按键盘上方向键 ← 或 → 可快速上下翻页，按键盘上的 Enter 键可回到本书目录页，按键盘上方向键 ↑ 可回到本页顶部！
————未阅读完？加入书签已便下次继续阅读！
none of another （it does not matter which has the negative
relation）； but in no other way。 Let M be predicated of no N； but of
all O。 Since； then； the negative relation is convertible； N will
belong to no M： but M was assumed to belong to all O： consequently N
will belong to no O。 This has already been proved。 Again if M
belongs to all N； but to no O； then N will belong to no O。 For if M
belongs to no O； O belongs to no M： but M （as was said） belongs to all
N： O then will belong to no N： for the first figure has again been
formed。 But since the negative relation is convertible； N will
belong to no O。 Thus it will be the same syllogism that proves both
conclusions。
It is possible to prove these results also by reductio ad
impossibile。
It is clear then that a syllogism is formed when the terms are so
related； but not a perfect syllogism； for necessity is not perfectly
established merely from the original premisses； others also are
needed。
But if M is predicated of every N and O； there cannot be a
syllogism。 Terms to illustrate a positive relation between the
extremes are substance； animal； man； a negative relation； substance；
animal； number…substance being the middle term。
Nor is a syllogism possible when M is predicated neither of any N
nor of any O。 Terms to illustrate a positive relation are line；
animal； man： a negative relation； line； animal； stone。
It is clear then that if a syllogism is formed when the terms are
universally related； the terms must be related as we stated at the
outset： for if they are otherwise related no necessary consequence
follows。
If the middle term is related universally to one of the extremes；
a particular negative syllogism must result whenever the middle term
is related universally to the major whether positively or
negatively； and particularly to the minor and in a manner opposite
to that of the universal statement： by 'an opposite manner' I mean； if
the universal statement is negative； the particular is affirmative： if
the universal is affirmative； the particular is negative。 For if M
belongs to no N； but to some O； it is necessary that N does not belong
to some O。 For since the negative statement is convertible； N will
belong to no M： but M was admitted to belong to some O： therefore N
will not belong to some O： for the result is reached by means of the
first figure。 Again if M belongs to all N； but not to some O； it is
necessary that N does not belong to some O： for if N belongs to all O；
and M is predicated also of all N； M must belong to all O： but we
assumed that M does not belong to some O。 And if M belongs to all N
but not to all O； we shall conclude that N does not belong to all O：
the proof is the same as the above。 But if M is predicated of all O；
but not of all N； there will be no syllogism。 Take the terms animal；
substance； raven； animal； white； raven。 Nor will there be a conclusion
when M is predicated of no O； but of some N。 Terms to illustrate a
positive relation between the extremes are animal； substance； unit：
a negative relation； animal； substance； science。
If then the universal statement is opposed to the particular； we
have stated when a syllogism will be possible and when not： but if the
premisses are similar in form； I mean both negative or both
affirmative； a syllogism will not be possible anyhow。 First let them
be negative； and let the major premiss be universal； e。g。 let M belong
to no N； and not to some O。 It is possible then for N to belong either
to all O or to no O。 Terms to illustrate the negative relation are
black； snow； animal。 But it is not possible to find terms of which the
extremes are related positively and universally； if M belongs to
some O； and does not belong to some O。 For if N belonged to all O； but
M to no N； then M would belong to no O： but we assumed that it belongs
to some O。 In this way then it is not admissible to take terms： our
point must be proved from the indefinite nature of the particular
statement。 For since it is true that M does not belong to some O； even
if it belongs to no O； and since if it belongs to no O a syllogism
is （as we have seen） not possible； clearly it will not be possible now
either。
Again let the premisses be affirmative； and let the major premiss as
before be universal； e。g。 let M belong to all N and to some O。 It is
possible then for N to belong to all O or to no O。 Terms to illustrate
the negative relation are white； swan； stone。 But it is not possible
to take terms to illustrate the universal affirmative relation； for
the reason already stated： the point must be proved from the
indefinite nature of the particular statement。 But if the minor
premiss is universal； and M belongs to no O； and not to some N； it
is possible for N to belong either to all O or to no O。 Terms for
the positive relation are white； animal； raven： for the negative
relation； white； stone； raven。 If the premisses are affirmative； terms
for the negative relation are white； animal； snow； for the positive
relation； white； animal； swan。 Evidently then； whenever the
premisses are similar in form； and one is universal； the other
particular； a syllogism can； not be formed anyhow。 Nor is one possible
if the middle term belongs to some of each of the extremes； or does
not belong to some of either； or belongs to some of the one； not to
some of the other； or belongs to neither universally； or is related to
them indefinitely。 Common terms for all the above are white； animal；
man： white； animal； inanimate。
It is clear then from what has been said that if the terms are related
to one another in the way stated； a syllogism results of necessity；
and if there is a syllogism； the terms must be so related。 But it is
evident also that all the syllogisms in this figure are imperfect： for
all are made perfect by certain supplementary statements； which either
are contained in the terms of necessity or are assumed as
hypotheses； i。e。 when we prove per impossibile。 And it is evident that
an affirmative conclusion is not attained by means of this figure； but
all are negative； whether universal or particular。
6
But if one term belongs to all； and another to none； of a third；
or if both belong to all； or to none； of it； I call such a figure
the third； by middle term in it I mean that of which both the
predicates are predicated； by extremes I mean the predicates； by the
major extreme that which is further from the middle； by the minor that
which is nearer to it。 The middle term stands outside the extremes；
and is last in position。 A syllogism cannot be perfect in this
figure either； but it may be valid whether the terms are related
universally or not to the middle term。
If they are universal； whenever both P and R belong to S； it follows
that P will necessarily belong to some R。 For； since the affirmative
statement is convertible； S will belong to some R： consequently
since P belongs to all S； and S to some R； P must belong to some R：
for a syllogism in the first figure is produced。 It is possible to
demonstrate this also per impossibile and by exposition。 For if both P
and R belong to all S； should one of the Ss； e。g。 N； be taken； both
P and R will belong to this； and thus P will belong to some R。
If R belongs to all S； and P to no S； there will be a syllogism to
prove that P will necessarily not belong to some R。 This may be
demonstrated in the same way as before by converting the premiss RS。
It migh