of its concepts. And in this all the properties of the parabola—that it is a conic section formed by cutting a cone parallel to its sides, that the area of any of its segments is equal to two-thirds of its circumscribed rectangle, etc.—are implied, and from it they may be deduced. Each one of its attributes is an implication of all the others. Our concepts of material objects, on the contrary, are never exhaustive, for their complement of attributes varies with our experience concerning them. These attributes are expressive of the relations between the object and other objects; and, the number of objects being unlimited, the synthesis of attributes is, of necessity, incomplete. And the interdependence of these attributes, as well as the connection between the objects themselves, or their representative images and concepts, has its origin in laws, of which the laws of the intellect are but a partial reflex. It is true that the concept of a material object contains elements whose interdependence is subjective (every intellectual operation, or rather its result, being in some form a synthesis of subjective and objective data); but even these are liable to determination by undigested empirical elements which are present along with them. Moreover, our knowledge of the attributes of a material body is not only imperfect, but these attributes are variable. This is obvious enough in the case of those properties which are usually designated as secondary qualities; every one knows that the thermic, optic, electric, or magnetic conditions of a body change at every moment. But, in fact, there is no property whatever, of a material body, which is strictly invariable, or the law of whose variation is fully known. For this reason, also, the concept of a material object can never expressly, or by implication, be a full complement of its attributes.
- I do not enter into the question whether or not the use of the word "concept," in reference to material objects, can in all cases be justified, and whether the distinction between representations and concepts is not, in many cases, including the case of "singular concepts," so called, very shadowy. In this connection, it is significant that the Germans use the expression "empirical concept" (Erfahrungsbegriff), as equivalent to "representation" (Vorstellung).
can be lines without breadth, is so nearly true, that our senses, when unassisted by art, cannot detect the error. Formerly, and until the invention of the micrometer, in the seventeenth century, it was impossible to detect it at all. Hence, the conclusions of the geometrician approximate so closely to truth, that we are justified in accepting them as true. The flaw is too minute to be perceived. But that there is a flaw, appears to roe certain. It appears certain that, whenever something is kept back in the premises, something must be wanting in the conclusion. In all such cases, the field of inquiry has not been entirely covered; and, part of the preliminary facts being suppressed, it must, I think, be admitted that complete truth is unattainable, and that no problem in geometry has yet been exhaustively solved." Whether Buckle was able to think of a line as the limit between two surfaces, and whether, in his opinion, such a limit has breadth (i. e., is itself a surface, so that we are driven from limit to limit ad infinitum), he does not tell us. Nor does he say whether or not, in view of the fact that the breadth of a line depends upon the material out of which it is constructed, or upon which it is drawn, there ought to be a pasteboard geometry, a wooden geometry, a stone geometry, and so on, as distinct sciences.