William Stanley Jevons

“ There is no more convincing proof of the soundness of knowledge than that it confers the gift of foresight. Auguste Comte said that “Prevision is the test of true theory;” I should say that it is one test of true theory, and that which is most likely to strike the public attention. Coincidence with fact is the test of true theory, but when the result of theory is announced before-hand, there can be no doubt as to the unprejudiced spirit in which the theorist interprets the results of his own theory. ”

“ We ought always to bear in mind that the mean of any series of observations is the best, that is, the most probable approximation to the truth, only in the absence of knowledge to the contrary. The selection of the mean rests entirely upon the probability that unknown causes of error will in the long run fall as often in one direction as the opposite, so that in drawing the mean they will balance each other. If we have any reason to suppose that there exists a tendency to error in one direction rather than the other, then to choose the mean would be to ignore that tendency. ”

“ But no one can suppose that patient labour alone will invariably lead to those conspicuous results which we attribute to genius. In every branch of science, literature, art, or industry, there are thousands of men and women who work with unceasing patience, and thereby ensure moderate success; but it would be absurd to suppose that equal amounts of intellectual labour yield equal results. A Newton may modestly attribute his discoveries to industry and patient thought, and there is reason to believe that genius is unconscious and unable to account for its own peculiar powers. ”

“ So far as object is different from object, knowledge is useless and inference impossible. But so far as object resembles object, we can pass from one to the other. In proportion as resemblance is deeper and more general, the commanding powers of knowledge become more wonderful. Identity in one or other of its phases is thus always the bridge by which we pass in inference from case to case; and it is my purpose in this treatise to trace out the various forms in which the one same process of reasoning presents itself in the ever-growing achievements of Scientific Method. ”

“ THEORY OF APPROXIMATION. In order that we may gain a true understanding of the kind, degree, and value of the knowledge which we acquire by experimental investigation, it is requisite that we should be fully conscious of its approximate character. We must learn to distinguish between what we can know and cannot know—between the questions which admit of solution, and those which only seem to be solved. Many persons may be misled by the expression exact science, and may think that the knowledge acquired by scientific methods admits of our reaching absolutely true laws, exact to the last degree. ”

“ Had the science of numbers been studied for no other purpose, it must have been developed for the calculation of probabilities. All our inferences concerning the future are merely probable, and a due appreciation of the degree of probability depends upon a comprehension of the principles of the subject. I am convinced that it is impossible to expound the methods of induction in a sound manner, without resting them upon the theory of probability. Perfect knowledge alone can give certainty, and in nature perfect knowledge would be infinite knowledge, which is clearly beyond our capacities. ”

“ But Arago, who had both discovered the phenomenon and personally investigated its conditions, declined to put forward publicly any theory at all.
At the same time we must not suppose that the truly philosophic mind can tolerate a state of doubt, while a chance of decision remains open. In science nothing like compromise is possible, and truth must be one. Hence, doubt is the confession of ignorance, and involves a painful feeling of incapacity. But doubt lies between error and truth, so that if we choose wrongly we are further away than ever from our goal. ”

“ There is no doubt in lightning as to the point it shall strike; in the greatest storm there is nothing capricious; not a grain of sand lies upon the beach, but infinite knowledge would account for its lying there ”

“ To apprehend the truth of special cases of inference does not constitute logic; we must apprehend them as cases of more general truths. The object of all science is the separation of what is common and general from what is accidental and different. In a system of logic, if anywhere, we should esteem this generality, and strive to exhibit clearly what is similar in very diverse cases. Hence the great value of general symbols by which we can represent the form of a reasoning process, disentangled from any consideration of the special subject to which it is applied. ”

“ There must, indeed, be no prejudice or bias distorting the mind, and causing it to pass over the unwelcome results of experiment. There must be that scrupulous honesty and flexibility of mind, which assigns adequate value to all evidence; indeed, the more a man loves his theory, the more scrupulous should be his attention to its faults. It is common in life to meet with some theorist, who, by long cogitation over a single theory, has allowed it to mould his mind, and render him incapable of receiving anything but as a contribution to the truth of his one theory. ”

“ All that we need to secure additions to our knowledge of nature is the erection of great laboratories, museums, and observatories, and the offering of pecuniary rewards to those who can invent new chemical compounds, detect new species, or discover new comets. Doubtless this is not the real meaning of the eminent men who are now urging upon Government the endowment of physical research. They can only mean that the greater the pecuniary and material assistance given to men of science, the greater the result which the available genius of the country may be expected to produce. ”

“ Such may not generally be the reflections of men of science, but I believe that we may thus describe the secret feelings of fear which the constant advance of scientific investigation excites in the minds of many. Is science, then, essentially atheistic and materialistic in its tendency? Does the uniform action of material causes, which we learn with an ever-increasing approximation to certainty, preclude the hypothesis of a benevolent Creator, who has not only designed the existing universe, but who still retains the power to alter its course from time to time? ”

