INFERENCE IN GENERAL. Ill 



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 sei-ves to bridge over. Yet no one has ever censured 

 writers on geometiy, for placing a list of these elementaiy genci-aliza- 

 tions at the head of their treatises, as a first exercise to the leanier of 

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

 hending a general truth. And tlie student of logic, in tiie discussion 

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

 spect intei-}5retation of words, and of exactly measuring the length and 

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

 ditions 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 Rea- 

 soning 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 ai'e cases of inference in the proper acceptation of the term, 

 those in which we set out from known tniths, to anive at others really 

 distinct from them. 



Reasoning, in the extended sense in which I use the terra, and in 

 which it is synonymous with Inference, is popularly said to be of two 

 kinds : reasoning from particulars to generals, and reasoning from gen- 

 erals to particulars ; the fonner being called Induction, the latter 

 Ratiocination or Syllogism, It will presently be shown that there is 

 a third species of reasoning, which falls imder neither of these descrip- 

 tions, and which,- nevertheless, is not only valid, but the foundation of 

 both the others. 



It is necessary to observe, that the expressions, reasoning from par- 

 ticulars to generals, and reasoning from generals to particulars, are 

 recommended by brevity rather than by precision, and do not ade- 

 quately mark, without the aid of a commentary, the distinction between 

 Induction and Ratiocination. The meaning intended by these expres- 

 sions is, that Induction is infemng a proposition from propositions less 

 general than itself, and Ratiocination is infeiTing 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 

 fi-om a general proposition, not alone (for from a single proposition 

 nothing can be concluded which is not involved in the terms), but by 

 combining it with other propositions, we infer a proposition of the 

 same degree of geuerahty wiih itself, or a less general proposition, or 

 a proposition merely individual, the process is Ratiocination. Wlien, 

 in short, the conclusion is more general than the largest of the prem- 

 isses, 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 wiU, however, be advantageous, iii a science which 



