Posterior Analytics   

to the basic truths. Similarly if A does not inhere in B, this can
be demonstrated if there is a middle term or a term prior to B in
which A does not inhere: otherwise there is no demonstration and a
basic truth is reached. There are, moreover, as many 'elements' of the
demonstrated conclusion as there are middle terms, since it is
propositions containing these middle terms that are the basic
premisses on which the demonstration rests; and as there are some
indemonstrable basic truths asserting that 'this is that' or that
'this inheres in that', so there are others denying that 'this is
that' or that 'this inheres in that'-in fact some basic truths will
affirm and some will deny being.
When we are to prove a conclusion, we must take a primary
essential predicate-suppose it C-of the subject B, and then suppose
A similarly predicable of C. If we proceed in this manner, no
proposition or attribute which falls beyond A is admitted in the
proof: the interval is constantly condensed until subject and
predicate become indivisible, i.e. one. We have our unit when the
premiss becomes immediate, since the immediate premiss alone is a
single premiss in the unqualified sense of 'single'. And as in other
spheres the basic element is simple but not identical in all-in a
system of weight it is the mina, in music the quarter-tone, and so
on--so in syllogism the unit is an immediate premiss, and in the
knowledge that demonstration gives it is an intuition. In
syllogisms, then, which prove the inherence of an attribute, nothing
falls outside the major term. In the case of negative syllogisms on
the other hand, (1) in the first figure nothing falls outside the
major term whose inherence is in question; e.g. to prove through a
middle C that A does not inhere in B the premisses required are, all B
is C, no C is A. Then if it has to be proved that no C is A, a
middle must be found between and C; and this procedure will never
vary.
(2) If we have to show that E is not D by means of the premisses,
all D is C; no E, or not all E, is C; then the middle will never
fall beyond E, and E is the subject of which D is to be denied in
the conclusion.
(3) In the third figure the middle will never fall beyond the limits
of the subject and the attribute denied of it.

24

Since demonstrations may be either commensurately universal or
particular, and either affirmative or negative; the question arises,
which form is the better? And the same question may be put in regard
to so-called 'direct' demonstration and reductio ad impossibile. Let
us first examine the commensurately universal and the particular
forms, and when we have cleared up this problem proceed to discuss
'direct' demonstration and reductio ad impossibile.
The following considerations might lead some minds to prefer
particular demonstration.
(1) The superior demonstration is the demonstration which gives us
greater knowledge (for this is the ideal of demonstration), and we
have greater knowledge of a particular individual when we know it in
itself than when we know it through something else; e.g. we know
Coriscus the musician better when we know that Coriscus is musical
than when we know only that man is musical, and a like argument
holds in all other cases. But commensurately universal
demonstration, instead of proving that the subject itself actually
is x, proves only that something else is x- e.g. in attempting to
prove that isosceles is x, it proves not that isosceles but only that
triangle is x- whereas particular demonstration proves that the
subject itself is x. The demonstration, then, that a subject, as such,
possesses an attribute is superior. If this is so, and if the
particular rather than the commensurately universal forms
demonstrates, particular demonstration is superior.