Durant 1926: The Logician (Bertrand Russell)

Reference: The Story of Philosophy

This paper presents Chapter X Section 3.1 from the book THE STORY OF PHILOSOPHY by WILL DURANT. The  contents are from the 1933 reprint of this book by TIME INCORPORATED by arrangement with Simon and Schuster, Inc.

The paragraphs of the original material (in black) are accompanied by brief comments (in color) based on the present understanding.

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III. BERTRAND RUSSELL

1. The Logician

We have kept for the last the youngest and the most virile of the European thinkers of our generation.

When Bertrand Russell spoke at Columbia University in 1914, he looked like his subject, which was epistemology—thin, pale, and moribund; one expected to see him die at every period. The Great War had just broken out, and this tender-minded, peace-loving philosopher had suffered from the shock of seeing the most civilized of continents disintegrate into barbarism. One imagined that he spoke of so remote a subject as “Our Knowledge of the External World” because he knew it was remote, and wished to be as far as possible from actualities that had become so grim. And then, seeing him again, ten years later, one was happy to find him, though fifty-two, hale and jolly, and buoyant with a still rebellious energy. This despite an intervening decade that had destroyed almost all his hopes, loosened all his friendships, and broken almost all the threads of his once sheltered and aristocratic life.

Bertrand Russell spoke at Columbia University in 1914 on epistemology, because being tender-minded and peace-loving, he wished to be as far as possible from actualities of World War I.

For he belongs to the Russells, one of the oldest and most famous families in England or the world, a family that has given statesmen to Britain for many generations. His grandfather, Lord John Russell, was a great Liberal Prime Minister who fought an unyielding battle for free trade, for universal free education, for the emancipation of the Jews, for liberty in every field. His father, Viscount Amberley, was a free-thinker, who did not over-burden his son with the hereditary theology of the West. He is now heir presumptive to the second Earl Russell but he rejects the institution of inheritance, and proudly earns his own living. When Cambridge dismissed him for his pacifism he made the world his university, and became a traveling Sophist (in the original sense of that once noble word), whom the world supported gladly.

Russell belonged to one of the oldest and most famous families in England. He rejected the institution of inheritance, and proudly earned his own living. He was dismissed from Cambridge for his pacifism.

There have been two Bertrand Russells: one who died during the war; and another who rose out of that one’s shroud, an almost mystic communist born out of the ashes of a mathematical logician. Perhaps there was a tender mystic strain in him always; represented at first by a mountain of algebraic formulae; and then finding a distorted expression in a socialism that has the ear-marks rather of a religion than of a philosophy. The most characteristic title among his books is Mysticism and Logic: a merciless attack on the illogicality of mysticism, followed by such a glorification of scientific method as makes one think of the mysticism of logic. Russell inherits the English positivist tradition, and is resolved to be tough-minded, because he knows that he cannot.

Russell inherited the English positivist tradition. He mercilessly attacked the illogicality of mysticism, and praised the scientific method.

Perhaps it was by an over-correction that he emphasized the virtues of logic, and made a divinity of mathematics. He impressed one, in 1914, as cold-blooded, as a temporarily animated abstraction, a formula with legs. He tells us that he never saw a motion-picture till he read Bergson’s cinematographic analogy for the intellect; then he reconciled himself to one performance, merely as a task in philosophy. Bergson’s vivid sense of time and motion, his feeling that all things were alive with a vital impetus; made no impression on Russell; it seemed to him a pretty poem and nothing more; for his part he would have no other god than mathematics. He had no liking for the classics; he argued vigorously, like another Spencer, for more science in education. The world’s woes, he felt, were largely due to mysticism, to culpable obscurity of thought; and the first law of morality should be, to think straight. “Better the world should perish than that I, or any other human being, should believe a lie; … that is the religion of thought, in whose scorching flames the dross of the world is being burnt away.”

Perhaps it was by an over-correction that he emphasized the virtues of logic, and made a divinity of mathematics. Bergson’s feeling that all things were alive with a vital impetus; made no impression on Russell. He had no liking for the classics; he argued for more science in education.

His passion for clarity drove him inevitably to mathematics; he was almost thrilled at the calm precision of this aristocratic science. “Mathematics, rightly viewed, possesses not only truth but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.” He believes that the progress of mathematics was the finest feature of the nineteenth century; specifically, “the solution of the difficulties which formerly surrounded the mathematical infinite is probably, the greatest achievement of which our age can boast.” In one century the old geometry which had held the fortress of mathematics for two thousand years was almost entirely destroyed; and Euclid’s text, the oldest school-book in the world, was at last superseded. “It is nothing less than a scandal that he should still be taught to boys in England.”

His passion for clarity drove him inevitably to mathematics; he was almost thrilled at the calm precision of this aristocratic science. He believed that the progress of mathematics was the finest feature of the nineteenth century.

