88 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? |
| 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. |
| 22309 | An idea can only be like another idea [Berkeley] |
| Full Idea: An idea can be like nothing but an idea. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §08), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 43 'Mean' | |
| A reaction: I take this to be relevant to the correspondence theory, but also to be one of Berkeley's best observations. We understand ideas, but we can't map them onto the world (because they are not maps!). ...But then how is one idea like another? Hm. |
| 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! |
| 6717 | Abstract ideas are impossible [Berkeley] |
| Full Idea: We have, I think, shown the impossibility of Abstract Ideas. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], Intro §21) | |
| A reaction: He achieves this by an attack on universals, offering the nominalist view that there are only particulars. There seems to be a middle ground, where universals don't actually exist, but there are settled conventional abstraction, beyond particulars. |
| 18876 | Berkeley does believe in trees, but is confused about what trees are [Berkeley, by Cameron] |
| Full Idea: I think that we should consider Berkeley as believing in trees; we should simply claim that he has false beliefs about what trees are. | |
| From: report of George Berkeley (The Principles of Human Knowledge [1710]) by Ross P. Cameron - Truthmakers, Realism and Ontology 'Realism' | |
| A reaction: I can be realist about spots before my eyes, or a ringing in my ears, but be (quite sensibly) unsure about what they are, so Cameron's suggestion sounds plausible. |
| 14429 | Classes are logical fictions, made from defining characteristics [Russell] |
| Full Idea: Classes may be regarded as logical fictions, manufactured out of defining characteristics. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], II n1) | |
| A reaction: I agree with this. The idea that in addition to the members there is a further object, the set containing them, is absurd. Sets are a tool for thinking about the world. |
| 14430 | If a relation is symmetrical and transitive, it has to be reflexive [Russell] |
| Full Idea: It is obvious that a relation which is symmetrical and transitive must be reflexive throughout its domain. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], II) | |
| A reaction: Compare Idea 13543! The relation will return to its originator via its neighbours, rather than being directly reflexive? |
| 14432 | 'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a [Russell] |
| Full Idea: The relation of 'asymmetry' is incompatible with the converse. …The relation 'husband' is asymmetrical, so that if a is the husband of b, b cannot be the husband of a. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], V) | |
| A reaction: This is to be contrasted with 'non-symmetrical', where there just happens to be no symmetry. |
| 6715 | Universals do not have single meaning, but attach to many different particulars [Berkeley] |
| Full Idea: There is no such thing as one precise and definite signification annexed to any general name, they all signifying indifferently a great number of particular ideas. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], Intro §18) | |
| A reaction: The term 'red' may be assigned to a range of colours, but we also recognise the precision of 'that red'. For 'electron', or 'three', or 'straight', the particulars are indistinguishable. |
| 6719 | No one will think of abstractions if they only have particular ideas [Berkeley] |
| Full Idea: He that knows he has no other than particular ideas, will not puzzle himself in vain to find out and conceive the abstract idea annexed to any name. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], Intro §24) | |
| A reaction: A nice point against universals. Maybe gods only think in particulars. One particular on its own could never suggest a universal. How are you going to spot patterns if you don't think in universals? Maths needs patterns. |
| 6714 | Universals do not have any intrinsic properties, but only relations to particulars [Berkeley] |
| Full Idea: Universality, so far as I can comprehend it, does not consist in the absolute, positive nature or conception of anything, but in the relation it bears to the particulars signified or represented by it. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], Intro §15) | |
| A reaction: I always think it is a basic principle in philosophy that some sort of essence must precede relations (and functions). What is it about universals that enables them to have a relation to particulars? |
| 6729 | Material substance is just general existence which can have properties [Berkeley] |
| Full Idea: The most accurate philosophers have no other meaning annexed to 'material substance' but the idea of being in general, together with the relative notion of its supporting accidents. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §17) | |
| A reaction: This is part of the attack on Aristotle's concept of 'substance', and is a nice way of dissolving the concept. 'Substance' will never reappear in physics, but modern philosopher have returned to it, as possibly inescapable in metaphysics. |
| 16636 | A die has no distinct subject, but is merely a name for its modes or accidents [Berkeley] |
| Full Idea: To me a die seems to be nothing distinct from those things which are termed its modes or accidents. And to say a die is hard, extended and square is not to attribute those qualities to a distinct subject, but only an explication of the word 'die'. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], n 49) | |
