20 Bertrand Russell Quotes on Logic

Bertrand Russell quotes on logic

5. Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true ... If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.

7. The number of syllables in the English names of finite integers tends to increase as the integers grow larger, and must gradually increase indefinitely, since only a finite number of names can be made with a given finite number of syllables. Hence the names of some integers must consist of at least nineteen syllables, and among these there must be a least. Hence 'the least integer not nameable in fewer than nineteen syllables' must denote a definite integer; in fact, it denotes 111, 777. But 'the least integer not nameable in fewer than nineteen syllables' is itself a name consisting of eighteen syllables; hence the least integer not nameable in fewer than nineteen syllables can be named in eighteen syllables, which is a contradiction. This contradiction was suggested to us by Mr. G. G. Berry of the Bodleian Library.

10. Every philosophical problem, when it is subjected to the necessary analysis and justification, is found either to be not really philosophical at all, or else to be, in the sense in which we are using the word, logical.

15. There is no logical impossibility in the hypothesis that the world sprang into being five minutes ago, exactly as it then was, with a population that 'remembered' a wholly unreal past. There is no logically necessary connection between events at different times; therefore nothing that is happening now or will happen in the future can disprove the hypothesis that the world began five minutes ago.

43. Many orthodox people speak as though it were the business of sceptics to disprove received dogmas rather than of dogmatists to prove them. This is, of course, a mistake. If I were to suggest that between the Earth and Mars there is a china teapot revolving about the sun in an elliptical orbit, nobody would be able to disprove my assertion provided I were careful to add that the teapot is too small to be revealed even by our most powerful telescopes. But if I were to go on to say that, since my assertion cannot be disproved, it is intolerable presumption on the part of human reason to doubt it, I should rightly be thought to be talking nonsense. If, however, the existence of such a teapot were affirmed in ancient books, taught as the sacred truth every Sunday, and instilled into the minds of children at school, hesitation to believe in its existence would become a mark of eccentricity and entitle the doubter to the attentions of the psychiatrist in an enlightened age or of the Inquisitor in an earlier time.

65. The rules of logic are to mathematics what those of structure are to architecture.

73. The true function of logic ... as applied to matters of experience ... is analytic rather than constructive; taken a priori, it shows the possibility of hitherto unsuspected alternatives more often than the impossibility of alternatives which seemed prima facie possible. Thus, while it liberates imagination as to what the world may be, it refuses to legislate as to what the world is.

74. The conception of the necessary unit of all that is resolves itself into the poverty of the imagination, and a freer logic emancipates us from the straitwaistcoated benevolent institution which idealism palms off as the totality of being.

79. The reason that I call my doctrine logical atomism is because the atoms that I wish to arrive at as the sort of last residue in analysis are logical atoms and not physical atoms. Some of them will be what I call 'particulars' - such things as little patches of color or sounds, momentary things - and some of them will be predicates or relations and so on.

81. In a logically perfect language, there will be one word and no more for every simple object, and everything that is not simple will be expressed by a combination of words, by a combination derived, of course, from the words for the simple things that enter in, one word for each simple component.

82. Reason is a harmonising, controlling force rather than a creative one.

93. The question of 'unreality,' which confronts us at this point, is a very important one. Misled by grammar, the great majority of those logicians who have dealt with this question have dealt with it on mistaken lines. They have regarded grammatical form as a surer guide in analysis than, in fact, it is. And they have not known what differences in grammatical form are important.

94. For want of the apparatus of propositional functions, many logicians have been driven to the conclusion that there are unreal objects. It is argued, e.g., by Meinong, that we can speak about 'the golden mountain,' 'the round square,' and so on; we can make true propositions of which these are the subjects; hence they must have some kind of logical being, since otherwise the propositions in which they occur would be meaningless. In such theories, it seems to me, there is a failure of that feeling for reality which ought to be preserved even in the most abstract studies. Logic, I should maintain, must no more admit a unicorn than zoology can; for logic is concerned with the real world just as truly as zoology, though with its more abstract and general features.

95. In obedience to the feeling of reality, we shall insist that, in the analysis of propositions, nothing 'unreal' is to be admitted. But, after all, if there is nothing unreal, how, it may be asked, could we admit anything unreal? The reply is that, in dealing with propositions, we are dealing in the first instance with symbols, and if we attribute significance to groups of symbols which have no significance, we shall fall into the error of admitting unrealities, in the only sense in which this is possible, namely, as objects described.

151. Since the world is what it is, it is clear that valid reasoning from sound principles cannot lead to error; but a principle may be so nearly true as to deserve theoretical respect, and yet may lead to practical consequences which we feel to be absurd. There is therefore a justification for common sense in philosophy, but only as showing that our theoretical principles cannot be quite correct so long as their consequences are condemned by an appeal to common sense which we feel to be irresistible. The theorist may retort that common sense is no more infallible than logic. But this retort, though made by Berkeley and Hume, would have been wholly foreign to Locke's intellectual temper.

155. The worse your logic, the more interesting the consequences to which it gives rise.

163. In a man whose reasoning powers are good, fallacious arguments are evidence of bias.

208. To choose one sock from each of infinitely many pairs of socks requires the Axiom of choice, but for shoes the Axiom is not needed.

214. If a 'religion' is defined to be a system of ideas that contains unprovable statements, then Godel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one.

219. Its enduring value was simply a deeper understanding of the central concepts of mathematics and their basic laws and interrelationships. Their total translatability into just elementary logic and a simple familiar two-place predicate, membership, is of itself a philosophical sensation.