The Life of Reason by George Santayana (i have read the book TXT) ๐
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- Author: George Santayana
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The applicability of mathematics is not vouched for by mathematics but by sense, and its application in some distant part of nature is not vouched for by mathematics but by inductive arguments about nature's uniformity, or by the character which the notion, "a distant part of nature," already possesses. Inapplicable mathematics, we are told, is perfectly thinkable, and systematic deductions, in themselves valid, may be made from concepts which contravene the facts of perception. We may suspect, perhaps, that even these concepts are framed by analogy out of suggestions found in sense, so that some symbolic relevance or proportion is kept, even in these dislocated speculations, to the matter of experience. It is like a new mythology; the purely fictitious idea has a certain parallelism and affinity to nature and moves in a human and familiar way. Both data and method are drawn from applicable science, elements of which even myth, whether poetic or mathematical, may illustrate by a sort of variant or fantastic reduplication.
The great glory of mathematics, like that of virtue, is to be useful while remaining free. Number and measure furnish an inexhaustible subject-matter which the mind can dominate and develop dialectically as it is the mind's inherent office to develop ideas. At the same time number and measure are the grammar of sense; and the more this inner logic is cultivated and refined the greater subtlety and sweep can be given to human perception. Astronomy on the one hand and mechanical arts on the other are fruits of mathematics by which its worth is made known even to the layman, although the born mathematician would not need the sanction of such an extraneous utility to attach him to a subject that has an inherent cogency and charm. Ideas, like other things, have pleasure in propagation, and even when allowance is made for birth-pangs and an occasional miscarriage, their native fertility will always continue to assert itself. The more ideal and frictionless the movement of thought is, the more perfect must be the physiological engine that sustains it. The momentum of that silent and secluded growth carries the mind, with a sense of pure disembodied vision, through the logical labyrinth; but the momentum is vital, for the truth itself does not move.
Whether the airy phantoms thus brought into being are valued and preserved by the world is an ulterior point of policy which the pregnant mathematician does not need to consider in bringing to light the legitimate burden of his thoughts. But were mathematics incapable of application, did nature and experience, for instance, illustrate nothing but Parmenides' Being or Hegel's Logic, the dialectical cogency which mathematics would of course retain would not give this science a very high place in the Life of Reason. Mathematics would be an amusement, and though apparently innocent, like a game of patience, it might even turn out to be a wasteful and foolish exercise for the mind; because to deepen habits and cultivate pleasures irrelevant to other interests is a way of alienating ourselves from our general happiness. Distinction and a curious charm there may well be in such a pursuit, but this quality is perhaps traceable to affinities and associations with other more substantial interests, or is due to the ingenious temper it denotes, which touches that of the wit or magician. Mathematics, if it were nothing more than a pleasure, might conceivably become a vice. Those addicted to it might be indulging an atavistic taste at the expense of their humanity. It would then be in the position now occupied by mythology and mysticism. Even as it is, mathematicians share with musicians a certain partiality in their characters and mental development. Masters in one abstract subject, they may remain children in the world; exquisite manipulators of the ideal, they may be erratic and clumsy in their earthly ways. Immense as are the uses and wide the applications of mathematics, its texture is too thin and inhuman to employ the whole mind or render it harmonious. It is a science which Socrates rejected for its supposed want of utility; but perhaps he had another ground in reserve to justify his humorous prejudice. He may have felt that such a science, if admitted, would endanger his thesis about the identity of virtue and knowledge.
Mathematical method has been the envy of philosophers, perplexed and encumbered as they are with the whole mystery of existence, and they have attempted at times to emulate mathematical cogency. Now the lucidity and certainty found in mathematics are not inherent in its specific character as the science of number or dimension; they belong to dialectic as a whole which is essentially elucidation. The effort to explain meanings is in most cases abortive because these meanings melt in our handsโa defeat which Hegel would fain have consecrated, together with all other evils, into necessity and law. But the merit of mathematics is that it is so much less Hegelian than life; that it holds its own while it advances, and never allows itself to misrepresent its original intent. In all it finds to say about the triangle it never comes to maintain that the triangle is really a square. The privilege of mathematics is simply to have offered the mind, for dialectical treatment, a material to which dialectical treatment could be honestly applied. This material consists in certain general aspects of sensationโits extensity, its pulsation, its distribution into related parts. The wakefulness that originally makes these abstractions is able to keep them clear, and to elaborate them infinitely without contradicting their essence.