| A reaction: This is apparently a reaction to Locke, and a final rejection of the medieval idea of a 'substance'. Unfortunately it leaves Berkeley with a 'bundle' view of objects (a typical empiricist account), which is even worse. |
| 14435 | The essence of individuality is beyond description, and hence irrelevant to science [Russell] |
| Full Idea: The essence of individuality always eludes words and baffles description, and is for that very reason irrelevant to science. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], VI) | |
| A reaction: [context needed for a full grasp of this idea] Russell seems to refer to essence as much as to individuality. The modern essentialist view is that essences are not beyond description after all. Fundamental physics is clearer now than in 1919. |
| 12197 | Inferring q from p only needs p to be true, and 'not-p or q' to be true [Russell] |
| Full Idea: In order that it be valid to infer q from p, it is only necessary that p should be true and that the proposition 'not-p or q' should be true. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XIV) | |
| A reaction: Rumfitt points out that this approach to logical consequences is a denial of any modal aspect, such as 'logical necessity'. Russell observes that for a good inference you must know the disjunction as a whole. Could disjunction be modal?... |
| 14450 | All forms of implication are expressible as truth-functions [Russell] |
| Full Idea: There is no need to admit as a fundamental notion any form of implication not expressible as a truth-function. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XIV) | |
| A reaction: Note that this is from a book about 'mathematical' philosophy. Nevertheless, it seems to have the form of a universal credo for Russell. He wasn't talking about conditionals here. Maybe conditionals are not implications (in isolation, that is). |
| 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. |
| 6722 | Perception is existence for my table, but also possible perception, by me or a spirit [Berkeley] |
| Full Idea: The table I write on I say exists, that is, I see and feel it; and if I were out of my study I should say it existed - meaning thereby that if I was in my study I might perceive it, or that some other spirit actually does perceive it. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §3) | |
| A reaction: Berkeley is always (understandably) labelled as an 'idealist', but this seems to be what we call 'phenomenalism', because it allows possible experiences as well as actual ones. See Ideas 5170 and 6522. |
| 6724 | The only substance is spirit, or that which perceives [Berkeley] |
| Full Idea: It is evident that there is not any other Substance than spirit, or that which perceives. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §7) | |
| A reaction: Weird. To say that this is 'evident' seems to be begging the question. Why should he assume that there is nothing more to reality than his perception of it? He seems strangely unimaginative. |
| 6723 | The 'esse' of objects is 'percipi', and they can only exist in minds [Berkeley] |
| Full Idea: The absolute existence of unthinking things with no relation to their being perceived is unintelligible to me; their 'esse' is 'percipi', nor is it possible they should have any existence out of the minds or thinking things which perceive them. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §3) | |
| A reaction: "Esse est percipi" (to be is to be perceived) is the well-known slogan associated with Berkeley. I cannot see how Berkeley can assert that the separate existence of things is impossible. He is the classic confuser of epistemology and ontology. |
| 6732 | When I shut my eyes, the things I saw may still exist, but in another mind [Berkeley] |
| Full Idea: When I shut my eyes, the things I saw may still exist, but it must be in another mind. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §90) | |
| A reaction: This strikes me as ridiculous. What kind of theory says that a table goes out of existence when someone forgets to look at it for a moment, but is then recreated in identical form? Epistemology is not ontology. |
| 6726 | No one can, by abstraction, conceive extension and motion of bodies without sensible qualities [Berkeley] |
| Full Idea: I desire any one to reflect and try whether he can, by any abstraction of thought, conceive the extension and motion of a body without any sensible qualities. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §10) | |
| A reaction: The rather geometrical view of objects found in Descartes and Russell is an attempt to do this. I don't think the fact that we can't really achieve it matters much. We divide primary from secondary qualities in our understanding, not in experience. |
| 6728 | Motion is in the mind, since swifter ideas produce an appearance of slower motion [Berkeley] |
| Full Idea: Is it not reasonable to say that motion is not without the mind, since if the succession of ideas in the mind become swifter the motion, it is acknowledged, shall appear slower without any alteration in any external object. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §14) | |
| A reaction: An intriguing argument, based on what is now the principle of slow-motion photography. Fast minds slow down movement, like great tennis players. By what right does Berkeley say that the external subject is unaltered? |
| 6727 | Figure and extension seem just as dependent on the observer as heat and cold [Berkeley] |
| Full Idea: If heat and cold are only affections of the mind (since the same body seems cold to one hand and warm to the other), why may we not argue that figure and extension also appear different to the same eye at different stations? | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §14) | |
