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Winds Of Doctrine By George Santayana Characters: 12028

Updated: 2017-12-06 00:03

"The solution of the difficulties which formerly surrounded the mathematical infinite is probably," says Mr. Russell, "the greatest achievement of which our own age has to boast.... It was assumed as self-evident, until Cantor and Dedekind established the opposite, that if, from any collection of things, some were taken away, the number of things left must always be less than the original number of things. This assumption, as a matter of fact, holds only of finite collections; and the rejection of it, where the infinite is concerned, has been shown to remove all the difficulties that hitherto baffled human reason in this matter." And he adds in another place: "To reconcile us, by the exhibition of its awful beauty, to the reign of Fate ... is the task of tragedy. But mathematics takes us still further from what is human, into the region of absolute necessity, to which not only the actual world, but every possible world, must conform; and even here it builds a habitation, or rather finds a habitation eternally standing, where our ideals are fully satisfied and our best hopes are not thwarted. It is only when we thoroughly understand the entire independence of ourselves, which belongs to this world that reason finds, that we can adequately realise the profound importance of its beauty."

Mathematics seems to have a value for Mr. Russell akin to that of religion. It affords a sanctuary to which to flee from the world, a heaven suffused with a serene radiance and full of a peculiar sweetness and consolation. "Real life," he writes, "is to most men a long second-best, a perpetual compromise between the ideal and the possible; but the world of pure reason knows no compromise, no practical limitations, no barrier to the creative activity embodying in splendid edifices the passionate aspiration after the perfect from which all great work springs. Remote from human passions, remote even from the pitiful laws of nature, the generations have gradually created an ordered cosmos where pure thought can dwell as in its natural home, and where one, at least, of our nobler impulses can escape from the dreary exile of the actual world." This study is one of "those elements in human life which merit a place in heaven." "The true spirit of delight, the exaltation, the sense of being more than man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry."

This enthusiastic language might have, I should think, an opposite effect upon some readers to that which Mr. Russell desires. It might make them suspect that the claim to know an absolute ideal necessity, so satisfying to one of our passionate impulses, might be prompted by the same conceit, and subject to the same illusion, as the claim to know absolute truth in religion. Beauty, when attributed to necessary relations between logical entities, casts a net of subjectivity over them; and at this net the omnivorous empiricist might be tempted to haul, until he fancied he had landed the whole miraculous draught of fishes. The fish, however, would have slipped through the meshes; and it would be only his own vital emotion, projected for a moment into the mathematical world, that he would be able to draw back and hug to his bosom. Eternal truth is as disconsolate as it is consoling, and as dreary as it is interesting: these moral values are, in fact, values which the activity of contemplating that sort of truth has for different minds; and it is no congruous homage offered to ideal necessity, but merely a private endearment, to call it beautiful or good. The case is not such as if we were dealing with existence. Existence is arbitrary; it is a questionable thing needing justification; and we, at least, cannot justify it otherwise than by taking note of some affinity which it may show to human aspirations. Therefore our private endearments, when we call some existing thing good or beautiful, are not impertinent; they assign to this chance thing its only assignable excuse for being, namely, the service it may chance to render to the spirit. But ideal necessity or, what is the same thing, essential possibility has its excuse for being in itself, since it is not contingent or questionable at all. The affinity which the human mind may develop to certain provinces of essence is adventitious to those essences, and hardly to be mentioned in their presence. It is something the mind has acquired, and may lose. It is an incident in the life of reason, and no inherent characteristic of eternal necessity.

The realm of essence contains the infinite multitude of Leibnitz's possible worlds, many of these worlds being very small and simple, and consisting merely of what might be presented in some isolated moment of feeling. If any such feeling, however, or its object, never in fact occurs, the essence that it would have presented if it had occurred remains possible merely; so that nothing can ever exist in nature or for consciousness which has not a prior and independent locus in the realm of essence. When a man lights upon a thought or is interested in tracing a relation, he does not introduce those objects into the realm of essence, but merely selects them from the plenitude of what lies there eternally. The ground of this selection lies, of course, in his human nature and circumstances; and the satisfaction he may find in so exercising his mind will be a consequence of his mental disposition and of the animal instincts beneath. Two and two would still make four if I were incapable of counting, or if I found it extremely painful to do so, or if I thought it naive and pre-Kantian of these numbers not to combine in a more vital fashion, and make five. So also, if I happen to enjoy counting, or to find the constancy of numbers sublime, and the reversibility of the processes connecting them consoling, in contrast to the irrevocable flux of living things, all this is due to my idiosyncrasy. It is no part of the essence of numbers to be con

genial to me; but it has perhaps become a part of my genius to have affinity to them.

