Aristotle - Works
[Translated under the editorship of W. D. Ross]
Organon I - Categories
2
Organon II - On Interpretation
47
Organon III - Prior Analytics
81
Organon IV - Posterior Analytics
221
Organon V - Topics
326
Organon VI - On Sophistical Refutations
533
Physics
602
On the Heavens
852
On Generation and Corruption
952
Meteorology
1033
On the Soul
1159
Parva Naturalia
1256
History of Animals
1389
On the Parts of Animals
1791
On the Motion of Animals
1966
On the Gait of Animals
1984
On the Generation of Animals
2 009
Metaphysics
2 205
Nicomachean Ethics
2 536
Politics
2 788
Athenian Constitution
3 050
Rhetoric
3 132
Poetics
3 308
Aristotle - Categories
[Translated by E. M. Edghill]
Things are said to be named 'equivocally' when, though they
have a common name, the definition corresponding with the
name differs for each. Thus, a real man and a figure in a picture
can both lay claim to the name 'animal'; yet these are
equivocally so named, for, though they have a common name,
the definition corresponding with the name differs for each. For
should any one define in what sense each is an animal, his
definition in the one case will be appropriate to that case only.
On the other hand, things are said to be named 'univocally'
which have both the name and the definition answering to the
name in common. A man and an ox are both 'animal', and these
are univocally so named, inasmuch as not only the name, but
also the definition, is the same in both cases: for if a man
should state in what sense each is an animal, the statement in
the one case would be identical with that in the other.
Things are said to be named 'derivatively', which derive their
name from some other name, but differ from it in termination.
Thus the grammarian derives his name from the word
'grammar', and the courageous man from the word 'courage'.
Forms of speech are either simple or composite. Examples of
the latter are such expressions as 'the man runs', 'the man
wins'; of the former 'man', 'ox', 'runs', 'wins'.
Of things themselves some are predicable of a subject, and are
never present in a subject. Thus 'man' is predicable of the
individual man, and is never present in a subject.
By being 'present in a subject' I do not mean present as parts
are present in a whole, but being incapable of existence apart
from the said subject.
Some things, again, are present in a subject, but are never
predicable of a subject. For instance, a certain point of
grammatical knowledge is present in the mind, but is not
predicable of any subject; or again, a certain whiteness may be
present in the body (for colour requires a material basis), yet it
is never predicable of anything.
Other things, again, are both predicable of a subject and present
in a subject. Thus while knowledge is present in the human
mind, it is predicable of grammar.
There is, lastly, a class of things which are neither present in a
subject nor predicable of a subject, such as the individual man
or the individual horse. But, to speak more generally, that which
is individual and has the character of a unit is never predicable
of a subject. Yet in some cases there is nothing to prevent such
being present in a subject. Thus a certain point of grammatical
knowledge is present in a subject.
When one thing is predicated of another, all that which is
predicable of the predicate will be predicable also of the subject.
Thus, 'man' is predicated of the individual man; but 'animal' is
predicated of 'man'; it will, therefore, be predicable of the
individual man also: for the individual man is both 'man' and
'animal'.
If genera are different and co-ordinate, their differentiae are
themselves different in kind. Take as an instance the genus
'animal' and the genus 'knowledge'. 'With feet', 'two-footed',
'winged', 'aquatic', are differentiae of 'animal'; the species of
knowledge are not distinguished by the same differentiae. One
species of knowledge does not differ from another in being
'two-footed'.
But where one genus is subordinate to another, there is nothing
to prevent their having the same differentiae: for the greater
class is predicated of the lesser, so that all the differentiae of
the predicate will be differentiae also of the subject.
Expressions which are in no way composite signify substance,
quantity, quality, relation, place, time, position, state, action, or
affection. To sketch my meaning roughly, examples of substance
are 'man' or 'the horse', of quantity, such terms as 'two cubits
long' or 'three cubits long', of quality, such attributes as 'white',
'grammatical'. 'Double', 'half, 'greater', fall under the category
of relation; 'in a the market place', 'in the Lyceum', under that of
place; 'yesterday', 'last year', under that of time. 'Lying', 'sitting',
are terms indicating position, 'shod', 'armed', state; 'to lance', 'to
cauterize', action; 'to be lanced', 'to be cauterized', affection.
No one of these terms, in and by itself, involves an affirmation;
it is by the combination of such terms that positive or negative
statements arise. For every assertion must, as is admitted, be
either true or false, whereas expressions which are not in any
way composite such as 'man', 'white', 'runs', 'wins', cannot be
either true or false.
Substance, in the truest and primary and most definite sense of
the word, is that which is neither predicable of a subject nor
present in a subject; for instance, the individual man or horse.
But in a secondary sense those things are called substances
within which, as species, the primary substances are included;
also those which, as genera, include the species. For instance,
the individual man is included in the species 'man', and the
genus to which the species belongs is 'animal'; these, therefore
- that is to say, the species 'man' and the genus 'animal, - are
termed secondary substances.
It is plain from what has been said that both the name and the
definition of the predicate must be predicable of the subject. For
instance, 'man' is predicted of the individual man. Now in this
case the name of the species man' is applied to the individual,
for we use the term 'man' in describing the individual; and the
definition of 'man' will also be predicated of the individual man,
for the individual man is both man and animal. Thus, both the
name and the definition of the species are predicable of the
individual.
With regard, on the other hand, to those things which are
present in a subject, it is generally the case that neither their
name nor their definition is predicable of that in which they are
present. Though, however, the definition is never predicable,
there is nothing in certain cases to prevent the name being
used. For instance, 'white' being present in a body is predicated
of that in which it is present, for a body is called white: the
definition, however, of the colour white' is never predicable of
the body.
Everything except primary substances is either predicable of a
primary substance or present in a primary substance. This
becomes evident by reference to particular instances which
occur. 'Animal' is predicated of the species 'man', therefore of
the individual man, for if there were no individual man of
whom it could be predicated, it could not be predicated of the
species 'man' at all. Again, colour is present in body, therefore in
individual bodies, for if there were no individual body in which
it was present, it could not be present in body at all. Thus
everything except primary substances is either predicated of
primary substances, or is present in them, and if these last did
not exist, it would be impossible for anything else to exist.
Of secondary substances, the species is more truly substance
than the genus, being more nearly related to primary substance.
For if any one should render an account of what a primary
substance is, he would render a more instructive account, and
one more proper to the subject, by stating the species than by
stating the genus. Thus, he would give a more instructive
account of an individual man by stating that he was man than
by stating that he was animal, for the former description is
peculiar to the individual in a greater degree, while the latter is
too general. Again, the man who gives an account of the nature
of an individual tree will give a more instructive account by
mentioning the species 'tree' than by mentioning the genus
'plant'.
Moreover, primary substances are most properly called
substances in virtue of the fact that they are the entities which
underlie every, else, and that everything else is either predicated
of them or present in them. Now the same relation which
subsists between primary substance and everything else
subsists also between the species and the genus: for the species
is to the genus as subject is to predicate, since the genus is
predicated of the species, whereas the species cannot be
predicated of the genus. Thus we have a second ground for
asserting that the species is more truly substance than the
genus.