| A reaction: If the assessment of the qualities of an object is entirely a matter of our experiences of it, there is no denying Berkeley on this. However, judgement goes beyond experience, into speculations, inferences, and explanations. |
| 6495 | Berkeley's idealism resulted from fear of scepticism in representative realism [Robinson,H on Berkeley] |
| Full Idea: It was fear of scepticism based upon representative realism that motivated Berkeley's idealism. | |
| From: comment on George Berkeley (The Principles of Human Knowledge [1710]) by Howard Robinson - Perception II.1 | |
| A reaction: Personally I side with Russell, who accepts representative realism, and also accepts that some degree of scepticism is unavoidable, but without getting excited about it. The key to everything is to be a 'fallibilist' about knowledge. |
| 6720 | Knowledge is of ideas from senses, or ideas of the mind, or operations on sensations [Berkeley] |
| Full Idea: The objects of knowledge are either ideas imprinted on the senses, or passions and operations of the mind, or ideas (formed by memory and imagination) compounding, dividing or barely representing the original perceptions. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §1) | |
| A reaction: This is the germ of Hume's 'associations' (Idea 2189). There is not much room here for synthetic a priori knowledge, as the a priori part seems to merely know the mind. Most of Russell's epistemology is contained in the last part of the sentence. |
| 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. |
| 23636 | Berkeley's idealism gives no grounds for believing in other minds [Reid on Berkeley] |
| Full Idea: I can find no principle in Berkeley's system, which affords me even probable ground to conclude that there are other intelligent beings, like myself. | |
| From: comment on George Berkeley (The Principles of Human Knowledge [1710]) by Thomas Reid - Essays on Intellectual Powers 2: Senses 10 | |
| A reaction: I agree, which means that Berkeley's position seems to entail solipsism, unless God is the Cartesian deus ex machina who rescues him from this wall of ignorance. |
| 6736 | I know other minds by ideas which are referred by me to other agents, as their effects [Berkeley] |
| Full Idea: The knowledge I have of other spirits is not immediate, as is the knowledge of my ideas; but depending on the intervention of ideas, by me referred to agents or spirits distinct from myself, as effects or concomitant signs. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §145) | |
| A reaction: This strikes me as gross intellectual dishonesty, since the argument Berkeley uses to assert other minds could equally be used to assert the existence of tables ('by me referred to agents distinct from myself, as effects'). Be a solipsist or a realist. |
| 6713 | If animals have ideas, and are not machines, they must have some reason [Berkeley] |
| Full Idea: If the brutes have any ideas at all, and are not bare machines (as some would have them), we cannot deny them to have some reason. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], Intro §11) | |
| A reaction: It seems possible to imagine a low level of mind, where a few ideas (or concepts) float around, but hardly anything worth the name of reason. However, a Darwinian view suggests that concepts must bestow an advantage, so the two go together. |
| 6491 | Berkeley replaced intentionality with an anti-abstractionist imagist theory of thought [Berkeley, by Robinson,H] |
| Full Idea: By Berkeley - with his anti-abstractionism and imagist theory of thought - the classical sense-datum conception was firmly established, and intentionality had disappeared as an intrinsic property, not only of perceptual states, but of all mental contents. | |
| From: report of George Berkeley (The Principles of Human Knowledge [1710]) by Howard Robinson - Perception 1.6 | |
| A reaction: Intentionality was originally a medieval concept, and was revived by Brentano in the late nineteenth century. Nowadays intentionality is taken for granted, but I still suspect that we could drop it, and talk of nothing but brain states caused by reality. |
| 6711 | The mind creates abstract ideas by considering qualities separated from their objects [Berkeley] |
| Full Idea: We are told that the mind being able to consider each quality of things singly, or abstracted from those other qualities with which it is united, does by that means frame to itself abstract ideas. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], Intro §7) | |
| A reaction: A helpful explanation of 'abstract' ideas. Berkeley gives colour and movement as examples. Fodor suggests that abstraction is the key strategy in empiricist epistemology. The difficulty is to decide whether the qualities are natural or conventional. |
| 10581 | I can only combine particulars in imagination; I can't create 'abstract' ideas [Berkeley] |
| Full Idea: Whether others can abstract their ideas, they best can tell. For myself, I find I have a faculty of imagining, or representing to myself, only the idea of those particular things I have perceived, and of compounding and dividing them. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], 10) | |
| A reaction: He is admitting mixing experiences, but always particulars, never abstract. His examples are 'man' and 'motion'. Compare Aristotle Idea 9067. Berkeley is, I think, trapped in a false imagistic view of thought. My image of Plato blurs young and old. |
| 6721 | Ideas are perceived by the mind, soul or self [Berkeley] |
| Full Idea: The thing which knows or perceives ideas is what I call mind, spirit, soul or myself. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §2) | |
