222 REASONING. 



explained, seem almost too obvious to require so 

 formal a statement, since the same amount of expla- 

 nation which is necessary to make the principles 

 intelligible, would enable the truths which they 

 convey to be apprehended in any particular case 

 which can occur. In this respect, however, these 

 axioms of logic are on a level with those of mathe- 

 matics. That things which are equal to the same 

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

 particular case as it is in the general statement : and 

 if no such general maxim had ever been 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 apprehending a general truth. 

 And the student of logic, in the discussion 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 attainment in science, and which it 

 is one of the primary objects of logical discipline to 

 cultivate. 



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

 province of Reasoning or Inference properly so called, 

 the cases in which the progress from one truth to 

 another is only apparent, 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 



