Sextus Empiricus: Logic 357
sign, and demonstration is a type of sign, it is necessary to suspend
judgement regarding demonstration. And indeed we shall find that the
arguments regarding the sign can be adapted for use against demonstra-
tion, since demonstration is supposed to be relative and revelatory of the
conclusion, and practically everything said by us regarding the sign
followed from this [line of argument]. 135. If, however, we must speak
specifically regarding demonstration, I shall concisely treat of the argu-
ment regarding it, first attempting to provide a little clarification regarding
what they say a demonstration is.
Demonstration, as they say, is an argument which, by means of agreed
upon premisses, according to conclusive deduction, reveals a non-evident
conclusion. What they mean will be made clearer by means of the follow-
ing. An argument is a complex of premisses and a conclusion. 136. The
premisses of the complex are said to be the propositions taken for the
establishment of the conclusion and the conclusion is the proposition
established by the premisses. For example, in the argument, 'if it is day,
it is light; but it is indeed day; therefore, it is light', the proposition
'therefore, it is light' is the conclusion and the rest are premisses. 137.
Some arguments are conclusive and some are non-conclusive; they are
conclusive whenever the conditional which starts from the conjunction
of the premisses and ends with the conclusion of the argument is sound.
For example, the above argument is conclusive, since, from the conjunc-
tion of its premisses 'if it is day, it is light' and 'it is day', 'it is light'
follows in this conditional 'it is day, and if it is day, it is light; <therefore,>
it is light.' Arguments that do not have this [structure] are non-conclusive.
- Some conclusive^36 arguments are true and some are not true; they
are true whenever not only the conditional formed from the conjunction
of the premisses and the conclusion is sound, as we said before, but
also the conjunction of the premisses, which is the antecedent of the
conditional, is true. A true conjunction is that which has all its conjuncts
true, as, for example, in 'it is day, and if it is day, it is light'. 139. Those
which are not like this are not true. For this argument 'if it is night, it
is dark; but indeed it is night; therefore, it is dark' when it is day, is
conclusive, since the conditional 'it is night and if it is night it is dark;
therefore, it is dark' is sound, but the argument is not true. For the
antecedent conjunction is false, viz. 'it is night and if it is night it is
dark' since it contains the falsehood 'it is night'. For a conjunction which
contains a false conjunct is false. Hence, they also say that a true argument
is one in which true premisses conclude to a true conclusion. - Again, some true arguments are demonstrative and some are non-
- See 11-3 (77-78).