The Basic Works of Aristotle (Modern Library Classics) (17 page)

26
     Since we understand the subjects with which syllogisms are concerned, what sort of conclusion is established in each figure, and in how many moods this is done, it is evident to us both what sort of problem is difficult and what sort is easy to prove.
(30)
For that which is concluded in many figures and through many moods is easier; that which is concluded in few figures and through few moods is more difficult to attempt. The universal affirmative is proved by means of the first figure only and by this in only one mood; the universal negative is proved both through the first figure and through the second,
(35)
through the first in one mood, through the second in two. The particular affirmative is proved through the first and through the last figure, in one mood through the first, in three moods through the last. The particular negative is proved in all the figures,
(40)
but once in the first, in two moods in the second, in three moods in the third.
[43a]
It is clear then that the universal affirmative is most difficult to establish, most easy to overthrow. In general, universals are easier game for the destroyer than particulars: for whether the predicate belongs to none or not to some, they are destroyed: and the particular negative is proved in all the figures,
(5)
the universal negative in two. Similarly with universal negatives: the original statement is destroyed, whether the predicate belongs to all or to some: and this we found possible in two figures. But particular statements can be refuted in one way only—by proving that the predicate belongs either to all or to none. But particular statements are easier to
establish:
for proof is possible in more figures and through more moods.
(10)
And in general we must not forget that it is possible to refute statements by means of one another, I mean, universal statements by means of particular, and particular statements by means of universal: but it is not possible to establish universal statements by means of particular, though it is possible to establish particular statements by means of universal. At the same time it is evident that it is easier to refute than to establish.
(15)

The manner in which every syllogism is produced, the number of the terms and premisses through which it proceeds, the relation of the premisses to one another, the character of the problem proved in each figure, and the number of the figures appropriate to each problem, all these matters are clear from what has been said.

27
     We must now state how we may ourselves always have a supply of syllogisms in reference to the problem proposed and by what road we may reach the principles relative to the problem: for perhaps we ought not only to investigate the construction of syllogisms,
(20)
but also to have the power of making them.

Of all the things which exist some are such that they cannot be predicated of anything else truly and universally,
(25)
e. g. Cleon and Callias, i. e. the individual and sensible, but other things may be predicated of them (for each of these is both man and animal); and some things are themselves predicated of others,
(30)
but nothing prior is predicated of them; and some are predicated of others, and yet others of them, e. g. man of Callias and animal of man. It is clear then that some things are naturally not stated of anything: for as a rule each sensible thing is such that it cannot be predicated of anything, save incidentally: for we sometimes say that that white object is Socrates, or that that which approaches is Callias.
(35)
We shall explain in another place
⁵⁹
that there is an upward limit also to the process of predicating: for the present we must assume this. Of these ultimate predicates it is not possible to demonstrate another predicate, save as a matter of opinion, but these may be predicated of other things. Neither can individuals be predicated of other things,
(40)
though other things can be predicated of them. Whatever lies between these limits can be spoken of in both ways: they may be stated of others, and others stated of them. And as a rule arguments and inquiries are concerned with these things.

