apply what we discover in some simple cases, as principles, by which, in a mathematical way, we may estimate the effects thereof in more involved cases. For it would be endless and impossible to bring every particular to direct and immediate observation. We said, in a mathematical way, to avoid all questions about the nature or quality of this force (attraction), which we would not be understood to determine by any hypothesis." 29 We are now prepared to consider Newton's somewhat more general statement of his method in the last pages of the Opticks, where the positivistic consequence of his experimentalism and rejection of hypothesis is especially stressed. ་་ These principles (mass, gravity, cohesion, etc.) I consider not as occult qualities, supposed to result from the specific forms of things, but as general laws of nature, by which the things themselves are formed; their truth appearing to us by phenomena, though their causes be not yet discovered. For these are manifest qualities, and their causes only are occult. And the Aristotelians gave the name of occult qualities not to manifest qualities, but to such qualities only as they supposed to lie hid in bodies, and to be the unknown causes of manifest effects; such as would be the causes of gravity, and of magnetic and electric attractions, and of fermentations, if we should suppose that these forces or actions arose from qualities unknown to us and incapable of being discovered and made manifest. Such occult qualities put a stop to the improvement of natural philosophy and therefore of late years have been rejected. To tell us that every species of things is endowed with an occult specific quality by which it acts and produces manifest effects, is to tell us nothing: But to derive two or three general principles of motion from phenomena, and afterwards to tell us how the properties and actions of all corporeal things follow from those manifest principles, would be a very great step in philosophy, though the causes of those principles were not yet discovered: and therefore I scruple not, to propose the principles of motion abovementioned, they being of very general extent, and leave their causes to be found out. "30 We shall return later to this fundamental contrast which Newton conceived to exist between his own method and that of the preceding Aristotelian and Cartesian systems, with the resulting confidence which 20 System of the World (Principles, Vol. III), p. 3. it gave him. An interesting question remains however to be asked about his method. Do not the very initial experiments and observations, as a result of which the mathematical behaviour of phenomena is defined, presuppose something which we can only speak of as an hypothesis, to direct those experiments to a successful issue? In the days of his early optical labours Newton would not have entirely refused assent; there are sometimes hypotheses which definitely “can be an aid to experiments.” 31 But in his classic writings even such guiding ideas seem to be denied place and function. Apparently we need an hypothesis only in this very general sense, namely the expectation that inasmuch as nature has hitherto revealed herself as being to a large extent, a simple and uniform mathematical order, there are exact quantitative aspects and laws in any group of phenomena which simplifying experiments will enable us to detect, and enlarged experiments reduce to their most general form. Thus Newton feels it possible to speak of his method as deducing principles of motion from phenomena 32, because these principles are exact and complete statements of the phenomena as far as their motion is concerned. And when induction is applied to these principles, their exactitude and completeness as a reduction of the phenomena are not at all lost; Newton simply means by it that they are expressed in their most general form as perceived to apply over a wider field. Thus there is no place for hypothesis in natural philosophy at all according to Newton's final view; we analyse phenomena to deduce their mathematical laws, of which those that are of wide applicability are rendered general by induction. The word induction does not derogate from the mathematical certainty of the results, and it must not mislead us when stressed in Newton's 31 Cf. p. 211, footnote. concluding statement of his method in the Opticks. It emphasizes his ultimate empiricism merely. "As in mathematics, so in natural philosophy, the investigation of difficult things by the method of analysis, ought ever to precede the method of composition. This analysis consists in making experiments and observations, and in drawing general conclusions from them by induction, and admitting of no objections against the conclusions, but such as are taken from experiments or other certain truths. For hypotheses are not to be regarded in experimental philosophy. And although the arguing from experiments. and observations by induction be no demonstration of general conclusions : yet it is the best way of arguing which the nature of things admits of, and may be looked upon as so much the stronger, by how much the induction is more general. And if no exception occur from phenomena, the conclusion may be pronounced generally. But if at any time afterwards any exception shall occur from experiments, it may then begin to be pronounced with such exceptions