Sextus Empiricus: Logic 361
ment, since he does not have an agreed upon procedure for judging
the conditional by means of which he will be able to judge the logical
consequence of the argument he is speaking about, will not be able to
say correctly and with judgement that it is defective by omission.
- Further, the argument said to be improper because of redundancy
is indiscernable from demonstrative arguments. For with respect to re-
dundancy, even the arguments touted by the Stoics as 'indemonstrable'
will be found to be non-conclusive. And when these [the indemonstrables]
are abolished the whole of dialectic is overturned. For these are the ones
they say are not in need of demonstration to establish themselves, but
seem to demonstrate the conclusiveness of the other arguments. That
they are redundant will be clear when we have set out the 'indemonstrable
arguments' and thus provided arguments for what we have said.^37 - They dream up many indemonstrables, but set forth these five
above all others; and the other arguments are thought to be reduced to
them. The first is that which concludes from the conditional and the
antecedent to the consequent, for example, 'if it is day, it is light; but it
is day; therefore, it is light.' The second is that which concludes from the
conditional and the contradictory of the consequent to the contradictory of
the antecedent, for example, 'if it is day, it is light; but it is not light;
therefore, it is not day.' 158. The third is that which concludes from the
denial of a conjunction and one of the conjuncts to the contradictory of
the other, for example, 'not: it is day and it is night; but it is day;
therefore, it is not night'. The fourth is that which concludes from a
disjunction and one of the disjuncts to the contradictory of the other,
for example, 'either it is day or it is night; but it is day; therefore, it is
not night'. The fifth is that which concludes from a disjunction and the
contradictory of one of its disjuncts to the other, for example, 'either it
is day or it is night; but it is not night; therefore, it is day'. - These then are the touted indemonstrables, all of which seem to
be non-conclusive by reason of redundancy. So, for instance, starting
with the first, either it is agreed that 'it is light' is logically connected to
its antecedent 'it is day' in the conditional 'if it is day, it is light' or it
is non-evident. But if it is non-evident, we will not grant that the condi-
tional is agreed upon. But if it is self-evident that, given that 'it is day'
it is also necessarily the case that 'it is light', then when we say 'it is
day', it is also concluded that 'it is light'; so that the argument 'it is day;
therefore it is light' is sufficient and the conditional 'if it is day, it is
light' is redundant. - 11-3 (80-81).