Some a is B
of
Converse

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Obverse
of
Converse
of 8 Some a is not b
Obverse
of
Converse

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Converse
of
Obverse 9 Some a is b
of
Contrapos

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Obverse
of
Converse
of 10 Some a is not B
Obverse
of
Contrapos

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In this table _a_ and _b_ stand for _not-A_ and _not-B_ and had better
be read thus: for _No A is b, No A is not-B_; for _All b is a_ (col. 6),
_All not-B is not-A_; and so on.

It may not, at first, be obvious why the process of alternately
obverting and converting any proposition should ever come to an end;
though it will, no doubt, be considered a very fortunate circumstance
that it always does end. On examining the results, it will be found that
the cause of its ending is the inconvertibility of O. For E., when
obverted, becomes A.; every A, when converted, degenerates into I.;
every I., when obverted, becomes O.; O cannot be converted, and to
obvert it again is merely to restore the former proposition: so that the
whole process moves on to inevitable dissolution. I. and O. are
exhausted by three transformations, whilst A. and E. will each endure
seven.

Except Obversion, Conversion and Contraposition, it has not been usual
to bestow special names on these processes or their results. But the
form in columns 7 and 10 (_Some a is B--Some a is not B_), where the
original predicate is affirmed or denied of the contradictory of the
original subject, has been thought by Dr. Keynes to deserve a
distinctive title, and he has called it the 'Inverse.' Whilst the
Inverse is one form, however, Inversion is not one process, but is
obtained by different processes from E. and A. respectively. In this it
differs from Obversion, Conversion, and Contraposition, each of which
stands for one process.

The Inverse form has been objected to on the ground that the inference
_All A is B .'. Some not-A is not B_, distributes _B_ (as predicate of a
negative proposition), though it was given as undistributed (as
predicate of an affirmative proposition). But Dr. Keynes defends it on
the ground that (1) it is obtained by obversions and conversions w