as occur. By this way of analysis we may proceed from compounds to ingredients, and from motions to the forces producing them; and in general, from effects to their causes, and from particular causes to more general ones, till the argument end in the most general. This is the method of analysis: and the synthesis consists in assuming the causes. discovered, and established as principles, and by them explaining the phenomena proceeding from them, and proving the explanations. In the first two books of these Optics, I proceeded by this analysis to discover and prove the original differences of the rays of light in respect of refrangibility, reflexibility, and colour, and their alternative fits of easy reflection and easy transmission, and the properties of bodies, both opaque and pellucid, on which their reflections and colours depend. And these discoveries being proved, may be assumed in the method of composition for explaining the phenomena arising from them: an instance of which method I gave in the end of the first book."33 It is abundantly clear from these earnest statements. that Newton conceived himself to have made a most remarkable methodological discovery, despite the fact that he was unable to state his method in its full generality. Galileo had set aside explanation in terms of the ultimate why of physical events in favour of explanation in terms of their immediate how, i.e., a mathematical formula expressing their processes. and motions. But Galileo still carried over many metaphysical prejudices from his ancestry, while for 33 Opticks p. 380, ff. Compare with a statement of method in Kepler, VII, 212. the rest he erected his mathematical method into a metaphysics, and was able (excepting a few passages) to follow no clear distinction in his works between the scientific study of perceived motions and these more ultimate ideas. In Descartes the metaphysic of mathematics was still more central and controlling ; the passion for a complete system of the universe still less surrendered. Boyle, for his part, was quite confident that ultimately the world is to be interpreted religiously, but as far as experimental science is concerned he was ready to stress the meagreness of human knowledge and its tentative and gradual progress. Inasmuch, however, as Boyle was not a mathematician, he saw no way to win certainty in science. Science is composed of hypotheses, which have, to be sure, been tested and verified as far as possible by experiments, but inasmuch as at any time a contrary experiment may appear, we must be satisfied with probabilism merely. Newton, as we have seen, was willing to grant the possibility of exceptions, but he was in no wise willing to grant that science was composed of hypotheses. Anything that is not immediately deduced from the phenomena is to be called an hypothesis and has no place in science, especially attempts to explain the nature of the forces and causes revealed in the phenomena of motion. Such explanations by their very nature are insusceptible of experimental verification. We know, for example, that certain motions take place in nature which we have been able to reduce to mathematical law, and regarding these motions as the effects of a certain kind of force, we call that force gravity. "But hitherto I have been unable to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses." 34 The ultimate nature of gravity is unknown; it is not necessary for science that it be known, for science seeks to understand how 34 Principles, II, 314. it acts, not what it is. For Newton, then, science was composed of laws stating the mathematical behaviour of nature solely-laws clearly deducible from phenomena and exactly verifiable in phenomena-everything further is to be swept out of science, which thus becomes a body of absolutely certain truth about the doings of the physical world. By his intimate union of the mathematical and experimental methods, Newton believed himself to have indissolubly allied the ideal exactitude of the one with the constant empirical reference of the other. Science is the exact mathematical formulation of the processes of the natural world. Speculation is at a discount, but motion has unconditionally surrendered to the conquering mind of man. Section 2.-The Doctrine of Positivism Now, someone will ask, if this be a correct portrayal of Newton's method, is there not a flagrant contradiction in such a phrase as 'the metaphysics of Newton'? Was not this rejection of hypothesis his most distinctive attainment, and did he not measurably succeed, at least in the main body of his works, in banning ideas about the nature of the universe at large? Is there not full justification for his claim to have discovered and used a method by which a realm of certain truth might be opened up and gradually widened quite independently of assumed solutions of ultimate problems? Newton, we are told, was the first great positivist 35. Following Galileo and Boyle, but more consistently, he turned his back on metaphysics in favour of a small but growing body of exact knowledge. With his work the era of great speculative systems ended and a new day of exactitude and promise for man's intellectual conquest of nature dawned. How, then, speak of him as a metaphysician? 35 Brewster, Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton, Edinburgh, 1855, Vol. II, p. 532. |