The Complete Aristotle (eng.)

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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.
    (2) The universal has not a separate being over against groups
of singulars. Demonstration nevertheless creates the opinion that
its function is conditioned by something like this-some separate
entity belonging to the real world; that, for instance, of triangle
or of figure or number, over against particular triangles, figures,
and numbers. But demonstration which touches the real and will not
mislead is superior to that which moves among unrealities and is
delusory. Now commensurately universal demonstration is of the
latter kind: if we engage in it we find ourselves reasoning after a
fashion well illustrated by the argument that the proportionate is
what answers to the definition of some entity which is neither
line, number, solid, nor plane, but a proportionate apart from all
these. Since, then, such a proof is characteristically commensurate
and universal, and less touches reality than does particular
demonstration, and creates a false opinion, it will follow that
commensurate and universal is inferior to particular
demonstration.
    We may retort thus. (1) The first argument applies no more to
commensurate and universal than to particular demonstration. If
equality to two right angles is attributable to its subject not qua
isosceles but qua triangle, he who knows that isosceles possesses
that attribute knows the subject as qua itself possessing the
attribute, to a less degree than he who knows that triangle has
that attribute. To sum up the whole matter: if a subject is proved
to possess qua triangle an attribute which it does not in fact
possess qua triangle, that is not demonstration: but if it does
possess it qua triangle the rule applies that the greater knowledge
is