The fourth dimension

104 THE FOURTH DIMENSION

the form s is P in the various moods. It is quite indeterminate how the circle representing s lies with regard to the circle representing Pp. It may lie inside, outside, or partly inside p. The same is true in the other figures 2 and 3. But when we come to the fourth figure, since M and s lie completely outside each other, there cannot lie inside s that part of P which lies inside mM Now we know by the major premiss that some of P does lie in M. Hence s cannot contain the whole of p. In words, some P is M, no M is S, therefore s does not contain the whole of p. If we take P as the subject, this gives us a conclusion in the mood 0 about Pp. Some P is not s. But it does not give us conclusion about s in any one of the four forms recognised in the syHogism and called its moods. Hence the breach of the continuity in the poiograph has enabled us to detect a lack of completeness in the relations which are considered in the syllogism.

To take an instance:—Some Americans (P) are of African stock (mM); No Aryans (Ss) are of African stock (mM); Aryans (S)do not include all of Americans (P).

In order to draw a conclusion about s we haye to admit the statement, ‘“s does not contain the whole of P,” as a valid logical form—it is a statement about s which can be made. The logie which gives us the form, “some P is not s,” and which does not allow us to give the exactly equivalent and equally primary form, “s does not contain the whole of P,” is artificial.

And I wish to point out that this artificiality leads to an error.

If one trusted to the mnemonic lines given above, one would conclude that no logical conclusion about s can be drawn from the statement, “some P are M, 00 M are S.”

But a conclusion can be drawn: s does not contain the whole of P.

It is not that the result is given expressed in another