1880.] expressing the common propositions of Logic. 37 



they are expressed in the same letters in each case, 8 and P 

 standing respectively for the subject and predicate of the original 

 proposition ; viz. no S is P. 



The analysis by which I should reach these various forms 

 would be somewhat of the following kind : 



I. In the first place we may regard the proposition as an 

 existential one. In this case what it does is to deny the existence 

 of a certain class, viz. of the things which are both S and P. 



II. We may cast the proposition into the form of an identity. 

 "What we then do is to make the terms of the proposition respectively 

 S and not-P, and to identify the former with an undetermined 

 part of the latter. The appropriate copula is then of course (=). 



III. Another plan is to regard the proposition as expressing 

 a consequence or implication : ' If S then not-P/ or, ' the presence 

 of S implies the absence of P.' This relation, of course, is not 

 convertible, for it does not follow that the absence of P implies 

 the presence of S. Accordingly, some kind of unsymmetrical 

 symbol becomes appropriate to represent the copula in this case. 



IV. Again, keeping more closely to the common expression 

 of the proposition, we may regard it as expressing a relation not, 

 as above, between S and not-P, but between S and P. This 

 relation is convertible, and we should therefore naturally seek in 

 this case for some symmetrical symbol. 



V. Again, we may couch the proposition in conceptualist or 

 notional phraseology, regarding P and S not as classes of things 

 but as attributes or groups of attributes. 



VI. Lastly, we may meet with nondescript attempts which 

 aim at little more than just translating the proposition as it stands, 

 or adopting some arbitrary notation to stand for it. 



Grouping them thus, we may arrange our species as follows : — 



( 1 >S1'=0 Boole. 



I. Existential 



II. Identity 



