EDUCATION AS A SCIENCE. 665 



contradiction to what has been already said respecting the greater labo- 

 riousness of general knowledge : but the contrariety is only appar- 

 ent. To contract an impression of one single individual, after plenty 

 of time given to attend to it, is the easiest supposable mental effort. 

 But such is the multiplicity of things, that we must learn to know and 

 remember vast numbers of individuals ; and we soon feel ourselves 

 overpowered by the never-ending demands upon us. We must know 

 many persons, many places, many houses, many natural objects ; and 

 our capability of memory is in danger of exhaustion before we have 

 done. Now comes in, however, the discovery of identities, whereby 

 the work is shortened. If a new individual is exactly the same as the 

 old, we are saved the labor of a new impression ; if there is a slight 

 difference, we have to learn that difference and no more. In actual ex- 

 perience, the case is that there are numerous agreements in the world, 

 but accompanied with differences ; and, while we have the benefit of 

 the agreements, we must take notice of the differences. What makes 

 a general notion difficult is that it represents a large number of objects 

 that, while agreeing in some respects, differ in others. This difficulty 

 is the price that we pay for an enormous saving in intellectual labor. 



The overcoming of isolation in the multitude of particulars, by 

 flashes of identity, is the progress of our knowledge in one direction ; 

 it is the satisfaction that we express when we say we understand or 

 can account for a thing. Lightning was accounted for when it was 

 identified with the electric spark : besides the exhilarating surprise at 

 the sameness of two facts in their nature so different and remote, men 

 had the further satisfaction of saying that they learned what lightning 

 is. Thus by discoveries of identity we are enabled to explain the world, 

 to assign the causes of things, to dissipate in part the mysteriousness 

 that everywhere surrounds us. 



When a discovery of identification is made among particulars hith- 

 erto looked upon as diverse, the interest created is all-sufficient to secure 

 our appreciation. This is the alluring side of generalities. The repug- 

 nant aspect of them is seen in the technicalities that are invented to 

 hold and express them general or abstract designations, diagrams, 

 and formulas. When it is proposed to indoctrinate the mind in these 

 things, by themselves, and at a stage when the condensing and explain- 

 ing power of the identities is as yet unawakened, the whole machinery 

 seems an uncouth jargon. Hence the attempt to afford relief to the 

 faculties by teaching the dry symbols of arithmetic and geometry, 

 through the aid of examples in the concrete, and in all the abstract 

 sciences to afford plenty of particulars to illustrate the generalities. 

 This is good so far ; but the real interest that overcomes the dryness 

 arises only when we can apply the generalities in tracing identities, in 

 solving difficulties, and in shortening labor ; an effect that comes soon- 

 est to those that have already some familiarity with the field where the 

 formulas are applicable. The liking for algebra and for geometry pro- 



