FUNCTIONS AND VALUE OF THE SYLLOGISM. 129 



which we lay down at the beginning of our reasonings, are merely 

 abi-idged statements in a kind of short hand, of the particular facts, 

 which, as occasion aiises, we either think we may proceed upon as 

 proved, or intend to assume. In any one demonstration it is enough 

 if we assume for a particular case, suitably selected, what by the state- 

 ment of the definition or principle we announce that we intend to 

 assume in all cases which may arise. The definition of the circle, 

 therefore, is to one of Euclid's demonstrations, exactly what, according 

 to Stewart, the axioms are ; that is, the demonstration does not depend 

 upon it, but yet if we deny it the demonstration fails. The proof does 

 not rest upon the general assumption, but upon a similar assumption 

 confined to the particular case : that case, however, being chosen as a 

 specimen or paradigm of the whole class of cases included in the theo- 

 rem, there can be no gi'ound for making the assumption in that case 

 which does not exist in every other ; and if you deny the assumption as 

 a general truth, you deny the right to make it in the particular instance. 

 There are, undoubtedly, the most ample reasons for stating both the 

 principles and the theorems in their general fonn, and these will be 

 explained presently, so far as explanation is requisite. But, that an 

 unpractised learner, even in making use of , one theorem to demon- 

 strate another, reasons rather from particular to particular tlian from 

 the general proposition, is manifest from the difiiculty he finds in ap- 

 plying a theorem to a case in which the configuration of the diagram 

 is exti'emely unlike that of the diagi'am by which the original theorem 

 was demonstrated. A difficulty which, except in cases of unusual 

 mental power, long practice can alone remove, and removes chiefly by 

 rendering us familiar with all the configurations consistent with the 

 general conditions of the theorem. 



§ 4. From the considerations now adduced, the following conclu- 

 sions seem to be established: All inference is from particulars to par- 

 ticulars : General propositions are mei-ely registers of such inferences 

 already made, and short formulae for making more : The major premiss 

 of a syllogism, consequently, is a formula of this description : and 

 the conclusion is not an inference drawn from the formula, but an in- 

 ference drawn according to the formula : the real logical antecedent, 

 or premisses, being the particular facts firom which the general propo- 

 sition was collected by induction.. Those facts, and the individual in- 

 stances which supplied them, may have been forgotten ; but a record 

 remains, not indeed descriptive of the facts themselves, but showing 

 how those cases may be distinguished respecting which the facts, when 

 known, were considered to warrant a given inference. According to 

 the indications of this record, we draw our conclusion ; which is, to all 

 intents and pui-poses, a conclusion from the forgotten facts. For this 

 it is essential that we should read the rccoi-d correctly : and the rules 

 of the syllogism are a set of precautions to insure our doing so. 



This \dew of the functions of the syllogism is confinned by the con- 

 sideration of precisely those cases which might be expected to be least 

 favorable to it, namely, those in which ratiocination is independent of 

 any previous induction. We have already obsei-\'ed that the syllogism, 

 in the ordinary course of our reasoning, is only the latter half of the 

 process of ti-avelling fi'om premisses to a conclusion. There are, how- 

 evex", some peculiai' cases in which it is the whole process. Particu- 



