Sextus Empiricus: Logic 359
when we state the second, the first no longer exists and the conclusion
does not yet exist. And when we put forth the conclusion, the premisses
no longer exist. Therefore, the parts of the argument do not coexist with
each other. For this reason, the argument will seem not to exist.
- Apart from these considerations, the conclusive argument is un-
graspable. For if this argument is judged from the logical consequence
of the conditional and the consequence in the conditional is a matter of
undecidable disagreement, and is probably ungraspable, as we suggested
in the argument regarding the sign, the conclusive argument too will be
ungraspable. 146. At any rate, the dialecticians say that an argument
becomes non-conclusive either because of logical disconnectedness or
omission, or being asserted in improper form or because of redundancy.
For example, there is logical disconnectedness whenever there is no
logical consequence between the premisses and between premisses and
the conclusion, as in 'if it is day, it is light; but wheat is sold in the market-
place; therefore, Dion is walking'. 147. [Non-conclusiveness] because of
redundancy occurs whenever a premisse is discovered to be redundant
for the argument's conclusiveness, as in 'if it is day, it is light; but it is
indeed day, and Dion is walking; therefore, it is light'. [Non-conclusive-
ness] because improper form occurs whenever the argument does not
have a conclusive form; for example, 'if it is day, it is light; but indeed
it is light; therefore, it is day' is non-conclusive, where the proper syllo-
gisms are, as they say: 'if it is day, it is light; but it is indeed day;
therefore, it is light' and 'if it is day, it is light; but it is not light;
therefore, it is not day'. 148. For since the conditional announces plainly
that if the antecedent holds the consequent follows, it is [only] reasonable
that when the antecedent is admitted the consequent too is inferred; and
if the consequent is denied, the antecedent is denied. For if the antecedent
held, the consequent would follow. But when the consequent is admitted,
the antecedent is not necessarily posited as well. For the conditional did
not promise that the antecedent followed on the consequent, but only
that the consequent followed on the antecedent. - For this reason, therefore, the argument that deduces the conclu-
sion from the conditional and the antecedent is said to be syllogistic; and
so is that which deduces the contradictory of the antecedent of the
conditional from the [positing of the] conditional and the contradictory
of the consequent. The argument, as in the case of the above, that deduces
the antecedent from the conditional and its consequent, is non-conclusive,
so that even though its premisses are true, it deduces something false
[i.e., it is day] when it [i.e., it is light] is said by lamplight at night. For
'if it is day, it is light' is a true conditional, but the additional statement
'but indeed it is light' is true; but the conclusion 'it is day' is false.