Prior Analytics - Book II
then D is subordinate to C, clearly B does not belong to it. But
that B does not belong to what is subordinate to A is not clear by
means of the syllogism. And yet B does not belong to E, if E is
subordinate to A. But while it has been proved through the syllogism
that B belongs to no C, it has been assumed without proof that B
does not belong to A, consequently it does not result through the
syllogism that B does not belong to E.
But in particular syllogisms there will be no necessity of inferring
what is subordinate to the conclusion (for a syllogism does not result
when this premiss is particular), but whatever is subordinate to the
middle term may be inferred, not however through the syllogism, e.g.
if A belongs to all B and B to some C. Nothing can be inferred about
that which is subordinate to C; something can be inferred about that
which is subordinate to B, but not through the preceding syllogism.
Similarly in the other figures. That which is subordinate to the
conclusion cannot be proved; the other subordinate can be proved, only
not through the syllogism, just as in the universal syllogisms what is
subordinate to the middle term is proved (as we saw) from a premiss
which is not demonstrated: consequently either a conclusion is not
possible in the case of universal syllogisms or else it is possible
also in the case of particular syllogisms.
It is possible for the premisses of the syllogism to be true, or
to be false, or to be the one true, the other false. The conclusion is
either true or false necessarily. From true premisses it is not
possible to draw a false conclusion, but a true conclusion may be
drawn from false premisses, true however only in respect to the
fact, not to the reason. The reason cannot be established from false
premisses: why this is so will be explained in the sequel.
First then that it is not possible to draw a false conclusion from