40 Mr Venn, On the various notations adopted for [Dec. 6, 



nothing else than Boole's vS = v'P, with the difference that the 

 arbitrary factor is put into the denominator instead of the nu- 

 merator (i.e. the factor multiplies by - and — , it does not divide 



K l J p 7T 



by p and 7r; there is no notion here of an inverse logical operation, 

 though Holland had realized it elsewhere). The consequent con- 

 dition as to the range of value of p and 7r is of course that they 

 must lie between 1 and go, just as in Boole's form v and v' lie 

 between 1 and 0. What we express symbolically therefore is 

 ' some S is some P,' where ' some' may range from none to all. So 

 far good. Where he goes astray is by interpreting the limiting 

 case S=0P (viz. when p = 1, it— oo) as meaning " all S is no P," 

 instead of " all S is nothing." The fact is that his form is extensible 

 enough to cover particular and universal affirmatives, with distri- 

 buted and undistributed premises ; but in order to make it stretch 

 so as to cover negative propositions we must either use a negative 

 predicate, not-P, or else join S and P together into one complex 

 subject and equate this to as in (1). 



All of these six concur in employing the equation symbol (=), 

 and rightly so, for what they represent is the identity of the 

 subject S with a portion of not-P. The two following must really 

 be considered to belong to the same general class, though actually 

 employing a different, and decidedly less suitable symbol, viz. 



(<)• 



9. This was employed by Drobisch in the first edition of his 

 Neue Darstellung der Logik (1836), but is omitted in later editions. 

 Two points deserve notice about it. First as regards the connecting 

 symbol itself. We are familiar with it in mathematics as meaning 

 'less than;' and it is here transferred to the signification 'is in- 

 cluded in/ or 'is identical with a part of.' It is therefore exactly 

 equivalent to the equation symbol when, as in the last examples, 

 this is affixed to a predicate affected by some indeterminate factor. 

 This transfer of the sign < does not seem to me a very convenient 

 or accurate one, though its signification is quite clear; it need 

 hardly be remarked that it here refers to the extent not the intent 

 of the terms S and P. Secondly, as regards the predicate, the 

 notation is curious as shewing the great difficulty which logicians 

 brought up in the old traditions had in realizing the conception of 

 a ' universe,' which could be represented by a single symbol. The 

 letter X does not here stand for really " all," for this would be to 

 introduce an " unendlicher Begriff," or "infinite term," quite alien 

 to old tradition. Drobisch only ventures symbolically to embrace 

 a finite but uncertain portion of this infinite universe. Let us then 

 take a class term X of uncertain extent, only demanding that its 



