[Logic by Carveth Read]@TWC D-Link book
Logic

CHAPTER VII
24/27

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).


<<Back  Index  Next>>

D-Link book Top

TWC mobile books