Of species themselves, except in the case of such as are genera,
no one is more truly substance than another. We should not
give a more appropriate account of the individual man by
stating the species to which he belonged, than we should of an
individual horse by adopting the same method of definition. In
the same way, of primary substances, no one is more truly
substance than another; an individual man is not more truly
substance than an individual ox.
It is, then, with good reason that of all that remains, when we
exclude primary substances, we concede to species and genera
alone the name 'secondary substance', for these alone of all the
predicates convey a knowledge of primary substance. For it is by
stating the species or the genus that we appropriately define
any individual man; and we shall make our definition more
exact by stating the former than by stating the latter. All other
things that we state, such as that he is white, that he runs, and
so on, are irrelevant to the definition. Thus it is just that these
alone, apart from primary substances, should be called
substances.
Further, primary substances are most properly so called,
because they underlie and are the subjects of everything else.
Now the same relation that subsists between primary substance
and everything else subsists also between the species and the
genus to which the primary substance belongs, on the one
hand, and every attribute which is not included within these, on
the other. For these are the subjects of all such. If we call an
individual man 'skilled in grammar', the predicate is applicable
also to the species and to the genus to which he belongs. This
law holds good in all cases.
It is a common characteristic of all sub. stance that it is never
present in a subject. For primary substance is neither present in
a subject nor predicated of a subject; while, with regard to
secondary substances, it is clear from the following arguments
(apart from others) that they are not present in a subject. For
'man' is predicated of the individual man, but is not present in
any subject: for manhood is not present in the individual man.
In the same way, 'animal' is also predicated of the individual
man, but is not present in him. Again, when a thing is present
in a subject, though the name may quite well be applied to that
in which it is present, the definition cannot be applied. Yet of
secondary substances, not only the name, but also the
definition, applies to the subject: we should use both the
definition of the species and that of the genus with reference to
the individual man. Thus substance cannot be present in a
subject.
Yet this is not peculiar to substance, for it is also the case that
differentiae cannot be present in subjects. The characteristics
'terrestrial' and 'two-footed' are predicated of the species 'man',
but not present in it. For they are not in man. Moreover, the
definition of the differentia may be predicated of that of which
the differentia itself is predicated. For instance, if the
characteristic 'terrestrial' is predicated of the species 'man', the
definition also of that characteristic may be used to form the
predicate of the species 'man': for 'man' is terrestrial.
The fact that the parts of substances appear to be present in the
whole, as in a subject, should not make us apprehensive lest we
should have to admit that such parts are not substances: for in
explaining the phrase 'being present in a subject', we stated'
that we meant 'otherwise than as parts in a whole'.
It is the mark of substances and of differentiae that, in all
propositions of which they form the predicate, they are
predicated univocally. For all such propositions have for their
subject either the individual or the species. It is true that,
inasmuch as primary substance is not predicable of anything, it
can never form the predicate of any proposition. But of
secondary substances, the species is predicated of the
individual, the genus both of the species and of the individual.
Similarly the differentiae are predicated of the species and of
the individuals. Moreover, the definition of the species and that
of the genus are applicable to the primary substance, and that
of the genus to the species. For all that is predicated of the
predicate will be predicated also of the subject. Similarly, the
definition of the differentiae will be applicable to the species
and to the individuals. But it was stated above that the word
'univocal' was applied to those things which had both name
and definition in common. It is, therefore, established that in
every proposition, of which either substance or a differentia
forms the predicate, these are predicated univocally.
All substance appears to signify that which is individual. In the
case of primary substance this is indisputably true, for the thing
is a unit. In the case of secondary substances, when we speak,
for instance, of 'man' or 'animal', our form of speech gives the
impression that we are here also indicating that which is
individual, but the impression is not strictly true; for a
secondary substance is not an individual, but a class with a
certain qualification; for it is not one and single as a primary
substance is; the words 'man', 'animal', are predicable of more
than one subject.
Yet species and genus do not merely indicate quality, like the
term 'white'; 'white' indicates quality and nothing further, but
species and genus determine the quality with reference to a
substance: they signify substance qualitatively differentiated.
The determinate qualification covers a larger field in the case of
the genus that in that of the species: he who uses the word
'animal' is herein using a word of wider extension than he who
uses the word 'man'.
Another mark of substance is that it has no contrary. What
could be the contrary of any primary substance, such as the
individual man or animal? It has none. Nor can the species or
the genus have a contrary. Yet this characteristic is not peculiar
to substance, but is true of many other things, such as quantity.
There is nothing that forms the contrary of 'two cubits long' or
of 'three cubits long', or of 'ten', or of any such term. A man may
contend that 'much' is the contrary of 'little', or 'great' of 'small',
but of definite quantitative terms no contrary exists.
Substance, again, does not appear to admit of variation of
degree. I do not mean by this that one substance cannot be
more or less truly substance than another, for it has already
been stated' that this is the case; but that no single substance
admits of varying degrees within itself. For instance, one
particular substance, 'man', cannot be more or less man either
than himself at some other time or than some other man. One
man cannot be more man than another, as that which is white
may be more or less white than some other white object, or as
that which is beautiful may be more or less beautiful than some
other beautiful object. The same quality, moreover, is said to
10
subsist in a thing in varying degrees at different times. A body,
being white, is said to be whiter at one time than it was before,
or, being warm, is said to be warmer or less warm than at some
other time. But substance is not said to be more or less that
which it is: a man is not more truly a man at one time than he
was before, nor is anything, if it is substance, more or less what
it is. Substance, then, does not admit of variation of degree.
The most distinctive mark of substance appears to be that,
while remaining numerically one and the same, it is capable of
admitting contrary qualities. From among things other than
substance, we should find ourselves unable to bring forward any
which possessed this mark. Thus, one and the same colour
cannot be white and black. Nor can the same one action be
good and bad: this law holds good with everything that is not
substance. But one and the selfsame substance, while retaining
its identity, is yet capable of admitting contrary qualities. The
same individual person is at one time white, at another black, at
one time warm, at another cold, at one time good, at another
bad. This capacity is found nowhere else, though it might be
maintained that a statement or opinion was an exception to the
rule. The same statement, it is agreed, can be both true and
false. For if the statement 'he is sitting' is true, yet, when the
person in question has risen, the same statement will be false.
The same applies to opinions. For if any one thinks truly that a
person is sitting, yet, when that person has risen, this same
opinion, if still held, will be false. Yet although this exception
may be allowed, there is, nevertheless, a difference in the
manner in which the thing takes place. It is by themselves
changing that substances admit contrary qualities. It is thus
that that which was hot becomes cold, for it has entered into a
different state. Similarly that which was white becomes black,
and that which was bad good, by a process of change; and in the
same way in all other cases it is by changing that substances
are capable of admitting contrary qualities. But statements and
11
opinions themselves remain unaltered in all respects: it is by
the alteration in the facts of the case that the contrary quality
comes to be theirs. The statement 'he is sitting' remains
unaltered, but it is at one time true, at another false, according
to circumstances. What has been said of statements applies
also to opinions. Thus, in respect of the manner in which the
thing takes place, it is the peculiar mark of substance that it
should be capable of admitting contrary qualities; for it is by
itself changing that it does so.
