1 62 Herbert Spencer 



positions of mathematical processes, but, as every one knows, 

 such processes can be carried on by a mere machine. Mr. 

 Spencer explains reasoning by considering only its lower 

 kinds. The apprehension of truths as 'true,' of related 

 things ds related, he altogether ignores. Comparisons of 

 relations are no doubt the materials of our reasoning — the 

 means of which we make use — -just as the inteUigence makes 

 use of sensible perceptions. Thus the highest and most 

 important truth is neglected by our author, and attention 

 directed exclusively to subordinate considerations. 



We have lately heard much concerning the inability of 

 certain savages to count more than five, or even three ; and 

 this fact has been advanced, with surprising shallowness, as 

 an indication of transition from the psychical powers of brutes 

 to the intelligence of man. But the slightest reflection is 

 enough to show that the real gulf lies between the animal 

 able to count two and the animal not able to count at all. 

 The difference between being able to count two and having 

 the integral calculus at one's fingers' ends is but a difference 

 of degree. That between the process of counting two con- 

 sciously, and an automatic quantitative segregation of objects, 

 is a difference of kind. We have not the sHghtest difficulty 

 n conceiving that a mere irrational ape might be created 

 with its nervous ganglia and nerve fibres so connected as to 

 turn out quadratic equations or to solve all the problems of 

 EucHd with ease and facihty. But such a creature would of 

 course have no rational knowledge of the action he performed 

 — no intellectual apprehension of his own psychical processes,^ 

 or of problems and equations as problems and equations. 



We may now attempt to summarise the results of such an 

 examination of Mr. Spencer's philosophy as we have found 

 compatible with our limits. 



It seems to us that that philosophy, in spite of the genius 

 of its expositor, possesses the following grave defects : — 



