Hinton - The Fourth Dimension.pdf

THE USE OF FOUR DIMENSIONS IN THOUGHT 93
And now we can represent the third variable in a precisely
similar way. We can take the conclusion as the third
variable, going through its four phases from the ground
plane upwards. Each of the small cubes at the base of
the whole cube has this true about it, whatever else may
be the case, that the conclusion is, in it, in the mood A.
Thus, to recapitulate, the first wall of sixteen small cubes,
the first of the four walls which , proceeding from left to
right, build up the whole cube, is characterised in each
part of it by this, that the major premiss is in the mood A.
The next wall denotes that the major premiss is in the
mood E, and so on. Proceeding from the front to the
back the first wall presents a region in every part of
which the minor premiss is in the mood A. The second
wall is a region throughout which the minor premiss is in
the mood E, and so on. In the layers, from the bottom
upwards, the conclusion goes through its various moods
beginning with A in the lowest, E in the second, I in the
third, O in the fourth.
In the general case, in which the variables represented
in the poiograph pass through a wide range of values, the
planes from which we measure their degrees of variation
in our experience are taken to be indefinitely extended.
In this case, however, all we are concerned with is the
finite region.
We have now to represent, by some limitation of the
complex we have obtained, the fact that not every combination
of premisses justifies any kind of conclusion.
This can be simply effected by marking the regions in
which, the premisses being such as are defined by the
positions, a conclusion which is valid is found.
Taking the conjunction of the major premisses, all M is
P, and the minor, all S is M, we conclude that all S is P.
Hence, that region must be marked in which we have the
conjunction of major premiss in mood A; minor premiss,