Prior Analytics - Book II
It is clear then that when the impossibility is not related to the
original terms, the false conclusion does not result on account of the
assumption. Or perhaps even so it may sometimes be independent. For if
it were laid down that A belongs not to B but to K, and that K belongs
to C and C to D, the impossible conclusion would still stand.
Similarly if one takes the terms in an ascending series.
Consequently since the impossibility results whether the first
assumption is suppressed or not, it would appear to be independent
of that assumption. Or perhaps we ought not to understand the
statement that the false conclusion results independently of the
assumption, in the sense that if something else were supposed the
impossibility would result; but rather we mean that when the first
assumption is eliminated, the same impossibility results through the
remaining premisses; since it is not perhaps absurd that the same
false result should follow from several hypotheses, e.g. that
parallels meet, both on the assumption that the interior angle is
greater than the exterior and on the assumption that a triangle
contains more than two right angles.
A false argument depends on the first false statement in it. Every
syllogism is made out of two or more premisses. If then the false
conclusion is drawn from two premisses, one or both of them must be
false: for (as we proved) a false syllogism cannot be drawn from two
premisses. But if the premisses are more than two, e.g. if C is
established through A and B, and these through D, E, F, and G, one
of these higher propositions must be false, and on this the argument
depends: for A and B are inferred by means of D, E, F, and G.
Therefore the conclusion and the error results from one of them.