39 



intension, as objects or 'units of thought,' this last being 

 tlie interpretation given by Professor Adamson in his article 

 on Logic in the new edition of the " Encyclopsedia Britan- 

 nica" (vol. xv., p. 801). 



Boole writes the proposition, 'all x is y' in the form 



x=^~ y, or x=vy, where - or -y is "an indefinite class sym- 

 bol," subject to the same fundamental law as the other 

 symbols, namely, v^=v. From this equation he deduces, by 

 the elimination of v, the equation x = xy, which is the form 

 in which Jevons always writes the universal affirmative 



proposition. In general, the symbol - or v indicates that 



all, some, or no7ie of the class to whose expression it is 

 affixed must be taken; but there are cases in which its 

 meaning is necessarily restricted. The subject is a very 

 large one, and I cannot discuss it here. Mr. Venn has sug- 

 gested that where the class is wholly indefinite, the symbol 



- should be used; and that where it is partially defined, or 



defined as meaning not none, v should be used. 



The idea that Boole's system starts from the doctrine of 

 the quantification of the predicate, as Jevons affirmed, or 

 that it is in any way bound up with that doctrine, has been 

 effectually disposed of by Mr. Yenn. He says truly, " If the 

 wit of man had sought about for some expression which 

 should unequivocally and even ostentatiously reject this 

 unfortunate doctrine, what better could be found than 



x = ~- y for such a purpose ? So far from quantifying the 



predicate by specifying whether we take some only or all 

 of it, we select a form which startles the ordinary logician 

 by the uncustomary language in which it announces that it 

 does not at all mean to state whether some only, or all, or 

 even none, is to be taken." Mr, Venn, in his Symbolic 



