1880.] expressing the common propositions of Logic. 47 



falling off from some of its predecessors, though Maimon has 

 contrived with more or less success to carry it through all the 

 syllogistic moods. One obvious inaccuracy is to be seen in the 

 use of the sign (= ). We have no right to adopt the equational 

 form unless the subject and predicate are identified, which they 

 are not in this case, the former being a part only of the latter. 



25. Ploucquet frequently uses this form in some of his logical 

 writings (e.g. Fundamenta Philosophic^ speculativce, 1704). It 

 must be observed that the sign ( — ) here stands for affirmation, 

 or rather for that and negation indifferently, the negation being 

 put into the subject, where N stands for nullum. It is therefore 

 merely a rendering of the common form ' No S is P,' whereas 

 8 — P would have stood for ' S is P.' 



26. A mere vagary on the part of Mr Chase (First Logic 

 Book, 1875) which should stand as a caution to non-mathematical 

 symbolic innovators. The sign ( — ) here is defined as standing 

 for negation, whilst + does duty for affirmation. So, to make quite 

 sure that we are really denying, he puts in the word no as well, 

 and writes it No $— P ; that is, No S is not P. 



On the employment of geometrical diagrams for the sensible re- 

 presentation of logical propositions. By John Venn, M.A., 



A few preliminary words will be desirable in order to point 

 out the limits of this notice. It is intended here to take account 

 of those schemes only which deal directly with propositions, and 

 which analyse them ; that is, which in some way or other 

 exhibit the relation of the subject to the predicate. Hence two 

 kinds of diagram of almost immemorial antiquity in Logic, will 

 have to be entirely rejected. The first of these is the so-called Por- 

 phyrian tree. This only represents the mutual relation of classes 

 to one another in the way of genus and species, by continued 

 subdivision ; and though of course giving rise to propositions 

 it cannot be said in any way to portray them. The other is 

 the triangle of which the three extremities are used to represent 

 the three terms of the syllogism. The same outline of a diagram 

 here serves for any kind of proposition, and all that is meant 

 to be illustrated by the figure, is, that we may by means of 

 reasoning connect the extremes A and C (so to say, along one 

 side) instead of connecting A with B, and then B with C (along 

 the two sides). In this sort of diagrams no kind of analysis of 

 propositions is attempted, and it can hardly be claimed for them 

 that they are any real aid to the mind in complicated trains 



