|
\#\_/ _/
\#####/ \_____/
pg175
It will be seen that, of the _four_ Classes, whose peculiar Sets of
Attributes are xy, xy', x'y, and x'y', only _three_ are here provided
with closed Compartments, while the _fourth_ is allowed the rest of the
Infinite Plane to range about in!

This arrangement would involve us in very serious trouble, if we ever
attempted to represent "No x' are y'." Mr. Venn _once_ (at p. 281)
encounters this awful task; but evades it, in a quite masterly fashion,
by the simple foot-note "We have not troubled to shade the outside of
this diagram"!

To represent _two_ Propositions (containing a common Term) _together_, a
_three_-letter Diagram is needed. This is the one used by Mr. Venn.

_____
_/ \_
_/___ x ___\_
_/| \_/ |\_
/ \_ / \ _/ \
| \|___|/ |
\_ m \_/ y _/
\_____/ \_____/

Here, again, we have only _seven_ closed Compartments, to accommodate
the _eight_ Classes whose peculiar Sets of Attributes are xym, xym', &c.

"With four terms in request," Mr. Venn says, "the most simple and
symmetrical diagram seems to me that produced by making four ellipses
intersect one another in the desired manner". This, however, provides
only _fifteen_ closed compartments.

b ____ ____ c
/ \ / \
a ___/___ \/ ___\___ d
/ \ \ /\ / / \
/ \ \/ \/ / \
\ \ /\ /\ / /
\ \/ \/ \/ /
\ /\ /\ /\ /
\ \ \/ \/ / /
\ \/\ /\/ /
\ /\_\/_/\ /
\__\______/__/

For _five_ letters, "the simplest diagram I can suggest," Mr. Venn says,
"is one like this (the small ellipse in the centre is to be regarded as
a portion of the _outside_ of c; i.e. its four component portions are
inside b and d but are no part of c). It must be admitted that such a
diagram is not quite so simple to draw as one might wish it to be; but
then consider what the alternative is of one undertakes to deal with
five terms and all their combinations--nothing short of the disagreeable
task of writing out, or in some way putting before us, all the 32
combinations involved."

b c d
______ ____ ______
______/_ \/ \/