103 ideas
| 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. |
| 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? |
| 14227 | We could refer to tables as 'xs that are arranged tablewise' [Inwagen] |
| Full Idea: We could paraphrase 'some chairs are heavier than some tables' as 'there are xs that are arranged chairwise and there are ys that are arranged tablewise and the xs are heavier than the ys'. | |
| From: Peter van Inwagen (Material Beings [1990], 11) | |
| A reaction: Liggins notes that this involves plural quantification. Being 'arranged tablewise' has become a rather notorious locution in modern ontology. We still have to retain identity, to pick out the xs. |
| 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. |
| 10662 | Mereology is 'nihilistic' (just atoms) or 'universal' (no restrictions on what is 'whole') [Inwagen, by Varzi] |
| Full Idea: Van Ingwagen writes of 'mereological nihilism' (that only mereological atoms exist) and of 'mereological universalism' (adhering to the principle of Unrestricted Composition). | |
| From: report of Peter van Inwagen (Material Beings [1990], p.72-) by Achille Varzi - Mereology 4.3 | |
| A reaction: They both look mereologically nihilistic to me, in comparison with an account that builds on 'natural' wholes and their parts. You can only be 'unrestricted' if you view the 'wholes' in your vast ontology as pretty meaningless (as Lewis does, Idea 10660). |
| 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? |
| 17587 | The 'Law' of Excluded Middle needs all propositions to be definitely true or definitely false [Inwagen] |
| Full Idea: I think the validity of the 'Law' of Excluded Middle depends on the assumption that every proposition is definitely true or definitely false. | |
| From: Peter van Inwagen (Material Beings [1990], 18) | |
| A reaction: I think this is confused. He cites vagueness as the problem, but that is a problem for Bivalence. If excluded middle is read as 'true or not-true', that leaves the meaning of 'not-true' open, and never mentions the bivalent 'false'. |
| 17558 | Variables are just like pronouns; syntactic explanations get muddled over dummy letters [Inwagen] |
| Full Idea: Explanations in terms of syntax do not satisfactorily distinguish true variables from dummy or schematic letters. Identifying variables with pronouns, however, provides a genuine explanation of what variables are. | |
| From: Peter van Inwagen (Material Beings [1990], 02) | |
| A reaction: I like this because it shows that our ordinary thought and speech use variables all the time ('I've forgotten something - what was it?'). He says syntax is fine for maths, but not for ordinary understanding. |
| 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) |
| 17583 | There are no heaps [Inwagen] |
| Full Idea: Fortunately ....there are no heaps. | |
| From: Peter van Inwagen (Material Beings [1990], 18) | |
| A reaction: This is the nihilist view of (inorganic) physical objects. If a wild view solves all sorts of problems, one should take it serious. It is why I take reductive physicalism about the mind seriously. (Well, it's true, actually) |
| 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. |
| 4045 | Children may have three innate principles which enable them to learn to count [Goldman] |
| Full Idea: It has been proposed (on the basis of observations) that young children have three innate principles of counting - one-to-one correspondence of number to item, stable order for numbers, and cardinality (which labels the nth item counted). | |
| From: Alvin I. Goldman (Phil Applications of Cognitive Science [1993], p.60) | |
| A reaction: I like the idea of observed patterns as central (which is the one-to-one principle). But the other two principles are plausible, and show why pure empiricism won't work. |
| 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. |
| 4044 | Rat behaviour reveals a considerable ability to count [Goldman] |
| Full Idea: Rats can determine the number of times they have pressed a lever up to at least twenty-four presses,…and can consistently turn down the fifth tunnel on the left in a maze. | |
| From: Alvin I. Goldman (Phil Applications of Cognitive Science [1993], p.58) | |
| A reaction: This seems to encourage an empirical view of maths (pattern recognition?) rather than a Platonic one. Or numbers are innate in rat brains? |
