characteristics of the real world. It was further assumed that others of our perceptions, as of colours, sounds, scents, were not perceptions of objectively existing characteristics of the real world, although they were correlated with such characteristics. This assumption was usual, but not universal. Boyle, for instance, did not hold it. The characteristics of the real world were completely definable mathematically. A complete mathematical description of the real world was the aim of science. Together with this was a strong insistence on the necessity of empirical observation. To assume certain principles and deduce their mathematical consequences was not sufficient. The results so obtained must be verified experimentally. And it was not quite clear that the characteristics so far discovered, as extension, etc., were sufficient to account for everything. Such phenomena as magnetism led to the invention of Æthers and influences" of considerable obscurity. The notion of the æther was also required to support the dogma that one piece of matter could not act on another piece of matter 66 at a distance." Motion, particularly on the Cartesian philosophy, was regarded as communicated wholly by contact. The æther, which filled all space not occupied by matter, was the medium by which the necessary shocks were transmitted. To make clear and definite the concepts of the mathematicians, to combine this achievement with complete adherence to the empirical method, and to vindicate the whole outlook by experimental investigation of particular cases. Even when they agreed with the mathematicians that phenomena could be ultimately reduced to mathematical relations between atoms in space and time, they also pointed out that a considerable control of such phenomena could be gained without making this reduction by stopping at directly perceived qualities, several links short, as it were, of the atomic end of the chain of causation. As against the extreme mathematician's tendency to deduce all phenomena by reasoning from a few general principles, they insisted upon the importance of experience. Boyle, in particular, found that the a priori reasoners sometimes arrived at conclusions which were contradicted by actual experimental evidence. Nevertheless, Boyle did not doubt the general world-view of the mathematicians. For Boyle, as much as for Galileo and Descartes, the world was a mathematical machine. The chief importance of these men for modern science was as protagonists of the empirical element in science. Science, to begin with, had a tendency to be rather too mathematical. Although their assumptions and technique were different, the early mathematicians were not wholly free from the failings of the scholastic philosophers they replaced. We may, therefore, summarize as follows the chief ingredients of the scientific outlook as it existed at the time Newton appeared. It was assumed that some of our perceptions, as of extension, motion, weight, were perceptions of objectively existing characteristics of the real world. It was further assumed that others of our perceptions, as of colours, sounds, scents, were not perceptions of objectively existing characteristics of the real world, although they were correlated with such characteristics. This assumption was usual, but not universal. Boyle, for instance, did not hold it. The characteristics of the real world were completely definable mathematically. A complete mathematical description of the real world was the aim of science. Together with this was a strong insistence on the necessity of empirical observation. To assume certain principles and deduce their mathematical consequences was not sufficient. The results so obtained must be verified experimentally. And it was not quite clear that the characteristics so far discovered, as extension, etc., were sufficient to account for everything. Such phenomena as magnetism led to the invention of Æthers " and "influences of considerable obscurity. The notion of the æther was also required to support the dogma that one piece of matter could not act on another piece of matter 66 at a distance." Motion, particularly on the Cartesian philosophy, was regarded as communicated wholly by contact. The æther, which filled all space not occupied by matter, was the medium by which the necessary shocks were transmitted. To make clear and definite the concepts of the mathematicians, to combine this achievement with complete adherence to the empirical method, and to vindicate the whole outlook by applying it with complete success to the description of phenomena, was the achievement of Isaac Newton. CHAPTER II THE NEWTONIAN CONCEPTIONS: SPACE, TIME, MASS THE ideal aim of science is to give a complete mathematical description of phenomena in terms of the fewest principles and entities. We have to find, under the baffling variety of nature, the essential and irreducible elements whose combinations produce that variety. The attempt can claim to be successful, so far, only for those sciences that ignore the chemical, living and mental properties of bodies. The primary concepts in terms of which the science of physics is constructed, such concepts as force, energy, mass, velocity, acceleration, momentum, etc., have to be supplemented by others in the science of chemistry and, for the sciences of life and mind, are so far from being sufficient, that they have hardly yet been found to be even relevant. The mathematical description of nature, therefore, is possible so far only for a limited region of phenomena. Whether such a description is even theoretically possible for the whole of nature is not a question that can be decided on this evidence. The doctrine of materialism is a doctrine that such a description is theoretic |