“ He who errs surely diverges from law, and it might be deemed hopeless out of error to draw truth. One of the most remarkable achievements of the human intellect is the establishment of a general theory which not only enables us among discrepant results to approximate to the truth, but to assign the degree of probability which fairly attaches to this conclusion. It would be a mistake indeed to suppose that this law is necessarily the best guide under all circumstances. Every measuring instrument and every form of experiment may have its own special law of error ”

“ All science, it has been said, at the outset, arises from the discovery of identity, and analogy is but one name by which we denote the deeper-lying cases of resemblance. I shall only try to point out at present how analogy between apparently diverse classes of phenomena often serves as a guide in discovery. We thus commonly gain the first insight into the nature of an apparently unique object, and thus, in the progress of a science, we often discover that we are treating over again, in a new form, phenomena which were well known to us in another form. ”

“ No apparent limit exists to the success of scientific method in weighing and measuring, and reducing beneath the sway of law, the phenomena both of matter and of mind. And if mental phenomena be thus capable of treatment by the balance and the micrometer, can we any longer hold that mind is distinct from matter? Must not the same inexorable reign of law which is apparent in the motions of brute matter be extended to the subtle feelings of the human heart? Are not plants and animals, and ultimately man himself, merely crystals, as it were, of a complicated form? ”

“ Go on as far as we will, in the subdivision of continuous quantity, yet we never get down to the absolute point. Thus scientific method leads us to the inevitable conception of an infinite series of successive orders of infinitely small quantities. If so, there is nothing impossible in the existence of a myriad universes within the compass of a needle’s point, each with its stellar systems, and its suns and planets, in number and variety unlimited. Science does nothing to reduce the number of strange things that we may believe. ”

“ The law of the conservation of energy, one of the widest of all physical generalisations, rests upon the same footing. The most that we can do by experiment is to show that the energy entering into any experimental combination is almost equal to what comes out of it, and more nearly so the more accurately we perform the measurements. Absolute equality is always a matter of assumption. We cannot even prove the indestructibility of matter; for were an exceedingly minute fraction of existing matter to vanish in any experiment, say one part in ten millions, we could never detect the loss. ”

“ Society, it is supposed, has now assumed so highly developed a form, that what was accomplished in past times by the solitary exertions of a great intellect, may now be worked out by the united labours of an army of investigators. Just as the well-organised power of a modern army supersedes the single-handed bravery of the mediæval knights, so we are to believe that the combination of intellectual labour has superseded the genius of an Archimedes, a Newton, or a Laplace. ”

“ It is of course by no means certain that everything which has been affirmed of a class is true of all objects afterwards referred to the class; for this would be a case of imperfect inference, which is never more than matter of probability. A definition can only make known a finite number of the qualities of an object, and it always remains possible that objects agreeing in those assigned qualities will differ in others. An individual cannot be defined, and can only be made known by the exhibition of the individual itself, or by a material specimen exactly representing it. ”

“ But if any person make a particular assertion, assigning place and time, then observation will either prove or disprove the alleged fact. If it is true that when a French observer professed to have seen a planet on the sun’s face, an observer in Brazil was carefully scrutinising the sun and failed to see it, we have a negative proof. False facts in science, it has been well said, are more mischievous than false theories. A false theory is open to every person’s criticism, and is ever liable to be judged by its accordance with facts. ”

“ The conclusions of scientific inference appear to be always of a hypothetical and provisional nature. Given certain experience, the theory of probability yields us the true interpretation of that experience and is the surest guide open to us. But the best calculated results which it can give are never absolute probabilities; they are purely relative to the extent of our information. It seems to be impossible for us to judge how far our experience gives us adequate information of the universe as a whole, and of all the forces and phenomena which can have place therein. ”

“ We pass from Perfect to Imperfect Induction when once we allow our conclusion to apply, at all events apparently, beyond the data on which it was founded. In making such a step we seem to gain a net addition to our knowledge; for we learn the nature of what was unknown. We reap where we have never sown. We appear to possess the divine power of creating knowledge, and reaching with our mental arms far beyond the sphere of our own observation. ”

“ No single law of nature can warrant us in making an absolute prediction. We must know all the laws of nature and all the existing agents acting according to those laws before we can say what will happen. To assume, then, that scientific method can take everything within its cold embrace of uniformity, is to imply that the Creator cannot outstrip the intelligence of his creatures, and that the existing Universe is not infinite in extent and complexity, an assumption for which I see no logical basis whatever. ”

“ 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. ”

“ Whether a particle of matter shall gravitate, depends not only upon the law of Newton, but also upon the distribution of surrounding particles. The theory of gravitation may perhaps be true throughout all time and in all parts of space, and the Creator may never find occasion to create those possible exceptions to it which I have asserted to be conceivable. Let this be as it may; our science cannot certainly determine the question. Certain it is, that the law of gravity does not alone determine the forces which may be brought to bear at any point of space. ”

“ In every act of inference or scientific method we are engaged about a certain identity, sameness, similarity, likeness, resemblance, analogy, equivalence or equality apparent between two objects. It is doubtful whether an entirely isolated phenomenon could present itself to our notice, since there must always be some points of similarity between object and object. But in any case an isolated phenomenon could be studied to no useful purpose. The whole value of science consists in the power which it confers upon us of applying to one object the knowledge acquired from like objects ”