Without examining whether, as maintained by J. S. Mill, all inference is actually from particular to particular (general propositions being under this hypothesis only simple reminders, brief formulæ serving as a base of operations) it is clear that we have in it the simplest form of mental progress from the known to the unknown. At the same time it is more than mere association, though transcending it only in degree. Association by similarity is not, as we have seen, identical with formation of generic images; this last implies fusion, mental synthesis. So, too, reasoning from particular to particular implies something more than simple association; it is a state of expectation equivalent to a conclusion in the empirical order; it is an anticipation. The animal which has burned itself in swallowing some steaming food, is on its guard in future against everything that gives off steam. Here we have more than simple association between two anterior experiences (steam, burning); and this state “differs from simple associative suggestion, by the fact that the mind is less occupied with the memory of past burns than with the expectation of a repetition of the same fact in the present instance; that is to say, that it does not so much recall the fact of having once been burnt as it draws the conclusion that it will be burnt.”[18]
Otherwise expressed, he is orientated less towards the past than towards the future. Granted that this tendency to believe that what has occurred once or twice will occur invariably, is a fruitful source of error, it remains none the less a logical operation (judgment or ratiocination) containing an element more than association: an inclusion of the future, an implicit affirmation expressed in an act. Doubtless, between these two processes,—association, inference from particular to particular—the difference is slight enough; yet in a study of genesis and evolution, it is just these transitional forms that are the most important.
Reasoning by analogy is of a far higher order. It is the principal logical instrument of the child and of primitive man: the substrate of all extension of language, of vulgar and empirical classifications, of myths, of the earliest, quasi-scientific knowledge.[19] It is the commencement of induction, differing from the latter, not in form, but in its imperfectly established content. “Two things are alike in one or several characteristics; a proposition stated is true of the one, therefore it is true of the other. A is analogous to B; m is true of A, therefore m is true of B also.” So runs the formula of J. S. Mill. The animal, or child, which when ill-treated by one person extends its hatred to all others that resemble the oppressor, reasons by analogy. Obviously this procedure from known to unknown will vary in degree,—from zero to the point at which it merges into complete induction.
With these general remarks, we may return to the logic of animals or rather to the sole kind of logic possible without speech. This is, and can only be, a logic of images (Romanes employs a synonymous expression, logic of recepts), which is to logic, properly so called, what generic images are to abstraction and to generalisation proper. This denomination is necessary; it enables us to form a separate category, well defined by the absence of language; it permits us, in speaking of judgment and ratiocination in animals, and in persons deprived of speech, to know exactly what meaning is intended.
It follows that there are two principal degrees in the logic of images.
1. Inference from particular to particular. The bird which finds bread upon the window, one morning, comes back next day at the same hour, finds it again, and continues to come. It is moved by an association of images, plus the state of awaiting, of anticipation, as described above.
2. Procedure by analogy. This (at least in its higher forms in animal intelligence) presupposes mental construction: the aim is definite, and means to attain it are invented. To this type I should refer the cases cited above of ants digging tunnels, forming bridges, etc. The ants are wont to practise these operations in their normal life; their virtue lies in the power of dissociation from their habitual conditions, from their familiar ant-heap, and of adaptation to new and unknown cases.
The logic of images has characteristics which pertain to it exclusively, and which may be summarised as follows:
1. As material it employs concrete representations or generic images alone, and cannot escape from this domain. It admits of fairly complex constructions, but not of substitution. The tyro finds no great difficulty in solving problems of elementary arithmetic (such as: 15 workmen build a wall 3 metres high in 4 days; how long will it take 4 men to build it?), because he uses the logic of signs, replacing the concrete facts by figures, and working out the relations of these. The logic of images is absolutely refractory to attempts at substitution. And while it thus acts by representation only, its progress even within this limit is necessarily very slow, encumbered, and embarrassed by useless details, for lack of adequate dissociation. At the same time it may, in the adult who is practised in ratiocination, become an auxiliary in certain cases; I am even tempted to regard it as the main auxiliary of constructive imagination. It would be worth while to ascertain, from authentic observations, what part it plays in the inventions of novelists, poets, and artists. In a polemic against Max Müller, who persists in affirming that it is radically impossible to think and reason without words, a correspondent remarks:
“Having been all my life since school-days engaged in the practice of architecture and civil engineering, I can assure Prof. Max Müller that designing and invention are done entirely by mental pictures. I find that words are only an encumbrance. In fact, words are in many cases so cumbersome that other methods have been devised for imparting knowledge. In mechanics the graphic method, for instance.”[20]