by Aristotle
no refutation is possible. For if a refutation were possible, a
syllogism must be possible; although if a syllogism is possible it
does not follow that a refutation is possible. Similarly refutation is
not possible if nothing is conceded universally: since the fields of
refutation and syllogism are defined in the same way.
21
It sometimes happens that just as we are deceived in the arrangement
of the terms, so error may arise in our thought about them, e.g. if it
is possible that the same predicate should belong to more than one
subject immediately, but although knowing the one, a man may forget
the other and think the opposite true. Suppose that A belongs to B and
to C in virtue of their nature, and that B and C belong to all D in
the same way. If then a man thinks that A belongs to all B, and B to
D, but A to no C, and C to all D, he will both know and not know the
same thing in respect of the same thing. Again if a man were to make a
mistake about the members of a single series; e.g. suppose A belongs
to B, B to C, and C to D, but some one thinks that A belongs to all B,
but to no C: he will both know that A belongs to D, and think that
it does not. Does he then maintain after this simply that what he
knows, he does not think? For he knows in a way that A belongs to C
through B, since the part is included in the whole; so that what he
knows in a way, this he maintains he does not think at all: but that
is impossible.
In the former case, where the middle term does not belong to the
same series, it is not possible to think both the premisses with
reference to each of the two middle terms: e.g. that A belongs to
all B, but to no C, and both B and C belong to all D. For it turns out
that the first premiss of the one syllogism is either wholly or
partially contrary to the first premiss of the other. For if he thinks
that A belongs to everything to which B belongs, and he knows that B
belongs to D, then he knows that A belongs to D. Consequently if again
he thinks that A belongs to nothing to which C belongs, he thinks that
A does not belong to some of that to which B belongs; but if he thinks
that A belongs to everything to which B belongs, and again thinks that
A does not belong to some of that to which B belongs, these beliefs
are wholly or partially contrary. In this way then it is not
possible to think; but nothing prevents a man thinking one premiss
of each syllogism of both premisses of one of the two syllogisms: e.g.
A belongs to all B, and B to D, and again A belongs to no C. An
error of this kind is similar to the error into which we fall
concerning particulars: e.g. if A belongs to all B, and B to all C,
A will belong to all C. If then a man knows that A belongs to
everything to which B belongs, he knows that A belongs to C. But
nothing prevents his being ignorant that C exists; e.g. let A stand
for two right angles, B for triangle, C for a particular diagram of
a triangle. A man might think that C did not exist, though he knew
that every triangle contains two right angles; consequently he will
know and not know the same thing at the same time. For the
expression 'to know that every triangle has its angles equal to two
right angles' is ambiguous, meaning to have the knowledge either of
the universal or of the particulars. Thus then he knows that C
contains two right angles with a knowledge of the universal, but not
with a knowledge of the particulars; consequently his knowledge will
not be contrary to his ignorance. The argument in the Meno that
learning is recollection may be criticized in a similar way. For it
never happens that a man starts with a foreknowledge of the
particular, but along with the process of being led to see the general
principle he receives a knowledge of the particulars, by an act (as it
were) of recognition. For we know some things directly; e.g. that
the angles are equal to two right angles, if we know that the figure
is a triangle. Similarly in all other cases.
By a knowledge of the universal then we see the particulars, but
we do not know them by the kind of knowledge which is proper to
them; consequently it is possible that we may make mistakes about
them, but not that we should have the knowledge and error that are
contrary to one another: rather we have the knowledge of the universal
but make a mistake in apprehending the particular. Similarly in the
cases stated above. The error in respect of the middle term is not
contrary to the knowledge obtained through the syllogism, nor is the
thought in respect of one middle term contrary to that in respect of
the other. Nothing prevents a man who knows both that A belongs to the
whole of B, and that B again belongs to C, thinking that A does not
belong to C, e.g. knowing that every mule is sterile and that this
is a mule, and thinking that this animal is with foal: for he does not
know that A belongs to C, unless he considers the two propositions
together. So it is evident that if he knows the one and does not
know the other, he will fall into error. And this is the relation of
knowledge of the universal to knowledge of the particular. For we know
no sensible thing, once it has passed beyond the range of our
senses, even if we happen to have perceived it, except by means of the
universal and the possession of the knowledge which is proper to the
particular, but without the actual exercise of that knowledge. For
to know is used in three senses: it may mean either to have
knowledge of the universal or to have knowledge proper to the matter
in hand or to exercise such knowledge: consequently three kinds of
error also are possible. Nothing then prevents a man both knowing
and being mistaken about the same thing, provided that his knowledge
and his error are not contrary. And this happens also to the man whose
knowledge is limited to each of the premisses and who has not
previously considered the particular question. For when he thinks that
the mule is with foal he has not the knowledge in the sense of its
actual exercise, nor on the other hand has his thought caused an error
contrary to his knowledge: for the error contrary to the knowledge
of the universal would be a syllogism.