| A reaction: The interest here is in making no distinction between 'mind' and 'self', which seems to ally Berkeley with Locke's view of personal identity, as continuity of consciousness. The addition of 'soul' tries to connect Locke to Christian thought. |
| 6716 | Language is presumably for communication, and names stand for ideas [Berkeley] |
| Full Idea: It is a received opinion that language has no other end but the communicating our ideas, and that every significant name stands for an idea. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], Intro §19) | |
| A reaction: This attitude to language has been widely discredited, partly by the observation that 'idea' is very ambiguous, and partly by the fans of meaning-as-use. Truth conditions seem to be ideas, and so are speaker's intentions. |
| 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. |
| 6718 | I can't really go wrong if I stick to wordless thought [Berkeley] |
| Full Idea: So long as I confine my thoughts to my own ideas divested of words, I do not see how I can easily be mistaken. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], Intro §22) | |
| A reaction: I think it was one of the great errors of twentieth century philosophy to say that Berkeley cannot do this, because thought needs language. Personally I think language lags along behind most our thinking, tidying up the mess. I believe in propositions. |
| 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'). |
| 6731 | No one can explain how matter affects mind, so matter is redundant in philosophy [Berkeley] |
| Full Idea: How matter should operate on a spirit, or produce any idea in it, is what no philosopher will pretend to explain; it is therefore evident there can be no use of matter in natural philosophy. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §50) | |
| A reaction: An intriguing argument for idealism, which starts in Cartesian dualism, but then discards the physical world because of the notorious interaction problem. Of course, if he had thought that matter and spirit were one (Spinoza) the problem vanishes. |
| 6730 | We discover natural behaviour by observing settled laws of nature, not necessary connections [Berkeley] |
| Full Idea: That food nourishes, sleep refreshes, and fire warms us; all this we know, not by discovering any necessary connexion between our ideas, but only by the observation of the settled laws of nature. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §31) | |
| A reaction: Hume is famous for this idea, but it is found in Hobbes too (Idea 2364), and is the standard empiricist view of causation. The word 'settled' I take to imply that the laws are contingent, because they could become unsettled at any time. |
| 15861 | The laws of nature are mental regularities which we learn by experience [Berkeley] |
| Full Idea: The set rules or established methods wherein the Mind we depend on excites in us the ideas of sense, are called the 'laws of nature'; and these we learn by experience, which teaches us that such and such ideas are attended with certain other ideas. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], 33) | |
| A reaction: He observes that the ideas of sense are more regular than other mental events, and attributes the rules to an Author. He is giving the standard empirical Humean view, with his own quirky idealist slant. |
| 6734 | If properties and qualities arise from an inward essence, we will remain ignorant of nature [Berkeley] |
| Full Idea: An inducement to pronouncing ourselves ignorant of the nature of things is the opinion that everything includes within itself the cause of its properties; or that there is in each object an inward essence which is the source whence its qualities flow. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §102) | |
| A reaction: This remains a good objection to essentialism - that while it remains quite a plausible picture of how nature operates, it makes the task of understanding nature hopeless. We can grasp imposed regular laws, but not secret inner essences. |
| 6735 | All motion is relative, so a single body cannot move [Berkeley] |
| Full Idea: There cannot be any motion other than relative; …if there was one only body in being it could not possibly move. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §112) | |
| A reaction: This seems to agree with with Leibniz in denying the Newton-Clarke idea of absolute space. See Idea 2100. Suppose there were two bodies racing towards one another, when one of them suddenly vanished? |
| 6733 | I cannot imagine time apart from the flow of ideas in my mind [Berkeley] |
| Full Idea: Whenever I attempt to frame a simple idea of time, abstracted from the succession of ideas in my mind, which flows uniformly and is participated in by all beings, I am lost and embrangled in inextricable difficulties. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §98) | |
| A reaction: 'Embrangled'! A nice statement of the idealist view of time, as entirely mental. I know what he means. However, surely he can manage to imagine a movement which continues when he shuts he eyes? Try blinking during a horse race. |
| 6737 | Particular evils are really good when linked to the whole system of beings [Berkeley] |
| Full Idea: Those particular things which, considered in themselves, appear to be evil, have the nature of good, when considered as linked with the whole system of beings. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §153) | |
| A reaction: This wildly contradicts the rest of Berkeley's philosophy, which is strictly empiricist, and rests wholly on actual experience. What experience does he have of the 'whole system of beings', and its making evil into actual good? |