The fourth dimension

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 Pp 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 first written is subject, the one written second is predicate, we have the following possibilities :—

Ist Figure. 2nd Figure. 3rd Figure. 4th Figure,

Major MP PM M P PM

Minor SM SM MS MS

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 premisses 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 sulid.