VI.] THE INDIRECT METHOD OF INFERENCE. 93 



A, B produce four combinations 



A, V>, C, „ eight 



A, B, C, D „ sixteen „ 



A. B, C, D, E „ thirty-two „ 



A, B, C, D, E, F „ sixty-four „ 



and so on. 



1 propose to call any such series of combinations the 

 Logical Alphabet. It holds in logical science a position 

 the importance of which cannot be exaggerated, and as 

 we proceed from logical to mathematical considerations, it 

 will become apparent that there is a close connection 

 between these combinations and the fundamental theorems 

 of mathematical science. For tlie convenience of the 

 reader who may wish to employ the Alphabet in logical 

 questions, I have had printed on the next page a complete 

 series of the combinations up to those of six terms. At 

 the very commencement, in the first column, is placed a 

 single letter X, which might seem to be superfluous. This 

 letter serves to denote that it is always some higher class 

 which is divided up. Thus the combination AB really 

 means APjX, or that part of some larger class, say X, 

 which has the qualities of A and B present. The letter 

 X is omitted in the greater part of the table merely for the 

 sake of brevity and clearness. In a later chapter on Com- 

 binations it will become apparent that the introduction of 

 this unit class is requisite in order to complete the 

 analogy with the Arithmetical Triangle there described. 

 The re-ider ought to bear in mind that though the Logical 

 Alpliabet seems to give mere lists of combinations, these 

 combinations are intended in every case to constitute the 

 development of a term of a proposition. Thus the four 

 combinations AB, Ab, aB, ab really mean that any class X 

 is described by the following proposition, 



X = XAB -I- XAb -I- XaB -I- Xab. 

 If we select the A's, we obtain the following proposition 



AX = XAB -I- XAb. 

 Thus whatever gToup of combinations we treat must be 

 conceived as part of a higher class, siimmwn genus or 

 universe symbolised in the term X ; but, bearing this in 

 mind, it is nei'dless to complicate our fornndie by always 

 introducing the letter. All inference consists in passing 

 from propositions to propositions, and combinations i>ci- se 



