ON VARIOUS POINTS OP THE ONYMATIC SYSTEM. 



469 



pose. Over and above the i-einforcement of preceding notions, that purpose is the compari- 

 son of extension and comprehension, or, as I prefer to say, of extent and intent. With the 

 above limitations the following table, to be immediately explained, contains all that is 

 necessary. 



II 



III 



IV 



) 

 ( 

 ( 

 ) 

 ( 



6 ) 



7 ) 



8i( 



)) ) 



(•( ( 



) ) ( pw D°; wp g: 



(•( ) pw °; wp Dg: 

 ) ) ) wp : WW =: 

 (•( ( wpD=::wwD=: 

 ) ) ( PP ~ wp := 

 (•( ) ppB:=wpD:= 



) )( ( 



( (•) ) 



( ) ( ) pp D- WW =: 



) (•) ( PP !i wwD=: 



( )( ( PP D-pwD — 



) (•) ) PP °.o pw — 



) ) ( )pp D- wpD— 



((•)(PP ° 



( () ) 



) )•( ( 



) ( ) ( PP ~ WW D 



( )•( ) PP r>:= WW 



) ( ) ) wpD_. WW D 



( )•( ( wp — • WW 



( ( ) ( pwD.- WW D" 



) )■( ) pw •— WW 



Take one of these readings, for instance 1.6) (•( (, say X) (■( ( Y, where X) may be 

 either 'Any part of X' or 'some whole of X' and the same of (Y. There are four read- 

 ings; WW (whole and whole), wp, pw, and pp. Of these pp and pw, about which no remark 

 follows, are unrestrictive readings, and give ) (•( ( with the middle spicule erased, or X)-( Y. 

 That is, ' Any part of X is exient of [not wholly contained in] any part of Y* and ' Any 

 part of X is exient of some whole of Y' mean simply that ' X is external of Y', or that 

 'noX is Y'; and the converse. But wp and ww are denials of a restrictive, and both 

 simply deny (D) that X and Y are penultimately identical. That is, ' some whole of X is 

 exient of any part of Y', and 'some whole of X is exient of some whole of Y', simply say, 

 ' It is not true that X and Y are coextensive and each taking up all the universe except one 

 individual object.' When X and Y are anything but coextensive, or, being coextensive, any- 

 thing but penultimate, some whole of X, X or X arid more, is not wholly within any part 

 of Y. 



Take the symbol IV. 4 as an example, X()-()Y. Omit the secondary spiculae : we 

 have X(')Y, which is the proposition symbolized. Read the secondary )•( as 'is out of, 

 ' is entirely excluded from', or ' entirely excludes'. Four readings are possible, from part to 

 part, PP, &c. These four readings are 



pp. Some part of X is out of some part of Y ; 

 WW, Any whole of X is out of any whole of Y ; 

 pw, Some part of X is out of any whole of Y ; 

 wp. Any whole of X is out of some part of Y. 



Of these the table tells us that only pw and wp are unrestrictive: that pp merely denies (D) 

 that X and Y are singular and identical ; and ww merely affirms that X and Y are singular 

 and contrary. But pw, which affirms that Y and anything, up to penultimacy, leaves out 

 some part of X, affirms, as we see, that all which is not Y is X. 



