CHAPTER VI. 



THE INDIRECT METHOD OF INFERENCE. 



THE forms of deductive reasoning as yet considered, are 

 mostly cases of Direct Deduction as distinguished from 

 those which we are -now about to treat. The method of 

 Indirect Deduction may be described as that which points 

 out what a thing is, by showing that it cannot be anything 

 else. We can define a certain space upon a map, either by 

 colouring that space, or by colouring all except the space ; 

 the first mode is positive, the second negative. The dif- 

 ference, it will be readily seen, is exactly analogous to that 

 between the direct and indirect proof in geometry. Euclid 

 often shows that two lines are equal, by showing that they 

 cannot be unequal, and the proof rests upon the known num- 

 ber of alternatives, greater, equal or less, which are alone 

 conceivable. In other cases, as for instance in the seventh 

 proposition of the first book, he shows that two lines must 

 meet in a particular point, by showing that they cannot 

 meet elsewhere. 



In logic we can always define with certainty the utmost 

 number of alternatives which are conceivable. The Law 

 of Duality (pp. 6, 88) enables us always to assert that any 

 quality or circumstance whatsoever is either present or 

 absent in anything. Whatever may be the meaning and 

 nature of the terms A and B it is certainly true that 



A = AB [ A6 

 B = AB I- aB. 



These are universal though tacit premises which may 

 be employed in the solution of every problem, and which 



