146 KEASONING. 



we may draw an exactly similar conclusion. The definition is a sort of 

 notice to ourselves and others, what assumptions we think ourselves en- 

 titled to make. And so in all cases, the general propositions, whether 

 called definitions, axioms, or laws of nature, which we lay down at the 

 beginning of our reasonings, are merely abridged statements, in a kind of 

 short-hand, of the particular facts, which, as occasion arises, we either 

 think we may proceed on as proved, or intend to assume. In any one 

 demonstration it is enough if we assume for a particular case suitably se- 

 lected, what by the statement 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, ac- 

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

 depend on it, but yet if we deny it the demonstration fails. The proof 

 does not rest on the general assumption, but on a similar assumption con- 

 fined to the particular case : that case, however, being chosen as a speci- 

 men or paradigm of the whole class of cases included in the theorem, there 

 can be no ground for making the assumption in that case which does not 

 exist in every other; and to deny the assumption as a general truth, is to 

 deny the right of making it in the particular instance. 



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

 principles and the theorems in their general form, and these will be ex- 

 plained presently, so far as explanation is requisite. But, that unpracticed 

 learners, even in making use of one theorem to demonstrate another, rea- 

 son rather from particular to particular than from the general proposition, 

 is manifest from the difficulty they find in applying a theorem to a case in 

 which the configuration of the diagram is extremely unlike that of the dia- 

 gram by which the original theorem was demonstrated. A difficulty 

 which, except in cases of unusual mental power, long practice can alone re- 

 move, and removes chiefly by rendering us familiar with all the configura- 

 tions consistent with the general conditions of the theorem. 



§ 4. From the considerations now adduced, the following conclusions 

 seem to be established. All inference is from particulars to particulars: 

 General propositions are merely registers of such inferences already made, 

 and short formulae for making more : The major premise of a syllogism, 

 consequently, is a formula of this description : and the conclusion is not an 

 inference drawn from the formula, but an inference drawn according to 

 the formula : the real logical antecedent, or premise, being the particular 

 facts from which the general proposition was collected by induction. 

 Those facts, and the individual instances 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 infer- 

 ence. According to the indications of this record we draw our conclusion : 

 which is, to all intents and purposes, a conclusion from the forgotten facts. 

 For this it is essential that we should read the record correctly: and the 

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



This view of the functions of the syllogism is confirmed by the consid- 

 eration of precisely those cases which might be expected to be least favor- 

 able to it, namely, those in which ratiocination is independent of any pre- 

 vious induction. We have already observed that the syllogism, in the or- 

 dinary course of our reasoning, is only the latter half of the process of 

 traveling from premises to a conclusion. There are, however, some pecul- 



