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of all but universally non…attributable to B； C…A will be true but C…B
false。 Again； actually that which is an attribute of no B will not
be an attribute of all A either； for if it be an attribute of all A；
it will also be an attribute of all B； which is contrary to
supposition； but if C be nevertheless assumed to be a universal
attribute of A； but an attribute of no B； then the premiss C…B is true
but the major is false。 The case is similar if the major is made the
negative premiss。 For in fact what is an attribute of no A will not be
an attribute of any B either； and if it be yet assumed that C is
universally non…attributable to A； but a universal attribute of B； the
premiss C…A is true but the minor wholly false。 Again； in fact it is
false to assume that that which is an attribute of all B is an
attribute of no A； for if it be an attribute of all B； it must be an
attribute of some A。 If then C is nevertheless assumed to be an
attribute of all B but of no A； C…B will be true but C…A false。
It is thus clear that in the case of atomic propositions erroneous
inference will be possible not only when both premisses are false
but also when only one is false。
17
In the case of attributes not atomically connected with or
disconnected from their subjects； （a） （i） as long as the false
conclusion is inferred through the 'appropriate' middle； only the
major and not both premisses can be false。 By 'appropriate middle' I
mean the middle term through which the contradictory…i。e。 the
true…conclusion is inferrible。 Thus； let A be attributable to B
through a middle term C： then； since to produce a conclusion the
premiss C…B must be taken affirmatively； it is clear that this premiss
must always be true； for its quality is not changed。 But the major A…C
is false； for it is by a change in the quality of A…C that the
conclusion becomes its contradictory…i。e。 true。 Similarly （ii） if
the middle is taken from another series of predication； e。g。 suppose D
to be not only contained within A as a part within its whole but
also predicable of all B。 Then the premiss D…B must remain
unchanged； but the quality of A…D must be changed； so that D…B is
always true； A…D always false。 Such error is practically identical
with that which is inferred through the 'appropriate' middle。 On the
other hand； （b） if the conclusion is not inferred through the
'appropriate' middle…（i） when the middle is subordinate to A but is
predicable of no B； both premisses must be false； because if there
is to be a conclusion both must be posited as asserting the contrary
of what is actually the fact； and so posited both become false： e。g。
suppose that actually all D is A but no B is D； then if these
premisses are changed in quality； a conclusion will follow and both of
the new premisses will be false。 When； however； （ii） the middle D is
not subordinate to A； A…D will be true； D…B false…A…D true because A
was not subordinate to D； D…B false because if it had been true； the
conclusion too would have been true； but it is ex hypothesi false。
When the erroneous inference is in the second figure； both premisses
cannot be entirely false； since if B is subordinate to A； there can be
no middle predicable of all of one extreme and of none of the other；
as was stated before。 One premiss； however； may be false； and it may
be either of them。 Thus； if C is actually an attribute of both A and
B； but is assumed to be an attribute of A only and not of B； C…A
will be true； C…B false： or again if C be assumed to be attributable
to B but to no A； C…B will be true； C…A false。
We have stated when and through what kinds of premisses error will
result in cases where the erroneous conclusion is negative。 If the
conclusion is affirmative； （a） （i） it may be inferred through the
'appropriate' middle term。 In this case both premisses cannot be false
since； as we said before； C…B must remain unchanged if there is to
be a conclusion； and consequently A…C； the quality of which is
changed； will always be false。 This is equally true if （ii） the middle
is taken from another series of predication； as was stated to be the
case also with regard to negative error； for D…B must remain
unchanged； while the quality of A…D must be converted； and the type of
error is the same as before。
（b） The middle may be inappropriate。 Then （i） if D is subordinate to
A； A…D will be true； but D…B false； since A may quite well be
predicable of several terms no one of which can be subordinated to
another。 If； however； （ii） D is not subordinate to A； obviously A…D；
since it is affirmed； will always be false； while D…B may be either
true or false； for A may very well be an attribute of no D； whereas
all B is D； e。g。 no science is animal； all music is science。 Equally
well A may be an attribute of no D； and D of no B。 It emerges； then；
that if the middle term is not subordinate to the major； not only both
premisses but either singly may be false。
Thus we have made it clear how many varieties of erroneous inference
are liable to happen and through what kinds of premisses they occur；
in the case both of immediate and of demonstrable truths。
18
It is also clear that the loss of any one of the senses entails
the loss of a corresponding portion of knowledge； and that； since we
learn either by induction or by demonstration； this knowledge cannot
be acquired。 Thus demonstration develops from universals； induction
from particulars； but since it is possible to familiarize the pupil
with even the so…called mathematical abstractions only through
induction…i。e。 only because each subject genus possesses； in virtue of
a determinate mathematical character； certain properties which can
be treated as separate even though they do not exist in isolation…it
is consequently impossible to come to grasp universals except
through induction。 But induction is impossible for those who have
not sense…perception。 For it is sense…perception alone which is
adequate for grasping the particulars： they cannot be objects of
scientific knowledge； because neither can universals give us knowledge
of them without induction； nor can we get it through induction without
sense…perception。
19
Every syllogism is effected by means of three terms。 One kind of
syllogism serves to prove that A inheres in C by showing that A
inheres in B and B in C； the other is negative and one of its
premisses asserts one term of another； while the other denies one