AND THE PROBABILITIES OF AUTHORITY AND ARGUMENT. 387 



Consequently, since there is the same probability that they shall have nothing in common when 

 IJL is on the right and /j.' on the left, the expression just written is tiie probability that /x and ju' shall 

 be quite clear of one another. 



The condition that a; and i' shall not have so much as i- in common, is expressed by saying 

 that ,r + x' less than I - /u - /i.' + v : v being less than /x and than /jl'. Hence, by similar reasoning 



(I -M -j/ + vY 



(1 -mXi-m) 



is the chance that ju and /m' have not so much as v in common. 



Under these new circumstances, if u and u! be each = — , the chance that thev are clear of one 

 64 '^ 10 • 



another is — , or it is 6-t to 17 in favour of it. That is, if a thousand persons were placed in a 

 81 



row, and two being selected at hazard, 100 sovereigns were given successively, beginning with the 

 first, and ion shillings successively, beginning with the second, it would now be about 6i to 17 that 

 no one received a guinea. 



Section IV. Oti the Syllogisw. 



There is much that is elegant and instructive about the theory of the four figures of the syllo- 

 gism, three of which belong to .Aristotle. And the magic words Barbara, Camestres, ^-c. are models 

 of notation, almost every letter of the moods in the three latter figures being a rule of direction. The 

 following old epitaph on a schoolman selects, I think, one of the best parts of the system for ridicule : 



Hie jacet raagister noster 

 Qui dispiitavit bis aut ter 

 In Barbara et Celarent 

 Ita ut omnes admirarent 

 In Fapesmo et Frisesoinorum 

 Orate pro animis eorum ! 



In proposing another system of classification, in connexion with the use of contraries, I 

 remark, first, that the ordinary method has two points of redundancy. The distinct use of the 

 two forms of a convertible proposition, X. Y and Y . X, ^F and YX, is made for the system 

 of figures, rather than the figures for it. It is desirable I think to confound them as much as pos- 

 sible ; so that each may never fail to suggest the other. In the next place, if the use of contraries 

 be introduced, every one of the twenty-four modes of predicating would claim admission into a 

 system of figures, and their number would be increased to thirty-two. 



Again, the first followers of Aristotle, in adopting the rule that no syllogism should be admitted 

 in which the conclusion was not the strongest the premises would allow — in rejecting for instance 

 "A') }' and Y)Z therefore XZ,"^ because X)Z also follows — did not adopt the equally 

 obvious rule of admitting no syllogism in which a weaker premiss would lead to as strong a con- 

 clusion. They retained, for instance, " T ) A' and Y ) Z therefore XZ ", though 1' ) X and YZ would 

 produce the same conclusion. Now 1 think it desirable to adopt the rule of producing the strongest 

 conclusion with the weakest premises, not only because it will turn out that by so doing the number 

 of forms is diminished, even when contraries are considered, but also because a better and clearer 

 diHtinctii>n is drawn lietween the necessary and the contingent. 



I also drop the distinction of minor and major terms and premises. Aristotle meant them to 

 ap|)ly only to affirmative propositions, in which the predicate includes the subject. But the use of 

 iheni wa- extended, to the utter destruction of the meaning in negative propositions, or worse, to the 



.io 2 



