queries to guide further experimental inquiry. The classic pronouncement on the rejection of hypothesis occurs at the end of the Principia. "Whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction. Thus it was that the impenetrability, the mobility, and the impulsive force of bodies, and the laws of motion and of gravitation, were discovered." 24 With these illuminating assertions in mind we must press as exceedingly important the fourth Rule of Reasoning in Philosophy, which, if read aright, absolves Newton from the charge of having accepted in his philosophy certain a priori principles, apparently assumed in the other three rules; although, to be sure, his guarded language, especially in the third rule, ought to dissuade us from any such complaint. The first rule is the principle of simplicity: "We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. To this purpose, the philosophers say, that nature does nothing in vain, and more is in vain when less will serve; for nature is pleased with simplicity, and affects not the pomp of superfluous The second rule is, that "to the same natural effects we must, as far as possible, assign the same causes." The later more mathematical expression of this principle is that where different events are expressed by the same equations, they must be regarded as produced by the same forces. third rule appears even more definitely than these to go beyond strict empirical principles. "The qualities of bodies, which admit neither intension nor remission causes." 25 24 Principles, II, 314. Cf. also Opticks, p. 380. The of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever." to Is not this a highly speculative assumption of the Cartesian sort, that it is legitimate to generalize ad infinitum the qualities discovered in the small realm of our experience; or is it perhaps a purely methodological postulate? Newton goes on explain that he regards this rule as nothing more than a combination of the experimental method with the first principle of the uniformity of nature. "For since the qualities of bodies are only known to us by experiments, we are to hold for universal all such as universally agree with experiments; and such as are not liable to diminution can never be quite taken away. We are certainly not to relinquish the evidence of experiments for the sake of dreams and vain fictions of our own devising; nor are we to recede from the analogy of nature, which uses to be simple, and always consonant to itself." We are thus brought back to the first two principles, that of the simplicity and uniformity of nature and the identity of causes where effects are the same. Are these apriorisms speculative assumptions about the structure of the universe, which make it always possible to reduce its phenomena to laws, especially mathematical laws; or were they to Newton a matter of method merely, to be used tentatively as a principle of further inquiry? It is perhaps impossible to answer this question with absolute confidence. At those times when the theological basis of Newton's science was uppermost in his mind, it is probable that he would have answered substantially as Galileo and Descartes did. But in his strictly scientific paragraphs the emphasis is overwhelmingly in favour of their tentative, positivistic character, hence the fourth rule of reasoning in philosophy, which we are now to quote, must be regarded as imposing definite limits on all of the other three. "In experimental philosophy we are to look upon propositions collected by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions. This rule we must follow, that the argument of induction may not be evaded by hypotheses." In other words, we have no metaphysical guarantee whatever against there appearing exceptions to even our most confidently adopted principles; empiricism is the ultimate test. That this applies to the basic principle of the simplicity and uniformity of nature itself appears from an interesting passage in the Opticks." That it should be so is very reasonable [i.e., that the theorem of the uniform proportion of the sines applies to all the rays of light], nature being ever conformable to herself; but an experimental proof is desired." 26 No deduction from an accepted principle, no matter how general or clearly derived from past phenomena, can therefore pass for absolute or physically certain, without careful and continued experimental verification. (D) Newton's Union of Mathematics and Experiment How, now, did Newton propose to unite the mathematical and experimental methods? A full statement of his position on this point can only be given after a careful examination of his practice, for his words are disappointingly inadequate. The best The best passage is in his letter to Oldenburg in response to Hook's attack, from which we have already quoted. "In the last place, I should take notice of a casual expression, which intimates a greater certainty in these things, than I ever promised, viz. the certainty of mathematical 26 P. 66. demonstrations. I said, indeed, that the science of colours was mathematical, and as certain as any other part of optics; but who knows not that optics, and many other mathematical sciences, depend as well on physical sciences, as on mathematical demonstrations? And the absolute certainty of a science cannot exceed the certainty of its principles. Now the evidence, by which I asserted the propositions of colours, is in the next words expressed to be from experiments, and so but physical: whence the propositions themselves can be esteemed no more than physical principles of a science. And if those principles be such, that on them a mathematician may determine all the phenomena of colours, that can be caused by refractions, and that by disputing or demonstrating after what manner, and how much, those refractions do separate or mingle the rays, in which several colours are originally inherent; I suppose the science of colours will be granted mathematical, and as certain as any part of optics. And that this may be done, I have good reason to believe, because ever since I became first acquainted with these principles, I have, with constant success in the events, made use of them for this purpose." 27 Here again, Newton's failure to rise to any higher degree of generality than that characteristic of his own practice is disappointingly evident; at the same time he is saying some important and instructive things. Certain propositions about colours are derived from experiments, which propositions become the principles of the science, and are of such a sort that mathematical demonstrations can be made from them of all the phenomena of colourrefraction. This somewhat clearer form of Newton's own conception of his modus operandi a painstaking study of his scientific biography will generalize and greatly illumine in detail. Newton's whole experimental-mathematical method 11 Opera, IV, 312. Oldenburg was Secretary of the Royal Society. would seem to be analysable, in the light of such a supplementary study, into three main steps. First, the simplification of phenomena by experiments, so that those characteristics of them that vary quantitatively, together with the mode of their variation, may be seized and precisely defined. This step has been practically neglected by later logicians, but it is clearly the way in which such fundamental concepts as refrangibility in optics and mass in physics were accurately fixed by Newton, and the simpler propositions about refraction, motion, and force discovered. Second, the mathematical elaboration of such propositions, usually by the aid of the calculus, in such a way as will express mathematically the operation of these principles in whatever quantities or relations they might be found. Third, further exact experiments must be made (1) to verify the applicability of these deductions in any new field and to reduce them to their most general form; (2) in the case of more complex phenomena, to detect the presence and determine the value of any additional, causes (in mechanics, forces) which can then themselves be subjected to quantitative treatment; and (3) to suggest, in cases where the nature of such additional causes remains obscure, an expansion of our present mathematical apparatus so as to handle them more effectively. Thus, for Newton, careful experimentation must occur at the beginning and end of every important scientific step, because it is always the sensisible facts that we are seeking to comprehend28; but the comprehension, so far as it is exact, must be expressed in the mathematical language. Hence by experiments we must discover those characteristics which can be handled in that language, and by experiments our conclusions must be verified. Our purpose is only to trace out the quantity and properties of this force [attraction] from the phenomena and to 20 Cf. Opticks, pp. 351, 364, ff. |