162 THE PRINCIPLES OF SCIENCE. 



of negatives. This table then presents the results of 

 a complete analysis of all the possible logical relations 

 arising in the case of three terms, and the old syllogism 

 forms but one out of fifteen typical forms. Generally 

 speaking every form can be converted into apparently 

 different propositions ; thus the fourth type A = B, B = BC 

 may appear in the form A = ABC, a = ab, or again in the 

 form of three propositions A = AB, B = BC, aB = aBc ; but 

 all these sets of premises yield identically the same series 

 of combinations, and are therefore of exactly equivalent 

 logical meaning. The fifth type, or Barbara, can also be 

 thrown into the equivalent forms A = ABC, aB = aBC and 

 A = AC, B = A I aBC. In other cases I have obtained the 

 very same logical conditions in four modes of statement. 

 As regards mere appearance and mode of statement, the 

 number of possible premises would be almost unlimited. 



The most remarkable of all the types of logical condition 

 is the fourteenth, namely A = BC I be. It is that which 

 expresses the division of a genus into two doubly marked 

 species, arid might be illustrated by the example ' Com- 

 ponent of the physical universe = matter, gravitating, or 

 not-matter (ether), not-gravitating.' 



It is capable of only two distinct logical variations, 

 namely, A BC I be and A = Be I bC. By transposition 

 or negative change of the letters we can indeed obtain 

 six different expressions of each of these propositions ; 

 but when their meanings are analysed, by working out 

 the combinations, they are found to be logically equiva- 

 lent to one or other of the above two. Thus the proposi- 

 tion A = BC I be can be written in any of the following 

 five other modes, 



a = 60 -I- Be, B = CAica, 6=cA|Ca, 

 C = ABIa6, c=aBtA6. 



I do not think it needful at present to publish the 

 complete table of 193 series of combinations and the 



