Hinton - The Fourth Dimension.pdf

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 P. 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 M. 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 O about P. Some P is not S.
But it does not give us conclusion about S in any one of
the four forms recognised in the syllogism 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 (M); no Aryans (S) are of African stock
(M); Aryans (S) do not include all of Americans (P).
In order to draw a conclusion about S we have 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 logic 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, no 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