THE THEORY OF SYLLOGISM, ETC. 



109 



Thomas' and 'John is |one who can persuade Thomas}.' The deduction of y = <p\j/z from 

 y = <p<v, #=\J/*is the formation of the composite copula = <p\f,. And thus may be seen the 

 analogy by which the instrumental part of inference may be described as the elimination of a 

 term by composition* of relations. For though in ordinary inference the concluding copula is 

 usually identical with those premised, yet it is no less true that the composition must have 

 taken place : X is Y, Y is Z, therefore X is that which is (= is) Z. 



Upon two given relations, there is but one species of affirmative syllogism, and two species 

 of opposing negative syllogisms ; that is, if the alternative relation be merely negative, and no 



- and .. 



correlative be permitted. If — 



compound relation ; and if and 



relations, the three syllogisms are 



First figure. 



(Y Z 



\X Y 



X.^TT^Z 



be the copular symbols, and that of the 



777 represent the negatives of the first 



and 



Second figure. 



fZ Y j 



|X— — Y \ 



X, 



Third figure. 



Y — — Z 

 Y X 



X Z 



The terms are here singular : if we make them cumulative, we introduce the usual laws of 

 quantity. And the three figures shew their primitive forms + +, + — , — r. If the correla- 

 tive copulae be introduced, the preceding theory of figure may be extended to the bicopular 

 syllogism. And we now see as follows ; — 



First, the fourth figure is dependent for its existence upon the entrance of the copular 

 correlative. I have always looked with surprise upon the arguments for and against the fourth 

 figure. If the inferences therein made be good inferences — if the man who can establish the 

 premises, does establish the conclusion, of Dimaris or Camenes, how can it be said that the 

 fourth figure is not to be used ? there it is, and it cannot be reasoned out of existence. But 

 in the above system, the fourth figure yields no true inference until the copular correlative is 

 allowed : this may be excluded from data by hypothesis, but on what principle of reason can 

 true consequences of data be excluded by hypothesis, and what is the correct English of the 

 word hypothesis, in such case ? There ought to be no bounds to any science, except such as 

 are determined by its data. 



Secondly, it appears that the affirmative syllogism gains its conclusion by composition, the 

 negative by resolution : the negative premise has a compound copular relation, which is to be 

 resolved. We see this plainly when different relations are compounded : just as a beginner in 

 algebra sees properties of a x b which would be much clouded by taking his initial examples 

 from a x a. Indeed, the forms of logic, stinted down to the Aristotelian syllogism, much 

 resemble those of an algebra in which all the letters are equal, and all equal to unity. For 

 example, taking our previous instance of composition, from ' Z can command Y, X cannot 

 control V we deduce X cannot persuade Z. And we must deduce it by resolving control 



* Or composition and resolution, but these two words never 

 finally mean more than one. Composition of an opponent is 

 resolution. Whether the words shall both occur or not de- 

 pends upon whether we begin on a narrow or a wide basis. 



Arithmeticians begin with multiplication and division, and end 

 by declaring them identical. The old geometers began with 

 composition of ratios, and never arrived at resolution, for they 

 had all resolutions in their compositions. 



