Interview by Bryan Magee
- Ayer on Russell and Frege (part 1)
- Ayer on Russell and Frege (part 2)
- Ayer on Russell and Frege (part 3)
- Ayer on Russell and Frege (part 4)
- Ayer on Russell and Frege (part 5)
Quotes from Bertrand Russell and comments upon them
“A proposition is just a symbol It is a complex symbol in the sense that it has parts which are also symbols: a symbol may be defined as complex when it has parts that are symbols. In a sentence containing several words, the several words are each symbols, and the sentence containing them is therefore a complex symbol in that sense. There is a good deal of importance to philosophy in the theory of symbolism, a good deal more that at one time I thought. I think the importance is almost always negative, i.e. the importance lies in the fact that unless you are fairly self-conscious about symbols, unless you are fairly aware of the relation of the symbol to what it symbolizes, you will find yourself attributing to the thing properties which only belong to the symbol. That, of course, is especially likely in very abstract studies such as philosophical logic, because the subject-matter that you are supposed to be thinking of is so exceedingly difficult and elusive that any person who has ever tried to think about it knows you do not think about it except perhaps once in six months for half a minute. The rest of the time you think about the symbols, because they are tangible, but the thing you are supposed to be thinking about is fearfully difficult and one does not often manage to think about it. The really good philosopher is the one who does once in six months think about it for a minute. Bad philosophers never do.”
—- Bertrand Russell in “The Philosophy of Logical Atomism” – Volume 8 of The Collected Papers of Bertrand Russell, page 166.
From page xli of the CPBR volume 5 – in a letter of 13 June 1905 to Lucy Donnelly BR wrote:
“For a long time I have been at intervals debating this conundrum: If two names or descriptions apply to the same object, whatever is true of the one is true or the other. Now George IV wished to know whether Scott was the author of Waverly. Hence, putting “Scott” on the place of “the author of Waverly”, we find that George IV wished to know whether Scott was Scott, which implies more interest in the Laws of Thought than was possible for the First Gentleman of Europe. This little puzzle was quite hard to solve; the solution, which I have now found, throws a flood of light on the foundations of mathematics and the whole problem of the relation of thought to things.”
The solution was published on “On Denoting”.
From “On Denoting” – page 423 of CPBR volume 4, BR wrote:
‘According to the view which I advocate, a denoting phrase is essentially part of a sentence, and does not, like most single words, have any significance on its own account. If I say “Scott was a man”, that is a statement of the form “x was a man”, and it has “Scott” for its subject”. But if I say “the author of Waverly was a man”, that is not a statement of the form “x was a man”, and does not have “the author of Waverly for its subject. … , we may put, in place of “the author of Waverly was a man” the following: “One and only one entity wrote Waverly, and that one was a man”.
… And speaking generally, suppose we wish to say that the author of Waverly had the property F, what we wish to say is equivalent to “One and only one entity wrote Waverly, and that one had the property F.”
… “Scott was the author of Waverly” (i.e. “Scott was identical with the author of Waverly”) becomes “One and only one entity wrote Waverly, and Scott was identical with that one”; or reverting to the wholly explicit form: “It is not always false of x that x wrote Waverly, that it is always true of y that if y wrote Waverly y is identical with x, and that Scott is identical with x.”
From “The Philosophy of Logical Atomism” by Bertrand Russell. Quoted by Bart Kosko, Fuzzy Thinking, p. 121.
“Everything is vague to a degree you do not realize till you have tried to make it precise.”
In Fuzzy Thinking, Kosko (p. 298) says:
“The term ‘vague’ comes from Bertrand Russell and his work on multivalued logic in the early part of the twentieth century.”
- [Note: Kosko mis-cites Russell’s 1923 paper “Vagueness” as in “Australian Journal of Philosophy”. It was actually in “The Australasian Journal of Psychology and Philosophy”. See The Collected Papers of Bertrand Russell, Volume 9, p. 145.]
His quotes it on page 92 of Fuzzy Thinking:
“All traditional logic habitually assumes that precise symbols are being employed. It is therefore not applicable to this terrestrial life, but only to an imagined celestial one. The law of excluded middle [A or not-A] is true when precise symbols are employed but it is not true when symbols are vague [fuzzy], as, in fact, all symbols are.”
- On page 94 of Fuzzy Thinking, Kosko describes Russell’s example of a sorites paradox. “Bertrand Russell used a man’s head of hair and asked whether the man was bald. Pluck out a hair and ask again. Keep plucking and asking and eventually, after a hundred thousand plucks or so, the man passes from nonbald to bald.”
On intension and extension in Introduction to Mathematical Philosophy by Bertrand Russell.
