INFERENCE IN GENERAL. 



107 



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 

 generalisations 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 ariy 

 considerable mental attainment, and 

 which it is one of the primary objects 

 of logical discipline to cultivate. 



§ 3. Having noticed, in order to ex- 

 clude from the province of Reasoning 

 or Inference properly so called, the 

 cases in which the progression 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 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 popu- 

 larly said to be of two kinds : reason- 

 ing 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 reasoning, which falls 

 underneitherof these descriptions, and 

 which, nevertheless, is not only valid, 

 butis thefoundation of both theothers. 



It is necessary to observe, that the 

 expressions, reasoning from particulars 

 to generals, and reasoning from gene- 

 rals to particulars, are recommended 

 by brevity rather than by precision, 

 and do not adequately mark, without 

 the aid of a commentary, the distinc- 

 tion between Induction (in the sense 

 now adverted to) and Ratiocination. 



The meaning intended by these ex- 

 pressions is, that Induction is inferring 

 a proposition from propositions less 

 general than itself, and Ratiocination 

 is inferring a proposition from proposi- 

 tions eqvxdly or m,ore general. When, 

 from the observation of a number of 

 individual instances, we ascend to a 

 general proposition, or when, by com- 

 bining a number of general proposi- 

 tions, we conclude from them another 

 proposition still more general, the pro- 

 cess, which is substantially the same 

 in both instances, is called Induction. 

 When from a general proposition, not 

 alone (for from a single proposition 

 nothing can be concluded which is not 

 involved in the terms), but by combin- 

 ing it with other propositions, 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 Ratiocina- 

 tion. Wlien, 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 indi- 

 vidual cases, and proceeds from them 

 to generals, it might seem most con- 

 formable 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 con- 

 structing our knowledge ; and should 

 tracederivative truths backward to the 

 truths from which they are deduced, 

 and on which they depend for their 

 evidence, before attempting to point 

 out the original spring from which both 

 ultimately take their rise. The ad- 

 vantages of this order of proceeding 

 in the present instance will manifest 

 themselves as we advance, in a man- 

 ner superseding the necessity of any 

 further justification or explanation. 



Of Induction, therefore, we shall 

 say no more at present, than that it 