We must select the premisses suitable to each problem in this manner: first we must lay down the subject and the definitions and the properties of the thing; next we must lay down those attributes which follow the thing, and again those which the thing follows, and those which cannot belong to it.
[43b]
But those to which it cannot belong need not be selected,
(5)
because the negative statement implied above is convertible. Of the attributes which follow we must distinguish those which fall within the definition, those which are predicated as properties, and those which are predicated as accidents, and of the latter those which apparently and those which really belong. The larger the supply a man has of these, the more quickly will he reach a conclusion; and in proportion as he apprehends those which are truer,
(10)
the more cogently will he demonstrate. But he must select not those which follow some particular but those which follow the thing as a whole e. g. not what follows a particular man but what
follows every man: for the syllogism proceeds through universal premisses.
(15)
If the statement is indefinite, it is uncertain whether the premiss is universal, but if the statement is definite, the matter is clear. Similarly one must select those attributes which the subject follows as wholes, for the reason given. But that which follows one must not suppose to follow as a whole, e. g. that every animal follows man or every science music, but only that it follows, without qualification,
(20)
as indeed we state it in a proposition: for the other statement is useless and impossible, e. g. that every man is every animal or justice is all good. But that which something follows receives the mark ‘every’. Whenever the subject, for which we must obtain the attributes that follow, is contained by something else, what follows or does not follow the highest term universally must not be selected in dealing with the subordinate term (for these attributes have been taken in dealing with the superior term; for what follows animal also follows man,
(25)
and what does not belong to animal does not belong to man); but we must choose those attributes which are peculiar to each subject. For some things are peculiar to the species as distinct from the genus; for species being distinct there must be attributes peculiar to each. Nor must we take as things which the superior term follows, those things which the inferior term follows,
(30)
e. g. take as subjects of the predicate ‘animal’ what are really subjects of the predicate ‘man’. It is necessary indeed, if animal follows man, that it should follow all these also. But these belong more properly to the choice of what concerns man. One must apprehend also normal consequents and normal antecedents; for propositions which obtain normally are established syllogistically from premisses which obtain normally,
(35)
some if not all of them having this character of normality. For the conclusion of each syllogism resembles its principles. We must not however choose attributes which are consequent upon all the terms:
⁶⁰
for no syllogism can be made out of such premisses. The reason why this is so will be clear in the sequel.
⁶¹

28
     If men wish to establish something about some whole,
(40)
they must look to the
subjects
of that which is being established (the subjects of which it happens to be asserted), and the
attributes
which follow that of which it is to be predicated. For if any of these subjects is the same as any of these attributes, the attribute originally in question
must belong to the subject originally in question.
⁶²
But if the purpose is to establish not a universal but a particular proposition, they must look for the terms of which the terms in question are predicable: for if any of these are identical, the attribute in question must belong to some of the subject in question.
⁶³
[44a]
Whenever the one term has to belong to none of the other, one must look to the consequents of the subject, and to those attributes which cannot possibly be present in the predicate in question:
⁶⁴
or conversely to the attributes which cannot possibly be present in the subject, and to the consequents of the predicate.
⁶⁵
If any members of these groups are identical,
(5)
one of the terms in question cannot possibly belong to any of the other. For sometimes a syllogism in the first figure results,
⁶⁶
sometimes a syllogism in the second. But if the object is to establish a particular negative proposition, we must find antecedents of the subject in question and attributes which cannot possibly belong to the predicate in question.
⁶⁷
If any members of these two groups are identical,
(10)
it follows that one of the terms in question does not belong to some of the other. Perhaps each of these statements will become clearer in the following way. Suppose the consequents of
A
are designated by
B,
the antecedents of
A
by
C,
attributes which cannot possibly belong to
A
by
D.
Suppose again that the attributes of
E
are designated by
F,
(15)
the antecedents of
E
by
G,
and attributes which cannot belong to
E
by
H.
If then one of the
C
s should be identical with one of the
F
s,
A
must belong to all
E:
for
F
belongs to all
E,
and
A
to all
C,
consequently
A
belongs to all
E.
If
C
and
G
are identical,
A
must belong to some of the
E
s: for
A
follows
C,
and
E
follows all
G.
(20)
If
F
and
D
are identical,
A
will belong to none of the
E
s by a prosyllogism: for since the negative proposition is convertible, and
F
is identical with
D, A
will belong to none of the
F
s, but
F
belongs to all
E.
Again, if
B
and
H
are identical,
A
will belong to none of the
E
s: for
B
will belong to all
A,
but to no
E:
for it was assumed to be identical with
H,
(25)
and
H
belonged to none of the
E
s. If
D
and
G
are identical,
A
will not belong to some of the
E
s: for it will not belong to
G,
because it does not belong to
D:
but
G
falls under
E:
consequently
A
will not belong to some of the
E
s.
(30)
If
B
is identical with
G,
there will be a converted syllogism: for
E
will belong to all
A,
since
B
belongs to
A
and
E
to
B
(for
B
was found to be identical with
G
): but that
A
should belong to all
E
is not
necessary, but it must belong to some
E
because it is possible to convert the universal statement into a particular.
(35)