If, then, a man should make this exception and contend that
statements and opinions are capable of admitting contrary
qualities, his contention is unsound. For statements and
opinions are said to have this capacity, not because they
themselves undergo modification, but because this modification
occurs in the case of something else. The truth or falsity of a
statement depends on facts, and not on any power on the part
of the statement itself of admitting contrary qualities. In short,
there is nothing which can alter the nature of statements and
opinions. As, then, no change takes place in themselves, these
cannot be said to be capable of admitting contrary qualities.
But it is by reason of the modification which takes place within
the substance itself that a substance is said to be capable of
admitting contrary qualities; for a substance admits within
itself either disease or health, whiteness or blackness. It is in
this sense that it is said to be capable of admitting contrary
qualities.
To sum up, it is a distinctive mark of substance, that, while
remaining numerically one and the same, it is capable of
admitting contrary qualities, the modification taking place
through a change in the substance itself.
Let these remarks suffice on the subject of substance.
12
Quantity is either discrete or continuous. Moreover, some
quantities are such that each part of the whole has a relative
position to the other parts: others have within them no such
relation of part to part.
Instances of discrete quantities are number and speech; of
continuous, lines, surfaces, solids, and, besides these, time and
place.
In the case of the parts of a number, there is no common
boundary at which they join. For example: two fives make ten,
but the two fives have no common boundary, but are separate;
the parts three and seven also do not join at any boundary. Nor,
to generalize, would it ever be possible in the case of number
that there should be a common boundary among the parts; they
are always separate. Number, therefore, is a discrete quantity.
The same is true of speech. That speech is a quantity is evident:
for it is measured in long and short syllables. I mean here that
speech which is vocal. Moreover, it is a discrete quantity for its
parts have no common boundary. There is no common
boundary at which the syllables join, but each is separate and
distinct from the rest.
A line, on the other hand, is a continuous quantity, for it is
possible to find a common boundary at which its parts join. In
the case of the line, this common boundary is the point; in the
case of the plane, it is the line: for the parts of the plane have
also a common boundary. Similarly you can find a common
boundary in the case of the parts of a solid, namely either a line
or a plane.
13
Space and time also belong to this class of quantities. Time,
past, present, and future, forms a continuous whole. Space,
likewise, is a continuous quantity; for the parts of a solid occupy
a certain space, and these have a common boundary; it follows
that the parts of space also, which are occupied by the parts of
the solid, have the same common boundary as the parts of the
solid. Thus, not only time, but space also, is a continuous
quantity, for its parts have a common boundary.
Quantities consist either of parts which bear a relative position
each to each, or of parts which do not. The parts of a line bear a
relative position to each other, for each lies somewhere, and it
would be possible to distinguish each, and to state the position
of each on the plane and to explain to what sort of part among
the rest each was contiguous. Similarly the parts of a plane
have position, for it could similarly be stated what was the
position of each and what sort of parts were contiguous. The
same is true with regard to the solid and to space. But it would
be impossible to show that the arts of a number had a relative
position each to each, or a particular position, or to state what
parts were contiguous. Nor could this be done in the case of
time, for none of the parts of time has an abiding existence, and
that which does not abide can hardly have position. It would be
better to say that such parts had a relative order, in virtue of one
being prior to another. Similarly with number: in counting, 'one'
is prior to 'two', and 'two' to 'three', and thus the parts of
number may be said to possess a relative order, though it would
be impossible to discover any distinct position for each. This
holds good also in the case of speech. None of its parts has an
abiding existence: when once a syllable is pronounced, it is not
possible to retain it, so that, naturally, as the parts do not abide,
they cannot have position. Thus, some quantities consist of
parts which have position, and some of those which have not.
14
Strictly speaking, only the things which I have mentioned
belong to the category of quantity: everything else that is called
quantitative is a quantity in a secondary sense. It is because we
have in mind some one of these quantities, properly so called,
that we apply quantitative terms to other things. We speak of
what is white as large, because the surface over which the
white extends is large; we speak of an action or a process as
lengthy, because the time covered is long; these things cannot
in their own right claim the quantitative epithet. For instance,
should any one explain how long an action was, his statement
would be made in terms of the time taken, to the effect that it
lasted a year, or something of that sort. In the same way, he
would explain the size of a white object in terms of surface, for
he would state the area which it covered. Thus the things
already mentioned, and these alone, are in their intrinsic nature
quantities; nothing else can claim the name in its own right,
but, if at all, only in a secondary sense.
Quantities have no contraries. In the case of definite quantities
this is obvious; thus, there is nothing that is the contrary of 'two
cubits long' or of 'three cubits long', or of a surface, or of any
such quantities. A man might, indeed, argue that 'much' was
the contrary of 'little', and 'great' of 'small'. But these are not
quantitative, but relative; things are not great or small
absolutely, they are so called rather as the result of an act of
comparison. For instance, a mountain is called small, a grain
large, in virtue of the fact that the latter is greater than others of
its kind, the former less. Thus there is a reference here to an
external standard, for if the terms 'great' and 'small' were used
absolutely, a mountain would never be called small or a grain
large. Again, we say that there are many people in a village, and
few in Athens, although those in the city are many times as
numerous as those in the village: or we say that a house has
many in it, and a theatre few, though those in the theatre far
outnumber those in the house. The terms 'two cubits long,
15
"three cubits long,' and so on indicate quantity, the terms 'great'
and 'small' indicate relation, for they have reference to an
external standard. It is, therefore, plain that these are to be
classed as relative.
Again, whether we define them as quantitative or not, they
have no contraries: for how can there be a contrary of an
attribute which is not to be apprehended in or by itself, but only
by reference to something external? Again, if 'great' and 'small'
are contraries, it will come about that the same subject can
admit contrary qualities at one and the same time, and that
things will themselves be contrary to themselves. For it
happens at times that the same thing is both small and great.
For the same thing may be small in comparison with one thing,
and great in comparison with another, so that the same thing
comes to be both small and great at one and the same time, and
is of such a nature as to admit contrary qualities at one and the
same moment. Yet it was agreed, when substance was being
discussed, that nothing admits contrary qualities at one and the
same moment. For though substance is capable of admitting
contrary qualities, yet no one is at the same time both sick and
healthy, nothing is at the same time both white and black. Nor
is there anything which is qualified in contrary ways at one and
the same time.
Moreover, if these were contraries, they would themselves be
contrary to themselves. For if 'great' is the contrary of 'small',
and the same thing is both great and small at the same time,
then 'small' or 'great' is the contrary of itself. But this is
impossible. The term 'great', therefore, is not the contrary of the
term 'small', nor 'much' of 'little'. And even though a man
should call these terms not relative but quantitative, they would
not have contraries.
