THE THEORY OF SYLLOGISM, ETC. 107 



Turning to Sir William Hamilton's system, I find that his peculiar syllogisms will not 

 follow this rule : but in the exemplar system it is preserved throughout. The fourth figure 

 is incapable of inference, as long as one inconvertible copula, and that only, is used. 



The copula being inconvertible, we may complete the modes of inference by allowing the 

 correlative copula; as ' X gives V ' Y is given by AT'. That is, whenever conversion is 

 necessary to turn the syllogism into + + of the first figure, H — of the second, or — + of the 

 third, the correlative copula must somewhere be introduced. 



The following addition to the poetry of logic may be euphonized by any one to his own 

 taste : the letter g, following a vowel, denotes that the premise (or conclusion) denoted by that 

 vowel takes the correlative copula. 



Barbara, Celagrent, Darii, Ferigoque prioris 



Cesareg, Camestres, Festinog, Baroko secundas 



Tertia Darapgi, Disagmis, Datigsi, Felapton 



Bokardo Ferison habet. Quarta insuper addit 



Bramantigp, Camegnes, Dimarigs, Fegsapo, Fregsison. 



This means, for example, that Fesapo may be read in the fourth figure under the additional 

 condition seen in Fegsapo, namely, that the copula of the first premise is to be correlative of 

 that used in the second premise and conclusion : and Darapgi in the third, if the second copula 

 used be correlative of the other. two. Thus 'all the piles supported arches; all the piles were 

 supported on gravel, therefore gravel did then support arches' is a good syllogism, and not 

 capable of reduction to an Aristotelian syllogism. The proposition ' support of support is 

 support' is necessary to the inference, which inference can only be obtained from a sorites, and 

 not then except by help of the dictum already quoted. It may be said that this is more than 

 an Aristotelian syllogism ; I maintain it to be less, if either. The outstanding copular relation 

 (always implied) of an Aristotelian syllogism is 'is that which is, gives is:' of the preceding 

 case, ' support of support is support.' The former demands transitive and convertible meaning 

 for is, or that is shall be its own correlative : the latter demands transitive meaning for support, 

 and the allowance of its correlative. 



The following table shews the way in which any combination of premises is to be read in 

 any figure, it being presumed, as in Sir William Hamilton's system, that every syllogism may 

 be read in any figure. 



I. + + + ( + ) _ _ _ (+) - 

 II. (+)++ + _ _ - +(-) 



III. + (+) + + -(-) - + - 

 IV. + + (+) + (-)- (-) + - 



These cases may be remembered as follows. Let + +, + -, - +, and , be called the 



primitive forms of the four figures : the fourth figure taking its root in an inconclusive form. 

 In every primitive form the correlative copula need not appear. When one premise of a 

 primitive form is altered, the necessity of a correlative copula is thrown upon the other : when 

 both, upon the conclusion. 



The principles laid down in Section I. enable us to make a still further enlargement. The 



14—2 