It is clear then that in every proposition which requires proof we must look to the aforesaid relations of the subject and predicate in question: for all syllogisms proceed through these. But if we are seeking consequents and antecedents we must look for those which are primary and most universal,
(40)
e. g. in reference to
E
we must look to
KF
rather than to
F
alone, and in reference to
A
we must look to
KC
rather than to
C
alone.
[44b]
For if
A
belongs to
KF,
it belongs both to
F
and to
E:
but if it does not follow
KF,
it may yet follow
F.
Similarly we must consider the antecedents of
A
itself: for if a term follows the primary antecedents, it will follow those also which are subordinate,
(5)
but if it does not follow the former, it may yet follow the latter.

It is clear too that the inquiry proceeds through the three terms and the two premisses, and that all the syllogisms proceed through the aforesaid figures. For it is proved that
A
belongs to
all E,
whenever an identical term is found among the
C
s and
F
s.
(10)
This will be the middle term;
A
and
E
will be the extremes. So the first figure is formed. And
A
will belong to
some E,
whenever
C
and
G
are apprehended to be the same. This is the last figure: for
G
becomes the middle term. And
A
will belong to
no E,
when
D
and
F
are identical. Thus we have both the first figure and the middle figure; the first, because
A
belongs to no
F,
since the negative statement is convertible,
(15)
and
F
belongs to all
E;
the middle figure because
D
belongs to no
A,
and to all
E.
And
A
will
not
belong to
some E,
whenever
D
and
G
are identical. This is the last figure: for
A
will belong to no
G,
and
E
will belong to all
G.
Clearly then all syllogisms proceed through the aforesaid figures,
(20)
and we must not select consequents of all the terms,
⁶⁸
because no syllogism is produced from them. For (as we saw)
⁶⁹
it is not possible at all to establish a proposition from consequents, and it is not possible to refute by means of a consequent of both the terms in question: for the middle term must belong to the one, and not belong to the other.

It is clear too that other methods of inquiry by selection of middle terms are useless to produce a syllogism,
(25)
e. g. if the consequents of the terms in question are identical, or if the antecedents of
A
are identical with those attributes which cannot possibly belong to
E,
or if those attributes are identical which cannot belong to either term: for no syllogism is produced by means of these. For if the consequents are identical,
(30)
e. g.
B
and
F,
we have the middle figure with
both premisses affirmative: if the antecedents of
A
are identical with attributes which cannot belong to
E,
e. g.
C
with
H,
we have the first figure with its minor premiss negative. If attributes which cannot belong to either term are identical, e. g.
C
and
H,
both premisses are negative,
(35)
either in the first or in the middle figure. But no syllogism is possible in this way.

It is evident too that we must find out which terms in this inquiry are identical, not which are different or contrary, first because the object of our investigation is the middle term,
(40)
and the middle term must be not diverse but identical. Secondly, wherever it happens that a syllogism results from taking contraries or terms which cannot belong to the same thing, all arguments can be reduced to the aforesaid moods, e. g. if
B
and
F
are contraries or cannot belong to the same thing.
[45a]
For if these are taken, a syllogism will be formed to prove that
A
belongs to none of the
E
s,
(5)
not however from the premisses taken but in the aforesaid mood. For
B
will belong to all
A
and to no
E.
Consequently
B
must be identical with one of the
H
s. Again, if
B
and
G
cannot belong to the same thing, it follows that
A
will not belong to some of the
E
s: for then too we shall have the middle figure: for
B
will belong to all
A
and to no
G.
(10)
Consequently
B
must be identical with some of the
H
s. For the fact that
B
and
G
cannot belong to the same thing differs in no way from the fact that
B
is identical with some of the
H
s: for that includes everything which cannot belong to
E.
(15)

It is clear then that from the inquiries taken by themselves no syllogism results; but if
B
and
F
are contraries
B
must be identical with one of the
H
s, and the syllogism results through these terms.
(20)
It turns out then that those who inquire in this manner are looking gratuitously for some other way than the necessary way because they have failed to observe the identity of the
B
s with the
H
s.