16
It is in the case of space that quantity most plausibly appears to
admit of a contrary. For men define the term 'above' as the
contrary of 'below', when it is the region at the centre they
mean by 'below'; and this is so, because nothing is farther from
the extremities of the universe than the region at the centre.
Indeed, it seems that in defining contraries of every kind men
have recourse to a spatial metaphor, for they say that those
things are contraries which, within the same class, are
separated by the greatest possible distance.
Quantity does not, it appears, admit of variation of degree. One
thing cannot be two cubits long in a greater degree than
another. Similarly with regard to number: what is 'three' is not
more truly three than what is 'five' is five; nor is one set of three
more truly three than another set. Again, one period of time is
not said to be more truly time than another. Nor is there any
other kind of quantity, of all that have been mentioned, with
regard to which variation of degree can be predicated. The
category of quantity, therefore, does not admit of variation of
degree.
The most distinctive mark of quantity is that equality and
inequality are predicated of it. Each of the aforesaid quantities
is said to be equal or unequal. For instance, one solid is said to
be equal or unequal to another; number, too, and time can have
these terms applied to them, indeed can all those kinds of
quantity that have been mentioned.
That which is not a quantity can by no means, it would seem,
be termed equal or unequal to anything else. One particular
disposition or one particular quality, such as whiteness, is by no
means compared with another in terms of equality and
inequality but rather in terms of similarity. Thus it is the
distinctive mark of quantity that it can be called equal and
unequal.
17
Those things are called relative, which, being either said to be of
something else or related to something else, are explained by
reference to that other thing. For instance, the word 'superior' is
explained by reference to something else, for it is superiority
over something else that is meant. Similarly, the expression
'double' has this external reference, for it is the double of
something else that is meant. So it is with everything else of
this kind. There are, moreover, other relatives, e.g. habit,
disposition, perception, knowledge, and attitude. The
significance of all these is explained by a reference to
something else and in no other way. Thus, a habit is a habit of
something, knowledge is knowledge of something, attitude is
the attitude of something. So it is with all other relatives that
have been mentioned. Those terms, then, are called relative, the
nature of which is explained by reference to something else, the
preposition 'of or some other preposition being used to indicate
the relation. Thus, one mountain is called great in comparison
with son with another; for the mountain claims this attribute by
comparison with something. Again, that which is called similar
must be similar to something else, and all other such attributes
have this external reference. It is to be noted that lying and
standing and sitting are particular attitudes, but attitude is itself
a relative term. To lie, to stand, to be seated, are not themselves
attitudes, but take their name from the aforesaid attitudes.
It is possible for relatives to have contraries. Thus virtue has a
contrary, vice, these both being relatives; knowledge, too, has a
contrary, ignorance. But this is not the mark of all relatives;
'double' and 'triple' have no contrary, nor indeed has any such
term.
18
It also appears that relatives can admit of variation of degree.
For 'like' and 'unlike', 'equal' and 'unequal', have the
modifications 'more' and 'less' applied to them, and each of
these is relative in character: for the terms 'like' and 'unequal'
bear 'unequal' bear a reference to something external. Yet,
again, it is not every relative term that admits of variation of
degree. No term such as 'double' admits of this modification. All
relatives have correlatives: by the term 'slave' we mean the
slave of a master, by the term 'master', the master of a slave; by
'double', the double of its hall; by 'half, the half of its double; by
'greater', greater than that which is less; by 'less,' less than that
which is greater.
So it is with every other relative term; but the case we use to
express the correlation differs in some instances. Thus, by
knowledge we mean knowledge the knowable; by the knowable,
that which is to be apprehended by knowledge; by perception,
perception of the perceptible; by the perceptible, that which is
apprehended by perception.
Sometimes, however, reciprocity of correlation does not appear
to exist. This comes about when a blunder is made, and that to
which the relative is related is not accurately stated. If a man
states that a wing is necessarily relative to a bird, the connexion
between these two will not be reciprocal, for it will not be
possible to say that a bird is a bird by reason of its wings. The
reason is that the original statement was inaccurate, for the
wing is not said to be relative to the bird qua bird, since many
creatures besides birds have wings, but qua winged creature. If,
then, the statement is made accurate, the connexion will be
reciprocal, for we can speak of a wing, having reference
necessarily to a winged creature, and of a winged creature as
being such because of its wings.
19
Occasionally, perhaps, it is necessary to coin words, if no word
exists by which a correlation can adequately be explained. If we
define a rudder as necessarily having reference to a boat, our
definition will not be appropriate, for the rudder does not have
this reference to a boat qua boat, as there are boats which have
no rudders. Thus we cannot use the terms reciprocally, for the
word 'boat' cannot be said to find its explanation in the word
'rudder'. As there is no existing word, our definition would
perhaps be more accurate if we coined some word like
'ruddered' as the correlative of 'rudder'. If we express ourselves
thus accurately, at any rate the terms are reciprocally
connected, for the 'ruddered' thing is 'ruddered' in virtue of its
rudder. So it is in all other cases. A head will be more accurately
defined as the correlative of that which is 'headed', than as that
of an animal, for the animal does not have a head qua animal,
since many animals have no head.
Thus we may perhaps most easily comprehend that to which a
thing is related, when a name does not exist, if, from that which
has a name, we derive a new name, and apply it to that with
which the first is reciprocally connected, as in the aforesaid
instances, when we derived the word 'winged' from 'wing' and
from 'rudder'.
All relatives, then, if properly defined, have a correlative. I add
this condition because, if that to which they are related is stated
as haphazard and not accurately, the two are not found to be
interdependent. Let me state what I mean more clearly. Even in
the case of acknowledged correlatives, and where names exist
for each, there will be no interdependence if one of the two is
denoted, not by that name which expresses the correlative
notion, but by one of irrelevant significance. The term 'slave,' if
defined as related, not to a master, but to a man, or a biped, or
anything of that sort, is not reciprocally connected with that in
relation to which it is defined, for the statement is not exact.
20
Further, if one thing is said to be correlative with another, and
the terminology used is correct, then, though all irrelevant
attributes should be removed, and only that one attribute left in
virtue of which it was correctly stated to be correlative with that
other, the stated correlation will still exist. If the correlative of
'the slave' is said to be 'the master', then, though all irrelevant
attributes of the said 'master', such as 'biped', 'receptive of
knowledge', 'human', should be removed, and the attribute
'master' alone left, the stated correlation existing between him
and the slave will remain the same, for it is of a master that a
slave is said to be the slave. On the other hand, if, of two
correlatives, one is not correctly termed, then, when all other
attributes are removed and that alone is left in virtue of which it
was stated to be correlative, the stated correlation will be found
to have disappeared.
For suppose the correlative of 'the slave' should be said to be
'the man', or the correlative of 'the wing"the bird'; if the
attribute 'master' be withdrawn from' the man', the correlation
between 'the man' and 'the slave' will cease to exist, for if the
man is not a master, the slave is not a slave. Similarly, if the
attribute 'winged' be withdrawn from 'the bird', 'the wing' will
no longer be relative; for if the so-called correlative is not
winged, it follows that 'the wing' has no correlative.
