240 ARISTOTELIAN LOGIC. [CHAP. XV. 



ther deductive reasoning can with propriety be regarded as con- 

 sisting only of elimination. I believe, upon careful examination, 

 the true answer to the former question to be, that it is always 

 theoretically possible so to resolve and combine propositions that 

 elimination may subsequently be effected by the syllogistic ca- 

 nons, but that the process of reduction would in many instances 

 be constrained and unnatural, and would involve operations 

 which are not syllogistic. To the second question I reply, that 

 reasoning cannot, except by an arbitrary restriction of its mean- 

 ing, be confined to the process of elimination. No definition can 

 suffice which makes it less than the aggregate of the methods 

 which are founded upon the laws of thought, as exercised upon 

 propositions ; and among those methods, the process of elimina- 

 tion, eminently important as it is, occupies only a place. 



Much of the error, as I cannot but regard it, which prevails 

 respecting the nature of the Syllogism and the extent of its 

 office, seems to be founded in a disposition to regard all those 

 truths in Logic as primary which possess the character of sim- 

 plicity and intuitive certainty, without- inquiring into the relation 

 which they sustain to other truths in the Science, or to general 

 methods in the Art, of Reasoning. Aristotle's dictum de omni et 

 nullo is a self-evident principle, but it is not found among those 

 ultimate laws of the reasoning faculty to which all other laws, 

 however plain and self-evident, admit of being traced, and from 

 which they may in strictest order of scientific evolution be de- 

 duced. For though of every science the fundamental truths are 

 usually the most simple of apprehension, yet is not that sim- 

 plicity the criterion by which their title to be regarded as funda- 

 mental must be judged. This must be sought for in the nature 

 and extent of the structure which they are capable of supporting. 

 Taking this view, Leibnitz appears to me to have judged cor- 

 rectly when he assigned to the " principle of contradiction" a 

 fundamental place in Logic ;* for we have seen the consequences 

 of that law of thought of which it is the axiomatic expression 

 (III. 15). But enough has been said upon the nature of deduc- 

 tive inference and upon its constitutive elements. The subject of 



* Nouveaux Essais sur 1'entendement humain. Liv. iv. cap. 2. Theodicee 

 Pt. I. sec. 44. 



