Hinton - The Fourth Dimension.pdf

THE USE OF FOUR DIMENSIONS IN THOUGHT 105
form. The mnemonic lines deny that any conclusion can
be drawn from premises in the moods I, E, respectively.
Thus a simple four-dimensional poiograph has enabled
us to detect a mistake in the mnemonic lines which have
been handed down unchallenged from mediæval times.
To discuss the subject of these lines more fully a logician
defending them would probably say that a particular
statement cannot be a major premiss; and so deny the
existence of the fourth figure in the combination of moods.
To take our instance: some Americans are of African
stock; no Aryans are of African stock. He would say
that the conclusion is some Americans are not Aryans;
and that the second statement is the major. He would
refuse to say anything about Aryans, condemning us to
an eternal silence about them, as far as these premisses
are concerned! But, if there is a statement involving
the relation of two classes, it must be expressible as a
statement about either of them.
To bar the conclusion, “Aryans do not include the
whole of Americans,” is purely a makeshift in favour of
a false classification.
And the argument drawn from the universality of the
major premiss cannot be consistently maintained. It
would preclude such combinations as major O, minor A,
conclusion O—i.e., such as some mountains (M) are not
permanent (P); all mountains (M) are scenery (S); some
scenery (S) is not permanent (P).
This is allowed in “Jevon’s Logic,” and his omission to
discuss I, E, O, in the fourth figure is inexplicable. A
satisfactory poiograph of the logical scheme can be made
by admitting the use of the words some, none, or all
about the predicate as well as about the subject. Then
we can express the statements, “Aryans do not include the
whole of Americans,” clumsily, but, when its obscurity
is fathomed, correctly, as “Some Aryans are not all