| 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! |
| 17578 | I reject talk of 'stuff', and treat it in terms of particles [Inwagen] |
| Full Idea: I have a great deal of difficulty with an ontology that includes 'stuffs' in addition to things. ...I prefer to replace talk of sameness of matter with talk of sameness of particles. | |
| From: Peter van Inwagen (Material Beings [1990], 14) | |
| A reaction: Van Inwagen is wedded to the idea that reality is composed of 'simples' - even if physicists seem now to talk of 'fields' as much as they do about objects in the fields. Has philosophy yet caught up with Maxwell? |
| 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. |
| 17582 | Singular terms can be vague, because they can contain predicates, which can be vague [Inwagen] |
| Full Idea: Since singular terms can contain predicates, and since vague predicates are common, vague singular terms are common. For 'the tallest man that Sally knows' there are lots of men for whom it is unclear whether Sally knows them. | |
| From: Peter van Inwagen (Material Beings [1990], 17) |
| 4048 | Infant brains appear to have inbuilt ontological categories [Goldman] |
| Full Idea: Infant behaviour implies inbuilt ontological categories of thing, place, event, path, action, sound, manner, amount and number. ...There is an algebra of relationships between them. | |
| From: Alvin I. Goldman (Phil Applications of Cognitive Science [1993], p.109) | |
| A reaction: Interesting. We would expect the categories in infant brains to have instrumental value, but we don't have to accept them as true. Adults (even Aristotle) are big infants. |
| 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. |
| 17556 | Material objects are in space and time, move, have a surface and mass, and are made of some stuff [Inwagen] |
| Full Idea: A thing is a material object if it occupies space and endures through time and can move about in space (literally move, unlike a shadow or wave or reflection) and has a surface and has a mass and is made of a certain stuff or stuffs. | |
| From: Peter van Inwagen (Material Beings [1990], 01) | |
| A reaction: It is not at all clear what electrons (which must count for him as 'simples') are made of. |
| 8264 | Maybe table-shaped particles exist, but not tables [Inwagen, by Lowe] |
| Full Idea: Van Ingwagen holds that although table-shaped collections of particles exist, tables do not. | |
| From: report of Peter van Inwagen (Material Beings [1990], Ch.13) by E.J. Lowe - The Possibility of Metaphysics 2.3 | |
| A reaction: I find this idea appealing. See the ideas of Trenton Merricks. When you get down to micro-level, it is hard to individuate a table among the force fields, and hard to distinguish a table from a smashed or burnt table. An ontology without objects? |
| 17565 | Nihilism says composition between single things is impossible [Inwagen] |
| Full Idea: Nihilism about objects says there is a Y such that the Xs compose it if and only if there is only one of the Xs. | |
| From: Peter van Inwagen (Material Beings [1990], 08) | |
| A reaction: He says that Unger, the best known 'nihilist' about objects, believes a different version - claiming there are composites, but they never make up the ordinary objects we talk about. |
| 14228 | If there are no tables, but tables are things arranged tablewise, the denial of tables is a contradiction [Liggins on Inwagen] |
| Full Idea: Van Inwagen says 'there are no tables', and 'there are tables' means 'there are some things arranged tablewise'. Presumably 'there are no tables' negates the latter claim, saying no things are arranged tablewise. But he should think that is false. | |
| From: comment on Peter van Inwagen (Material Beings [1990], 10) by David Liggins - Nihilism without Self-Contradiction 3 | |
| A reaction: Liggins's nice paper shows that Van Inwagen is in a potential state of contradiction when he starts saying that there are no tables, but that there are things arranged tablewise, and that they amount to tables. Liggins offers him an escape. |
| 14468 | Actions by artefacts and natural bodies are disguised cooperations, so we don't need them [Inwagen] |
| Full Idea: All the activities apparently carried out by shelves and stars and other artefacts and natural bodies can be understood as disguised cooperative activities. And, therefore, we are not forced to grant existence to any artefacts or natural bodies. | |
