1880.] representation of logical propositions. 49 



se positum, nenipe subjectum conclusionis in minore propositione 

 positum Diagramma est tale : — 



Animal , 



a — b 



sentit 



homo 

 f." 



There is nothing in this, — the only diagram of the sort which 

 he gives, — even to suggest the distinction between affirmative 

 and negative, universal and particular, which is the least we 

 can look for in these sensible illustrations. 



The first logician apparently to make free use of diagrams 

 was Chr. Weise, rector of Zittau, who died in 1708. He seems 

 to have published some works on logic himself, but his system is 

 said to be given in the Nucleus Logicae Weisianae of J. C. Lange, 

 (1712). I have not succeeded in seeing this work, but judging by 

 what Lambert says of it {Architectonik, I. 128), I gather that 

 he makes free use of circles and squares for the purpose of repre- 

 senting propositions. Hamilton (Logic, I. 256) confirms this 

 statement. 



In the only work of Lange's to which I have been able to ob- 

 tain access, viz. his Inventuni novum Quadratilogici, there is nothing 

 which strikes me as of any great merit. There are a number of 

 geometrical figures represented, both plane and solid, but the 

 author does not seem to have grasped the essential conception of 

 illustrating in this way the mutual intersection, or otherwise, of 

 two or more classes by means of his figures. All that he repre- 

 sents is continued sub-division: e.g. that of A into B and C, of B 

 into D and E, and G into F and G, and so forth. This he sets 

 forth by a parallelogram for A ; under it is put a similar one 

 divided into two equal parts to denote B and C, the next in order 

 having four divisions and so forth. All that this properly repre- 

 sents is the doctrine of Division or continued Dichotomy; i.e. the 

 entire exclusion of B by C, and the entire inclusion of D and E 

 in B, and so forth. There is no attempt to represent the various 

 relations of two terms, B and C, to one another, as set forth in 

 the various forms of proposition which have B and G for their 

 subject and predicate. 



We now come to Euler's well-known circles which were first 

 described in his Lettres a nne Princesse d'Allemagne (Letters 102 

 — 105). The weak point about these consists in the fact that 

 they only illustrate in strictness the actual relations of classes to 

 one another. Accordingly they will not fit in with the propositions 

 of common logic, but demand the constitution of a new group of 

 appropriate elementary propositions. This defect must have been 

 noticed from the first in the case of the particular affirmative and 



VOL iv. pt.i 4 



