PRIMARY CONCEPTS OF MODERN SCIENCE. 101 



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 circum- 

 scribed rectangle, etc. — are implied, and from it they may be deduced. 

 Each one of its attributes is an implication of all the others. Our con- 

 cepts 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 inter- 

 dependence 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 ele- 

 ments whose interdependence is subjective (every intellectual opera- 

 tion, 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, elec- 

 tric, or magnetic conditions of a body change at every moment. But, 

 in fact, there is no property whatever, of a material body, w T hich 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. 1 



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 geome- 

 try, a wooden geometry, a stone geometry, and so on, as distinct sciences. 



1 1 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 be- 

 tween 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),^ equivalent to "repre- 

 sentation " ( Vorstettung). 



