DESCRIPTION OF A NOTATION FOR THE 





Individual Terms. 



The fundamental formulas relatin 



noted by capitals. 



(95.) 

 (96.) 



g to individuality are two. Individual or. i, 



fc*. 



lf*>0 *r=xj r x'-yx"-kx"4r*to. 



y 



X 



yX. 



We have also the following which are easily deducible from the se two: 



(97.) 



(y,*)x 



(yX),(zX) . 



(98.) Xtfo = X#X. 



(99.) [X] 



( 100.) f* 



I 



X. 



We have already seen that 



/* 



, provided that \x\ > 



i . 



As an example of the use of the formula? we have thus far obtained, let us inws- 



| 



tigate the logical relations between "benefactor of a lover of every servant of every 

 woman," " that which stands to every servant of some woman in the relation of ben- 

 efactor of a lover of him," "benefactor of every lover of some servant of a worn n, 

 "benefactor of every lover of every servant of every woman," etc. 

 In the first place, then, we have by (95) 



sw 



S (W' -k W" -fc- W" -k- etc.) = *W -fc- sW + $W m -V etc 



5 W 



S W + W" 4- W" + etc. = ,W . W" yS W f e tc. 



From the last equation we have by (96) 



s w 



(«W'),(*\H,(*W"'), etc. 



Now by (31) 



// 



x "V x ' "fe" etc - — z f ,z", x '"> etc. -fc- etc. , 



or 



(101.) 



it 



2', 



where II' and 2' signify that the addition and multiplication with commas are to be 

 used. From this it follows that 



(102.) s" 



S\V . 



If w vanishes, this equation fails, because in that case (95) does not hold 

 From (102) we have 



(103.) 



(Is) 



W 



Isvr . 





