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'healthy' is substituted for 'health' and 'diseased' for 'disease'。
For it is not true to say that being healthy cannot belong to one
who is diseased。 But unless this is assumed no conclusion results；
save in respect of possibility： but such a conclusion is not
impossible： for it is possible that health should belong to no man。
Again the fallacy may occur in a similar way in the middle figure： 'it
is not possible that health should belong to any disease； but it is
possible that health should belong to every man； consequently it is
not possible that disease should belong to any man'。 In the third
figure the fallacy results in reference to possibility。 For health and
diseae and knowledge and ignorance； and in general contraries； may
possibly belong to the same thing； but cannot belong to one another。
This is not in agreement with what was said before： for we stated that
when several things could belong to the same thing； they could
belong to one another。
It is evident then that in all these cases the fallacy arises from
the setting out of the terms： for if the things that are in the
conditions are substituted； no fallacy arises。 It is clear then that
in such premisses what possesses the condition ought always to be
substituted for the condition and taken as the term。
35
We must not always seek to set out the terms a single word： for we
shall often have complexes of words to which a single name is not
given。 Hence it is difficult to reduce syllogisms with such terms。
Sometimes too fallacies will result from such a search； e。g。 the
belief that syllogism can establish that which has no mean。 Let A
stand for two right angles； B for triangle； C for isosceles
triangle。 A then belongs to C because of B： but A belongs to B without
the mediation of another term： for the triangle in virtue of its own
nature contains two right angles； consequently there will be no middle
term for the proposition AB； although it is demonstrable。 For it is
clear that the middle must not always be assumed to be an individual
thing； but sometimes a complex of words； as happens in the case
mentioned。
36
That the first term belongs to the middle； and the middle to the
extreme； must not be understood in the sense that they can always be
predicated of one another or that the first term will be predicated of
the middle in the same way as the middle is predicated of the last
term。 The same holds if the premisses are negative。 But we must
suppose the verb 'to belong' to have as many meanings as the senses in
which the verb 'to be' is used； and in which the assertion that a
thing 'is' may be said to be true。 Take for example the statement that
there is a single science of contraries。 Let A stand for 'there
being a single science'； and B for things which are contrary to one
another。 Then A belongs to B； not in the sense that contraries are the
fact of there being a single science of them； but in the sense that it
is true to say of the contraries that there is a single science of
them。
It happens sometimes that the first term is stated of the middle；
but the middle is not stated of the third term； e。g。 if wisdom is
knowledge； and wisdom is of the good； the conclusion is that there
is knowledge of the good。 The good then is not knowledge； though
wisdom is knowledge。 Sometimes the middle term is stated of the third；
but the first is not stated of the middle； e。g。 if there is a
science of everything that has a quality； or is a contrary； and the
good both is a contrary and has a quality； the conclusion is that
there is a science of the good； but the good is not science； nor is
that which has a quality or is a contrary； though the good is both
of these。 Sometimes neither the first term is stated of the middle；
nor the middle of the third； while the first is sometimes stated of
the third； and sometimes not： e。g。 if there is a genus of that of
which there is a science； and if there is a science of the good； we
conclude that there is a genus of the good。 But nothing is
predicated of anything。 And if that of which there is a science is a
genus； and if there is a science of the good； we conclude that the
good is a genus。 The first term then is predicated of the extreme； but
in the premisses one thing is not stated of another。
The same holds good where the relation is negative。 For 'that does
not belong to this' does not always mean that 'this is not that'；
but sometimes that 'this is not of that' or 'for that'； e。g。 'there is
not a motion of a motion or a becoming of a becoming； but there is a
becoming of pleasure： so pleasure is not a becoming。' Or again it
may be said that there is a sign of laughter； but there is not a
sign of a sign； consequently laughter is not a sign。 This holds in the
other cases too； in which the thesis is refuted because the genus is
asserted in a particular way； in relation to the terms of the
thesis。 Again take the inference 'opportunity is not the right time：
for opportunity belongs to God； but the right time does not； since
nothing is useful to God'。 We must take as terms opportunity…right
time…God： but the premiss must be understood according to the case
of the noun。 For we state this universally without qualification； that
the terms ought always to be stated in the nominative； e。g。 man； good；
contraries； not in oblique cases； e。g。 of man； of a good； of
contraries； but the premisses ought to be understood with reference to
the cases of each term…either the dative； e。g。 'equal to this'； or the
genitive； e。g。 'double of this'； or the accusative； e。g。 'that which
strikes or sees this'； or the nominative； e。g。 'man is an animal'；
or in whatever other way the word falls in the premiss。
37
The expressions 'this belongs to that' and 'this holds true of that'
must be understood in as many ways as there are different
categories； and these categories must be taken either with or
without qualification； and further as simple or compound： the same
holds good of the corresponding negative expressions。 We must consider
these points and define them better。
38
A term which is repeated in the premisses ought to be joined to
the first extreme； not to the middle。 I mean for example that if a
syllogism should be made proving that there is knowledge of justice；
that it is good； the expression 'that it is good' （or 'qua good'）
should be joined to the first term。 Let A stand for 'knowledge that it
is good'； B for good； C for justice。 It is true to predicate A of B。
For of the good there is knowledge that it is good。 Also it is true to
predicate B of C。 For justice is identical with a good。 In this way an
analysis of the argument can be made。 But if the expression 'that it
is good' were added to B； the conclusion will not follow： for A will
be true of B； but B will not be true of C。 For to predicate of justice
the term 'good that it is good' is false and not intelligible。
Similarly if it should be proved that the healthy is an object of
knowledge qua good； of goat…stag an object of knowledge qua not
existing； or man perishable qua an object of sense： in every case in
which an addition is made to the predicate； the addition must be
joined to the extreme。
The position of the terms is not the same when something is
established without qualification and when it is qualified by some
attribute or condition； e。g。 when the good is proved to be an object
of knowledge and when it is proved to be an object of knowledge that
it is good。 If it has been proved to be an object of knowledge without
qualification； we must put as middle term 'that which is'； but if we
add the qualification 'that it is good'； the middle term must be 'that
which is something'。 Let A stand for 'knowledge that it is something'；
B stand for 'something'； and C stand for 'good'。 It is true to
predicate A of B： for ex hypothesi there is a science of that which is
something； that it is something。 B too is true of C： for that which
C represents is something。 Consequently A is true of C： there will
then be knowledge of the good； that it is good： for ex hypothesi the
term 'something' indicates the thing's special nature。 But if
'being' were taken as middle and 'being' simply were joined to the
extreme； not 'being something'； we should n