Given perplexity as to the cause of any phenomenon, what is our natural first step? We may describe it as searching for a clue: we look carefully at the circumstances with a view to finding some means of assimilating what perplexes us to what is already within our knowledge. Our next step is to make a guess, or conjecture, or, in scientific language, a hypothesis. We exercise our Reason or Nous, or Imagination, or whatever we choose to call the faculty, and try to conceive some cause that strikes us as sufficient to account for the phenomenon. If it is not at once manifest that this cause has really operated, our third step is to consider what appearances ought to present themselves if it did operate. We then return to the facts in question, and observe whether those appearances do present themselves. If they do, and if there is no other way of accounting for the effect in all its circumstances, we conclude that our guess is correct, that our hypothesis is proved, that we have reached a satisfactory explanation.
These four steps or stages may be distinguished in most protracted inquiries into cause. They correspond to the four stages of what Mr. Jevons calls the Inductive Method par excellence, Preliminary Observation, Hypothesis, Deduction and Verification. Seeing that the word Induction is already an overloaded drudge, perhaps it would be better to call these four stages the Method of Explanation. The word Induction, if we keep near its original and most established meaning, would apply strictly only to the fourth stage, the Verification, the bringing in of the facts to confirm our hypothesis. We might call the method the Newtonian method, for all four stages are marked in the prolonged process by which he made good his theory of Gravitation.
To give the name of Inductive Method simply to all the four stages of an orderly procedure from doubt to a sufficient explanation is to encourage a widespread misapprehension. There could be no greater error than to suppose that only the senses are used in scientific investigation. There is no error that men of science are so apt to resent in the mouths of the non-scientific. Yet they have partly brought it on themselves by their loose use of the word Induction, which they follow Bacon in wresting from the traditional meaning of Induction, using it to cover both Induction or the bringing in of facts—an affair mainly of Observation—and Reasoning, the exercise of Nous, the process of constructing satisfactory hypotheses. In reaction against the popular misconception which Bacon encouraged, it is fashionable now to speak of the use of Imagination in Science. This is well enough polemically. Imagination as commonly understood is akin to the constructive faculty in Science, and it is legitimate warfare to employ the familiar word of high repute to force general recognition of the truth. But in common usage Imagination is appropriated to creative genius in the Fine Arts, and to speak of Imagination in Science is to suggest that Science deals in fictions, and has discarded Newton's declaration Hypotheses non fingo. In a fight for popular respect, men of science may be right to claim for themselves Imagination; but in the interests of clear understanding, the logician must deplore that they should defend themselves from a charge due to their abuse of one word by making an equally unwarrantable and confusing extension of another.
Call it what we will, the faculty of likely guessing, of making probable hypotheses, of conceiving in all its circumstances the past situation or the latent and supramicroscopical situation out of which a phenomenon has emerged, is one of the most important of the scientific man's special gifts. It is by virtue of it that the greatest advancements of knowledge have been achieved, the cardinal discoveries in Molar and Molecular Physics, Biology, Geology, and all departments of Science. We must not push the idea of stages in explanatory method too far: the right explanation may be reached in a flash. The idea of stages is really useful mainly in trying to make clear the various difficulties in investigation, and the fact that different men of genius may show different powers in overcoming them. The right hypothesis may occur in a moment, as if by simple intuition, but it may be tedious to prove, and the gifts that tell in proof, such as Newton's immense mathematical power in calculating what a hypothesis implies, Darwin's patience in verifying, Faraday's ingenuity in devising experiments, are all great gifts, and may be serviceable at different stages. But without originality and fertility in probable hypothesis, nothing can be done.
