Abstract Ideas, that is, General Conceptions, certainly do exist, however Metaphysics may decide as to their composition. They represent in our minds the whole classes of things called by the general names; and, being implied in the mental operation whereby classes are formed, viz. in the comparison of phenomena, to ascertain in what they agree, cannot be dispensed with in induction, since such a comparison is a necessary preliminary to an induction, and more than two objects cannot well be compared without a type, in which capacity conceptions serve.
But, though implied in the comparison, it does not follow that, as Dr. Whewell supposes, they must have existed in the mind prior to comparison. Sometimes, but only sometimes, they are pre-existent to the comparison of the particular facts in question, being, as was Kepler's hypothesis of an ellipse, familiar conceptions borrowed from different facts, and superinduced, to use Dr. Whewell's expression, on the facts in question. But even such conceptions are the results of former comparisons of individual facts. And much more commonly (and these are the more difficult cases in science) conceptions are not pre-existent even in this sense; but they have to be got (e.g. the Idea of Polarity) by abstraction, that is, by comparison, from among the very phenomena which they afterwards serve to arrange, or, as Dr. Whewell says, to connect. They seem to be pre-existent; but this is only because the mind keeps ever forming conceptions from the facts, which at the time are before it, and then tentatively applies these conceptions (which it is always remodelling, dropping some which are found not to suit after-found facts, and generalising others by a further effort of abstraction) as types of comparison for phenomena subsequently presented to it; so that, being found in these later stages of the comparison already in the mind, they appear in the character simply of types, and not as being also themselves results of comparison. Really they are always both; and the term comparison expresses as well their origin as (and this far more exactly than to connect or to superinduce) their function.
Dr. Whewell says that conceptions must be appropriate and clear. They must, indeed, be appropriate relatively to the purpose in view (for appropriateness is only relative); but they cannot avoid being appropriate (though one may be more so than another) if our comparison of the objects has led to a conception corresponding to any real agreement in the facts: the ancients' and schoolmen's conceptions were often absolutely inappropriate, because grounded on only apparent agreement. So, again, they must be clear in the following sense; that is to say, a sufficient number of facts must have been carefully observed, and accurately remembered. It is also a condition (and one implied in the latter qualities) of clearness, that the conception should be determinate, that is, that we should know precisely what agreements we include in it, and never vary the connotation except consciously.
Activity, carefulness, and accuracy in the observing and comparing faculties are therefore needed; the first quality to produce appropriateness, and the latter two, clearness. Moreover, scientific imagination, i.e. the faculty of mentally arranging known elements into new combinations, is necessary for forming true conceptions; and the mind should be stored with previously acquired conceptions, kindred to the subject of inquiry, since a comparison of the facts themselves often fails to suggest the principle of their agreement; just as, in seeking for anything lost, we often have to ask ourselves in what places it may be hid, that we may search for it there.
CHAPTER III.
NAMING AS SUBSIDIARY TO INDUCTION.
As reasoning is from particulars to particulars, and consists simply in recognising one fact as a mark of another, or a mark of a mark of another, the only necessary conditions of the exertion of the reasoning power are senses, to perceive that two facts are conjoined; and association, as the law by which one of the two facts raises up the idea of the other. The existence of artificial signs is not a third necessary condition. It is only, however, the rudest inductions (and of such even brutes are capable) that can be made without language or other artificial signs. Without such we could avail ourselves but little of the experience of others; and (except in cases involving our intenser sensations or emotions) of none of our own long past experience. It is only through the medium of such permanent signs that we can register uniformities; and the existence of uniformities is necessary to justify an inference, even in a single case, and they can be ascertained once for all.
General names are not, as some have argued, a mere contrivance to economise words. For, if there were a name for every individual object, but no general names, we could not record one uniformity, or the result of a single comparison. To effect this, all indeed, that are indispensable, are the abstract names of attributes; but, in fact, men have always given general names to objects also.