| From: Peter van Inwagen (Material Beings [1990], 12) | |
| A reaction: In 'the crowd tore her to pieces' are we forced to accept the existence of a crowd? We can't say 'Jack tore her to pieces' and 'Jill tore her to pieces'. If a plural quantification is unavoidable, we have to accept the plurality. Perhaps. |
| 17571 | Every physical thing is either a living organism or a simple [Inwagen] |
| Full Idea: The thesis about composition and parthood that I am advocating has far-reaching ontological consequences: that every physical thing is either a living organism or a simple. | |
| From: Peter van Inwagen (Material Beings [1990], 10) | |
| A reaction: A 'simple' is a placeholder for anything considered to be a fundamental unit of existence (such as an electron or a quark). This amazingly sharp distinction strikes me as utterly implausible. There is too much in the middle ground. |
| 17562 | The statue and lump seem to share parts, but the statue is not part of the lump [Inwagen] |
| Full Idea: Those who believe that the statue is distinct from the lump should concede that whatever shares a part with the statue shares a part with the lump but deny that the statue is a part of the lump. | |
| From: Peter van Inwagen (Material Beings [1990], 05) | |
| A reaction: Standard mereology says if they share all their parts then they are the same thing, so it is hard to explain how they are 'distinct'. The distinction is only modal - that they could be separated (by squashing, or by part substitution). |
| 17574 | If you knead clay you make an infinite series of objects, but they are rearrangements, not creations [Inwagen] |
| Full Idea: If you can make a (random) gollyswoggle by accident by kneading clay, then you must be causing the generation and corruption of a series of objects of infinitesimal duration. ...We have not augmented the furniture of the world but only rearranged it. | |
| From: Peter van Inwagen (Material Beings [1990], 13) | |
| A reaction: Van Inwagen's final conclusion is a bit crazy, but I am in sympathy with his general scepticism about what sorts of things definitively constitute 'objects'. He overrates simples, and he overrates lives. |
| 17531 | I assume matter is particulate, made up of 'simples' [Inwagen] |
| Full Idea: I assume in this book that matter is ultimately particulate. Every material being is composed of things that have no proper parts: 'elementary particles' or 'mereological atoms' or 'metaphysical simples'. | |
| From: Peter van Inwagen (Material Beings [1990], Pref) | |
| A reaction: It may be that modern physics doesn't support this, if 'fields' is the best term for what is fundamental. Best to treat his book as hypothetical - IF there are just simples, proceed as follows. |
| 17560 | If contact causes composition, do two colliding balls briefly make one object? [Inwagen] |
| Full Idea: If composition just requires contact, if I cause the cue ball to rebound from the eight ball, do I thereby create a short-lived object shaped like two slightly flattened spheres in contact? | |
| From: Peter van Inwagen (Material Beings [1990], 03) | |
| A reaction: [compressed] |
| 17561 | If bricks compose a house, that is at least one thing, but it might be many things [Inwagen] |
| Full Idea: If composition just requires contact, that tells us that the bricks of a house compose at least one thing; it does not tell us that they also compose at most one thing. | |
| From: Peter van Inwagen (Material Beings [1990], 04) |
| 17566 | I think parthood involves causation, and not just a reasonably stable spatial relationship [Inwagen] |
| Full Idea: I propose that parthood essentially involves causation. Too many philosophers have supposed that objects compose something when and only when they stand in some (more or less stable) spatial relationship to one another. | |
| From: Peter van Inwagen (Material Beings [1990], 09) | |
| A reaction: I have to say that I like this, even though it comes from a thinker who is close to nihilism about ordinary non-living objects. He goes on to say that only a 'life' provides the right sort of causal relationship. |
| 14230 | We can deny whole objects but accept parts, by referring to them as plurals within things [Inwagen, by Liggins] |
