_Sometimes when A is B, C is D;_
E. _If A is B, C is not D;_
O. _Sometimes when A is B, C is not D._

But I. and O. are rarely used.

As for Disjunctives, it is easy to distinguish the two quantities thus:

A. _Either A is B, or C is D;_
I. _Sometimes either A is B or C is D._

But I. is rarely used. The distinction of quality, however, cannot be
made: there are no true negative forms; for if we write--

_Neither is A B, nor C D,_

there is here no alternative predication, but only an Exponible
equivalent to _No A is B, and No C is D_. And if we write--

_Either A is not B, or C is not D,_

this is affirmative as to the alternation, and is for all methods of
treatment equivalent to A.

Logicians are divided in opinion as to the interpretation of the
conjunction 'either, or'; some holding that it means 'not both,' others
that it means 'it may be both.' Grammatical usage, upon which the
question is sometimes argued, does not seem to be established in favour
of either view. If we say _A man so precise in his walk and conversation
is either a saint or a consummate hypocrite_; or, again, _One who is
happy in a solitary life is either more or less than man_; we cannot in
such cases mean that the subject may be both. On the other hand, if it
be said that _the author of 'A Tale of a Tub' is either a misanthrope or
a dyspeptic_, the alternatives are not incompatible. Or, again, given
that _X. is a lunatic, or a lover, or a poet_, the three predicates have
much congruity.

It has been urged that in Logic, language should be made as exact and
definite as possible, and that this requires the exclusive
interpretation 'not both.' But it seems a better argument, that Logic
(1) should be able to express all meanings, and (2), as the science of
evidence, must not assume more than is given; to be on the safe side, it
must in doubtful cases assume the least, just as it generally assumes a
preindesignate term to be of particular quantity; and, therefore
'either, or' means 'one, or the other, or both.'

However, when both the alternative propositions have the same subject,
as _Either A is B, or A is C_, if the two predicates are contrary or
contradictory terms (as 'saint' and 'hypocrite,' or 'saint' and
'not-saint'), they cannot in their nature be predicable in the same way
of the same subject; and, therefore, in such a case 'either, or' means
one or the other, but not both in the same relation. Hence