108 THE PRINCIPLES OF SCIENCE. 



become apparent that there is a close connection between 

 these combinations and the most fundamental theorems of 

 mathematical science. For the convenience of the reader 

 who may wish to employ the abecedarium 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 ABX, 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 

 Combinations it will become apparent that the intro- 

 duction of this unit class is requisite in order to com- 

 plete the analogy with the Arithmetical Triangle there 

 described. 



The reader ought to bear in mind that though the 

 abecedarium seems to give mere lists of combinations, 

 these combinations are intended in every case to con- 

 stitute the development of a term of a proposition. 

 Thus the four combinations AB, A&, aB, ab really mean 

 that any class X is described by the following proposition, 



X = X (AB I Ab | aB ! ab). 

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



AX = X(AB I Aft). 



Thus whatever group of combinations we treat must be 

 conceived as part of a higher class, summum genus or 

 universe symbolised in the term X ; but bearing this in 

 mind, it is needless to complicate our formulae by always 

 introducing the letter. All inference consists in passing 

 from propositions to propositions, and combinations per se 

 have no meaning. They are consequently to be regarded 

 in all cases as forming parts of propositions. 



