CH. XV.] TEE COMPOSITION OF MIND. 105 



posed in consciousness, and recognized as equal or unequal ; 

 but in the second case the relations contemplated consist of 

 so many simple relations heterogeneously combined, that they 

 can only through a very indirect process be juxtaposed in 

 consciousness, and hence are only approximately recognized 

 as like or unlike. That this is the only essential difference 

 between quantitative reasoning and qualitative reasoning is 

 shown by the fact that all qualitative reasoning is vaguely 

 quantitative, while all quantitative reasoning begins by being 

 qualitative. For example — to cite Mr, Spencer's admirable 

 illustration — when a brewer describes a vat of fermeuting 

 wort as containing carbonic acid, he makes a qualitative 

 statement ; yet some rude notion of quantity is involved in it. 

 " He thinks of the carbonic acid as more, certainly, than a 

 cubic foot; less, certainly, than the total capacity of the vat: 

 the quantity is thought of as in some ratio to the quantity of 

 wort." On the other hand, " a man who has walked a mile 

 in fifteen minutes, and, observing that he has a quarter of a 

 mile still to go, infers the time it will take to reach his desti- 

 nation, does not primarily infer three minutes omd three 

 quarters: he primarily infers a short time — a time indefinitely 

 conceived as certainly less than ten minutes, and certainly 

 more than one." Doubtlftss he may in an instant proceed to 

 calculate the exact length of the time ; yet, as it will not be 

 denied that even before calculating he has a vague notion 

 of the interval, it must be admitted that his inference, though 

 ultimately quantitative, is, at the outset, only qualitative. 

 Between the two kinds of reasoning, therefore, the only differ- 

 ence is the degree of definiteness to which they are re- 

 spectively developed. 



Bearing in mind these mutually harmonious conclusions — 

 which alike imply the assertion that, between the highest and 

 the lowest kinds of reasoning employed by civilized man, the 

 difference consists solely in the complexit}'' of the relations 

 contemplated, and in the greater or less definiteness with 



