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.