330 MEMOIRS OF THE 



and the other is infinity; for as l 00 is indeterminate in ordinary algebra, so it will 

 be shown hereafter to be here, so that to remove the correlate by the product of an 

 infinite series of ones is to leave it indeterminate. Accordingly, 



m,oo 



should be regarded as expressing some man. Any term, then, is properly to be 

 regarded as having an infinite number of commas, all or some of which are neu- 

 tralized by zeros. 



"Something" may then be expressed by 



/ 



QO 



I shall for brevity frequently express this by an antique figure one ( i ). 

 "Anything" by 



/o. 



1 shall often also write a straight 1 for anything. 



It is obvious that multiplication into a multiplicand indicated by a comma is com- 

 mutative,* that is, 



This multiplication is effectively the same as that of Boole in his logical calculus. 

 Boole's unity is my 1 , that is, it denotes whatever is. 



The sum x -\- x generally denotes no logical term. But x,^ -f- x )(X> may be 

 considered as denoting some two #'s. It is natural to write 



and 



x i X /& . X j 



oo ? 



where the dot shows that this multiplication is invertible. We may also use the 

 antique figures so that 



just as 



^•X.jtfi j.X * 



/«. = I . 



Then 2 alone will denote some two things. But this multiplication is not in gener 

 commutative, and only becomes so when it affects a relative which imparts a relatic 

 such that a thing only bears it to one thing, and one thing alone bears it to a thin 



* It will often be convenient to speak of the whole operation of affixing a comma and then multiplying as a com- 

 mutative multiplication, the sign for which is the comma. But though this is allowable, we shall fall into confusion 

 at once if we ever forget that in point of fact it is not a different multiplication, only it is multiplication by a relative 

 whose meaning — or rather whose syntax — has been slightly altered ; and that the comma is really the sign of this 



term 