| Full Idea: Van Inwagen's claim that nothing has parts causes incredulity. ..But the problem is not with endorsing the sentence 'Some things have parts'; it is with interpreting this sentence by means of singular resources rather than plural ones. | |
| From: report of Peter van Inwagen (Material Beings [1990], 7) by David Liggins - Nihilism without Self-Contradiction | |
| A reaction: Van Inwagen notoriously denies the existence of normal physical objects. Liggins shows that modern formal plural quantification gives a better way of presenting his theory, by accepting tables and parts of tables as plurals of basic entities. |
| 17557 | Special Composition Question: when is a thing part of something? [Inwagen] |
| Full Idea: The Special Composition Question asks, In what circumstances is a thing a (proper) part of something? | |
| From: Peter van Inwagen (Material Beings [1990], 02) | |
| A reaction: [He qualifies this formulation as 'misleading'] It's a really nice basic question for the metaphysics of objects. |
| 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. |
| 17564 | The essence of a star includes the released binding energy which keeps it from collapse [Inwagen] |
| Full Idea: I think it is part of the essence of a star that the radiation pressures that oppose the star's tendency to gravitational collapse has its source in the release of no-longer-needed nuclear binding energy when colliding nuclei fuse in the star's hot core. | |
| From: Peter van Inwagen (Material Beings [1990], 07) | |
| A reaction: A perfect example of giving the essence of something as the bottom level of its explanation. This even comes from someone who doesn't really believe in stars! |
| 17575 | The persistence of artifacts always covertly involves intelligent beings [Inwagen] |
| Full Idea: Statements that are apparently about the persistence of artifacts make covert reference to the dispositions of intelligent beings to maintain certain arrangements of matter. | |
| From: Peter van Inwagen (Material Beings [1990], 13) | |
| A reaction: If you build a self-sustaining windmill that pumps water, that seems to have an identity of its own, apart from the intentions of whoever makes it and repairs it. The function of an artefact is not just the function we want it to have. |
| 17577 | When an electron 'leaps' to another orbit, is the new one the same electron? [Inwagen] |
| Full Idea: Is the 'new' electron in the lower orbit the one that was in the higher orbit? Physics, as far as I can tell, has nothing to say about this. | |
| From: Peter van Inwagen (Material Beings [1990], 14) | |
| A reaction: I suspect that physicists would say that philosophers are worrying about such questions because they haven't grasped the new conceptual scheme that emerged in 1926. The poor mutts insist on hanging on to 'objects'. |
| 17589 | If you reject transitivity of vague identity, there is no Ship of Theseus problem [Inwagen] |
| Full Idea: If you have rejected the Principle of the Transitivity of (vague) Identity, it is hard to see how the problem of the Ship of Theseus could arise. | |
| From: Peter van Inwagen (Material Beings [1990], 18) | |
| A reaction: I think this may well be the best solution to the whole problem |
| 17588 | We should talk of the transitivity of 'identity', and of 'definite identity' [Inwagen] |
| Full Idea: In some contexts, the principle of 'the transitivity of identity' should be called 'the transitivity of definite identity'. | |
| From: Peter van Inwagen (Material Beings [1990], 18) | |
| A reaction: He is making room for a person to retain identity despite having changed. Applause from me. |
| 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). |
| 17572 | Actuality proves possibility, but that doesn't explain how it is possible [Inwagen] |
| Full Idea: A proof of actuality is a proof of possibility, but that does not invariably explain the possibility whose existence it demonstrates, for we may know that a certain thing is actual (and hence possible) but have no explanation of how it could be possible. | |
| From: Peter van Inwagen (Material Beings [1990], 12) | |
| A reaction: I like this, because my project is to see all of philosophy in terms of explanation rather than of description. |
| 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. |
| 17579 | Counterparts reduce counterfactual identity to problems about similarity relations [Inwagen] |
