# Bertrand Russell

1872 - 1970

## A Quote by Bertrand Arthur William Russell on conformity, mathematics, and necessity

Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.

Source: N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.

## A Quote by Bertrand Arthur William Russell on mathematics

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.

Source: Mysticism and Logic and Other Essays

## A Quote by Bertrand Arthur William Russell on age, discovery, facts, logic, mathematics, and principles

The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists in the analysis of Symbolic Logic itself.

Source: Principles of Mathematics. 1903.

## A Quote by Bertrand Arthur William Russell on achievement, science, and world

Almost everything that distinguishes the modern world from earlier centuries is attibutable to science, which achieved its most spectacular triumphs in the seventeenth century.

Source: Bertrand Russell, History of Western Philosophy, Allen & Unwin, London, 1979, p 512.

## A Quote by Bertrand Arthur William Russell on belief, choice, clarity, confession, decisions, impossibility, inclusion, language, logic, problems, questions, sharing, truth, virtue, work, and writers

It seems clear that there must be some way of defining logic otherwise than in relation to a particular logical language. The fundamental characteristic of logic, obviously, is that which is indicated when we say that logical propositions are true in virtue of their form. The question of demonstrability cannot enter in, since every proposition which, in one system, is deduced from the premises, might, in another system, be itself taken as a premise. If the proposition is complicated, this is inconvenient, but it cannot be impossible. All the propositions that are demonstrable in any admissible logical system must share with the premises the property of being true in virtue of their form; and all propositions which are true in virtue of their form ought to be included in any adequate logic. Some writers, for example Carnap in his "Logical Syntax of Language," treat the whole matter as being more a matter of linguistic choice than I can believe it to be. In the above mentioned work, Carnap has two logical languages, one of which admits the multiplicative axiom and the axiom of infinity, while the other does not. I cannot myself regard such a matter as one to be decided by our arbitrary choice. It seems to me that these axioms either do, or do not, have the characteristic of formal truth which characterises logic, and that in the former event every logic must include them, while in the latter every logic must exclude them. I confess, however, that I am unable to give any clear account of what is meant by saying that a proposition is "true in virtue of its form." But this phrase, inadequate as it is, points, I think, to the problem which must be solved if an adequate definition of logic is to be found.

Source: the Introduction to the second edition of The Principles of Mathematics, Russell

## A Quote by Bertrand Arthur William Russell on life and possessions

It is preoccupation with possessions, more than anything else, that prevents us from living freely and nobly.

## A Quote by Bertrand Arthur William Russell on acceptance, certainty, discovery, expectation, faith, kindness, knowledge, mathematics, people, religion, rest, security, teachers, thought, work, and world

I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers expected me to accept, were full of fallacies, and that, if certainty were indeed discoverable in mathematics, it would be in a new field of mathematics, with more solid foundations than those that had hitherto been thought secure. But as the work proceeded, I was continually reminded of the fable about the elephant and the tortoise. having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was no more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.

Source: Portraits from Memory.

## A Quote by Bertrand Arthur William Russell on animals, argument, belief, certainty, dogs, life, and plants

"But," you might say, "none of this shakes my belief that 2 and 2 are 4." You are quite right, except in marginal cases - and it is only in marginal cases that you are doubtful whether a certain animal is a dog or a certain length is less than a meter. Two must be two of something, and the proposition "2 and 2 are 4" is useless unless it can be applied. Two dogs and two dogs are certainly four dogs, but cases arise in which you are doubtful whether two of them are dogs. "Well, at any rate there are four animals," you may say. But there are microorganisms concerning which it is doubtful whether they are animals or plants. "Well, then living organisms," you say. But there are things of which it is doubtful whether they are living organisms or not. You will be driven into saying: "Two entities and two entities are four entities." When you have told me what you mean by "entity," we will resume the argument.

Source: N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.

## A Quote by Bertrand Arthur William Russell on awareness, education, facts, future, greatness, individuality, intelligence, knowledge, life, mind, organize, past, people, power, religion, present, time, value, and wishes

If I had the power to organize higher education as I should wish it to be, I should seek to substitute for the old orthodox religions - which appeal to few among the young, and those as a rule the least intelligent and the most obscurantist - something which is perhaps hardly to be called religion, since it is merely a focusing of attention upon well-ascertained facts. I should seek to make young people vividly aware of the past, vividly realizing that the future of man will in all likelihood be immeasurably longer than his past, profoundly conscious of the minuteness of the planet upon which we live and of the fact that life on this planet is only a temporary incident; and at the same time with these facts which tend to emphasize the insignificance of the individual, I should present quite another set of facts designed to impress upon the mind of the young the greatness of which the individual is capable, and the knowledge that throughout all the depths of stellar space nothing of equal value is known to us. . . .

Source: The Conquest of Happiness