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.



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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.



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