“A class or collection may be defined in two ways that at first sight seem quite distinct. We may enumerate its members, as when we say, “The collection I mean is Brown, Jones, and Robinson.” Or we may mention a defining property, as when we speak of “mankind” or “the inhabitants of London.” The definition which enumerates is called a definition by “extension,” and the one which mentions a defining property is called a definition by “intension.” Of these two kinds of definition, the one by intension is logically more fundamental. This is shown by two considerations: (1) that the extensional definition can always be reduced to an intensional one; (2) that the intensional one often cannot even theoretically be reduced to the extensional one. Each of these points needs a word of explanation.
(1) Brown, Jones, and Robinson all of them possess a certain property which is possessed by nothing else in the whole universe, namely, the property of being either Brown or Jones or Robinson. This property can be used to give a definition by intension of the class consisting of Brown and Jones and Robinson. Consider such a formula as “x is Brown or x is Jones or x is Robinson.” This formula will be true for just three x’s, namely, Brown and Jones and Robinson. In this respect it resembles a cubic equation with its three roots. It may be taken as assigning a property common to the members of the class consisting of these three [page 13] men, and peculiar to them. A similar treatment can obviously be applied to any other class given in extension.
(2) It is obvious that in practice we can often know a great deal about a class without being able to enumerate its members. No one man could actually enumerate all men, or even all the inhabitants of London, yet a great deal is known about each of these classes. This is enough to show that definition by extension is not necessary to knowledge about a class. But when we come to consider infinite classes, we find that enumeration is not even theoretically possible for beings who only live for a finite time. We cannot enumerate all the natural numbers: they are 0, 1, 2, 3, and so on. At some point we must content ourselves with “and so on.” We cannot enumerate all fractions or all irrational numbers, or all of any other infinite collection. Thus our knowledge in regard to all such collections can only be derived from a definition by intension.
These remarks are relevant, when we are seeking the definition of number, in three different ways. In the first place, numbers themselves form an infinite collection, and cannot therefore be defined by enumeration. In the second place, the collections having a given number of terms themselves presumably form an infinite collection: it is to be presumed, for example, that there are an infinite collection of trios in the world, for if this were not the case the total number of things in the world would be finite, which, though possible, seems unlikely. In the third place, we wish to define “number” in such a way that infinite numbers may be possible; thus we must be able to speak of the number of terms in an infinite collection, and such a collection must be defined by intension, i.e. by a property common to all its members and peculiar to them.
For many purposes, a class and a defining characteristic of it are practically interchangeable. The vital difference between the two consists in the fact that 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. Men [page 14] may be defined as featherless bipeds, or as rational animals, or (more correctly) by the traits by which Swift delineates the Yahoos. It is this fact that a defining characteristic is never unique which makes classes useful; otherwise we could be content with the properties common and peculiar to their members.2 Any one of these properties can be used in place of the class whenever uniqueness is not important.”
Many problems occur if one refuses to acknowledge intensions as several 20th and 21st century philosophers have. Russell above has given the principal reasons that they are needed.
CPBR 5 pp. 451-452.
“Thus a belief, if this view [a belief is not a single thing related to a fact] is adopted, will not consist of one idea with a complex object, but will consist of several related ideas. That is, if we believe (say) that A is B, we shall have the ideas of A and of B, and these ideas will be related in a certain manner; but we shall not have a sinle complex idea which can be described as the idea of `A is B`. A belief will then differ from an idea or presentation by the fact that it will consist of several interrelated ideas. Certain ideas standing in certain relations will be called the belief that so-and-so. In the event of the objects standing in he corresponding relation, we shall say that the belief is true, or that it is belief in a fact. In the event of the objects not standing in the corresponding relation, there will be no objective complex corresponding to the belief, and the belief is belief in nothing, though it is not `thinking of nothing`, because it is thinking of the objects of the ideas which constitute the belief. Thus it would seem that the argument that false beliefs must be beliefs in something is not conclusive in favour of objective falsehood.”
From Philosophical Essays, p. 155:
“The theory of judgment [belief] which I am advocating is, that judgment is not a dual relation of mind to a single objective, but a multiple relation of the mind to the various other terms with which the judgment is concerned. Thus if I judge that A loves B, that is not a relation of me to `A`s love for B`, but a relation between me and A and love and B. If it were a relation of me to `A`s love for B`, it would be impossible unless there were such a thing s `A`s love for B`, i.e. unless A loved B, i.e. unless the judgment were true; but in fact false judgments are possible. When the judgment is taken as a relation between me and A and love and B, the mere fact that the the judgement occurs does not involve any relation between its objects A and love and B; thus the possibility of false judgments is fully allowed for.”
Another quote from Bertrand Russell. Quoted in Fuzzy Thinking, p. 241.
“The most savage controversies are those about matters as to which there is no good evidence either way.”