They may be the rough edges of the building, showing where the next construction is to be. Whether it is to be growth or failure, however, can only be empirically determined: but it needed the humble-mindedness of Maxwell to see in the optimistic 19th century, the theoretical importance of these signs of possible limits to scientific ad vance. The third of the series of postulates is that our sensations must come to us in such an order as to reveal the laws really present. The possibility of other orders in our sensations has best been brought out, I think, in Mr. Norman Campbell's book, Physics: The Elements, where he makes it clear how great a part in the setting in fruitful order of our sensory observations is played by comparison with other observers. I shall not develop this postulate further, but refer only to one point: namely, that the need for this postulate discloses the possibility that just as there may be chaotic regions in space, so also there may be regions in time where science is impossible. 5 I will conclude this brief sketch of what is implied in the notion of intelligibility in scientific thought by referring back to what was said at the beginning about the tendency towards more generalized forms of scientific philosophising. Modern science is taking more and more abstract forms. For full grasp of its vast operations one must stand away from the process and view it as a whole. Further, as addition is made to the superstructure of science, it is increasingly necessary to pay attention to the foundations on which it rests. That is why our philosophising on science must, within the limits of our powers, be made both wider and deeper. A. E. HEATH UNIVERSITY COLLEGE OF SWANSEA, WALES. W KANTIAN RELATIVITY HILE it is an oft repeated statement that Kant effected a "Copernican revolution", or thought that he had done so, there is a rather general confusion as to why he called it "Copernican". In fact, the criticism is sometimes made that, in its anthropocentricism, it is Ptolemaic rather than Copernican. Norman Kemp Smith1 has shown that Kant's analogy is well chosen and accurate. Copernicus explained the apparently objective movements of the planets and the sun as projections, with reference to the frame of the fixed stars, of our own motion. The extension of this principle of explanation to a vastly wider field of knowledge constitutes Kant's "Copernican revolution”, and amounts to a very general theory of relativity. The study of this relativity in the field of space, time, and motion is the object of the following discussion. The close relation which Kantian relativity bears to the Einstein theory and modern physics, though familiar to specialists, deserves a more widespread and general notice than it has hitherto received. At any rate, such a study may serve to place Kant in perspective, and to humanize what is often felt to be the most abstract part of his system. In Newton and Leibniz Kant found conflicting teachers. Newton had distinguished absolute and relative space, absolute and relative time, absolute and relative motion. 1Smith, Norman Kemp, A Commentary to Kant's Critique of Pure Reason, p. 22-25. Leibniz had made them all relative, for, according to his view, apart from objects existing or conceived, space and time do not exist. Newton associates this relational view with popular notions and prejudices. He says: "I do not define time, space, place, and motion, as being well known to all. Only I must observe that the vulgar conceive these quantities under no other notions but from the relation they bear to sensible objects. And thence arise prejudices for the removal of which it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common." "I. Absolute, true, and mathematical time, of itself and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent and common time is some sensible and external. measure of duration by means of motion, which is commonly used instead of true time, such as an hour, a day, a month, a year. "II. Absolute space, in its own nature, and without regard to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of absolute space, which our senses determine by the position of bodies; and which is vulgarly taken for immovable space; such as the dimensions of subterranean, or aerial, or celestial space determined by its position in respect of the earth." Similarly Newton draws the distinction between absolute and relative position, and absolute and relative motion. Though he states these propositions dogmatically as facts they are probably no more than axioms which seemed to him self-evident, and which aided him in clear thinking. It is still possible, in spite of the most recent contributions to science, to adopt as one's foundation axioms the Newtonian space and time, and the Euclidean geometry. They may not 2Newton's Principia, Daniel Adee, 1846, pp. 77-78. be the neatest or most simple axioms, and their self-evidence is no longer conceded, but they can hardly be successfully overthrown. The corollaries are that the world is infinite in extent, that it is infinitely complex at all stages, and that it has no limits in time." In other words, it leaves us in a position of being unable fully to comprehend our world in its extent, complexity, or duration. It solves the antinomies of Kant by denying the thesis-that the world is finite-and asserting the antithesis-that the world is infinite. Although for all practical purposes we may adopt the axioms of absolute space and time, there are difficulties involved which are more easily passed by than solved. Since all points of reference and all measurements are relative to human limitations and purposes, where shall be found the basis for the immovable space and the evenly flowing time? Newton felt the difficulty and took refuge in the theory of an all-pervading and immovable ether. This seemed so satisfactory that very little doubt was cast upon it, especially in view of the wave theory of light, till the negative results of the Michelson and Morley experiment of 1887 shook the confidence of the experimenters and the expectant world. As for time, the conception of an absolute time, in relation to which all specific times stand, seemed to be demanded by the then recent discovery of Roemer of the fact that light requires time for its propagation through space. To Newton this fact appeared conclusively to prove that there is a flow of time independent of any personal reference. It seemed to overthrow all theories which made time a matter of the succession of impressions or the mere strung-outness of experience or the relation of events of the world. The fact that all calculations had to be checked and Newton, however, thought it not inconceivable that God had created the world at a definite time. *Roemer discovered that light requires time for its propagation and calculated its velocity in 1675; the Principia was published in 1686. amended by taking account of the velocity of light seemed to give space and time an absoluteness that was inescapable. Difficulties, however, were forced upon Newton's notice from the fact that no human observer can get a point of view that is in any sense absolute. Newton's reply was that absolute space and time are indeed beyond human perception and experience, but that they are God's sensorium. What for man is a vague conception and beyond his perception is for God a matter of clear perception. In the Optics he says: "Do not these phenomena of nature make it clear, that there is a being incorporeal, living, omnipresent, who in infinite space as his sensorium sees, discerns and understands everything most intimately and with absolute perfection."" This, of course, is the exact reverse of the position of Leibniz, his most illustrious contemporary and critic. Leibniz, beginning at the other end, and working from the nature of God to the necessary nature of the world, holds that space is in the world, not the world in space; that space and time are our confused way of reflecting the universe, whereas for God space and time do not exist; that space and time are merely the order of coexistence and succession respectively; that they are therefore entirely relative and are mere modes of our perception. Kant, therefore, found in these two predecessors conflicting teachers. Newton was in the ascendancy and exerted the more direct influence, especially in the earlier works. Kant's earlier papers are nearly all on subjects connected with physics, mathematics, and astronomy, reflecting the Newtonian influence. His power of independent and constructive thinking, however, was soon manifested. In 1763 his paper on "The Conception of Negative QuantiQuoted from H. Wildon Carr, The Principle of Relativity, p. 21. |