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！
true to say that that which necessarily does not belong to some of the
As may possibly not belong to any A； just as it is not true to say
that what necessarily belongs to some A may possibly belong to all
A。 If any one then should claim that because it is not possible for
C to belong to all D； it necessarily does not belong to some D； he
would make a false assumption： for it does belong to all D； but
because in some cases it belongs necessarily； therefore we say that it
is not possible for it to belong to all。 Hence both the propositions
'A necessarily belongs to some B' and 'A necessarily does not belong
to some B' are opposed to the proposition 'A belongs to all B'。
Similarly also they are opposed to the proposition 'A may belong to no
B'。 It is clear then that in relation to what is possible and not
possible； in the sense originally defined； we must assume； not that
A necessarily belongs to some B； but that A necessarily does not
belong to some B。 But if this is assumed； no absurdity results：
consequently no syllogism。 It is clear from what has been said that
the negative proposition is not convertible。
This being proved； suppose it possible that A may belong to no B and
to all C。 By means of conversion no syllogism will result： for the
major premiss； as has been said； is not convertible。 Nor can a proof
be obtained by a reductio ad absurdum： for if it is assumed that B can
belong to all C； no false consequence results： for A may belong both
to all C and to no C。 In general； if there is a syllogism； it is clear
that its conclusion will be problematic because neither of the
premisses is assertoric； and this must be either affirmative or
negative。 But neither is possible。 Suppose the conclusion is
affirmative： it will be proved by an example that the predicate cannot
belong to the subject。 Suppose the conclusion is negative： it will
be proved that it is not problematic but necessary。 Let A be white；
B man； C horse。 It is possible then for A to belong to all of the
one and to none of the other。 But it is not possible for B to belong
nor not to belong to C。 That it is not possible for it to belong； is
clear。 For no horse is a man。 Neither is it possible for it not to
belong。 For it is necessary that no horse should be a man； but the
necessary we found to be different from the possible。 No syllogism
then results。 A similar proof can be given if the major premiss is
negative； the minor affirmative； or if both are affirmative or
negative。 The demonstration can be made by means of the same terms。
And whenever one premiss is universal； the other particular； or both
are particular or indefinite； or in whatever other way the premisses
can be altered； the proof will always proceed through the same
terms。 Clearly then； if both the premisses are problematic； no
syllogism results。
18
But if one premiss is assertoric； the other problematic； if the
affirmative is assertoric and the negative problematic no syllogism
will be possible； whether the premisses are universal or particular。
The proof is the same as above； and by means of the same terms。 But
when the affirmative premiss is problematic； and the negative
assertoric； we shall have a syllogism。 Suppose A belongs to no B；
but can belong to all C。 If the negative proposition is converted； B
will belong to no A。 But ex hypothesi can belong to all C： so a
syllogism is made； proving by means of the first figure that B may
belong to no C。 Similarly also if the minor premiss is negative。 But
if both premisses are negative； one being assertoric； the other
problematic； nothing follows necessarily from these premisses as
they stand； but if the problematic premiss is converted into its
complementary affirmative a syllogism is formed to prove that B may
belong to no C； as before： for we shall again have the first figure。
But if both premisses are affirmative； no syllogism will be
possible。 This arrangement of terms is possible both when the relation
is positive； e。g。 health； animal； man； and when it is negative； e。g。
health； horse； man。
The same will hold good if the syllogisms are particular。 Whenever
the affirmative proposition is assertoric； whether universal or
particular； no syllogism is possible （this is proved similarly and
by the same examples as above）； but when the negative proposition is
assertoric； a conclusion can be drawn by means of conversion； as
before。 Again if both the relations are negative； and the assertoric
proposition is universal； although no conclusion follows from the
actual premisses； a syllogism can be obtained by converting the
problematic premiss into its complementary affirmative as before。
But if the negative proposition is assertoric； but particular； no
syllogism is possible； whether the other premiss is affirmative or
negative。 Nor can a conclusion be drawn when both premisses are
indefinite； whether affirmative or negative； or particular。 The
proof is the same and by the same terms。
19
If one of the premisses is necessary； the other problematic； then if
the negative is necessary a syllogistic conclusion can be drawn； not
merely a negative problematic but also a negative assertoric
conclusion； but if the affirmative premiss is necessary； no conclusion
is possible。 Suppose that A necessarily belongs to no B； but may
belong to all C。 If the negative premiss is converted B will belong to
no A： but A ex hypothesi is capable of belonging to all C： so once
more a conclusion is drawn by the first figure that B may belong to no
C。 But at the same time it is clear that B will not belong to any C。
For assume that it does： then if A cannot belong to any B； and B
belongs to some of the Cs； A cannot belong to some of the Cs： but ex
hypothesi it may belong to all。 A similar proof can be given if the
minor premiss is negative。 Again let the affirmative proposition be
necessary； and the other problematic； i。e。 suppose that A may belong
to no B； but necessarily belongs to all C。 When the terms are arranged
in this way； no syllogism is possible。 For （1） it sometimes turns
out that B necessarily does not belong to C。 Let A be white； B man；
C swan。 White then necessarily belongs to swan； but may belong to no
man； and man necessarily belongs to no swan； Clearly then we cannot
draw a problematic conclusion； for that which is necessary is
admittedly distinct from that which is possible。 （2） Nor again can
we draw a necessary conclusion： for that presupposes that both
premisses are necessary； or at