AND ON LOGIC IN GENERAL. iZl? 



XXXVI. The syllogism is inference of the relation which exists between two terms, as 

 a necessary consequence of their relations to the same third, or middle, term. When the 

 relations are onymatic, so may be called the syllogism. 



The perception of the validity of a syllogism is the perception of the combination of two 

 relations into one. This is frequently the case even in the common mode of stating a syl- 

 logism, in which premises (the two expressions of simple relation) and conclusion (the expres- 

 sion of the compound relation) are stated in the arithmetical whole. If the common form be 

 not compelled to accept the name of a syllogism of first intention, it is because the act of mind 

 in forming the conclusion may be based on notions of second intention. 



Some pairs of relations combine into one relation. Thus a species of a species is a species : 

 but a species of a copartient may be any one of the eight relations. 



The major term of a syllogism is that term of the conclusion to which the other is related, 

 or the predicate: the subject of the conclusion is the minor term. The major term is the one 

 to which the action of tiie syllogism points: in this way. We see that X )) Y and Y )■( Z 

 give X )•( Z, which may be expressed thus: — the species of an external of Z is an external 

 of Z : here Z is the major term. But in reading backwards, as ' The external of a genus of 

 X is an external of X,' we see that X is the major term. 



The natural character oi the first Jigure will now be seen, as the most simple expression of 

 the combination of relations : but it is somewhat obscured by the usual order of writing the 

 premises. The fourth figure is less natural, because it converts the expected relation. The 

 second and third figures are less natural, because they do not present the relations to be com- 

 bined, but one of them and the converse of the other. 



Ever}' syllogism may be read, with reference to one set of terms, in sixteen ways. For 

 any term may be changed into its contrary, and the proper change of relation made : this 

 gives eight ways of reading; and inversion of order gives eight more. But when we drop the 

 terms, and consider merely combination of relation, the sixteen are only two repetitions of the 

 same eight, when both premises are universal. 



Two universal premises always give a conclusion, universal when the middle term is of 

 different quantities in the two premises, particular, when of the same. A universal premise 

 coupled with a particular always gives a conclusion when the middle term is of different 

 quantities in the two ; and not otherwise. But universal premises with a particular conclu- 

 sion would allow as strong a conclusion if either premise be properly weakened into a par- 

 ticular : hence I called such a syllogism strengthened. A syllogism with a premise stronger 

 than needful for the conclusion, or with a conclusion weaker than needful from the premises, is 

 a logical argument, but one which should not be allowed to stand in the same class with the 

 fundamental'' syllogism which has all that can be got from premises which are no stronger than 



ig a witches' cauldron: I accept the phrase. Algebra is a 

 witches' cauldron. It has two handles, + and —. By these we 

 lift on the fire, at once, the distinctions of addition and sub- 

 traction, multiplication and division, up and down, north and 

 south, east and west, loss and gain, before and after, gravity 

 and levity, attraction and repulsion, &c. &c. &c. They all 

 boil together, and the results are magical. The spell was 



impaired by the long time which certain toots (of negative 

 quantities) took to boil; but they are now quite done. The 

 logical cauldron, of which I have some further knowledge, I 

 hope to set boiling at some future time. 



• Had this distinction been made from the beginning, it 

 would have been seen that it is as necessary to a fundamental 

 syllogism that the middle term should enter once particularly. 



Vol. X. Pakt I. 28 



