Posterior Analytics   

that form; in which case the proof lays down as its major premiss that
the major is truly affirmed of the middle but falsely denied. It makes
no difference, however, if we add to the middle, or again to the minor
term, the corresponding negative. For grant a minor term of which it
is true to predicate man-even if it be also true to predicate
not-man of it--still grant simply that man is animal and not
not-animal, and the conclusion follows: for it will still be true to
say that Callias--even if it be also true to say that
not-Callias--is animal and not not-animal. The reason is that the
major term is predicable not only of the middle, but of something
other than the middle as well, being of wider application; so that the
conclusion is not affected even if the middle is extended to cover the
original middle term and also what is not the original middle term.
The law that every predicate can be either truly affirmed or truly
denied of every subject is posited by such demonstration as uses
reductio ad impossibile, and then not always universally, but so far
as it is requisite; within the limits, that is, of the genus-the
genus, I mean (as I have already explained), to which the man of
science applies his demonstrations. In virtue of the common elements
of demonstration-I mean the common axioms which are used as
premisses of demonstration, not the subjects nor the attributes
demonstrated as belonging to them-all the sciences have communion with
one another, and in communion with them all is dialectic and any
science which might attempt a universal proof of axioms such as the
law of excluded middle, the law that the subtraction of equals from
equals leaves equal remainders, or other axioms of the same kind.
Dialectic has no definite sphere of this kind, not being confined to a
single genus. Otherwise its method would not be interrogative; for the
interrogative method is barred to the demonstrator, who cannot use the
opposite facts to prove the same nexus. This was shown in my work on
the syllogism.

12

If a syllogistic question is equivalent to a proposition embodying
one of the two sides of a contradiction, and if each science has its
peculiar propositions from which its peculiar conclusion is developed,
then there is such a thing as a distinctively scientific question, and
it is the interrogative form of the premisses from which the
'appropriate' conclusion of each science is developed. Hence it is
clear that not every question will be relevant to geometry, nor to
medicine, nor to any other science: only those questions will be
geometrical which form premisses for the proof of the theorems of
geometry or of any other science, such as optics, which uses the
same basic truths as geometry. Of the other sciences the like is true.
Of these questions the geometer is bound to give his account, using
the basic truths of geometry in conjunction with his previous
conclusions; of the basic truths the geometer, as such, is not bound
to give any account. The like is true of the other sciences. There
is a limit, then, to the questions which we may put to each man of
science; nor is each man of science bound to answer all inquiries on
each several subject, but only such as fall within the defined field
of his own science. If, then, in controversy with a geometer qua
geometer the disputant confines himself to geometry and proves
anything from geometrical premisses, he is clearly to be applauded; if
he goes outside these he will be at fault, and obviously cannot even
refute the geometer except accidentally. One should therefore not
discuss geometry among those who are not geometers, for in such a
company an unsound argument will pass unnoticed. This is
correspondingly true in the other sciences.
Since there are 'geometrical' questions, does it follow that there
are also distinctively 'ungeometrical' questions? Further, in each
special science-geometry for instance-what kind of error is it that
may vitiate questions, and yet not exclude them from that science?