§ [52]. But though the abstractness involved in scientific description is open and deliberate, we must come to a more precise understanding of it, if we are to draw any conclusion as to what it involves. In his "Principles of Human Knowledge," the English philosopher Bishop Berkeley raises the question as to the universal validity of mathematical demonstrations. If we prove from the image or figure of an isosceles right triangle that the sum of its angles is equal to two right angles, how can we know that this proposition holds of all triangles?
"To which I answer, that, though the idea I have in view whilst I make the demonstration be, for instance, that of an isosceles rectangular triangle whose sides are of a determinate length, I may nevertheless be certain it extends to all other rectilinear triangles, of what sort or bigness soever. And that because neither the right angle, nor the equality, nor determinate length of the sides are at all concerned in the demonstration. It is true the diagram I have in view includes all these particulars; but then there is not the least mention made of them in the proof of the proposition."[140:6]
Of the total conditions present in the concrete picture of a triangle, one may in one's calculations neglect as many as one sees fit, and work with the remainder. Then, if one has clearly distinguished the conditions used, one may confidently assert that whatever has been found true of them holds regardless of the neglected conditions. These may be missing or replaced by others, provided the selected or (for any given investigation) essential conditions are not affected. That which is true once is true always, provided time is not one of its conditions; that which is true in one place is true everywhere, provided location is not one of its conditions. But, given any concrete situation, the more numerous the conditions one ignores in one's calculations, the less adequate are one's calculations to that situation. The number of its inhabitants, and any mathematical operation made with that number, is true, but only very abstractly true of a nation. A similar though less radical abstractness appertains to natural science. Simple qualities of sound or color, and distinctions of beauty or moral worth, together with many other ingredients of actual experience attributed therein to the objects of nature, are ignored in the mechanical scheme. There is a substitution of certain mechanical arrangements in the case of the first group of properties, the simple qualities of sense, so that they may be assimilated to the general scheme of events, and their occurrence predicted. But their intrinsic qualitative character is not reckoned with, even in psychology, where the physiological method finally replaces them with brain states. Over and above these neglected properties of things there remain the purposive activities of thought. It is equally preposterous to deny them and to describe them in mechanical terms. It is plain, then, that natural science calculates upon the basis of only a fraction of the conditions that present themselves in actual experience. Its conclusions, therefore, though true so far as they go, and they may be abstractly true of everything, are completely true of nothing.
But Scientific Truth is Valid for Reality.
§ [53]. Such, in brief, is the general charge of inadequacy which may be urged against natural science, not in the spirit of detraction, but for the sake of a more sound belief concerning reality. The philosopher falls into error no less radical than that of the dogmatic scientist, when he charges the scientist with untruth, and attaches to his concepts the predicate of unreality. The fact that the concepts of science are selected, and only inadequately true of reality, should not be taken to mean that they are sportive or arbitrary. They are not "devices" or abbreviations, in any sense that does not attach to such symbolism as all thought involves. Nor are they merely "hypothetical," though like all thought they are subject to correction.[142:7] The scientist does not merely assert that the equation for energy is true if nature's capacity for work be measurable, but that such is actually the case. The statistician does not arrive at results contingent upon the supposition that men are numerable, but declares his sums and averages to be categorically true. Similarly scientific laws are true; only, to be sure, so far as they go, but with no condition save the condition that attaches to all knowledge, viz., that it shall not need correction. The philosophy of science, therefore, is not the adversary of science, but supervenes upon science in the interests of the ideal of final truth. No philosophy of science is sound which does not primarily seek by an analysis of scientific concepts to understand science on its own grounds. Philosophy may understand science better than science understands itself, but only by holding fast to the conviction of its truth, and including it within whatever account of reality it may be able to formulate.
Relative Practical Value of Science and Philosophy.
§ [54]. Though philosophy be the most ancient and most exalted of human disciplines, it is not infrequently charged with being the most unprofitable. Science has amassed a fortune of information, which has facilitated life and advanced civilization. Is not philosophy, on the other hand, all programme and idle questioning? In the first place, no questioning is idle that is logically possible. It is true that philosophy shows her skill rather in the asking than in the answering of questions. But the formal pertinence of a question is of the greatest significance. No valid though unanswered question can have a purely negative value, and especially as respects the consistency or completeness of truth. But, in the second place, philosophy with all its limitations serves mankind as indispensably as science. If science supplies the individual with means of self-preservation, and the instruments of achievement, philosophy supplies the ideals, or the objects of deliberate construction. Such reflection as justifies the adoption of a fundamental life purpose is always philosophical. For every judgment respecting final worth is a judgment sub specie eternitatis. And the urgency of life requires the individual to pass such judgments. It is true that however persistently reflective he may be in the matter, his conclusion will be premature in consideration of the amount of evidence logically demanded for such a judgment. But he must be as wise as he can, or he will be as foolish as conventionality and blind impulse may impel him to be. Philosophy determines for society what every individual must practically determine upon for himself, the most reasonable plan of reality as a whole which the data and reflection of an epoch can afford. It is philosophy's service to mankind to compensate for the enthusiasm and concentration of the specialist, a service needed in every "present day." Apart from the philosopher, public opinion is the victim of sensationalism, and individual opinion is further warped by accidental propinquity. It is the function of philosophy to interpret knowledge for the sake of a sober and wise belief. The philosopher is the true prophet, appearing before men in behalf of that which is finally the truth. He is the spokesman of the most considerate and comprehensive reflection possible at any stage in the development of human thought. Owing to a radical misconception of function, the man of science has in these later days begun to regard himself as the wise man, and to teach the people. Popular materialism is the logical outcome of this determination of belief by natural science. It may be that this is due as much to the indifference of the philosopher as to the forwardness of the scientist, but in any case the result is worse than conservative loyalty to religious tradition. For religion is corrected surely though slowly by the whole order of advancing truth. Its very inflexibility makes it proof against an over-emphasis upon new truth. It has generally turned out in time that the obstinate man of religion was more nearly right than the adaptable intellectual man of fashion. But philosophy, as a critique of science for the sake of faith, should provide the individual religious believer with intellectual enlightenment and gentleness. The quality, orderliness, and inclusiveness of knowledge, finally determine its value; and the philosopher, premature as his synthesis may some day prove to be, is the wisest man of his own generation. From him the man of faith should obtain such discipline of judgment as shall enable him to be fearless of advancing knowledge, because acquainted with its scope, and so intellectually candid with all his visions and his inspirations.