The dispute between Mill and Whewell as to the place and value of hypotheses in science was in the main a dispute about words. Mill did not really undervalue hypothesis, and he gave a most luminous and accurate account of the conditions of proof. But here and there he incautiously spoke of the "hypothetical method" (by which he meant what we have called the method of Explanation) as if it were a defective kind of proof, a method resorted to by science when the "experimental methods" could not be applied. Whether his language fairly bore this construction is not worth arguing, but this was manifestly the construction that Whewell had in his mind when he retorted, as if in defence of hypotheses, that "the inductive process consists in framing successive hypotheses, the comparison of these with the ascertained facts of nature, and the introduction into them of such modifications as the comparison may render necessary". This is a very fair description of the whole method of explanation. There is nothing really inconsistent with it in Mill's account of his "hypothetical method"; only he erred himself or was the cause of error in others in suggesting, intentionally or unintentionally, that the Experimental Methods were different methods of proof. The "hypothetical method," as he described it, consisting of Induction, Ratiocination, and Verification, really comprehends the principles of all modes of observation, whether naturally or artificially experimental. We see this at once when we ask how the previous knowledge is got in accordance with which hypotheses are framed. The answer must be, by Observation. However profound the calculations, it must be from observed laws, or supposed analogues of them, that we start. And it is always by Observation that the results of these calculations are verified.
Both Mill and Whewell, however, confined themselves too exclusively to the great hypotheses of the Sciences, such as Gravitation and the Undulatory Theory of Light. In the consideration of scientific method, it is a mistake to confine our attention to these great questions, which from the multitude of facts embraced can only be verified by prolonged and intricate inquiry. Attempts at the explanation of the smallest phenomena proceed on the same plan, and the verification of conjectures about them is subject to the same conditions, and the methods of investigation and the conditions of verification can be studied most simply in the smaller cases. Further, I venture to think it a mistake to confine ourselves to scientific inquiry in the narrow sense, meaning thereby inquiry conducted within the pale of the exact sciences. For not merely the exact sciences but all men in the ordinary affairs of life must follow the same methods or at least observe the same principles and conditions, in any satisfactory attempt to explain.
Tares appear among the wheat. Good seed was sown: whence, then, come the tares? "An enemy has done this." If an enemy has actually been observed sowing the tares, his agency can be proved by descriptive testimony. But if he has not been seen in the act, we must resort to what is known in Courts of Law as circumstantial evidence. This is the "hypothetical method" of science. That the tares are the work of an enemy is a hypothesis: we examine all the circumstances of the case in order to prove, by inference from our knowledge of similar cases, that thus, and thus only, can those circumstances be accounted for. Similarly, when a question is raised as to the authorship of an anonymous book. We first search for a clue by carefully noting the diction, the structure of the sentences, the character and sources of the illustration, the special tracks of thought. We proceed upon the knowledge that every author has characteristic turns of phrase and imagery and favourite veins of thought, and we look out for such internal evidence of authorship in the work before us. Special knowledge and acumen may enable us to detect the authorship at once from the general resemblance to known work. But if we would have clear proof, we must show that the resemblance extends to all the details of phrase, structure and imagery: we must show that our hypothesis of the authorship of XYZ explains all the circumstances. And even this is not sufficient, as many erroneous guesses from internal evidence may convince us. We must establish further that there is no other reasonable way of accounting for the matter and manner of the book; for example, that it is not the work of an imitator. An imitator may reproduce all the superficial peculiarities of an author with such fidelity that the imitation can hardly be distinguished from the original: thus few can distinguish between Fenton's work and Pope's in the translation of the Odyssey. We must take such known facts into account in deciding a hypothesis of authorship. Such hypotheses can seldom be decided on internal evidence alone: other circumstantial evidence—other circumstances that ought to be discoverable if the hypothesis is correct—must be searched for.
The operation of causes that are manifest only in their effects must be proved by the same method as the operation of past causes that have left only their effects behind them. Whether light is caused by a projection of particles from a luminous body or by an agitation communicated through an intervening medium cannot be directly observed. The only proof open is to calculate what should occur on either hypothesis, and observe whether this does occur. In such a case there is room for the utmost calculating power and experimental ingenuity. The mere making of the general hypothesis or guess is simple enough, both modes of transmitting influence, the projection of moving matter and the travelling of an undulation or wave movement, being familiar facts. But it is not so easy to calculate exactly how a given impulse would travel, and what phenomena of ray and shadow, of reflection, refraction and diffraction ought to be visible in its progress. Still, no matter how intricate the calculation, its correspondence with what can be observed is the only legitimate proof of the hypothesis.