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！
demonstrated in the same way as before by converting the premiss RS。
It might be proved also per impossibile； as in the former cases。 But
if R belongs to no S； P to all S； there will be no syllogism。 Terms
for the positive relation are animal； horse； man： for the negative
relation animal； inanimate； man。
Nor can there be a syllogism when both terms are asserted of no S。
Terms for the positive relation are animal； horse； inanimate； for
the negative relation man； horse； inanimate…inanimate being the middle
term。
It is clear then in this figure also when a syllogism will be
possible and when not； if the terms are related universally。 For
whenever both the terms are affirmative； there will be a syllogism
to prove that one extreme belongs to some of the other； but when
they are negative； no syllogism will be possible。 But when one is
negative； the other affirmative； if the major is negative； the minor
affirmative； there will be a syllogism to prove that the one extreme
does not belong to some of the other： but if the relation is reversed；
no syllogism will be possible。 If one term is related universally to
the middle； the other in part only； when both are affirmative there
must be a syllogism； no matter which of the premisses is universal。
For if R belongs to all S； P to some S； P must belong to some R。 For
since the affirmative statement is convertible S will belong to some
P： consequently since R belongs to all S； and S to some P； R must also
belong to some P： therefore P must belong to some R。
Again if R belongs to some S； and P to all S； P must belong to
some R。 This may be demonstrated in the same way as the preceding。 And
it is possible to demonstrate it also per impossibile and by
exposition； as in the former cases。 But if one term is affirmative；
the other negative； and if the affirmative is universal； a syllogism
will be possible whenever the minor term is affirmative。 For if R
belongs to all S； but P does not belong to some S； it is necessary
that P does not belong to some R。 For if P belongs to all R； and R
belongs to all S； then P will belong to all S： but we assumed that
it did not。 Proof is possible also without reduction ad impossibile；
if one of the Ss be taken to which P does not belong。
But whenever the major is affirmative； no syllogism will be
possible； e。g。 if P belongs to all S and R does not belong to some
S。 Terms for the universal affirmative relation are animate； man；
animal。 For the universal negative relation it is not possible to
get terms； if R belongs to some S； and does not belong to some S。
For if P belongs to all S； and R to some S； then P will belong to some
R： but we assumed that it belongs to no R。 We must put the matter as
before。' Since the expression 'it does not belong to some' is
indefinite； it may be used truly of that also which belongs to none。
But if R belongs to no S； no syllogism is possible； as has been shown。
Clearly then no syllogism will be possible here。
But if the negative term is universal； whenever the major is
negative and the minor affirmative there will be a syllogism。 For if P
belongs to no S； and R belongs to some S； P will not belong to some R：
for we shall have the first figure again； if the premiss RS is
converted。
But when the minor is negative； there will be no syllogism。 Terms
for the positive relation are animal； man； wild： for the negative
relation； animal； science； wild…the middle in both being the term
wild。
Nor is a syllogism possible when both are stated in the negative；
but one is universal； the other particular。 When the minor is
related universally to the middle； take the terms animal； science；
wild； animal； man； wild。 When the major is related universally to
the middle； take as terms for a negative relation raven； snow；
white。 For a positive relation terms cannot be found； if R belongs
to some S； and does not belong to some S。 For if P belongs to all R；
and R to some S； then P belongs to some S： but we assumed that it
belongs to no S。 Our point； then； must be proved from the indefinite
nature of the particular statement。
Nor is a syllogism possible anyhow； if each of the extremes
belongs to some of the middle or does not belong； or one belongs and
the other does not to some of the middle； or one belongs to some of
the middle； the other not to all； or if the premisses are
indefinite。 Common terms for all are animal； man； white： animal；
inanimate； white。
It is clear then in this figure also when a syllogism will be
possible； and when not； and that if the terms are as stated； a
syllogism results of necessity； and if there is a syllogism； the terms
must be so related。 It is clear also that all the syllogisms in this
figure are imperfect （for all are made perfect by certain
supplementary assumptions）； and that it will not be possible to
reach a universal conclusion by means of this figure； whether negative
or affirmative。
7
It is evident also that in all the figures； whenever a proper
syllogism does not result； if both the terms are affirmative or
negative nothing necessary follows at all； but if one is
affirmative； the other negative； and if the negative is stated
universally； a syllogism always results relating the minor to the
major term； e。g。 if A belongs to all or some B； and B belongs to no C：
for if the premisses are converted it is necessary that C does not
belong to some A。 Similarly also in the other figures： a syllogism
always results by means of conversion。 It is evident also that the
substitution of an indefinite for a particular affirmative will effect
the same syllogism in all the figures。
It is clear too that all the imperfect syllogisms are made perfect
by means of the first figure。 For all are brought to a conclusion
either ostensively or per impossibile。 In both ways the first figure
is formed： if they are made perfect ostensively； because （as we saw）
all are brought to a conclusion by means of conversion； and conversion
produces the first figure： if they are proved per impossibile； because
on the assumption of the false statement the syllogism comes about
by means of the first figure； e。g。 in the last figure； if A and B
belong to all C； it follows that A belongs to some B： for if A
belonged to no B； and B belongs to all C； A would belong to no C：
but （as we stated） it belongs to all C。 Similarly also with the rest。
It is possible also to reduce all syllogisms to the universal
syllogisms in the first figure。 Those in the second figure are clearly
made perfect by these； though not all in the same way； the universal
syllogisms are made perfect by converting the negative premiss； each
of the particular syllogisms by reductio ad impossibile。 In the
first figure particular syllogisms are indeed made perfect by
themselves； but it is possible also to prove them by means of the
second figure； reducing them ad impossibile； e。g。 if A belongs to
all B； and B to some C； it follows that A belongs to some C。 For if it
belonged to no C； and belongs to all B； then B will belong to no C：
this we know by means of the second figure。 Similarly also
demonstration will be possible in the case of the negative。 For if A
belongs to no B； and B belongs to some C； A will not belong to some C：
for if it belonged to all C； and belongs to no B； then B will belong
to no C： and this （as we saw） is the middle figure。 Consequently；
since all syllogisms in the middle figure can be reduced to
unive