undoubtedly is—then every increase or diminution of this bundle is in effect the formation of a new concept; and Mill's objection that we cannot think by means of concepts, because in reasoning we bring before the mind a varying number of the attributes composing them, is seen to be founded on the mistaken assumption that for every object there is but one corresponding concept, the truth being that an object may be represented in thought by concepts without number. For every object is the first link in innumerable chains of abstractions varying in kind and diverging in direction with the comparisons instituted between it and other objects; and each of the links beyond the first is a concept under which the object may, in scholastic phrase, be subsumed. A horse, for example, may be considered mechanically as a system of levers and strings, a self-regulating locomotive, a machine, etc., or as a thousand pounds moving at the rate of 2.40 per mile, a heavy body, etc.; or, chemically, as a congeries of calcium and magnesium phosphates, carbonates, and fluorids, with albumine, fibrine, and similar substances, as a compound of oxygen, hydrogen, carbon, nitrogen, sulphur, phosphorus, calcium, magnesium, silicon, etc.; or, zoologically, as a solipede, an ungulate, a mammal, an animal, etc.; or, economically, as a beast of burden, a domestic animal—and so on, indefinitely. The formation of concepts like these is incident to all productive reasoning about individual things, and their fixation by means of language (speaking of language in the comprehensive sense of all symbols by which forms of thought may be represented) an indispensable condition of the progress of scientific knowledge, or, indeed, knowledge of any sort.
On the other hand, the most obstinate conceptualist will not deny that, before any one of these concepts can stand as the representative of an actual, concrete object, it must be supplemented with all those circumstances of singularity or particularity which were left behind in the progress of abstraction.
On closer examination, however, the war of words between Mill and his antagonists proves to be a real contest of principles. The elaboration of the data of experience into concepts implies an establishment of relations between these data in conformity to laws not immediately derivable from this experience itself—a mental digestion of the crude material of sense; and this is, in Mill's opinion, inadmissible in view of the purely sensational origin of all knowledge. Mill has an instinctive horror of every thing which purports to be something else than a deliverance of sense, and contends that in our thought we are at all times conversant, not with abstractions, but with facts. Whether this be true or not, depends upon the meaning of the word "facts," irrespective of the necessary reservation that all the facts about which we know any thing at all are the facts of consciousness. A satisfactory discussion of this topic (to which very valuable contributions have been made by Mr. Ferrier) is beyond the scope of my inquiry;