94 



By an additional letter (g) introduced into the usual words of 

 syllogism, the places of the correlative copula may be remembered, 

 as in Barbara, Celagrent, &c; : a g being made to accompany any 

 member of the syllogism in which the correlative copula must be 

 employed. 



This theory is applied equally to the Aristotelian system, to Sir 

 William Hamilton's (though not of universal application in the cu- 

 mular form), and to Mr. De Morgan's system of contraries. The 

 extensions required by the use of a merely transitive copula, in the 

 last-mentioned system, are discussed ; and mention is made of the 

 tricopular system, in which the leading copula and its correlative 

 have an intermediate or middle relation, equally connected with 

 both ; as in > = and < of the mathematicians. 



The next step is the assertion that it is not necessary that any 

 two of the three copulse of a syllogism should be the same ; all that 

 is requisite is that, in affirmative syllogisms, the copular relation in 

 the conclusion should be compounded of those in the premises. The 

 instrumental part of inference is described by Mr. De Morgan as the 

 elimination of a term by composition (including resolution) of relations, 

 which leads to the conclusion that whenever a negative premise occurs, 

 there is a resolution of a compound relation. This resolution is shown 

 in a case (among others) of the ordinary copula, in which, however, 

 it would hardly strike the mind more forcibly than would the pro- 

 perties of powers in algebra if every letter represented unity. Mr. 

 De Morgan shows (in an addition) that in some isolated cases of in- 

 ference which are not reducible to ordinary syllogism, logicians have 

 had recourse to what amounts to composition of relations. 



Mr. De Morgan next points out that the copular relation, in 

 affirmative propositions, need not be restricted as applying to one 

 instance only of the predicate ; and shows that the removal of this 

 usual restriction entirely removes all his objections to Sir William 

 Hamilton's form of his own system. 



Section VI. On the application of the theory of probabilities to some 

 questions of evidence. — This inquiry was suggested by the apparent 

 (but only apparent) error of the logicians, who seem to lean towards 

 the maxim that, when the subject and predicate are unknown, the 

 universal and particular propositions * Every X is Y,' ' Some Xs are 

 not Ys,' are a priori of equal probability. The difficulty is one which 

 occurs in the following case : — If a good witness, drawing a card 

 from a pack, were to announce the seven of spades, his credit would 

 not be lowered, though he would have asserted an event against which 

 it was 51 to 1 a priori. A common person gives the true answer, 

 ' Why not the seven of spades as well as any other ? ' Many readers 

 of works on probability would be inclined to say ' That is not the 

 question ; why the seven of spades rather than some one or another 

 of the fifty-one others ? ' The retort is fallacious : it rubs out the 

 distinctive marks from the other fifty-one cards, and writes on each 

 of them ' not the seven of spades ' as its only exponent. Laplace 

 has chosen two problems, in one of which the distinctive marks 

 exist, and not in the other ; and, neglecting the consideration of the 

 first one, has founded his remarks upon the deterioration of evidence 



