tastes, these odours, and these sounds, demand other than size, figure, number, and slow or rapid motion, I do not believe; and I judge that, if the ears, the tongue, and the nostrils were taken away, the figure, the numbers, and the motions would indeed remain, but not the odours, nor the tastes nor the sounds, which, without the living animal, I do not believe are anything else than names, just as tickling is precisely nothing but a name if the armpit and the nasal membrane be removed." Galileo assumes, then, that amongst the characteristics we attribute to the real world are some that would remain "without the living animal" and some that would not. The first class of characteristics, size, motion, etc., are quantitative, and this seems to be one of the reasons why they are preferred. Galileo's assumption that they exist "without the living animal" is not justified by his arguments and, indeed, rests on grounds which were only later made explicit and which have never been made logically irrefragable. It will be noted that, in this argument, Galileo does not mention mass amongst the characteristics of his real world. But he was quite aware of the fact that the characteristics of size, shape and motion were not sufficient to enable phenomena to be mathematically described. He was aware of the importance of weight. That bodies of the same size, shape, and motion could have different weights was a fact about them that one had to take into consideration in attempting a mathematical description of their behaviour. The characteristics of the real world were size, shape, weight and motion. This real world was, Galileo believed, atomic in structure. Therefore, in Galileo's view, the real world consisted of atoms possessing size, shape and weight, and these atoms were in motion. From their combinations the material universe arose. The atomic motions were produced by force, but on the ultimate nature of force Galileo, with a reserve most extraordinary in his time, refused to speculate. In this view of the world which, in its main lines, has been the scientific view for centuries, the notion of cause has undergone a profound transformation, and the notions of space and time have acquired an importance they never before possessed. On the pre-scientific view the cause of a phenomenon was found by asking why it occurred. Thus some bodies fell downwards and some others, as flames, soared upwards, because each body tended towards its natural place. For Galileo the cause of a phenomenon was found by asking how it occurred. The list of preceding conditions which were always followed by the phenomenon in question was the cause of the phenomenon. The cause was transferred, as it were, from the end to the beginning of the process. Motion, which, on this view, was an important and fundamental characteristic of the real world, involves the notions of time and space. Time and space, therefore, became fundamental in the new outlook. Spatial relations between bodies were supposed to conform to the principles of geometry-Euclidean geometry. Time, also, was regarded as something that could be exactly formulated mathematically. It was his grasp of the mathematical nature of time that led Galileo to devise more exact clocks. We have, then, the real world conceived as consisting of bodies located in space and time and possessing no characteristics but those that can be given mathematical formulation. The scientific task was thus clearly defined; it was to account for all the variety of phenomena in terms of these fundamental concepts. The Galilean analysis of the real world has, as we have said, dominated science until quite recent times, chiefly through the influence of Isaac Newton. Newton adopted, extended, and made more explicit the fundamental Galilean concepts. But that the Galilean analysis was not inevitable is shown by the work of Descartes. Descartes was, if possible, even more convinced than Galileo that the key to the operations of nature was to be found in mathematics. But he elaborated a theory in terms of a somewhat different set of fundamental entities. He tried to account for phenomena in terms of the geometrical property of extension and the property of motion, without importing the notion of weight or of mass. Galileo had found that the notions of extension and motion were not sufficient, by themselves, to describe the observed behaviour of bodies. He therefore imported other fundamental notions, such as weight and momentum. Obviously, therefore, the Cartesian analysis was bound to fail. Descartes overcame this difficulty by inventing an Æther," a universal medium whose vortical motions explained those features of phenomena which could not be derived from bare extension and motion. The properties of this æther were left vague. It amounted to no more than an evasion of the problem of determining the necessary and sufficient characteristics of nature that should allow of the complete mathematical description of the observed behaviour of bodies. Newton, with his truer instinct, recognised the insufficiency of the Cartesian conceptions, and adopted those of Galileo. The scientific outlook was very largely due, as we have seen, to the predilections of the mathematician. The metaphysic assumed by these men-that Nature must be essentially mathematical in character -was nothing but an expression of their predilection. The harmful effects of this assumption are most apparent in the case of Descartes, who deduced erroneous laws of nature from quite gratuitous a priori assumptions. Even Galileo, as we have said, was inclined to think that mathematical deductions did not require experimental confirmation. None of these men, great as they were, manifested the scientific mind in complete purity. But, together with these great mathematical legislators, there existed men of a very different type, who made their indispensable contribution to the formation of the modern scientific outlook. These were the empiricists, such men as Gilbert, Harvey, Boyle. Their characteristic note was their insistence upon the 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. 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. For 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 |