in their elements ABSTRACT-CONCRETE SCIENCE (Mechanics, Physics, Chemistry, etc.) in their totalities CONCRETE SCIENCE (Astronomy, Geology, Biology, Psychology, Sociology, etc.) It is needful to define the words _abstract_ and _concrete_ as thus used; since they are sometimes used with other {79} meanings. M. Comte divides Science into abstract and concrete; but the divisions which he distinguishes by these names are quite unlike those above made. Instead of regarding some Sciences as wholly abstract, and others as wholly concrete, he regards each Science as having an abstract part, and a concrete part. There is, according to him, an abstract mathematics and a concrete mathematics—an abstract biology and concrete biology. He says:—“Il faut distinguer, par rapport à tous les ordres de phénomènes, deux genres de sciences naturelles: les unes abstraites, générales, ont pour objet la découverte des lois qui régissent les diverses classes de phénomènes, en considérant tous les cas qu’on peut concevoir; les autres concrètes, particulières, descriptives, et qu’on désigne quelquefois sous le nom de sciences naturelles proprement dites, consistent dans l’application de ces lois a l’histoire effective des différens êtres existans.” And to illustrate the distinction, he names general physiology as abstract, and zoology and botany as concrete. Here it is manifest that the words _abstract_ and _general_ are used as synonymous. They have, however, different meanings; and confusion results from not distinguishing their meanings. Abstractness means _detachment from_ the incidents of particular cases. Generality means _manifestation in_ numerous cases. On the one hand, the essential nature of some phenomenon is considered, apart from disguising phenomena. On the other hand, the frequency of the phenomenon, with or without disguising phenomena, is the thing considered. Among the phenomena presented by numbers, which are purely ideal, the two coincide; but excluding these, an abstract truth is not realizable to perception in any case of which it is asserted, whereas a general truth is realizable to perception in every case of which it is asserted. Some illustrations will make the distinction clear. Thus it is an abstract truth that the angle contained in a semi-circle is a right angle—abstract in the sense that though it does not hold of {80} actually-constructed semi-circles and angles, which are always inexact, it holds of the ideal semi-circles and angles abstracted from real ones; but this is not a general truth, either in the sense that it is commonly manifested in Nature, or in the sense that it is a space-relation that comprehends many minor space-relations: it is a quite special space-relation. Again, that the momentum of a body causes it to move in a straight line at a uniform velocity, is an