INDUCTIVE LOGICAL PROBLEM. 129 



type, or Barbara, can also be thrown into the equivalent 

 form A=ABC, aB=aBC. In other cases I have obtained 

 the very same logical conditions in four modes of state- 

 ment. As regards mere appearance and mode of state- 

 ment, the number of possible premises Avould be almost 

 unlimited. 



The most remarkable of all the types of logical condi- 

 tions is the fourteenth, namely A=BC-\- be. It is that 

 which expresses the division of a genus into two doubly 

 marked species, and might be illustrated by the example — 

 Component of the physical Universe = Matter, gravitating, 

 •I- Not matter (ether), not gravitating. 



It is capable of only two distinct logical variations, 

 namely A==BC •!• be and A=Bc •!■ bC. By transposition, or 

 negative change of the letters, we can indeed obtain six dif- 

 ferent expressions of each of these propositions ; but when 

 their meanings are analyzed by working out the combina- 

 tions, they are found to be logically equivalent to one or the 

 other of the above two. Thus the proposition A=BC -I- be 

 can be written in any of the following five other modes : — 



a=bO-YBc, B=CAlc«, b=cA-\-Ca, 

 C=ABla6, c=aB + Ab. 



I do not think it needful at present to publish the com- 

 plete table of 193 series of combinations and the premises 

 corresponding to each. Such a table enables us by mere 

 inspection to learn the laws obeyed by any set of combina- 

 tions of three things, and is to logic what a table of factors 

 and prime numbers is to the theory of numbers, or a table 

 of integrals to the higher mathematics. The table already 

 given above (p. 128) would enable a person with but little 

 labour to discover the law of any combinations. If there be 

 seven combinations (one contradicted) the law must be of 

 the eighth type, and the proper variety will be apparent ; 

 if there be six combinations (two contradicted), either the 



SER. III. VOL. V. K 