Thus it is essential that the correlated terms should be exactly
designated; if there is a name existing, the statement will be
easy; if not, it is doubtless our duty to construct names. When
the terminology is thus correct, it is evident that all correlatives
are interdependent.
Correlatives are thought to come into existence simultaneously.
This is for the most part true, as in the case of the double and
the half. The existence of the half necessitates the existence of
that of which it is a half. Similarly the existence of a master
21
necessitates the existence of a slave, and that of a slave implies
that of a master; these are merely instances of a general rule.
Moreover, they cancel one another; for if there is no double it
follows that there is no half, and vice versa; this rule also
applies to all such correlatives. Yet it does not appear to be true
in all cases that correlatives come into existence
simultaneously. The object of knowledge would appear to exist
before knowledge itself, for it is usually the case that we acquire
knowledge of objects already existing; it would be difficult, if
not impossible, to find a branch of knowledge the beginning of
the existence of which was contemporaneous with that of its
object.
Again, while the object of knowledge, if it ceases to exist,
cancels at the same time the knowledge which was its
correlative, the converse of this is not true. It is true that if the
object of knowledge does not exist there can be no knowledge:
for there will no longer be anything to know. Yet it is equally
true that, if knowledge of a certain object does not exist, the
object may nevertheless quite well exist. Thus, in the case of the
squaring of the circle, if indeed that process is an object of
knowledge, though it itself exists as an object of knowledge, yet
the knowledge of it has not yet come into existence. Again, if all
animals ceased to exist, there would be no knowledge, but there
might yet be many objects of knowledge.
This is likewise the case with regard to perception: for the
object of perception is, it appears, prior to the act of perception.
If the perceptible is annihilated, perception also will cease to
exist; but the annihilation of perception does not cancel the
existence of the perceptible. For perception implies a body
perceived and a body in which perception takes place. Now if
that which is perceptible is annihilated, it follows that the body
is annihilated, for the body is a perceptible thing; and if the
body does not exist, it follows that perception also ceases to
22
exist. Thus the annihilation of the perceptible involves that of
perception.
But the annihilation of perception does not involve that of the
perceptible. For if the animal is annihilated, it follows that
perception also is annihilated, but perceptibles such as body,
heat, sweetness, bitterness, and so on, will remain.
Again, perception is generated at the same time as the
perceiving subject, for it comes into existence at the same time
as the animal. But the perceptible surely exists before
perception; for fire and water and such elements, out of which
the animal is itself composed, exist before the animal is an
animal at all, and before perception. Thus it would seem that
the perceptible exists before perception.
It may be questioned whether it is true that no substance is
relative, as seems to be the case, or whether exception is to be
made in the case of certain secondary substances. With regard
to primary substances, it is quite true that there is no such
possibility, for neither wholes nor parts of primary substances
are relative. The individual man or ox is not defined with
reference to something external. Similarly with the parts: a
particular hand or head is not defined as a particular hand or
head of a particular person, but as the hand or head of a
particular person. It is true also, for the most part at least, in the
case of secondary substances; the species 'man' and the species
'ox' are not defined with reference to anything outside
themselves. Wood, again, is only relative in so far as it is some
one's property, not in so far as it is wood. It is plain, then, that in
the cases mentioned substance is not relative. But with regard
to some secondary substances there is a difference of opinion;
thus, such terms as 'head' and 'hand' are defined with reference
to that of which the things indicated are a part, and so it comes
about that these appear to have a relative character. Indeed, if
23
our definition of that which is relative was complete, it is very
difficult, if not impossible, to prove that no substance is relative.
If, however, our definition was not complete, if those things only
are properly called relative in the case of which relation to an
external object is a necessary condition of existence, perhaps
some explanation of the dilemma may be found.
The former definition does indeed apply to all relatives, but the
fact that a thing is explained with reference to something else
does not make it essentially relative.
From this it is plain that, if a man definitely apprehends a
relative thing, he will also definitely apprehend that to which it
is relative. Indeed this is self-evident: for if a man knows that
some particular thing is relative, assuming that we call that a
relative in the case of which relation to something is a
necessary condition of existence, he knows that also to which it
is related. For if he does not know at all that to which it is
related, he will not know whether or not it is relative. This is
clear, moreover, in particular instances. If a man knows
definitely that such and such a thing is 'double', he will also
forthwith know definitely that of which it is the double. For if
there is nothing definite of which he knows it to be the double,
he does not know at all that it is double. Again, if he knows that
a thing is more beautiful, it follows necessarily that he will
forthwith definitely know that also than which it is more
beautiful. He will not merely know indefinitely that it is more
beautiful than something which is less beautiful, for this would
be supposition, not knowledge. For if he does not know
definitely that than which it is more beautiful, he can no longer
claim to know definitely that it is more beautiful than
something else which is less beautiful: for it might be that
nothing was less beautiful. It is, therefore, evident that if a man
apprehends some relative thing definitely, he necessarily knows
that also definitely to which it is related.
24
Now the head, the hand, and such things are substances, and it
is possible to know their essential character definitely, but it
does not necessarily follow that we should know that to which
they are related. It is not possible to know forthwith whose
head or hand is meant. Thus these are not relatives, and, this
being the case, it would be true to say that no substance is
relative in character. It is perhaps a difficult matter, in such
cases, to make a positive statement without more exhaustive
examination, but to have raised questions with regard to details
is not without advantage.
8
By 'quality' I mean that in virtue of which people are said to be
such and such.
Quality is a term that is used in many senses. One sort of
quality let us call 'habit' or 'disposition'. Habit differs from
disposition in being more lasting and more firmly established.
The various kinds of knowledge and of virtue are habits, for
knowledge, even when acquired only in a moderate degree, is, it
is agreed, abiding in its character and difficult to displace,
unless some great mental upheaval takes place, through disease
or any such cause. The virtues, also, such as justice, self-
restraint, and so on, are not easily dislodged or dismissed, so as
to give place to vice.
By a disposition, on the other hand, we mean a condition that is
easily changed and quickly gives place to its opposite. Thus,
heat, cold, disease, health, and so on are dispositions. For a man
is disposed in one way or another with reference to these, but
quickly changes, becoming cold instead of warm, ill instead of
well. So it is with all other dispositions also, unless through
25
lapse of time a disposition has itself become inveterate and
almost impossible to dislodge: in which case we should perhaps
go so far as to call it a habit.
It is evident that men incline to call those conditions habits
which are of a more or less permanent type and difficult to
displace; for those who are not retentive of knowledge, but
volatile, are not said to have such and such a 'habit' as regards
knowledge, yet they are disposed, we may say, either better or
worse, towards knowledge. Thus habit differs from disposition
in this, that while the latter in ephemeral, the former is
permanent and difficult to alter.
Habits are at the same time dispositions, but dispositions are
not necessarily habits. For those who have some specific habit
may be said also, in virtue of that habit, to be thus or thus
disposed; but those who are disposed in some specific way have
not in all cases the corresponding habit.
