Hinton - The Fourth Dimension.pdf

92
THE FOURTH DIMENSION
letters E, I, O, in the same way show the mood characterising
the minor premise in the rows opposite these letters.
We still have to exhibit the conclusion. To do this we
must consider the conclusion as a third variable, characterised
in its different varieties by four moods—this being
the syllogistic classification. The introduction of a third
variable involves a change in our type of representation.
Before we started with the regions to the right of a
certain line as representing successively the major premiss
in its moods; now we must start with the regions to the
N
R
M
L
A E I O
Fig. 52.
right of a certain plane. Let LMNR be
the plane face of a cube, fig. 52, and let
the cube be divided into four parts by
vertical sections parallel to LMNR. The
variable, the major premiss, is represented
by the successive regions
which occur to the right of the plane
LMNR—that region to which A stands opposite, that
slice of the cube, is significative of the mood A. This
whole quarter-part of the cube represents that for every
part of it the major premiss is in the mood A.
In a similar manner the next section, the second with
the letter E opposite it, represents that for every one of
the sixteen small cubic spaces in it, the major premiss is
in the mood E. The third and fourth compartments made
by the vertical sections denote the major premise in the
moods I and O. But the cube can be divided in other
ways by other planes. Let the division, of which four
stretch from the front face, correspond to the minor
premiss. The first wall of sixteen cubes, facing the
observer, has as its characteristic that in each of the small
cubes, whatever else may be the case, the minor premiss is
in the mood A. The variable—the minor premiss—varies
through the phases A, E, I, O, away from the front face of the
cube, or the front plane of which the front face is a part.