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.
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.
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.”36
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.”37 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.”38 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.”39
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.40
What draws Russell to mathematics is, again, its rigid impersonality and objectivity: here, and here alone, is eternal truth, and absolute knowledge; these à 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 à 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 proportions 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 à 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.”41 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.”42
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.