Beyond six letters Mr. Venn does not go.
[§ 7.]
My Method of Diagrams.
My Method of Diagrams resembles Mr. Venn’s, in having separate Compartments assigned to the various Classes, and in marking these Compartments as occupied or as empty; but it differs from his Method, in assigning a closed area to the Universe of Discourse, so that the Class which, under Mr. Venn’s liberal sway, has been ranging at will through Infinite Space, is suddenly dismayed to find itself “cabin’d, cribb’d, confined”, in a limited Cell like any other Class! Also I use rectilinear, instead of curvilinear, Figures; and I mark an occupied Cell with a ‘I’ (meaning that there is at least one Thing in it), and an empty Cell with a ‘O’ (meaning that there is no Thing in it).
For two letters, I use this Diagram, in which the North Half is assigned to ‘x’, the South to ‘not-x’ (or ‘x′’), the West to y, and the East to y′. Thus the N.W. Cell contains the xy-Class, the N.E. Cell the xy′-Class, and so on.
For three letters, I subdivide these four Cells, by drawing an Inner Square, which I assign to m, the Outer Border being assigned to m′. I thus get eight Cells that are needed to accommodate the eight Classes, whose peculiar Sets of Attributes are xym, xym′, &c.
This last Diagram is the most complex that I use in the Elementary Part of my ‘Symbolic Logic.’ But I may as well take this opportunity of describing the more complex ones which will appear in Part II.
[pg177]For four letters (which I call a, b, c, d) I use this Diagram; assigning the North Half to a (and of course the rest of the Diagram to a′), the West Half to b, the Horizontal Oblong to c, and the Upright Oblong to d. We have now got 16 Cells.