Another sort of quality is that in virtue of which, for example,
we call men good boxers or runners, or healthy or sickly: in fact
it includes all those terms which refer to inborn capacity or
incapacity. Such things are not predicated of a person in virtue
of his disposition, but in virtue of his inborn capacity or
incapacity to do something with ease or to avoid defeat of any
kind. Persons are called good boxers or good runners, not in
virtue of such and such a disposition, but in virtue of an inborn
capacity to accomplish something with ease. Men are called
healthy in virtue of the inborn capacity of easy resistance to
those unhealthy influences that may ordinarily arise; unhealthy,
in virtue of the lack of this capacity. Similarly with regard to
softness and hardness. Hardness is predicated of a thing
because it has that capacity of resistance which enables it to
withstand disintegration; softness, again, is predicated of a
thing by reason of the lack of that capacity.
26
A third class within this category is that of affective qualities
and affections. Sweetness, bitterness, sourness, are examples of
this sort of quality, together with all that is akin to these; heat,
moreover, and cold, whiteness, and blackness are affective
qualities. It is evident that these are qualities, for those things
that possess them are themselves said to be such and such by
reason of their presence. Honey is called sweet because it
contains sweetness; the body is called white because it contains
whiteness; and so in all other cases.
The term 'affective quality' is not used as indicating that those
things which admit these qualities are affected in any way.
Honey is not called sweet because it is affected in a specific way,
nor is this what is meant in any other instance. Similarly heat
and cold are called affective qualities, not because those things
which admit them are affected. What is meant is that these said
qualities are capable of producing an 'affection' in the way of
perception. For sweetness has the power of affecting the sense
of taste; heat, that of touch; and so it is with the rest of these
qualities.
Whiteness and blackness, however, and the other colours, are
not said to be affective qualities in this sense, but - because
they themselves are the results of an affection. It is plain that
many changes of colour take place because of affections. When
a man is ashamed, he blushes; when he is afraid, he becomes
pale, and so on. So true is this, that when a man is by nature
liable to such affections, arising from some concomitance of
elements in his constitution, it is a probable inference that he
has the corresponding complexion of skin. For the same
disposition of bodily elements, which in the former instance
was momentarily present in the case of an access of shame,
might be a result of a man's natural temperament, so as to
produce the corresponding colouring also as a natural
characteristic. All conditions, therefore, of this kind, if caused by
27
certain permanent and lasting affections, are called affective
qualities. For pallor and duskiness of complexion are called
qualities, inasmuch as we are said to be such and such in virtue
of them, not only if they originate in natural constitution, but
also if they come about through long disease or sunburn, and
are difficult to remove, or indeed remain throughout life. For in
the same way we are said to be such and such because of these.
Those conditions, however, which arise from causes which may
easily be rendered ineffective or speedily removed, are called,
not qualities, but affections: for we are not said to be such
virtue of them. The man who blushes through shame is not said
to be a constitutional blusher, nor is the man who becomes pale
through fear said to be constitutionally pale. He is said rather to
have been affected.
Thus such conditions are called affections, not qualities.
In like manner there are affective qualities and affections of the
soul. That temper with which a man is born and which has its
origin in certain deep-seated affections is called a quality. I
mean such conditions as insanity, irascibility, and so on: for
people are said to be mad or irascible in virtue of these.
Similarly those abnormal psychic states which are not inborn,
but arise from the concomitance of certain other elements, and
are difficult to remove, or altogether permanent, are called
qualities, for in virtue of them men are said to be such and
such.
Those, however, which arise from causes easily rendered
ineffective are called affections, not qualities. Suppose that a
man is irritable when vexed: he is not even spoken of as a bad-
tempered man, when in such circumstances he loses his
temper somewhat, but rather is said to be affected. Such
conditions are therefore termed, not qualities, but affections.
28
The fourth sort of quality is figure and the shape that belongs to
a thing; and besides this, straightness and curvedness and any
other qualities of this type; each of these defines a thing as
being such and such. Because it is triangular or quadrangular a
thing is said to have a specific character, or again because it is
straight or curved; in fact a thing's shape in every case gives rise
to a qualification of it.
Rarity and density, roughness and smoothness, seem to be
terms indicating quality: yet these, it would appear, really
belong to a class different from that of quality. For it is rather a
certain relative position of the parts composing the thing thus
qualified which, it appears, is indicated by each of these terms.
A thing is dense, owing to the fact that its parts are closely
combined with one another; rare, because there are interstices
between the parts; smooth, because its parts lie, so to speak,
evenly; rough, because some parts project beyond others.
There may be other sorts of quality, but those that are most
properly so called have, we may safely say, been enumerated.
These, then, are qualities, and the things that take their name
from them as derivatives, or are in some other way dependent
on them, are said to be qualified in some specific way. In most,
indeed in almost all cases, the name of that which is qualified is
derived from that of the quality. Thus the terms 'whiteness',
'grammar', 'justice', give us the adjectives 'white', 'grammatical',
'just', and so on.
There are some cases, however, in which, as the quality under
consideration has no name, it is impossible that those
possessed of it should have a name that is derivative. For
instance, the name given to the runner or boxer, who is so
called in virtue of an inborn capacity, is not derived from that of
any quality; for lob those capacities have no name assigned to
them. In this, the inborn capacity is distinct from the science,
29
with reference to which men are called, e.g. boxers or wrestlers.
Such a science is classed as a disposition; it has a name, and is
called 'boxing' or 'wrestling' as the case may be, and the name
given to those disposed in this way is derived from that of the
science. Sometimes, even though a name exists for the quality,
that which takes its character from the quality has a name that
is not a derivative. For instance, the upright man takes his
character from the possession of the quality of integrity, but the
name given him is not derived from the word 'integrity'. Yet this
does not occur often.
We may therefore state that those things are said to be
possessed of some specific quality which have a name derived
from that of the aforesaid quality, or which are in some other
way dependent on it.
One quality may be the contrary of another; thus justice is the
contrary of injustice, whiteness of blackness, and so on. The
things, also, which are said to be such and such in virtue of
these qualities, may be contrary the one to the other; for that
which is unjust is contrary to that which is just, that which is
white to that which is black. This, however, is not always the
case. Red, yellow, and such colours, though qualities, have no
contraries.
If one of two contraries is a quality, the other will also be a
quality. This will be evident from particular instances, if we
apply the names used to denote the other categories; for
instance, granted that justice is the contrary of injustice and
justice is a quality, injustice will also be a quality: neither
quantity, nor relation, nor place, nor indeed any other category
but that of quality, will be applicable properly to injustice. So it
is with all other contraries falling under the category of quality.
Qualities admit of variation of degree. Whiteness is predicated
of one thing in a greater or less degree than of another. This is
30
also the case with reference to justice. Moreover, one and the
same thing may exhibit a quality in a greater degree than it did
before: if a thing is white, it may become whiter.
