INFERENCE IN GENERAL. 125 



one has ever censured writers on geometry, for placing a list of these ele- 

 mentary 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 discus- 

 sion even of such truths as we have cited above, acquires habits of cir- 

 cumspect interpretation of words, and of exactly measuring the length and 

 breadth of his assertions, which are among the most indispensable condi- 

 tions 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 province of Reasoning 

 or Inference properly so called, the cases in which the pi'ogression from one 

 truth to another is only apparent, the logical consequent being a mere rep- 

 etition 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 distinct 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 : rea- 

 soning from particulars to generals, and reasoning from generals to partic- 

 ulars ; the former being called Induction, the latter Ratiocination or Syllo- 

 gism. It will presently be shown that there is a third species of reasoning, 

 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 from particii- 

 lars to generals, and reasoning from generals to particulars, are recom- 

 mended by brevity rather than by precision, and do not adequately mark, 

 without the aid of a commentary, the distinction between Induction (in the 

 sense now adverted to) and Ratiocination. The meaning intended by these 

 expressions is, that Induction is inferring a proposition from propositions 

 less general than itself, and Ratiocination is inferring a proposition from 

 propositions equally or more general. When, from the observation of a 

 number of individual instances, we ascend to a general proposition, or when, 

 by combining a number of general propositions, we conclude from them 

 another proposition still more general, the process, which is substantially 

 the same in both instances, is called Induction. When from a general prop- 

 osition, not alone (for from a single proposition nothing can be concluded 

 which is not involved in the terms), but by combining it with other propo- 

 sitions, we infer a proposition of the same degree of generality with itself, 

 or a less general proposition, or a proposition merely individual, the process 

 is Ratiocination. When, in short, the conclusion is more general than the 

 largest of the premises, the argument is commonly called Induction ; when 

 less general, or equally general, it is Ratiocination. 



As all experience begins with individual cases, and proceeds from them 

 to generals, it might seem most conformable to the natural order of thought 

 that Induction should be treated of before we touch upon Ratiocination, 

 It will, however, be advantageous, in a science which aims at tracing our 

 acquired knowledge to its sources, that the inquirer should commence with 

 the latter rather than with the earlier stages of the process of constructing 

 our knowledge; and should trace derivative truths backward to the truths 

 from which they are deduced, and on which they depend tor their evidence 

 before attempting to point out the original spring from which both ulti- 

 mately take their rise. The advantages of this order of proceeding in tlio 

 present instance will manifest themselves as we advance, in a manner su- 

 perseding the necessity of any further justification or explanation. 



