THE THEORY OF SYLLOGISM, ETC. 93 



copula, turns a universal into another and inconsistent universal, and a particular into another 

 and a consistent particular : as A")) F into A(.)F, or A(.)F into X).)Y. An alteration of 

 either of the terms into its contrary, must count as alteration of the quantity of that term, 

 and the copula. 



To carry this a little further, observe that though all the particulars consist with one 

 another, or may exist together, yet they take distinctions, when looked at as to probability, 

 which have some resemblance to those existing among the universals either as probabilities or 

 as certainties. Take the universal X))Y, and change both quantities : it becomes A((F. If 

 the latter be true, it is in favour of X))Y rather than otherwise. Do the same with AQF, it 

 becomes A)(F: if the second be true, it is also rather a presumption for X()Y than otherwise. 

 The more things there are which are neither X nor Y, the smaller the number of instances of 

 the universe within which all the As and all the Ys are contained ; and the greater the proba- 

 bility of X()Y. Now take the universal X))Y and alter one quantity and the copula: we 

 have AQF and A).(F, both absolutely inconsistent with X))Y. Do the same with A()F: 

 we have X).)Y and A(.(F, neither inconsistent with A()F, but both diminishing its pro- 

 bability. This observation is of some wortli in classification : it may justify us in extending the 

 general name of concomitants to particulars in which both quantities differ, and opponents to 

 those in which one quantity and the copula differ ; and will help us to system. 



Now let a proposition be considered as having two sides, on each of which a change of 

 quantity counts as one, and a change of copula as one for each side. Changes of quantity 

 then may be represented by l|o and o|l, change of copula is l|l, and changes of term are 2|l 

 and l|2. The utmost amount of change is 4J4, which restores the original : thus o?(..(y is 

 X))Y affected by 4J4, and it is X))Y itself. And it will be found that l|o and o|l always pro- 

 duce a superior universal or an inferior particular, that l|l produces a concomitant, 2|l or l|2 

 an opponent, 2J2 a contrary ; and so on. 



When contraries are allowed, all inference may be made to consist in declaration of agree- 

 ment. The disagreement of two things, because one agrees and the other disagrees with a 

 third, may be made to fall under the other and more simple case ; not indeed, as the easiest rule 

 of thought, but as the best basis of a classification. This X agrees with this F; this Z does 

 not agree with this Y ; therefore this X does not agree with this Z — may be stated as, This X 

 agrees with this Y, something not this Z agrees with this Y, therefore this X agrees with 

 something not this Z. And the universe, explicitly divided into this Z and other things, is a 

 provision for the definite understanding of the manner in which the second proposition is 

 transformed. 



Accordingly, agreement between Xs and Ys, Ys and Zs leads to agreement between As 

 and Zs, if the number of agreements be altogether more than there are Ys. Restricted as we 

 are now to the case of the universal and the indefinite particular, one of the propositions must 

 mention all the Fs. So that the fundamental syllogisms, from which all the rest are derived 

 by every introduction of contraries, seem to be 



J l A 1 A l X))Y))Z = X))Z or )))) = )) 

 A' A' A' A((F((Z = A((Z or (((( = (( 



A()F))Z = A()Z or ())) = () 7,^,7, 

 X((Y()Z = X()Z or ((() = () ^'7,7, 



A l AJ t X((Y))Z = X()Z or (()) = (). 



