The conclusion, therefore, is Some S is not P.
It must be admitted that this is very complex, and that it would be a serious matter if in the first instance we had to work through all the different moods in this manner.[374] Still, for purposes of illustration, this very complexity has a certain advantage. It shews how many relations between three terms in respect of extension are left to us, even with two premisses given.
[374] Ueberweg, however, takes the trouble to establish in this way the validity of the valid moods in the various figures. Thomson (Laws of Thought, pp. 189, 190) introduces comparative simplicity by the use of dotted lines. His diagrams are, however, incorrect.
289. The application of Lambert’s diagrammatic scheme to syllogistic reasonings.—As applied to syllogisms, Lambert’s lines are much less cumbrous than Euler’s circles. The main point to notice is that it is in general necessary that the line standing for the middle term should not be dotted over any part of its extent.[375] This condition can be satisfied by selecting the appropriate alternative form in the case of A, I, and O propositions, as given in section [127]. As examples we may represent Barbara, Baroco, Datisi, and Fresison by Lambert’s method.
[375] The following representation of Barbara,
illustrates the kind of error that is likely to result if the above precaution is neglected. If this representation were correct we should be justified in inferring Some P is not S as well as All S is P.
290. The application of Dr Venn’s diagrammatic scheme to syllogistic reasonings.—Syllogisms in Barbara, Camestres, Datisi, and Bocardo may be taken in order to shew how Dr Venn’s diagrams can be used to illustrate syllogistic reasonings.