Hinton - The Fourth Dimension.pdf

THE USE OF FOUR DIMENSIONS IN THOUGHT 95
The view of these four squares which the plane creature
would have would not be such as ours. He would not
see the interior of the four squares represented above, but
each would be entirely contained within its outline, the
internal boundaries of the separate small squares he could
not see except by removing the outer squares.
We are now ready to introduce the fourth variable
involved in the syllogism.
In assigning letters to denote the terms of the syllogism
we have taken S and P to represent the subject and
predicate in the conclusion, and thus in the conclusion
their order is invariable. But in the premisses we have
taken arbitrarily the order all M is P, and all S is M.
There is no reason why M instead of P should not be the
predicate of the major premiss, and so on.
Accordingly we take the order of the terms in the premisses
as the fourth variable. Of this order there are four
varieties, and these varieties are called figures.
Using the order in which the letters are written to
denote that the letter written first is subject, the one
written second is predicate, we have the following possibilities:—
1st Figure. 2nd Figure. 3rd Figure. 4th Figure.
Major M P P M M P P M
Minor S M S M M S M S
There are therefore four possibilities with regard to
this fourth variable as with regard to the premisses.
We have used up our dimensions of space in representing
the phases of the premises and the conclusion in
respect of mood, and to represent in an analogous manner
the variations in figure we require a fourth dimension.
Now in bringing in this fourth dimension we must
make a change in our origins of measurement analogous
to that which we made in passing from the plane to the
solid.