Though this is generally the case, there are exceptions. For if we
should say that justice admitted of variation of degree,
difficulties might ensue, and this is true with regard to all those
qualities which are dispositions. There are some, indeed, who
dispute the possibility of variation here. They maintain that
justice and health cannot very well admit of variation of degree
themselves, but that people vary in the degree in which they
possess these qualities, and that this is the case with
grammatical learning and all those qualities which are classed
as dispositions. However that may be, it is an incontrovertible
fact that the things which in virtue of these qualities are said to
be what they are vary in the degree in which they possess them;
for one man is said to be better versed in grammar, or more
healthy or just, than another, and so on.
The qualities expressed by the terms 'triangular' and
'quadrangular' do not appear to admit of variation of degree,
nor indeed do any that have to do with figure. For those things
to which the definition of the triangle or circle is applicable are
all equally triangular or circular. Those, on the other hand, to
which the same definition is not applicable, cannot be said to
differ from one another in degree; the square is no more a circle
than the rectangle, for to neither is the definition of the circle
appropriate. In short, if the definition of the term proposed is
not applicable to both objects, they cannot be compared. Thus it
is not all qualities which admit of variation of degree.
Whereas none of the characteristics I have mentioned are
peculiar to quality, the fact that likeness and unlikeness can be
predicated with reference to quality only, gives to that category
its distinctive feature. One thing is like another only with
31
reference to that in virtue of which it is such and such; thus this
forms the peculiar mark of quality.
We must not be disturbed because it may be argued that,
though proposing to discuss the category of quality, we have
included in it many relative terms. We did say that habits and
dispositions were relative. In practically all such cases the genus
is relative, the individual not. Thus knowledge, as a genus, is
explained by reference to something else, for we mean a
knowledge of something. But particular branches of knowledge
are not thus explained. The knowledge of grammar is not
relative to anything external, nor is the knowledge of music, but
these, if relative at all, are relative only in virtue of their genera;
thus grammar is said be the knowledge of something, not the
grammar of something; similarly music is the knowledge of
something, not the music of something.
Thus individual branches of knowledge are not relative. And it
is because we possess these individual branches of knowledge
that we are said to be such and such. It is these that we actually
possess: we are called experts because we possess knowledge in
some particular branch. Those particular branches, therefore, of
knowledge, in virtue of which we are sometimes said to be such
and such, are themselves qualities, and are not relative. Further,
if anything should happen to fall within both the category of
quality and that of relation, there would be nothing
extraordinary in classing it under both these heads.
Action and affection both admit of contraries and also of
variation of degree. Heating is the contrary of cooling, being
heated of being cooled, being glad of being vexed. Thus they
32
admit of contraries. They also admit of variation of degree: for it
is possible to heat in a greater or less degree; also to be heated
in a greater or less degree. Thus action and affection also admit
of variation of degree. So much, then, is stated with regard to
these categories.
We spoke, moreover, of the category of position when we were
dealing with that of relation, and stated that such terms derived
their names from those of the corresponding attitudes.
As for the rest, time, place, state, since they are easily
intelligible, I say no more about them than was said at the
beginning, that in the category of state are included such states
as 'shod', 'armed', in that of place 'in the Lyceum' and so on, as
was explained before.
10
The proposed categories have, then, been adequately dealt with.
We must next explain the various senses in which the term
'opposite' is used. Things are said to be opposed in four senses:
(i) as correlatives to one another, (ii) as contraries to one
another, (iii) as privatives to positives, (iv) as affirmatives to
negatives.
Let me sketch my meaning in outline. An instance of the use of
the word 'opposite' with reference to correlatives is afforded by
the expressions 'double' and 'half; with reference to contraries
by 'bad' and 'good'. Opposites in the sense of 'privatives' and
'positives' are' blindness' and 'sight'; in the sense of
affirmatives and negatives, the propositions 'he sits', 'he does
not sit'.
33
(i) Pairs of opposites which fall under the category of relation
are explained by a reference of the one to the other, the
reference being indicated by the preposition 'of or by some
other preposition. Thus, double is a relative term, for that which
is double is explained as the double of something. Knowledge,
again, is the opposite of the thing known, in the same sense;
and the thing known also is explained by its relation to its
opposite, knowledge. For the thing known is explained as that
which is known by something, that is, by knowledge. Such
things, then, as are opposite the one to the other in the sense of
being correlatives are explained by a reference of the one to the
other.
(ii) Pairs of opposites which are contraries are not in any way
interdependent, but are contrary the one to the other. The good
is not spoken of as the good of the had, but as the contrary of
the bad, nor is white spoken of as the white of the black, but as
the contrary of the black. These two types of opposition are
therefore distinct. Those contraries which are such that the
subjects in which they are naturally present, or of which they
are predicated, must necessarily contain either the one or the
other of them, have no intermediate, but those in the case of
which no such necessity obtains, always have an intermediate.
Thus disease and health are naturally present in the body of an
animal, and it is necessary that either the one or the other
should be present in the body of an animal. Odd and even,
again, are predicated of number, and it is necessary that the one
or the other should be present in numbers. Now there is no
intermediate between the terms of either of these two pairs. On
the other hand, in those contraries with regard to which no
such necessity obtains, we find an intermediate. Blackness and
whiteness are naturally present in the body, but it is not
necessary that either the one or the other should be present in
the body, inasmuch as it is not true to say that everybody must
be white or black. Badness and goodness, again, are predicated
34
of man, and of many other things, but it is not necessary that
either the one quality or the other should be present in that of
which they are predicated: it is not true to say that everything
that may be good or bad must be either good or bad. These pairs
of contraries have intermediates: the intermediates between
white and black are grey, sallow, and all the other colours that
come between; the intermediate between good and bad is that
which is neither the one nor the other.
Some intermediate qualities have names, such as grey and
sallow and all the other colours that come between white and
black; in other cases, however, it is not easy to name the
intermediate, but we must define it as that which is not either
extreme, as in the case of that which is neither good nor bad,
neither just nor unjust.
(iii) 'privatives' and 'Positives' have reference to the same
subject. Thus, sight and blindness have reference to the eye. It is
a universal rule that each of a pair of opposites of this type has
reference to that to which the particular 'positive' is natural. We
say that that is capable of some particular faculty or possession
has suffered privation when the faculty or possession in
question is in no way present in that in which, and at the time
at which, it should naturally be present. We do not call that
toothless which has not teeth, or that blind which has not sight,
but rather that which has not teeth or sight at the time when by
nature it should. For there are some creatures which from birth
are without sight, or without teeth, but these are not called
toothless or blind.
To be without some faculty or to possess it is not the same as
the corresponding 'privative' or 'positive'. 'Sight' is a 'positive',
'blindness' a 'privative', but 'to possess sight' is not equivalent
to 'sight', 'to be blind' is not equivalent to 'blindness'. Blindness
is a 'privative', to be blind is to be in a state of privation, but is
35
not a 'privative'. Moreover, if 'blindness' were equivalent to
'being blind', both would be predicated of the same subject; but
though a man is said to be blind, he is by no means said to be
blindness.