Perhaps the source of most of the innovations in modern mathematics is the rejection of axioms; and Russell delights in men who challenge “self-evident truths” and insist upon the demonstration of the obvious. He was rejoiced to hear that parallel lines may somewhere meet, and that the whole may be no greater than one of its parts. He likes to startle the innocent reader with such puzzles as this: the even numbers are but half of all numbers, and yet there are just as many of them as there are numbers altogether,—since for every number there is its even double. Indeed, this is the whole point about that hitherto indefinable thing, the mathematical infinite: it is a whole containing parts that have as many terms or items as the whole.—The reader may follow this tangent if the spirit moves him.*

*Not that one would recommend Russell’s mathematical volumes to the lay reader. The Introduction to Mathematical Philosophy sets out with a specious intelligibility, but soon makes demands which only a specialist in mathematics can meet. Even the little book on The Problems of Philosophy, though intended to be popular, is difficult, and unnecessarily epistemological; the larger volume, Mysticism and Logic, is much clearer and closer to the earth. The Philosophy of Leibnitz is a fine exposition of a great thinker, ignored in these limited pages. The twin volumes on The Analysis of Mind and The Analysis of Matter will serve to bring the reader up to date with certain aspects of psychology and physics. The post-war books are easy reading; and though they suffer from the confusion natural to a man whose idealism is slipping into disillusionment, they are interesting and worth while. Why Men Fight? is still the best of these tracts for the times. Roads to Freedom is a genial survey of social philosophies as old as Diogenes, which Russell rediscovers with all the enthusiasm of a Columbus.

Perhaps the source of most of the innovations in modern mathematics is the rejection of axioms; and Russell delighted in men who challenge “self-evident truths” and insist upon the demonstration of the obvious. 

What draws Russell to mathematics is, again, its rigid impersonality and objectivity; here, and here alone, is eternal truth, and absolute knowledge; these a priori theorems are the “Ideas” of Plato, the “eternal order” of Spinoza, the substance of the world. The aim of philosophy should be to equal the perfection of mathematics by confining itself to statements similarly exact, and similarly true before all experience. “Philosophical propositions … must be a priori,” says this strange positivist. Such propositions will refer not to things but to relations, and to universal relations. They will be independent of specific “facts” and events; if every particular in the world were changed, these propositions would still be true. E. g., “if all A’s are B’s, and X is A, then X is a B”: this is true whatever A may be; it reduces to a universal and a priori form the old syllogism about the mortality of Socrates; and it would be true if no Socrates, even if nobody at all, had ever existed. Plato and Spinoza were right: “the world of universals may also be described as the world of being. The world of being is unchangeable, rigid, exact, delightful to the mathematician, the logician, the builder of metaphysical systems, and all who love perfection more than life.” To reduce all philosophy to such mathematical form, to take all specific content out of it, to compress it (voluminously) into mathematics—this was the ambition of this new Pythagoras.

“People have discovered how to make reasoning symbolic, as it is in algebra, so that deductions can be effected by mathematical rules. … 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. … 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.”

What draws Russell to mathematics is, again, its rigid impersonality and objectivity; here, and here alone, is eternal truth, and absolute knowledge; these a priori theorems are the “Ideas” of Plato, the “eternal order” of Spinoza, the substance of the world. They refer not to things but to universal relations. 

And perhaps (if one may rudely interrupt exposition with opinion) this description does no great injustice to mathematical philosophy. It is a splendid game for those who like it; guaranteed to “kill time” as rapidly as chess; it is a new form of solitaire, and should be played as far as possible from the contaminating touch of things. It is remarkable that after writing several volumes of this learned moonshine, Bertrand Russell should suddenly come down upon the surface of this planet, and begin to reason very passionately about war, and government, and socialism, and revolution,—and never once make use of the impeccable formulae piled like Pelion upon Ossa in his Principia Mathematica. Nor has anyone else, observably, made use of them. To be useful, reasoning must be about things, and must keep in touch with them at every step. Abstractions have their use as summaries; but as implements of argument they require the running test and commentary of experience. We are in danger here of a scholasticism beside which the giant Summa’s of medieval philosophy would be models of pragmatic thought.

But what use are these impeccable formulae in Russell’s Principia Mathematica when they cannot be used to solve the real problems of war, and government, and socialism, and revolution? To be useful, reasoning must be about things, and must keep in touch with them at every step. 

From such a starting point, Bertrand Russell was almost fated to pass into agnosticism. He found so much in Christianity that could not be phrased in mathematics, that he abandoned it all except its moral code. He speaks scornfully of a civilization that persecutes men who deny Christianity, and imprisons those who take it seriously. He can find no God in such a contradictory world; rather, only a humorous Mephistopheles could have produced it, and in a mood of exceptional deviltry. He follows Spencer in his vision of the end of the world, and rises to eloquence in describing the Stoic’s resignation to the ultimate defeat of every individual and every species. We talk of evolution and progress; but progress is an egotistical phrase and evolution is but one half of an unmoral cycle of events terminating in dissolution and death. “Organic life, we are told, has developed gradually from the protozoon to the philosopher; and this development, we are assured, is indubitably an advance. Unfortunately, it is the philosopher; not the protozoon, who gives us this assurance.”  The “free man” cannot comfort himself with childish hopes and anthropomorphic gods; he has to keep his courage up even though he knows that in the end he too must die, that all things must die. Nevertheless, he will not surrender; if he cannot win, he can at least enjoy the fight; and by the knowledge that foresees his own defeat he stands superior to the blind forces that will destroy him. His worship will go not to these brute powers without, that by their aimless persistence conquer him, and tear down every home and every civilization that he builds; but to those creative powers within him that struggle on in the face of failure, and raise for at least some centuries the frail beauty of carved and pictured things, and the majestic ruins of the Parthenon. 

This was the starting point of Russell’s philosophy. The “free man” cannot comfort himself with childish hopes and anthropomorphic gods; he has to keep his courage up even though he knows that in the end he too must die, that all things must die. His worship will go to those creative powers within him that struggle on in the face of failure.

Such was the philosophy of Bertrand Russell-before the war.

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