The principles of science

by William Stanley Jevons

Error of the Baconian Method.

Hundreds of investigators may be constantly engaged in experimental inquiry; they may compile numberless note-books full of scientific facts, and endless tables of numerical results; but, if the views of induction here maintained be true, they can never by such work alone rise to new and great discoveries. By a system of research they may work out deductively the details of a previous discovery, but to arrive at a new principle of nature is another matter. Francis Bacon spread abroad the notion that to advance science we must begin by accumulating facts, and then draw from them, by a process of digestion, successive laws of higher and higher generality. In protesting against the false method of the scholastic logicians, he exaggerated a partially true philosophy, until it became as false as that which preceded it. His notion of scientific method was a kind of scientific bookkeeping. Facts were to be indiscriminately gathered from every source, and posted in a ledger, from which would emerge in time a balance of truth. It is difficult to imagine a less likely way of arriving at great discoveries. The greater the array of facts, the less is the probability that they will by any routine system of classification disclose the laws of nature they embody. Exhaustive classification in all possible orders is out of the question, because the possible orders are practically infinite in number.

It is before the glance of the philosophic mind that facts must display their meaning, and fall into logical order. The natural philosopher must therefore have, in the first place, a mind of impressionable character, which is affected by the slightest exceptional phenomenon. His associating and identifying powers must be great, that is, a strange fact must suggest to his mind whatever of like nature has previously come within his experience. His imagination must be active, and bring before his mind multitudes of relations in which the unexplained facts may possibly stand with regard to each other, or to more common facts. Sure and vigorous powers of deductive reasoning must then come into play, and enable him to infer what will happen under each supposed condition. Lastly, and above all, there must be the love of certainty leading him diligently and with perfect candour, to compare his speculations with the test of fact and experiment.

Freedom of Theorising.

It would be an error to suppose that the great discoverer seizes at once upon the truth, or has any unerring method of divining it. In all probability the errors of the great mind exceed in number those of the less vigorous one. Fertility of imagination and abundance of guesses at truth are among the first requisites of discovery; but the erroneous guesses must be many times as numerous as those which prove well founded. The weakest analogies, the most whimsical notions, the most apparently absurd theories, may pass through the teeming brain, and no record remain of more than the hundredth part. There is nothing really absurd except that which proves contrary to logic and experience. The truest theories involve suppositions which are inconceivable, and no limit can really be placed to the freedom of hypothesis.

Kepler is an extraordinary instance to this effect. No minor laws of nature are more firmly established than those which he detected concerning the orbits and motions of planetary masses, and on these empirical laws the theory of gravitation was founded. Did we not learn from his own writings the multitude of errors into which he fell, we might have imagined that he had some special faculty of seizing on the truth. But, as is well known, he was full of chimerical notions; his favourite and long-studied theory was founded on a fanciful analogy between the planetary orbits and the regular solids. His celebrated laws were the outcome of a lifetime of speculation, for the most part vain and groundless. We know this because he had a curious pleasure in dwelling upon erroneous and futile trains of reasoning, which most persons consign to oblivion. But Kepler’s name was destined to be immortal, on account of the patience with which he submitted his hypotheses to comparison with observation, the candour with which he acknowledged failure after failure, and the perseverance and ingenuity with which he renewed his attack upon the riddles of nature.

Next after Kepler perhaps Faraday is the physical philosopher who has given us the best insight into the progress of discovery, by recording erroneous as well as successful speculations. The recorded notions, indeed, are probably but a tithe of the fancies which arose in his active brain. As Faraday himself said—“The world little knows how many of the thoughts and theories which have passed through the mind of a scientific investigator, have been crushed in silence and secrecy by his own severe criticism and adverse examination; that in the most successful instances not a tenth of the suggestions, the hopes, the wishes, the preliminary conclusions have been realised.”

Nevertheless, in Faraday’s researches, published in the Philosophical Transactions, in minor papers, in manuscript note-books, or in other materials, made known in his interesting life by Dr. Bence Jones, we find invaluable lessons for the experimentalist. These writings are full of speculations which we must not judge by the light of subsequent discovery. It may perhaps be said that Faraday committed to the printing press crude ideas which a friend would have counselled him to keep back. There was occasionally even a wildness and vagueness in his notions, which in a less careful experimentalist would have been fatal to the attainment of truth. This is especially apparent in a curious paper concerning Ray-vibrations; but fortunately Faraday was aware of the shadowy character of his speculations, and expressed the feeling in words which must be quoted. “I think it likely,” he says,‍[478] “that I have made many mistakes in the preceding pages, for even to myself my ideas on this point appear only as the shadow of a speculation, or as one of those impressions upon the mind, which are allowable for a time as guides to thought and research. He who labours in experimental inquiries knows how numerous these are, and how often their apparent fitness and beauty vanish before the progress and development of real natural truth.” If, then, the experimentalist has no royal road to the discovery of the truth, it is an interesting matter to consider by what logical procedure he attains the truth.

If I have taken a correct view of logical method, there is really no such thing as a distinct process of induction. The probability is infinitely small that a collection of complicated facts will fall into an arrangement capable of exhibiting directly the laws obeyed by them. The mathematician might as well expect to integrate his functions by a ballot-box, as the experimentalist to draw deep truths from haphazard trials. All induction is but the inverse application of deduction, and it is by the inexplicable action of a gifted mind that a multitude of heterogeneous facts are ranged in luminous order as the results of some uniformly acting law. So different, indeed, are the qualities of mind required in different branches of science, that it would be absurd to attempt to give an exhaustive description of the character of mind which leads to discovery. The labours of Newton could not have been accomplished except by a mind of the utmost mathematical genius; Faraday, on the other hand, has made the most extensive additions to human knowledge without passing beyond common arithmetic. I do not remember meeting in Faraday’s writings with a single algebraic formula or mathematical problem of any complexity. Professor Clerk Maxwell, indeed, in the preface to his new Treatise on Electricity, has strongly recommended the reading of Faraday’s researches by all students of science, and has given his opinion that though Faraday seldom or never employed mathematical formulæ, his methods and conceptions were not the less mathematical in their nature.‍[479] I have myself protested against the prevailing confusion between a mathematical and an exact science,‍[480] yet I certainly think that Faraday’s experiments were for the most part qualitative, and that his mathematical ideas were of a rudimentary character. It is true that he could not possibly investigate such a subject as magne-crystallic action without involving himself in geometrical relations of some complexity. Nevertheless I think that he was deficient in mathematical deductive power, that power which is so highly developed by the modern system of mathematical training at Cambridge.

Faraday was acquainted with the forms of his celebrated lines of force, but I am not aware that he ever entered into the algebraic nature of those curves, and I feel sure that he could not have explained their forms as depending on the resultant attractions of all the magnetic particles. There are even occasional indications that he did not understand some of the simpler mathematical doctrines of modern physical science. Although he so clearly foresaw the correlation of the physical forces, and laboured so hard with his own hands to connect gravity with other forces, it is doubtful whether he understood the doctrine of the conservation of energy as applied to gravitation. Faraday was probably equal to Newton in experimental skill, and in that peculiar kind of deductive power which leads to the invention of simple qualitative experiments; but it must be allowed that he exhibited little of that mathematical power which enabled Newton to follow out intuitively the quantitative results of a complicated problem with such wonderful facility. Two instances, Newton and Faraday, are sufficient to show that minds of widely different conformation will meet with suitable regions of research. Nevertheless, there are certain traits which we may discover in all the highest scientific minds.