viii CONCEPTUAL RECONSTRUCTION 143 



ence between two values, each being regarded as a value 

 momentarily possessed, and by reducing the difference 

 indefinitely near to vanishing point. This approximative 

 method was, until recently, taken to be the logical basis of 

 the calculus, which was therefore conceived as resting upon 

 a fictitious resolution of the continuous into the discrete. 

 In this resolution there was an unavoidable element of 

 error which was harmless, because it could always be 

 reduced below any finite magnitude, but served to show 

 the ultimate incapacity of the human mind to grapple with 

 the real by rational methods. Theoretically it could only 

 be justified by the assumption of infinitesimal magnitudes, 

 an assumption which could be shown to involve contradic- 

 tions. More modern analysis shows that the calculus gives 

 an exact reconstruction of the continuous depending on the 

 distinction between the limit of a series of values and any 

 actual value within such a series. The theory of the 

 calculus defines the limit with precision and without assum- 

 ing infinitesimal magnitudes, and proves that it is not the 

 approximate but the exact and unambiguous measure of 

 continuous variation. Thus, in this instance again it 

 would appear that while the first movement of thought 

 breaks up the continuous into the discrete, its final aim is 

 to surmount this point of view with the fictions involved, 

 and to equate its concepts with the continua which actual 

 experience yields. 



What is said of the physical continuum applies without 

 essential modification to the continuous, or at any rate, 

 exceedingly subtle and gradual variations of character 

 which the real world presents. Here, again, common 

 sense, guided by practical interests of correlation, gathers 

 together a certain section of experience under concepts, 

 which thus possess, not so much an exact fixity as a certain 

 range of meaning. This laxity is intolerable to abstract 

 thought, which, accordingly, selects some particular case 

 and hardens it into a type, to which any new case must 

 either conform or not conform. As an alternative, using 

 experience but using it badly, it takes an instance falling 

 under the concept, and (since the concept is assumed to be 

 one and indivisible) asserts anything that it finds in this 