But he who thinks the essence of good is the essence of bad will
think the same thing to be the essence of good and the essence of bad.
Let A stand for the essence of good and B for the essence of bad,
and again C for the essence of good. Since then he thinks B and C
identical, he will think that C is B, and similarly that B is A,
consequently that C is A. For just as we saw that if B is true of
all of which C is true, and A is true of all of which B is true, A
is true of C, similarly with the word 'think'. Similarly also with the
word 'is'; for we saw that if C is the same as B, and B as A, C is the
same as A. Similarly therefore with 'opine'. Perhaps then this is
necessary if a man will grant the first point. But presumably that
is false, that any one could suppose the essence of good to be the
<
br /> essence of bad, save incidentally. For it is possible to think this in
many different ways. But we must consider this matter better.
22
Whenever the extremes are convertible it is necessary that the
middle should be convertible with both. For if A belongs to C
through B, then if A and C are convertible and C belongs everything to
which A belongs, B is convertible with A, and B belongs to
everything to which A belongs, through C as middle, and C is
convertible with B through A as middle. Similarly if the conclusion is
negative, e.g. if B belongs to C, but A does not belong to B,
neither will A belong to C. If then B is convertible with A, C will be
convertible with A. Suppose B does not belong to A; neither then
will C: for ex hypothesi B belonged to all C. And if C is
convertible with B, B is convertible also with A, for C is said of
that of all of which B is said. And if C is convertible in relation to
A and to B, B also is convertible in relation to A. For C belongs to
that to which B belongs: but C does not belong to that to which A
belongs. And this alone starts from the conclusion; the preceding
moods do not do so as in the affirmative syllogism. Again if A and B
are convertible, and similarly C and D, and if A or C must belong to
anything whatever, then B and D will be such that one or other belongs
to anything whatever. For since B belongs to that to which A
belongs, and D belongs to that to which C belongs, and since A or C
belongs to everything, but not together, it is clear that B or D
belongs to everything, but not together. For example if that which
is uncreated is incorruptible and that which is incorruptible is
uncreated, it is necessary that what is created should be
corruptible and what is corruptible should have been created. For
two syllogisms have been put together. Again if A or B belongs to
everything and if C or D belongs to everything, but they cannot belong
together, then when A and C are convertible B and D are convertible.
For if B does not belong to something to which D belongs, it is
clear that A belongs to it. But if A then C: for they are convertible.
Therefore C and D belong together. But this is impossible. When A
belongs to the whole of B and to C and is affirmed of nothing else,
and B also belongs to all C, it is necessary that A and B should be
convertible: for since A is said of B and C only, and B is affirmed
both of itself and of C, it is clear that B will be said of everything
of which A is said, except A itself. Again when A and B belong to
the whole of C, and C is convertible with B, it is necessary that A
should belong to all B: for since A belongs to all C, and C to B by
conversion, A will belong to all B.
