46 Mr Venn, On the various notations adopted for [Dec. G, 



It is rather curious that Segner, whose work Lambert had 

 read (Brief wechsel, I.), could have set him right here. He has 

 expressly discussed almost exactly the same question, and realized 

 its logical bearings clearly, though he did not reach the very 

 important symbolic step of introducing the inverse or division 

 sign to mark it. He stated this theorem : Given that two classes 

 indicated by composite terms, AB and CD, have something in 

 common, and we abstract an attribute from each, say A and C, 

 then the resultant classes, B and D, must also have something 

 in common. But such community may be of any one of four 

 kinds which he marks respectively by B = D, B<D, B> D, 

 B x D ; that is, coextension, inclusion of B in D, inclusion of 

 D in B, and intersection. 



23. The above expression will be found described in Lambert's 

 Deutscher gelehrter Briefiuechsel, I. 37 ; and in the Nova Act. 

 Erudit. 1765. The present one is a slight modification of it 

 given in his Log. Abhandlungen, I. 98. The general idea is 

 exactly the same. Abstract sufficient attributes from P until 

 only those are left which are common to it and to 8. This does 

 not yield an identity as before, for S is now more determinate 

 than P, but it makes the remaining attributes of P included in 



P 



those of S. Interpreted therefore in intension, we have ' All — 



is 8,' and this we express, by use of the sign >, in the form 



P 



S> — . Another equivalent form given by Lambert, and which 



• c 



the reader will readily interpret for himself, is — < P. It is 



obvious that in order to get an identity of subject and predicate, 

 instead of a mere inclusion of one by the other, we must abstract 

 from both of them, as in (22). 



The three remaining forms are of little speculative interest ; 

 indeed No. (25) is only inserted as a curiosity of symbolic mis- 

 management. 



24. This is a form employed by S. Maimon (Versuch einer 

 neuen Logih, 1794). The negative sign here indicates, as in 

 several other systems, the contradictory of a class, so that (— P) 

 means not-P. The term x is intended to represent an arbitrary 

 logical factor or determination. Hence the interpretation is, 

 " 8, howsoever determined, is not-P " ; i. e. by no kind of 

 qualification can we reduce it to any part of P. Of course the 

 qualification here can only be in the way of logical determination : 

 not abstraction, as in the two preceding. There are a variety of 

 serious defects in this notation, and it represents altogether a great 



