122 THE PRINCIPLES OF SCIENCE. 



The lower line contains all the combinations which are 

 inconsistent with either premise ; we have carried out in 

 a mechanical manner that exclusion of self-contradictories 

 which was formerly done upon the slate or paper. Ac- 

 cordingly, from the remaining combinations in the upper 

 line we can draw any inference which the premises yield. 

 If we raise the A's we find only one, and that is C, so that 

 A must be C. If we select the c's we again find only 

 one which is a and also 6, so that we prove that not-C is 

 iiot-xl and not-B. 



When a disjunctive proposition occurs among the 

 premises the requisite movements become rather more 

 complicated. Take the disjunctive argument 



A is either B or C or D, 



A is not C and not D, 



Therefore A is B. 

 The premises are represented accurately as follows : 



A = ABI AC! AD (i) 



A = Ac (2) 



^ 



As there are four terms we choose the series of sixteen 

 combinations and place them on the highest ledge of the 

 board but one. We raise the a's and lower the b's. But 

 we are not to reject all the A&'s as contradictory, because 

 by the first premise A's may be either B's or C's or D's. 

 Accordingly out of the Afr's we must select the cs, and 

 out of these again the d's, so that only Kbcd will remain 

 to be rejected finally. Joining all the other fifteen com- 

 binations together again we raise the as and lower the 

 AC's, and thus reject the combinations inconsistent with 

 (2) ; similarly we reject the AD's which are inconsistent 

 with (3). It will be found that there remain in addition 

 to all the eight combinations containing a only one con- 

 taining A, namely 