| Full Idea: Counterpart Theory essentially reduces all problems about counterfactual identity to problems about choosing appropriate similarity relations. That is, Counterpart Theory essentially eliminates problems of counterfactual identity as such. | |
| From: Peter van Inwagen (Material Beings [1990], 14) |
| 17590 | A merely possible object clearly isn't there, so that is a defective notion [Inwagen] |
| Full Idea: The notion of a merely possible object is an even more defective notion than the notion of a borderline object; after all, a merely possible object is an object that definitely isn't there. | |
| From: Peter van Inwagen (Material Beings [1990], 19) |
| 17591 | Merely possible objects must be consistent properties, or haecceities [Inwagen] |
| Full Idea: Talk of merely possible objects may be redeemed in either maximally consistent sets of properties or in haecceities. | |
| From: Peter van Inwagen (Material Beings [1990], 19) |
| 4043 | Elephants can be correctly identified from as few as three primitive shapes [Goldman] |
| Full Idea: An elephant may be fully represented by nine primitive shapes ('geons'), but it may require as few as three geons in appropriate relations to be correctly identified. | |
| From: Alvin I. Goldman (Phil Applications of Cognitive Science [1993], p.7) | |
| A reaction: Encouraging the idea of the mind as a maker of maps and models |
| 4049 | The way in which colour experiences are evoked is physically odd and unpredictable [Goldman] |
| Full Idea: A unique yellow experience may be evoked with monochrome light of 580nm, or a mixture of 540nm and 670nm. ..Our interpretation of colour experience is a highly idiosyncratic artefact of our visual system. | |
| From: Alvin I. Goldman (Phil Applications of Cognitive Science [1993], p.117) | |
| A reaction: This confirms what I have always thought - that colour (as qualia) is strictly a feature of minds, not of the world. |
| 4047 | Gestalt psychology proposes inbuilt proximity, similarity, smoothness and closure principles [Goldman] |
| Full Idea: Gestalt psychology claims that there are at least four unlearned factors in perceptual grouping - the principles of proximity (close things), of similarity, of good continuation (extending lines in a smooth course), and closure (which completes figures). | |
| From: Alvin I. Goldman (Phil Applications of Cognitive Science [1993], p.103) | |
| A reaction: This offers a bridge between Hume's associationism and rationalist claims of innate ideas |
| 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. |
| 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. |
| 17563 | The strong force pulls, but also pushes apart if nucleons get too close together [Inwagen] |
| Full Idea: The strong force doesn't always pull nucleons together, but pushes them apart if they get too close. | |
| From: Peter van Inwagen (Material Beings [1990], 07) | |
| A reaction: Philosophers tend to learn their physics from other philosophers. But that's because philosophers are brilliant at picking out the interesting parts of physics, and skipping the boring stuff. |
| 17559 | Is one atom a piece of gold, or is a sizable group of atoms required? [Inwagen] |
| Full Idea: A physicist once told me that of course a gold atom was a piece of gold, and a physical chemist has assured me that the smallest possible piece of gold would have to be composed of sixteen or seventeen atoms. | |
| From: Peter van Inwagen (Material Beings [1990], 01) | |
| A reaction: The issue is at what point all the properties that we normally begin to associate with gold begin to appear. One water molecule can hardly have a degree of viscosity or liquidity. |
| 17586 | At the lower level, life trails off into mere molecular interaction [Inwagen] |
| Full Idea: The lives of the lower links of the Great Chain of Being trail off into vague, temporary episodes of molecular interaction. | |
| From: Peter van Inwagen (Material Beings [1990], 18) | |
| A reaction: His case involves conceding all sorts of vagueness to life, but asserting the utter distinctness of the full blown cases of more elaborate life. I don't really concede the distinction. |
| 17568 | A tumour may spread a sort of life, but it is not a life, or an organism [Inwagen] |
| Full Idea: A tumour is not an organism (or a parasite) and there is no self-regulating event that is its life. It does not fill one space, but is a locus within which a certain sort of thing is happening: the spreading of a certain sort of (mass-term) life. | |
