viii CONCEPTUAL RECONSTRUCTION 141 



us observe further, that this fallacy has two main forms. 

 The crudest is that of simply taking the ascertainable part 

 for the whole, e.g. the measurable desire for gain as the only 

 motive that counts in the conduct of business. A more 

 subtle and pervasive fallacy is that of the complementary 

 partial analysis. Here the given concrete is resolved into 

 elements which are in reality mere abstractions. They 

 harden into independent entities, and, when the first that 

 are so separated are seen to be inadequate, the missing 

 elements are similarly precipitated and transformed to the 

 requisite degree of self-sufficiency. The result is a recon- 

 struction which is related to reality much as an exceedingly 

 ingenious automaton to the living being which it simulates. 

 One great family of fallacies of this order arises in the 

 effort to render continuous reality in discrete thought. The 

 fixity which the concept needs in order to be easily handled 

 as a unity in inference, contrasts with the actual continuity 

 which experience yields. Hence, abstract thought will 

 resolve a continuum like space into an assemblage of points, 

 or time into a succession of instants, or motion into a succes- 

 sive occupation of positions. The point is the boundary 

 of a line (or, what comes to the same thing, of a segment 

 of a line), just as the line is a boundary of a figure. It has, 

 as Euclid justly remarks, no parts and no magnitude, 

 because it is not a division of the line, but an abstraction 

 within it the abstraction of its end or beginning, which 

 can neither be perceived, nor strictly speaking conceived 

 apart from that which begins or ends. But the point also 

 figures as the goal of an analysis which would treat space 

 as a whole consisting of separate elements. For this 

 purpose, either it must receive magnitude which contra- 

 dicts its essential purpose, or the spatial perception must be 

 declared to contain a contradiction, and we get the Zenonian 

 dialectics by which extension, motion, and, indeed, dura- 

 tion as well, are shown to be impossible. Modern mathe- 

 matics yields a reconstruction on its own lines through 

 its conception of infinity. No finite number of points 

 arranged in order, each next to its fellow, builds up the 

 continuous line. Only an infinite number can do this, and 

 the infinity is of such a character that it breaks out between 



