INFERENCE IN GENERAL. 181 



apprehended in any particular case which can occur. In this 

 respect, however, these axioms of logic are on a level with 

 those of mathematics. That things which are equal to the 

 same thing are equal to one another, is as obvious in any par 

 ticular case as it is in the general statement : and if no such 

 general maxim had ever heen laid down, the demonstrations in 

 Euclid would never have halted for any difficulty in stepping 

 across the gap which this axiom at present serves to bridge 

 over. Yet no one has ever censured writers on geometry, for 

 placing a list of these elementary generalizations at the head 

 of their treatises, as a first exercise to the learner of the faculty 

 which will be required in him at every step, that of appre 

 hending a general truth. And the student of logic, in the dis 

 cussion even of such truths as we have cited above, acquires 

 habits of circumspect interpretation of words, and of exactly 

 measuring the length and breadth of his assertions, which are 

 among the most indispensable conditions of any considerable 

 mental attainment, and which it is one of the primary objects 

 of logical discipline to cultivate. 



3. Having noticed, in order to exclude from the pro 

 vince of Reasoning or Inference properly so called, the cases 

 in which the progression from one truth to another is only ap 

 parent, the logical consequent being a mere repetition of the 

 logical antecedent ; we now pass to those which are cases of 

 inference in the proper acceptation of the term, those in which 

 we set out from known truths, to arrive at others really dis 

 tinct from them. 



Reasoning, in the extended sense in which I use the term, 

 and in which it is synonymous with Inference, is popularly 

 said to be of two kinds : reasoning from particulars to generals, 

 and reasoning from generals to particulars ; the former being 

 called Induction, the latter Ratiocination or Syllogism. It 

 will presently be shown that there is a third species of rea 

 soning, which falls under neither of these descriptions, and 

 which, nevertheless, is not only valid, but is the foundation of 

 both the others. 



It is necessary to observe, that the expressions, reasoning 



