324 



MEMOIRS OF THE AMERICAN ACADEMY 



means every Frenchman is a man, but there are men besides Frenchmen. Drobisch 

 has used this sign in the same sense.* It will follow from these significations of 



and <[ that the sign 



(or <, "as small as") will 



mean "is." 



Thus, 



f 



m 



me 



4 , 



• 



every Frenchman is a man," without saying whether there 



any oth 



men or not. So 



m 



I 



will mean that every mother of anything is a lover of the same thing; although 



this interpretation 



deg 



nticipates a convention to be made further 



The 



grnifications of 



= and < plainly conform to the indispensable cond 

 Upon the transitive character of these relations the syllogism depends, for by 

 of it, from ■ 



f 



m 



and 



we can infer that 



m 



a 



f^a; 



that 



from 



every Frenchnu 



adopted fulfil all absolute 



ery Frenchman being a man and 



every man being an 



But not only do the significations of 



animal, that 

 and <* here 



being very nearly the same as the common significations 



quirements, but they have the supererogatory virtue of 



Equality is, in fact, nothing 



but the identity of two numbers; numbers that are equal are those which are pred 



cable of the same 

 predicable of the 



just as terms that are identical are th 



So 



5<7 



f < m is to say that Frenchmen 



)se which are 

 say that 5 is part of 7, just 



part of men. Indeed, if f < 



then the number of Frenchmen is less than the number of men, and if v = p, then 

 the number of Vice-Presidents is equal to the number of Presidents of the Senate ; 

 so that the numbers may always be substituted for the terms themselves, in case no 



of operation 



the equations or inequalities 



TJie Signs for Addition. 



The sign of addition is taken by Boole 



that 



+ y 



denotes everything denoted by x, and, besides, everytl 



denoted by y. Thus 



m -f- w 



Ane tnim edition contains nothing of the sort. 



