AND MULTIPLICATION OF LOGICAL RELATI VES. 221 



the multiplicand of tlie reciprocal syllogism. Of course, 

 when any syllogism is inconclusive, its reciprocal is in- 

 conclusive, and conversely. The vacant squares, as before, 

 indicate inconclusive syllogisms. 



It will be seen that the entire table is divided into six- 

 teen squares of sixteen syllogisms each. The top left-hand 

 square is the same as that on page 209. The bottom right- 

 hand square is the same as that on page 207, except 

 that the syllogisms which there have zero products are 

 here inconclusive. 



In interpreting those syllogisms which contain factors 

 with zero index, it must be remembered that when we 

 deal with inclusion and coinclusion, exclusion and co- 

 exclusion, &c., the unexpressed middle term is understood 

 to be always the same ; that is to say, it is the same thing 

 which is included or excluded. For instance, the syllogism 



iVxiV°=iV. 



A and B are excludents of each other, 



B and C are coexeludents of A, 



A and C are excludents of each other. 



The analogy of all terms with zero index to unity fails 

 without this convention. But we adhere to this only as 

 between a term and its own zero power, not as between 

 one term and the zero power of another. This will 

 explain the only unsymmetrical or anomalous-looking 

 results in the table. We have seen (page 211) that 

 coincludents \_{L~^)°'\ of any third term are participants 

 [w] of each other. Consequently 



(L-')° X hz=n°, and w x {L-')° = n° ; 