And how, may I ask, has it become a part of my genius? Simply because nature, of which I am a part, and to which all my ideas must refer if they are to be relevant to my destiny, happens to have mathematical form. Nature had to have some form or other, if it was to exist at all; and whatever form it had happened to take would have had its prior place in the realm of essence, and its essential and logical relations there. That particular part of the realm of essence which nature chances to exemplify or to suggest is the part that may be revealed to me, and that is the predestined focus of all my admirations. Essence as such has no power to reveal itself, or to take on existence; and the human mind has no power or interest to trace all essence. Even the few essences which it has come to know, it cannot undertake to examine exhaustively; for there are many features nestling in them, and many relations radiating from them, which no one needs or cares to attend to. The implications which logicians and mathematicians actually observe in the terms they use are a small selection from all those that really obtain, even in their chosen field; so that, for instance, as Mr. Russell was telling us, it was only the other day that Cantor and Dedekind observed that although time continually eats up the days and years, the possible future always remains as long as it was before. This happens to be a fact interesting to mankind. Apart from the mathematical puzzles it may help to solve, it opens before existence a vista of perpetual youth, and the vital stress in us leaps up in recognition of its inmost ambition. Many other things are doubtless implied in infinity which, if we noticed them, would leave us quite cold; and still others, no doubt, are inapprehensible with our sort and degree of intellect. There is of course nothing in essence which an intellect postulated ad hoc would not be able to apprehend; but the kind of intellect we know of and possess is an expression of vital adjustments, and is tethered to nature.

That a few eternal essences, then, with a few of their necessary relations to one another, do actually appear to us, and do fascinate our attention and excite our wonder, is nothing paradoxical. This is merely what was bound to happen, if we became aware of anything at all; for the essence embodied in anything is eternal and has necessary relations to some other essences. The air of presumption which there might seem to be in proclaiming that mathematics reveals what has to be true always and everywhere, vanishes when we remember that everything that is true of any essence is true of it always and everywhere. The most trivial truths of logic are as necessary and eternal as the most important; so that it is less of an achievement than it sounds when we say we have grasped a truth that is eternal and necessary.

This fact will be more clearly recognised, perhaps, if we remember that the cogency of our ideal knowledge follows upon our intent in fixing its object. It hangs on a virtual definition, and explicates it. We cannot oblige anybody or anything to reproduce the idea which we have chosen; but that idea will remain the idea it is whether forgotten or remembered, exemplified or not exemplified in things. To penetrate to the foundation of being is possible for us only because the foundation of being is distinguishable quality; were there no set of differing characteristics, one or more of which an existing thing might appropriate, existence would be altogether impossible. The realm of essence is merely the system or chaos of these fundamental possibilities, the catalogue of all exemplifiable natures; so that any experience whatsoever must tap the realm of essence, and throw the light of attention on one of its constituent forms. This is, if you will, a trivial achievement; what would be really a surprising feat, and hardly to be credited, would be that the human mind should grasp the constitution of nature; that is, should discover which is the particular essence, or the particular system of essences, which actual existence illustrates. In the matter of physics, truly, we are reduced to skimming the surface, since we have to start from our casual experiences, which form the most superficial stratum of nature, and the most unstable. Yet these casual experiences, while they leave us so much in the dark as to their natural basis and environment, necessarily reveal each its ideal object, its specific essence; and we need only arrest our attention upon it, and define it to ourselves, for an eternal possibility, and some of its intrinsic characters, to have been revealed to our thought.

Whatever, then, a man's mental and moral habit might be, it would perforce have affinity to some essence or other; his life would revolve about some congenial ideal object; he would find some sorts of form, some types of relation, more visible, beautiful, and satisfying than others. Mr. Russell happens to have a mathematical genius, and to find comfort in laying up his treasures in the mathematical heaven. It would be highly desirable that this temperament should be more common; but even if it were universal it would not reduce mathematical essence to a product of human attention, nor raise the "beauty" of mathematics to part of its essence. I do not mean to suggest that Mr. Russell attempts to do the latter; he speaks explicitly of the value of mathematical study, a point in ethics and not directly in logic; yet his moral philosophy is itself so much assimilated to logic that the distinction between the two becomes somewhat dubious; and as Mr. Russell will never succeed in convincing us that moral values are independent of life, he may, quite against his will, lead us to question the independence of essence, with that blind gregarious drift of all ideas, in this direction or in that, which is characteristic of human philosophising.

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