| From: Peter van Inwagen (Material Beings [1990], 09) |
| 17581 | Being part of an organism's life is a matter of degree, and vague [Inwagen] |
| Full Idea: Being caught up in the life of an organism is, like being rich or being tall, a matter of degree, and is in that sense a vague condition. | |
| From: Peter van Inwagen (Material Beings [1990], 17) | |
| A reaction: Van Inwagen is trying to cover himself, given that he makes a sharp distinction between living organisms, which are unified objects, and everything else, which isn't. There may be a vague centre to a 'life', as well as vague boundaries. |
| 17567 | A flame is like a life, but not nearly so well individuated [Inwagen] |
| Full Idea: A flame, though it is a self-maintaining event, does not seem to be nearly so well individuated as a life. | |
| From: Peter van Inwagen (Material Beings [1990], 09) | |
| A reaction: This is to counter the standard problem that if you attempt to define 'life', fire turns out to tick nearly all the same boxes. The concept of 'individuated' often strikes me as unsatisfactory. How does a bonfire fail to be individuated? |
| 17576 | If God were to 'reassemble' my atoms of ten years ago, the result would certainly not be me [Inwagen] |
| Full Idea: If God were to 'reassemble' the atoms that composed me ten years ago, the resulting organism would certainly not be me. | |
| From: Peter van Inwagen (Material Beings [1990], 13) | |
| A reaction: What is obvious to Van Inwagen is not obvious to me. He thinks lives are special. Such examples just leave us bewildered about what counts as 'the same', because our concept of sameness wasn't designed to deal with such cases. |
| 17584 | Some events are only borderline cases of lives [Inwagen] |
| Full Idea: There are events of which it is neither definitely true nor definitely false that those events are lives. I do not see how we can deny this. | |
| From: Peter van Inwagen (Material Beings [1990], 18) | |
| A reaction: Very frustrating, since this is my main objection to Van Inwagen's distinction between unified lives and mere collections of simples. Some boundaries are real enough, despite their vagueness, and others indicate that there is no real distinction. |
| 17569 | Unlike waves, lives are 'jealous'; it is almost impossible for them to overlap [Inwagen] |
| Full Idea: A wave is not a 'jealous' event. Lives, however, are jealous. It cannot be that the activities of the Xs constitute at one and the same time two lives. Only in certain special cases can two lives overlap. | |
| From: Peter van Inwagen (Material Beings [1990], 09) |
| 17580 | One's mental and other life is centred on the brain, unlike any other part of the body [Inwagen] |
| Full Idea: One's life - not simply one's mental life - is centered in the activity of the simples that virtually compose one's brain in a way in which it is not centered in the activity of any of the other simples that compose one. | |
| From: Peter van Inwagen (Material Beings [1990], 15) | |
| A reaction: This justifies the common view that 'one follows one's brain'. I take that to mean that my brain embodies my essence. I would read 'centered on' as 'explains'. |
| 17570 | The chemical reactions in a human life involve about sixteen elements [Inwagen] |
| Full Idea: There are sixteen or so chemical elements involved in those chemical reactions that collectively constitute the life of a human being. | |
| From: Peter van Inwagen (Material Beings [1990], 09) |
| 17585 | Life is vague at both ends, but could it be totally vague? [Inwagen] |
| Full Idea: Individual human lives are infected with vagueness at both ends. ...But could there be a 'borderline life'? | |
| From: Peter van Inwagen (Material Beings [1990], 18) | |
| A reaction: Van Inwagen says (p.239) that there may be wholly vague lives, though it would suit his case better if there were not. |
| 17573 | There is no reason to think that mere existence is a valuable thing [Inwagen] |
| Full Idea: There is no reason to suppose - whatever Saint Anselm and Descartes may have thought - that mere existence is a valuable thing. | |
| From: Peter van Inwagen (Material Beings [1990], 12) | |
| A reaction: This is one of the simplest and most powerful objections to the Ontological Argument. God's existence may be of great value, but the existence of Hitler wasn't. |