Complete Works of Lewis Carroll (203 page)

8

9

Figs.
1 and 3 give

10

11

12

Figs.
1 and 4 give

13

From this group (Figs.
5 to 13) we have, by disregarding
m
, to find the relation of
x
and
y
.
On examination we find that Figs.
5, 10, 13 express the relation of entire mutual exclusion; that Figs.
6, 11 express partial inclusion and partial exclusion; that Fig.
7 expresses coincidence; that Figs.
8, 12 express entire inclusion of
x
in
y
; and that Fig.
9 expresses entire inclusion of
y
in
x
.

We thus get five Biliteral Diagrams for
x
and
y
, viz.

14

15

16

17

18

where the only Proposition, represented by them all, is “Some not-
y
are not-
x
,” i.e.
“Some persons, who are not gamblers, are not philosophers”——a result which Euler would hardly have regarded as a
valuable
one, since he seems to have assumed that a Proposition of this form is
always
true!

(4)
Solution by Venn’s Method of Diagrams.

The following Solution has been kindly supplied to me Mr.
Venn himself.

”The Minor Premiss declares that some of the constituents in
my
′
must be saved: mark these constituents with a cross.