The fourth dimension

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 4. 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 4.

The next wall denotes that the major premiss is in the mood F, 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 £, and so on. In the layers, from the bottom upwards, the conclusion goes through its various moods beginning with a in the lowest, B in the second, I in the third, 0 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 representation 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 premiss, all M is p, and the minor, all s is M, we conclude that all Ss is P, Hence, that region must be marked in which we have the conjunction of major premiss in mood A; minor premiss,