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Obverse 2 No A is b Some A is not b All A is b Some A is b

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Converse 3 Some B is A Some B is A No B is A

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Obverse of 4 Some B is not a Some B is not a All B is a Converse

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Contra-
positive 5 No b is A Some b is A Some b is A

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Obverse of 6 All b is a Some b is not a Some b is not a Contrapos

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Converse of Obverse 7 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.