a butterfly (which is pretty bizarre!), but not into a cathedral. Why? She says this idea denies change. |
| 7948 | A statue and its matter have different persistence conditions, so they are not identical [Macdonald,C] |
| Full Idea: Because a statue and the lump of matter that constitute it have different persistence conditions, they are not identical. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.4) | |
| A reaction: Maybe being a statue is a relational property? All the relational properties of a thing will have different persistence conditions. Suppose I see a face in a bowl of sugar, and you don't? |
| 7929 | A substance is either a bundle of properties, or a bare substratum, or an essence [Macdonald,C] |
| Full Idea: The three main theories of substance are the bundle theory (Leibniz, Berkeley, Hume, Ayer), the bare substratum theory (Locke and Bergmann), and the essentialist theory. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: Macdonald defends the essentialist theory. The essentialist view immediately appeals to me. Properties must be OF something, and the something must have the power to produce properties. So there. |
| 7941 | Each substance contains a non-property, which is its substratum or bare particular [Macdonald,C] |
| Full Idea: A rival to the bundle theory says that, for each substance, there is a constituent of it that is not a property but is both essential and unique to it, this constituent being referred to as a 'bare particular' or 'substratum'. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: This doesn't sound promising. It is unclear what existence devoid of all properties could be like. How could it 'have' its properties if it was devoid of features (it seems to need property-hooks)? It is an ontological black hole. How do you prove it? |
| 7942 | The substratum theory explains the unity of substances, and their survival through change [Macdonald,C] |
| Full Idea: If there is a substratum or bare particular within a substance, this gives an explanation of the unity of substances, and it is something which can survive intact when a substance changes. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: [v. compressed wording] Many problems here. The one that strikes me is that when things change they sometimes lose their unity and identity, and that seems to be decided entirely from observation of properties, not from assessing the substratum. |
| 7943 | A substratum has the quality of being bare, and they are useless because indiscernible [Macdonald,C] |
| Full Idea: There seems to be no way of identifying a substratum as the bearer of qualities without qualifiying it as bare (having the property of being bare?), ..and they cannot be used to individuate things, because they are necessarily indiscernible. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: The defence would probably be a priori, claiming an axiomatic necessity for substrata in our thinking about the world, along with a denial that bareness is a property (any more than not being a contemporary of Napoleon is a property). |
| 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. |
| 7927 | At different times Leibniz articulated three different versions of his so-called Law [Macdonald,C] |
| Full Idea: There are three distinct versions of Leibniz's Law, all traced to remarks made by Leibniz: the Identity of Indiscernibles (same properties, same thing), the Indiscernibility of Identicals (same thing, same properties), and the Substitution Principle. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.2) | |
| A reaction: The best view seems to be to treat the second one as Leibniz's Law (and uncontroversially true), and the first one as being an interesting but dubious claim. |
| 7928 | The Identity of Indiscernibles is false, because it is not necessarily true [Macdonald,C] |
| Full Idea: One common argument to the conclusion that the Principle of the Identity of Indiscernibles is false is that it is not necessarily true. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.2 n32) | |
| A reaction: This sounds like a good argument. If you test the Principle with an example ('this butler is the murderer') then total identity does not seem to necessitate identity, though it strongly implies it (the butler may have a twin etc). |
| 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). |
| 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. |
| 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. |
| 7947 | In continuity, what matters is not just the beginning and end states, but the process itself [Macdonald,C] |
| Full Idea: What matters to continuity is not just the beginning and end states of the process by which a thing persists, perhaps through change, but the process itself. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.4) | |
| A reaction: This strikes me as being a really important insight. Compare Idea 4931. If this is the key to understanding mind and personal identity, it means that the concept of a 'process' must be a central issue in ontology. How do you individuate a process? |
| 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. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |