Hinton - The Fourth Dimension.pdf

94
THE FOURTH DIMENSION
mood A; conclusion, mood A. This is the cube occupying
the lowest left-hand cover of the large cube.
Proceeding in this way, we find that the regions which
must be marked are those shown in fig. 53.
To discuss the case shown in the marked
cube which appears at the top of fig. 53.
Here the major premise is in the second
wall to the right—it is in the mood E and
minor
is of the type no M is P. The minor
premiss is in the mood characterised by
the third wall from the front. It is of
the type some S is M. From these premisses we draw
the conclusion that some S is not P, a conclusion in the
mood O. Now the mood O of the conclusion is represented
in the top layer. Hence we see that the marking is
correct in this respect.
It would, of course, be possible to represent the cube on
a plane by means of four
squares, as in fig. 54, if we
1
major
Fig. 53.
2 3 4
Fig. 54.
consider each square to represent
merely the beginning
of the region it stands for.
Thus the whole cube can be
represented by four vertical
squares, each standing for a
kind of vertical tray, and the
markings would be as shown. In No. 1 the major premiss
is in mood A for the whole of the region indicated by the
vertical square of sixteen divisions; for number 2 it is in the
mood E, and so on.
A creature confined to a plane would have to adopt some
such disjunctive way of representing the whole cube. He
would be obliged to represent that which we see as a
whole in separate parts, and each part would merely
represent, would not be, that solid content which we see.