it seems
necessary to admit that the conjunction 'either, or' may sometimes
require one interpretation, sometimes the other; and the rule is that it
implies the further possibility 'or both,' except when both alternatives
have the same subject whilst the predicates are contrary or
contradictory terms.

If, then, the disjunctive _A is either B or C_ (_B_ and _C_ being
contraries) implies that both alternatives cannot be true, it can only
be adequately rendered in hypotheticals by the two forms--(1) _If A is
B, it is not C_, and (2)_If A is not B, it is C_. But if the disjunctive
_A is either B or C_ (_B_ and _C_ not being contraries) implies that
both may be true, it will be adequately translated into a hypothetical
by the single form, _If A is not B, it is C_. We cannot translate it
into--_If A is B, it is not C_, for, by our supposition, if '_A is B_'
is true, it does not follow that '_A is C_' must be false.

Logicians are also divided in opinion as to the function of the
hypothetical form. Some think it expresses doubt; for the consequent
depends on the antecedent, and the antecedent, introduced by 'if,' may
or may not be realised, as in _If the sky is clear, the night is cold_:
whether the sky is, or is not, clear being supposed to be uncertain. And
we have seen that some hypothetical propositions seem designed to draw
attention to such uncertainty, as--_If there is a resisting medium in
space_, etc. But other Logicians lay stress upon the connection of the
clauses as the important matter: the statement is, they say, that the
consequent may be inferred from the antecedent. Some even declare that
it is given as a necessary inference; and on this ground Sigwart rejects
particular hypotheticals, such as _Sometimes when A is B, C is D_; for
if it happens only sometimes the connexion cannot be necessary. Indeed,
it cannot even be probably inferred without further grounds. But this is
also true whenever the antecedent and consequent are concerned with
different matter. For example, _If the soul is simple, it is
indestructible_. How do you know that? Because _Every simple substance
is indestructible_. Without this further ground there can be no
inference. The fact is that conditional forms often cover assertions
that are not true complex propositions but a sort of euthymemes (chap.
xi. Sec. 2), arguments abbreviated and rhetorically disguised. Thus: _If
patience is a virtue there are painful virtues_--an example from Dr.