Sextus Empiricus: Logic 353
to be false, since it has a true antecedent and a false consequent, if it is
day and I am silent; 111. whereas 'if the partless elements of things do
not exist, the partless elements of things do exist' is true, for according
to him, the false antecedent 'the partless elements of things do not exist'
is followed by the true consequent 'the partless elements of things do
exist'. Those who introduce the notion of logical connectedness say that
a conditional is sound whenever the contradictory of the consequent is in
conflict with its antecedent. So, according to them, the above-mentioned
conditionals will be unsound, but 'if it is day, it is day' is true [i.e., sound].
- Those who judge [the correct answer] by implicit [entailment] say
that the conditional is true where the consequent is contained virtually
in the antecedent. According to them, 'if it is day, it is day' and all such
doubled^35 conditionals will probably be false, for it is impossible for
something to be contained [virtually] in itself.
- So, it would perhaps seem impossible to decide this disagreement.
For we shall not be trusted if we express a preference for one of the
positions either without a demonstration or with a demonstration. For
a demonstration seems to be sound whenever the conclusion follows
from the conjunction of its premisses as a consequent follows from its
antecedent. For example, 'if it is day, it is light; but it is day; therefore,
it is light'. 114. But since what we are investigating is how we may judge
the following of a consequent from an antecedent, the circular mode is
adduced. For, in order that the judgement about the conditional should
be demonstrated, the conclusion [must] follow the premisses of the dem-
onstration, as we said before. And, again, in order that this should be
confirmed, one must have already decided about the conditional and
[logical] following [or consequence], which is absurd. 115. Therefore,
the sound conditional is ungraspable.
But even the antecedent is subject to doubt. For the antecedent, as
they say, is the principal [i.e., first] part of the conditional that begins
with a truth and ends with a truth. 116. But if the sign reveals the
consequent, either that consequent is self-evident or non-evident. If,
then, it is self-evident, it will not need something to reveal it, but will
be grasped along with it and will not be signified by it, for which reason
[the antecedent] is not a sign of [the consequent]. If, however, it is non-
evident, since there has been an undecided disagreement regarding which
of these are true and which false, and, in general, whether any of them
are true, it will be non-evident whether the consequent of the conditional
is true. With this follows that it is non-evident whether the principal
[i.e., first] part [of the conditional] is the antecedent.
- Reading diphoroumenon.
