in possessing rotundity. 'Having rotundity' is thus intensively included in 'apple,' while 'apples' are extensively included in 'having rotundity.'
The above are obvious examples of concrete and abstract ideas respectively, but in other cases it has seemed to many logicians impossible to draw this important distinction with clearness. This I believe to be due to the two facts: (1) that there is a certain class of grammatically abstract names which do not convey logically abstract ideas; and (2) that concrete ideas must be taken to include, not only the ideas of natural material entities, but the ideas of (a) certain natural features, which are neither material parts nor abstract qualities, and (6) certain conventional quasi-entities, especially those involved in mathematical and logical constructions. These categories are non-material and are frequently regarded as abstract; but they are concrete, not abstract, in what I take to be the proper sense of the terms. They are subjects which form centers of relationship to other cognate subjects; not pure modes, in which indefinitely numerous and otherwise unrelated subjects can share.
1. A few grammatically abstract names do not refer to any definite modes, but to the whole group of qualities and relations belonging to some concrete object or class. They really mean all which might be predicated of an object or class, if our knowledge of it were perfect. Concreteness is an abstract name which does not mean anything abstract, but refers to the totality of parts, qualities, and relations, which coinhere in some entity or quasi-entity—the totality which is it. Substantiality usually means consisting in ponderable and resisting substance, but in its logical sense it would seem to mean the concreteness, or total nature, of any particular object which does so consist. It would thus cover the totality of qualities and of relations, internal or external, which belong to such an object, and which, in the case of any complex object, are due partly to its chemical ingredients and their physical conditions, but also to its actual shape and dimensions and its internal mechanical or vital structure. Humanity (when it does not mean historical mankind, or, as with Comte, the bulk of historical mankind as co-operating
