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



what length it should be drawn, resolving this however by the 

 consideration that the unit of length being at our choice, any 

 length will do if the unit be chosen accordingly. In the latter 

 part of the Neues Organon, — where he is dealing with questions of 

 Probability, and the numerically, or rather proportionately, definite 

 syllogism, — the length of the lines which represent the extent 

 of the concepts becomes very important. So little was he pre- 

 pared to regard the diagram as referring solely to the purely 

 logical considerations of presence and absence of class charac- 

 teristics, of inclusion and exclusion of classes by one another. 



Of course if considerations of this kind were to be taken 

 into account it would follow almost necessarily that circles should 

 be abandoned in the formation of our diagrams ; since their 

 relative magnitude, or rather the relative magnitude of the figures 

 produced by their intersection, is not at all an easy matter of 

 intuitive observation. We should be reduced to the choice of 

 lines or parallelograms, so that the almost exclusive employment 

 of Eulerian circles has caused this quantitative application to 

 be much less adopted than would otherwise probably have been 

 the case. This, however, is what has been done quite recently 

 by F. A. Lange (Logische Studien), who in one of his Essays has 

 made considerable use of diagrammatic methods in illustration 

 of the Logic of Probability*. But I cannot regard the success 

 of such a plan as encouraging. For the alternative forced upon us 

 is this : — If we adhere to geometrical figures that are continuous, 

 then the shapes of the various subdivisions soon become com- 

 plicated ; for, by the time we have reached four or even three 

 terms, their combinations would result in yielding awkward com- 

 partments, whose relative areas could not be estimated intuitively. 

 If, on the other hand, we take our stand on having ultimate 

 compartments whose relative magnitudes admit of ready com- 

 putation we are driven to abandon continuous figures. Our ABC 

 compartment, say, instead of being enclosed in a ring fence is 

 scattered about the field like an ill-arranged German principality 

 of olden times, and its component portions require to be brought 

 together in order to collect the whole before the eye. We draw a 

 parallelogram to stand for A, and divide it into its B and not-5 

 parts. If we divide each of these again into their C and not-C 

 parts, we shall find that the B and not-i?, the C and not-C com- 

 partments will not lie in juxtaposition with one another, and 



* Every student of Probability is of course familiar enough with the converse 

 case, viz. that of reducing spatial relations to symbolic statement. "Whenever we 

 compute the chance that a ball dropped at random upon a frame work will strike 

 such and such a partition we are employing the same analogy as when we resort 

 to diagrammatic representation of one of these quantitative logical propositions. 





