54 Mr Venn, On geometrical diagrams fur the [Dec. 6, 



of the extent of the two terms is not here indicative of identity ; 

 for the line G is thus only drawn under B and not made coincident 

 with it. This was noticed at once by Ploucquet, whose theory of 

 propositions turned entirely on the identity of subject and pre- 

 dicate and consequent quantification of the predicate. He main- 

 tains that Lambert would do better to draw the second line, in an 

 affirmative proposition, wholly or partially coincident with the 

 first, and so secure this identity (Sammlung, p. 182). Since how- 

 ever the help to the eye would then be nearly lost, such an 

 alteration wou'd simply result in a poor and faulty imitation of 

 the Eulerian scheme. 



Lambert however did not stop here. Like most other clear 

 thinkers he recognized the flaw in all these methods, viz. that we 

 cannot represent the uncertain distribution of the predicate, but 

 employ one and the same diagram for "All A is B", whether the 

 predicate be ' all ' or only ' some ' B. He endeavoured to remedy 

 this defect by the employment of dotted lines, thus : 



B 





This means that A certainly covers a part of B, viz. the continuous 

 part; and may cover the rest, viz. the dotted part, the dots repre- 

 senting our uncertainty. In this case the scheme answers fairly 

 well, such use of dots not being open to the objection maintainable 

 against it when circles are employed. But when he comes to 

 extend this to particular propositions his use of dotted lines ceases 

 to be consistent or even, to me, intelligible. One would have 

 expected him to write ' some A is B ' thus, 



B 



A 



for by different filling in of the lines Ave could cover the case 

 of there being ' B which was not A,' and so forth. But he does 

 draw it 



B 



A 



which might consistently be interpreted to cover the case of 

 ' no A is B,' as well as suggesting the possibility of there being 

 no A at all. 



Lambert's use however of this modification of his scheme is so 

 obscure, and, when he comes to work out the syllogistic figures 

 in detail, is so partially adhered to, that it does not seem worth 



