man must be either mortal or immortal, but it is not necessary that
man should be a mortal animal-this is begged: and this is what ought
to have been proved syllogistically. And again, taking A as mortal
animal, B as footed, C as footless, and D as man, he assumes in the
same way that A inheres either in B or in C (for every mortal animal
is either footed or footless), and he assumes A of D (for he assumed
man, as we saw, to be a mortal animal); consequently it is necessary
that man should be either a footed or a footless animal; but it is not
necessary that man should be footed: this he assumes: and it is just
this again which he ought to have demonstrated. Always dividing then
in this way it turns out that these logicians assume as middle the
universal term, and as extremes that which ought to have been the
subject of demonstration and the differentiae. In conclusion, they
do not make it clear, and show it to be necessary, that this is man or
whatever the subject of inquiry may be: for they pursue the other
method altogether, never even suspecting the presence of the rich
supply of evidence which might be used. It is clear that it is neither
possible to refute a statement by this method of division, nor to draw
a conclusion about an accident or property of a thing, nor about its
genus, nor in cases in which it is unknown whether it is thus or thus,
e.g. whether the diagonal is incommensurate. For if he assumes that
every length is either commensurate or incommensurate, and the
diagonal is a length, he has proved that the diagonal is either
incommensurate or commensurate. But if he should assume that it is
incommensurate, he will have assumed what he ought to have proved.
He cannot then prove it: for this is his method, but proof is not
possible by this method. Let A stand for 'incommensurate or
commensurate', B for 'length', C for 'diagonal'. It is clear then that
this method of investigation is not suitable for every inquiry, nor is
it useful in those cases in which it is thought to be most suitable.
From what has been said it is clear from what elements
demonstrations are formed and in what manner, and to what points we
must look in each problem.
32
Our next business is to state how we can reduce syllogisms to the
aforementioned figures: for this part of the inquiry still remains. If
we should investigate the production of the syllogisms and had the
power of discovering them, and further if we could resolve the
syllogisms produced into the aforementioned figures, our original
problem would be brought to a conclusion. It will happen at the same
time that what has been already said will be confirmed and its truth
made clearer by what we are about to say. For everything that is
true must in every respect agree with itself First then we must
attempt to select the two premisses of the syllogism (for it is easier
to divide into large parts than into small, and the composite parts
are larger than the elements out of which they are made); next we must
inquire which are universal and which particular, and if both
premisses have not been stated, we must ourselves assume the one which
is missing. For sometimes men put forward the universal premiss, but
do not posit the premiss which is contained in it, either in writing
or in discussion: or men put forward the premisses of the principal
syllogism, but omit those through which they are inferred, and
invite the concession of others to no purpose. We must inquire then
whether anything unnecessary has been assumed, or anything necessary
has been omitted, and we must posit the one and take away the other,
until we have reached the two premisses: for unless we have these,
we cannot reduce arguments put forward in the way described. In some
arguments it is easy to see what is wanting, but some escape us, and
appear to be syllogisms, because something necessary results from what
has been laid down, e.g. if the assumptions were made that substance
is not annihilated by the annihilation of what is not substance, and
that if the elements out of which a thing is made are annihilated,
then that which is made out of them is destroyed: these propositions
substance; this has not however been drawn by syllogism from the
propositions assumed, but premisses are wanting. Again if it is
necessary that animal should exist, if man does, and that substance
should exist, if animal does, it is necessary that substance should
exist if man does: but as yet the conclusion has not been drawn
syllogistically: for the premisses are not in the shape we required.
We are deceived in such cases because something necessary results from
what is assumed, since the syllogism also is necessary. But that which
is necessary is wider than the syllogism: for every syllogism is
necessary, but not everything which is necessary is a syllogism.
Consequently, though something results when certain propositions are
assumed, we must not try to reduce it directly, but must first state
the two premisses, then divide them into their terms. We must take
that term as middle which is stated in both the remisses: for it is
necessary that the middle should be found in both premisses in all the
figures.
If then the middle term is a predicate and a subject of predication,
or if it is a predicate, and something else is denied of it, we
shall have the first figure: if it both is a predicate and is denied
of something, the middle figure: if other things are predicated of it,
or one is denied, the other predicated, the last figure. For it was
thus that we found the middle term placed in each figure. It is placed
similarly too if the premisses are not universal: for the middle
term is determined in the same way. Clearly then, if the same term
is not stated more than once in the course of an argument, a syllogism
cannot be made: for a middle term has not been taken. Since we know
what sort of thesis is established in each figure, and in which the
universal, in what sort the particular is described, clearly we must
not look for all the figures, but for that which is appropriate to the
thesis in hand. If the thesis is established in more figures than one,
we shall recognize the figure by the position of the middle term.
33
Men are frequently deceived about syllogisms because the inference
is necessary, as has been said above; sometimes they are deceived by
the similarity in the positing of the terms; and this ought not to
escape our notice. E.g. if A is stated of B, and B of C: it would seem
that a syllogism is possible since the terms stand thus: but nothing
necessary results, nor does a syllogism. Let A represent the term
'being eternal', B 'Aristomenes as an object of thought', C
'Aristomenes'. It is true then that A belongs to B. For Aristomenes as
an object of thought is eternal. But B also belongs to C: for
Aristomenes is Aristomenes as an object of thought. But A does not
belong to C: for Ari
stomenes is perishable. For no syllogism was
made although the terms stood thus: that required that the premiss
AB should be stated universally. But this is false, that every
Aristomenes who is an object of thought is eternal, since
Aristomenes is perishable. Again let C stand for 'Miccalus', B for
'musical Miccalus', A for 'perishing to-morrow'. It is true to
predicate B of C: for Miccalus is musical Miccalus. Also A can be
predicated of B: for musical Miccalus might perish to-morrow. But to
state A of C is false at any rate. This argument then is identical
with the former; for it is not true universally that musical
Miccalus perishes to-morrow: but unless this is assumed, no
syllogism (as we have shown) is possible.
This deception then arises through ignoring a small distinction. For
if we accept the conclusion as though it made no difference whether we
said 'This belong to that' or 'This belongs to all of that'.
34
Men will frequently fall into fallacies through not setting out
the terms of the premiss well, e.g. suppose A to be health, B disease,
C man. It is true to say that A cannot belong to any B (for health
belongs to no disease) and again that B belongs to every C (for
every man is capable of disease). It would seem to follow that
health cannot belong to any man. The reason for this is that the terms
are not set out well in the statement, since if the things which are
in the conditions are substituted, no syllogism can be made, e.g. if
'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