When, of two opposites A and B, A is preferable to B, and
similarly D is preferable to C, then if A and C together are
preferable to B and D together, A must be preferable to D. For A is an
object of desire to the same extent as B is an object of aversion,
since they are opposites: and C is similarly related to D, since
they also are opposites. If then A is an object of desire to the
same extent as D, B is an object of aversion to the same extent as C
(since each is to the same extent as each-the one an object of
aversion, the other an object of desire). Therefore both A and C
together, and B and D together, will be equally objects of desire or
aversion. But since A and C are preferable to B and D, A cannot be
equally desirable with D; for then B along with D would be equally
desirable with A along with C. But if D is preferable to A, then B
must be less an object of aversion than C: for the less is opposed
to the less. But the greater good and lesser evil are preferable to
the lesser good and greater evil: the whole BD then is preferable to
the whole AC. But ex hypothesi this is not so. A then is preferable to
D, and C consequently is less an object of aversion than B. If then
every lover in virtue of his love would prefer A, viz. that the
beloved should be such as to grant a favour, and yet should not
grant it (for which C stands), to the beloved's granting the favour
(represented by D) without being such as to grant it (represented by
B), it is clear that A (being of such a nature) is preferable to
granting the favour. To receive affection then is preferable in love
to sexual intercourse. Love then is more dependent on friendship
than on intercourse. And if it is most dependent on receiving
affection, then this is its end. Intercourse then either is not an end
at all or is an end relative to the further end, the receiving of
affection. And indeed the same is true of the other desires and arts.
23
It is clear then how the terms are related in conversion, and in
respect of being in a higher degree objects of aversion or of
desire. We must now state that not only dialectical and
demonstrative syllogisms are formed by means of the aforesaid figures,
but also rhetorical syllogisms and in general any form of
persuasion, however it may be presented. For every belief comes either
through syllogism or from induction.
Now induction, or rather the syllogism which springs out of
induction, consists in establishing syllogistically a relation between
one extreme and the middle by means of the other extreme, e.g. if B is
the middle term between A and C, it consists in proving through C that
A belongs to B. For this is the manner in which we make inductions.
For example let A stand for long-lived, B for bileless, and C for
the particular long-lived animals, e.g. man, horse, mule. A then
belongs to the whole of C: for whatever is bileless is long-lived. But
B also ('not possessing bile') belongs to all C. If then C is
convertible with B, and the middle term is not wider in extension,
it is necessary that A should belong to B. For it has already been
proved that if two things belong to the same thing, and the extreme is
convertible with one of them, then the other predicate will belong
to the predicate that is converted. But we must apprehend C as made up
of all the particulars. For induction proceeds through an
enumeration of all the cases.
Such is the syllogism which establishes the first and immediate
premiss: for where there is a middle term the syllogism proceeds
through the middle term; when there is no middle term, through
induction. And in a way induction is opposed to syllogism: for the
latter proves the major term to belong to the third term by means of
the middle, the former proves the major to belong to the middle by
means of the third. In the order of nature, syllogism through the
middle term is prior and better known, but syllogism through induction
is clearer to us.
24
We have an 'example' when the major term is proved to belong to
the middle by means of a term which resembles the third. It ought to
be known both that the middle belongs to the third term, and that
the first belongs to that which resembles the third. For example let A
be evil
, B making war against neighbours, C Athenians against Thebans,
D Thebans against Phocians. If then we wish to prove that to fight
with the Thebans is an evil, we must assume that to fight against
neighbours is an evil. Evidence of this is obtained from similar
cases, e.g. that the war against the Phocians was an evil to the
Thebans. Since then to fight against neighbours is an evil, and to
fight against the Thebans is to fight against neighbours, it is
clear that to fight against the Thebans is an evil. Now it is clear
that B belongs to C and to D (for both are cases of making war upon
one's neighbours) and that A belongs to D (for the war against the
Phocians did not turn out well for the Thebans): but that A belongs to
B will be proved through D. Similarly if the belief in the relation of
the middle term to the extreme should be produced by several similar
cases. Clearly then to argue by example is neither like reasoning from
part to whole, nor like reasoning from whole to part, but rather
reasoning from part to part, when both particulars are subordinate
to the same term, and one of them is known. It differs from induction,
because induction starting from all the particular cases proves (as we
saw) that the major term belongs to the middle, and does not apply the
syllogistic conclusion to the minor term, whereas argument by
example does make this application and does not draw its proof from
all the particular cases.
25
By reduction we mean an argument in which the first term clearly
belongs to the middle, but the relation of the middle to the last term
is uncertain though equally or more probable than the conclusion; or
again an argument in which the terms intermediate between the last
term and the middle are few. For in any of these cases it turns out
that we approach more nearly to knowledge. For example let A stand for
what can be taught, B for knowledge, C for justice. Now it is clear
that knowledge can be taught: but it is uncertain whether virtue is
knowledge. If now the statement BC is equally or more probable than
AC, we have a reduction: for we are nearer to knowledge, since we have