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qualified sense； but universally。 Finally； the first figure has no
need of the others； while it is by means of the first that the other
two figures are developed； and have their intervals closepacked
until immediate premisses are reached。
Clearly； therefore； the first figure is the primary condition of
knowledge。
15
Just as an attribute A may （as we saw） be atomically connected
with a subject B； so its disconnexion may be atomic。 I call 'atomic'
connexions or disconnexions which involve no intermediate term；
since in that case the connexion or disconnexion will not be
mediated by something other than the terms themselves。 It follows that
if either A or B； or both A and B； have a genus； their disconnexion
cannot be primary。 Thus： let C be the genus of A。 Then； if C is not
the genus of B…for A may well have a genus which is not the genus of
B…there will be a syllogism proving A's disconnexion from B thus：
all A is C；
no B is C；
therefore no B is A。
Or if it is B which has a genus D； we have
all B is D；
no D is A；
therefore no B is A； by syllogism；
and the proof will be similar if both A and B have a genus。 That the
genus of A need not be the genus of B and vice versa； is shown by
the existence of mutually exclusive coordinate series of
predication。 If no term in the series ACD。。。is predicable of any
term in the series BEF。。。；and if G…a term in the former series…is
the genus of A； clearly G will not be the genus of B； since； if it
were； the series would not be mutually exclusive。 So also if B has a
genus； it will not be the genus of A。 If； on the other hand； neither A
nor B has a genus and A does not inhere in B； this disconnexion must
be atomic。 If there be a middle term； one or other of them is bound to
have a genus； for the syllogism will be either in the first or the
second figure。 If it is in the first； B will have a genus…for the
premiss containing it must be affirmative： if in the second； either
A or B indifferently； since syllogism is possible if either is
contained in a negative premiss； but not if both premisses are
negative。
Hence it is clear that one thing may be atomically disconnected from
another； and we have stated when and how this is possible。
16
Ignorance…defined not as the negation of knowledge but as a positive
state of mind…is error produced by inference。
（1） Let us first consider propositions asserting a predicate's
immediate connexion with or disconnexion from a subject。 Here； it is
true； positive error may befall one in alternative ways； for it may
arise where one directly believes a connexion or disconnexion as
well as where one's belief is acquired by inference。 The error；
however； that consists in a direct belief is without complication； but
the error resulting from inference…which here concerns us…takes many
forms。 Thus； let A be atomically disconnected from all B： then the
conclusion inferred through a middle term C； that all B is A； will
be a case of error produced by syllogism。 Now； two cases are possible。
Either （a） both premisses； or （b） one premiss only； may be false。
（a） If neither A is an attribute of any C nor C of any B； whereas
the contrary was posited in both cases； both premisses will be
false。 （C may quite well be so related to A and B that C is neither
subordinate to A nor a universal attribute of B： for B； since A was
said to be primarily disconnected from B； cannot have a genus； and A
need not necessarily be a universal attribute of all things。
Consequently both premisses may be false。） On the other hand； （b）
one of the premisses may be true； though not either indifferently
but only the major A…C since； B having no genus； the premiss C…B
will always be false； while A…C may be true。 This is the case if；
for example； A is related atomically to both C and B； because when the
same term is related atomically to more terms than one； neither of
those terms will belong to the other。 It is； of course； equally the
case if A…C is not atomic。
Error of attribution； then； occurs through these causes and in
this form only…for we found that no syllogism of universal attribution
was possible in any figure but the first。 On the other hand； an
error of non…attribution may occur either in the first or in the
second figure。 Let us therefore first explain the various forms it
takes in the first figure and the character of the premisses in each
case。
（c） It may occur when both premisses are false； e。g。 supposing A
atomically connected with both C and B； if it be then assumed that
no C is and all B is C； both premisses are false。
（d） It is also possible when one is false。 This may be either
premiss indifferently。 A…C may be true； C…B false…A…C true because A
is not an attribute of all things； C…B false because C； which never
has the attribute A； cannot be an attribute of B； for if C…B were
true； the premiss A…C would no longer be true； and besides if both
premisses were true； the conclusion would be true。 Or again； C…B may
be true and A…C false； e。g。 if both C and A contain B as genera； one
of them must be subordinate to the other； so that if the premiss takes
the form No C is A； it will be false。 This makes it clear that whether
either or both premisses are false； the conclusion will equally be
false。
In the second figure the premisses cannot both be wholly false；
for if all B is A； no middle term can be with truth universally
affirmed of one extreme and universally denied of the other： but
premisses in which the middle is affirmed of one extreme and denied of
the other are the necessary condition if one is to get a valid
inference at all。 Therefore if； taken in this way； they are wholly
false； their contraries conversely should be wholly true。 But this
is impossible。 On the other hand； there is nothing to prevent both
premisses being partially false； e。g。 if actually some A is C and some
B is C； then if it is premised that all A is C and no B is C； both
premisses are false； yet partially； not wholly； false。 The same is
true if the major is made negative instead of the minor。 Or one
premiss may be wholly false； and it may be either of them。 Thus；
supposing that actually an attribute of all A must also be an
attribute of all B； then if C is yet taken to be a universal attribute
of all but universally non…attributable to B； C…A will be true but C…B
false。 Again； actually that which