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of experiments. If we inductively infer a general truth from a collection of instances, our collection of instances is never a complete one, and may not include some really exceptional cases; the law we infer from them is therefore too broadly stated, and is so far an hypothesis. When also we deductively infer the existence of a particular fact from a general law which governs it, the instance is only an hypothetical one until its existence is proved by experiment or observation; and our belief in it ought not to be certain until it has been proved by actual observation of nature.

Although quantitative reasoning is extremely important, little is here said about it, because this treatise is almost entirely restricted to a qualitative view of research. But quantitative inference may be superadded to purely logical reasoning; for instance, when we say, most metals are fusible, and most metals are ductile; or, some ductile metals are fusible, and some fusible metals are ductile, we begin to employ quantitative ideas, because the equivalent idea of most' is more than half;' and the word 'most' may mean any proportion more than fifty or less than one hundred per cent. The quantification of knowledge and inference is also of extreme value in questions of proof, and the fundamental question in such a case is, what amount of evidence is sufficient? Practically, a preponderance of proof determines us, and the human mind has no choice in the matter.

6

As all departments of knowledge assist in developing each other, so a searching study of the use of the reasoningpower and other intellectual faculties in original scientific research, shows that the developments of science, and the ways in which they are effected, reflect much light upon the proper functions and modes of action of each of our intellectual powers.

CHAPTER XXXVII.

NECESSITY OF IMAGINATIVE POWER.

It is one

THE meaning of the term imagination or conception is usually limited to the formation of new ideas, but is sometimes applied to the formation of old ones. of the most complex of mental actions, and has been defined as the faculty of the mind by which it either bodies forth the forms of things unknown, or produces original thoughts or new combinations of ideas from materials stored up in the memory.' It may also be defined as the highest degree of original action of the mind in a particular subject. It is often special or limited in its sphere of operation, being usually confined to some particular subject or art, such as that of architecture, sculpture, painting, music, poetry, eloquence, the drama, the conception of mechanical and other inventions, scientific explanations, hypotheses, theories, &c.; but it is only in reference to its action in scientific research that the following remarks are particularly intended to apply.

The essential characteristic of the highest imagination is originality, and on this account imagination is sometimes called the creative faculty.'

When we pass from the known to the unknown by an act of imagination, we first conceive known ideas, and then by purely mental acts compare, infer, divide, combine, or permutate them, and in each case, from a resulting new mental conception, and this is the so-called 'creative' process. The kind of mental action in such a case is precisely the same as when the resulting conception is not a new one; but its degree is greater because we have to

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Overcome the mental persistency of old associations of ideas, and the momentum of habitual currents of thought, before we can conceive new ideas.

Imagination is not a special mental faculty or mode of mental action, nor a simple action of the mind like that of comparison or inference, but a high degree of activity of special combinations of the simple mental powers. The products of its action are called conceptions, or original ideas, in order to distinguish them from other perceptions. Great imaginative power is, in fact, closely associated with genius,' and the two may be considered together.

High imaginative power requires for its full exercise great inherited nervous impressibility for the ideas of a particular subject, and a well-disciplined mind, richly stored with truthful ideas relating to that subject. In original scientific research, we must have inherently acute senses and perception, and a fertile and rapidly-acting intellect. The tendency to the particular subject is a congenital gift, like the instinct of animals, and is more common in subjects which, like music and painting, depend upon a high degree of refinement of the senses than in those requiring great reasoning power, because the latter depend upon a greater variety of acquirements and more intellectual action. In each case, however, the more complete and accurate the knowledge of the particular subject, the more perfect the action of the imagination; and such knowledge cannot be obtained by intuition. Truthful mental conception is based upon experience, and is largely limited by nature. It is only by possession of true views of the great principles of nature, as well as by inherited acuteness to ideas and impressions of natural phenomena, that a scientific investigator is enabled to imagine and discover the true hypothetical explanation of a novel

1 See p. 241.

phenomenon or fact, and the new truths of nature implied in it; and this combination of intuitive sensibility and extensive accurate knowledge is a rare gift, and constitutes the essence of scientific genius. The highest efforts of scientific imagination require acute and accurate perception, ready and faithful memory, instant power of comparison and detection of similarities and differences, sound inference, ready and rapid analysis, combination, and permutation of ideas, and immediate perception of new truths evolved by each of these. Much of the successful action of the imagination depends upon the fact that all knowledge sheds a light beyond itself; and it is by observing the reflection of this light, as it were, upon associated ideas, that the mind perceives, and the imagination is said to conceive, new truths.

The most valuable exercise of this power in scientific research is in the conception of important new truths, such as those which are embodied in the great laws and principles of nature; and in such cases it acts preeminently as the divine faculty,' when combined with the prophetic intellect. As also each general law or principle includes a great number of instances, and as the conception of the idea of it is usually founded upon a single, or only a few instances, so the conception of such a truth is more or less an hypothesis until it has been sufficiently proved.

Many original researches are based upon pure hypotheses or questions to be answered, and these are usually the direct results of thought and imagination in a wellstored mind. Unscientific persons often mistake such hypotheses for science itself, the scaffolding for the building. Science is truth, but hypotheses are only a preliminary to science, and may be true or untrue; pure hypotheses add nothing to real knowledge.

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In the act of invention during original research, whether it be that of forming new hypotheses, new questions. to be tested, or new causes, explanations, or theories, we try to imagine as many possibilities or suppositions as we can, and then select the best one.

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'In every inductive inference an act of invention is requisite. The invention of a new conception in every inductive inference is generally overlooked.' It is a thought which, once breathed forth, permeates all men's minds. All fancy they nearly or quite knew it before."1

In order, then, to discover scientific truths, suppositions consisting either of new conceptions, or of new combinations of old ones, are to be made, till we find one which succeeds in binding together the facts. But how are we to find this?' For this purpose we must both carefully observe the phenomena, and steadily trace the consequences of our assumptions till we can bring the two into comparison."

2

'The character of the true philosopher. is, not that he never conjectures hazardously, but that his conjectures are clearly conceived, and brought into rigid contact with facts. He sees and compares distinctly the ideas and the things-the relations of his notions to each other and to phenomena. Under these conditions it is not only excusable, but necessary to him to snatch at every semblance of general rule, to try all promising forms of simplicity and symmetry. Hence, advances in knowledge are not commonly made without the previous exercise of some boldness and license in guessing. The discovery of new truths requires, undoubtedly, minds careful and scrupulous in examining what is suggested; but it requires, no less, such as are quick and fertile in suggesting. What is

1 Whewell, Philosophy of the Inductive Sciences, vol. ii. pp. 217, 218. 2 Ibid. vol. ii. pp. 210, 211.