Hinton - The Fourth Dimension.pdf

THE USE OF FOUR DIMENSIONS IN THOUGHT 97
which the remaining variables run through their full
range of varieties.
Now, if we want to measure in respect of the moods of
the major premiss, we must let the minor premiss, the
conclusion, run through their range, and also the order
of the terms. That is we must take as a basis of measurement
in respect to the moods of the major that which
represents the variation of the moods of the minor, the
conclusion and the variation of the figures.
Now the variation of the moods of the minor and of the
conclusion are represented in the square face on the left
of the cube. Here are all varieties of the minor premiss
and the conclusion. The varieties of the figures are
represented by stages in a motion proceeding at right
angles to all space directions, at right angles consequently
to the face in question, the left-hand face of the cube.
Consequently letting the left-hand face move in this
direction we get a cube, and in this cube all the varieties
of the minor premiss, the conclusion, and the figure are
represented.
Thus another cubic base of measurement is given to
the cube, generated by movement of the left-hand square
in the fourth dimension.
We find the other bases in a similar manner, one in the
cube generated by the front square moved in the fourth
dimension so as to generate a cube. From this cube
variations in the mood of the minor are measured. The
fourth base is that found by moving the bottom square of
the cube in the fourth dimension. In this cube the
variations of the major, the minor, and the figure are given.
Considering this as a basis in the four stages proceeding
from it, the variations in the moods of the conclusion are
given.
Any one of these cubic bases can be represented in space,
and then the higher solid generated from them lies out of