For this reason it is always a false step in mathematical science, a step over its brink into the abyss beyond, when we try to reduce its elements to anything not essentially sensible. Intuition must continue to furnish the subject of discourse, the axioms, and the ultimate criteria and sanctions. Calculation and transmutation can never make their own counters or the medium in which they move. So that space, number, continuity, and every other elementary intuition remains at bottom opaqueโopaque, that is, to mathematical science; for it is no paradox, but an obvious necessity, that the data of a logical operation should not be producible by its workings. Reason would have nothing to do if it had no irrational materials. Saint Augustine's rhetoric accordingly coveredโas so often with himโa profound truth when he said of time that he knew what it was when no one asked him, but if any one asked him he did not know; which may be restated by saying that time is an intuition, an aspect of crude experience, which science may work with but which it can never arrive at.
When a concretion is formed in discourse and an intent is attained in consciousness, predicates accrue to the subject in a way which is perfectly empirical. Dialectic is not retrospective; it does not consist in recovering ground previously surveyed. The accretion of new predicates comes in answer to chance questions, questions raised, to be sure, about a given theme. The subject is fixed by the mind's intent and it suffices to compare any tentative assertion made about it with that intent itself to see whether the expression suggested for it is truly dialectical and thoroughly honest. Dialectic verifies by reconsideration, by equation of tentative results with fixed intentions. It does not verify, like the sciences of existence, by comparing a hypothesis with a new perception. In dialectic no new perception is wanted; the goal is to understand the old fact, to give it an aureole and not a progeny. It is a transubstantiation of matter, a passage from existence to eternity. In this sense dialectic is "synthetic a priori"; it analyses an intent which demanded further elucidation and had fixed the direction and principle of its expansion. If this intent is abandoned and a new subject is introduced surreptitiously, a fallacy is committed; yet the correct elucidation of ideas is a true progress, nor could there be any progress unless the original idea were better expressed and elicited as we proceeded; so that constancy in intent and advance in explication are the two requisites of a cogent deduction.
The question in dialectic is always what is true, what can be said, about this; and the demonstrative pronoun, indicating an act of selective attention, raises the object it selects to a concretion in discourse, the relations of which in the universe of discourse it then proceeds to formulate. At the same time this dialectical investigation may be full of surprises. Knowledge may be so truly enriched by it that knowledge, in an ideal sense, only begins when dialectic has given some articulation to being. Without dialectic an animal might follow instinct, he might have vivid emotions, expectations, and dreams, but he could hardly be said to know anything or to guide his life with conscious intent. The accretions that might come empirically into any field of vision would not be new predicates to be added to a known thing, unless the logical and functional mantle of that thing fell upon them and covered them. While the right of particulars to existence is their own, granted them by the free grace of heaven, their ability to enlarge our knowledge on any particular subjectโtheir relevance or incidence in discourseโhangs on their fulfilling the requirements which that subject's dialectical nature imposes on all its expressions.
It is on this ground, for instance, that the image of a loaf of bread is so far from being the loaf of bread itself. External resemblance is nothing; even psychological derivation or superposition is nothing; the intent, rather, which picks out what that object's function and meaning shall be, alone defines its idea; and this function involves a locus and a status which the image does not possess. Such admirable iridescence as the image might occasionally put onโin the fine arts, for instanceโwould not constitute any iridescence or transformation in the thing; nor would identity of aspect preserve the thing if its soul, if its utility, had disappeared. Herein lies the ground for the essential or functional distinction between primary and secondary qualities in things, a distinction which a psychological scepticism has so hastily declared to be untenable. If it was discovered, said these logicians, that space was perceived through reading muscular sensations, space, and the muscles too, were thereby proved to be unreal. This remarkable sophism passed muster in the philosophical world for want of attention to dialectic, which might so easily have shown that what a thing means is spatial distinction and mechanical efficacy, and that the origin of our perceptions, which are all equally bodily and dependent on material stimulation, has nothing to do with their respective claims to hypostasis. It is intent that makes objects objects; and the same intent, defining the function of things, defines the scope of those qualities which are essential to them. In the flux substances and shadows drift down together; it is reason that discerns the difference.
Purposes need dialectical articulation as much as essences do, and without an articulate and fixed purpose, without an ideal, action would collapse into mere motion or conscious change. It is notably in this region that elucidation constitutes progress; for to understand the properties of number may be less important than empirically to count; but to see and feel the values of things in all their distinction and fulness is the
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