To be in a state of 'possession' is, it appears, the opposite of
being in a state of 'privation', just as 'positives' and 'privatives'
themselves are opposite. There is the same type of antithesis in
both cases; for just as blindness is opposed to sight, so is being
blind opposed to having sight.
That which is affirmed or denied is not itself affirmation or
denial. By 'affirmation' we mean an affirmative proposition, by
'denial' a negative. Now, those facts which form the matter of
the affirmation or denial are not propositions; yet these two are
said to be opposed in the same sense as the affirmation and
denial, for in this case also the type of antithesis is the same.
For as the affirmation is opposed to the denial, as in the two
propositions 'he sits', 'he does not sit', so also the fact which
constitutes the matter of the proposition in one case is opposed
to that in the other, his sitting, that is to say, to his not sitting.
It is evident that 'positives' and 'privatives' are not opposed
each to each in the same sense as relatives. The one is not
explained by reference to the other; sight is not sight of
blindness, nor is any other preposition used to indicate the
relation. Similarly blindness is not said to be blindness of sight,
but rather, privation of sight. Relatives, moreover, reciprocate; if
blindness, therefore, were a relative, there would be a
reciprocity of relation between it and that with which it was
correlative. But this is not the case. Sight is not called the sight
of blindness.
That those terms which fall under the heads of 'positives' and
'privatives' are not opposed each to each as contraries, either, is
plain from the following facts: Of a pair of contraries such that
36
they have no intermediate, one or the other must needs be
present in the subject in which they naturally subsist, or of
which they are predicated; for it is those, as we proved,' in the
case of which this necessity obtains, that have no intermediate.
Moreover, we cited health and disease, odd and even, as
instances. But those contraries which have an intermediate are
not subject to any such necessity. It is not necessary that every
substance, receptive of such qualities, should be either black or
white, cold or hot, for something intermediate between these
contraries may very well be present in the subject. We proved,
moreover, that those contraries have an intermediate in the
case of which the said necessity does not obtain. Yet when one
of the two contraries is a constitutive property of the subject, as
it is a constitutive property of fire to be hot, of snow to be white,
it is necessary determinately that one of the two contraries, not
one or the other, should be present in the subject; for fire
cannot be cold, or snow black. Thus, it is not the case here that
one of the two must needs be present in every subject receptive
of these qualities, but only in that subject of which the one
forms a constitutive property. Moreover, in such cases it is one
member of the pair determinately, and not either the one or the
other, which must be present.
In the case of 'positives' and 'privatives', on the other hand,
neither of the aforesaid statements holds good. For it is not
necessary that a subject receptive of the qualities should always
have either the one or the other; that which has not yet
advanced to the state when sight is natural is not said either to
be blind or to see. Thus 'positives' and 'privatives' do not belong
to that class of contraries which consists of those which have
no intermediate. On the other hand, they do not belong either to
that class which consists of contraries which have an
intermediate. For under certain conditions it is necessary that
either the one or the other should form part of the constitution
of every appropriate subject. For when a thing has reached the
37
stage when it is by nature capable of sight, it will be said either
to see or to be blind, and that in an indeterminate sense,
signifying that the capacity may be either present or absent; for
it is not necessary either that it should see or that it should be
blind, but that it should be either in the one state or in the
other. Yet in the case of those contraries which have an
intermediate we found that it was never necessary that either
the one or the other should be present in every appropriate
subject, but only that in certain subjects one of the pair should
be present, and that in a determinate sense. It is, therefore,
plain that 'positives' and 'privatives' are not opposed each to
each in either of the senses in which contraries are opposed.
Again, in the case of contraries, it is possible that there should
be changes from either into the other, while the subject retains
its identity, unless indeed one of the contraries is a constitutive
property of that subject, as heat is of fire. For it is possible that
that that which is healthy should become diseased, that which
is white, black, that which is cold, hot, that which is good, bad,
that which is bad, good. The bad man, if he is being brought into
a better way of life and thought, may make some advance,
however slight, and if he should once improve, even ever so
little, it is plain that he might change completely, or at any rate
make very great progress; for a man becomes more and more
easily moved to virtue, however small the improvement was at
first. It is, therefore, natural to suppose that he will make yet
greater progress than he has made in the past; and as this
process goes on, it will change him completely and establish
him in the contrary state, provided he is not hindered by lack of
time. In the case of 'positives' and 'privatives', however, change
in both directions is impossible. There may be a change from
possession to privation, but not from privation to possession.
The man who has become blind does not regain his sight; the
man who has become bald does not regain his hair; the man
who has lost his teeth does not grow his grow a new set.
38
(iv) Statements opposed as affirmation and negation belong
manifestly to a class which is distinct, for in this case, and in
this case only, it is necessary for the one opposite to be true and
the other false.
Neither in the case of contraries, nor in the case of correlatives,
nor in the case of 'positives' and 'privatives', is it necessary for
one to be true and the other false. Health and disease are
contraries: neither of them is true or false. 'Double' and 'half
are opposed to each other as correlatives: neither of them is
true or false. The case is the same, of course, with regard to
'positives' and 'privatives' such as 'sight' and 'blindness'. In
short, where there is no sort of combination of words, truth and
falsity have no place, and all the opposites we have mentioned
so far consist of simple words.
At the same time, when the words which enter into opposed
statements are contraries, these, more than any other set of
opposites, would seem to claim this characteristic. 'Socrates is
ill' is the contrary of 'Socrates is well', but not even of such
composite expressions is it true to say that one of the pair must
always be true and the other false. For if Socrates exists, one
will be true and the other false, but if he does not exist, both
will be false; for neither 'Socrates is ill' nor 'Socrates is well' is
true, if Socrates does not exist at all.
In the case of 'positives' and 'privatives', if the subject does not
exist at all, neither proposition is true, but even if the subject
exists, it is not always the fact that one is true and the other
false. For 'Socrates has sight' is the opposite of 'Socrates is blind'
in the sense of the word 'opposite' which applies to possession
and privation. Now if Socrates exists, it is not necessary that
one should be true and the other false, for when he is not yet
able to acquire the power of vision, both are false, as also if
Socrates is altogether non-existent.
39
But in the case of affirmation and negation, whether the subject
exists or not, one is always false and the other true. For
manifestly, if Socrates exists, one of the two propositions
'Socrates is ill', 'Socrates is not ill', is true, and the other false.
This is likewise the case if he does not exist; for if he does not
exist, to say that he is ill is false, to say that he is not ill is true.
Thus it is in the case of those opposites only, which are opposite
in the sense in which the term is used with reference to
affirmation and negation, that the rule holds good, that one of
the pair must be true and the other false.
11
That the contrary of a good is an evil is shown by induction: the
contrary of health is disease, of courage, cowardice, and so on.
But the contrary of an evil is sometimes a good, sometimes an
evil. For defect, which is an evil, has excess for its contrary, this
also being an evil, and the mean, which is a good, is equally the
contrary of the one and of the other. It is only in a few cases,
however, that we see instances of this: in most, the contrary of
an evil is a good.
In the case of contraries, it is not always necessary that if one
exists the other should also exist: for if all become healthy there
will be health and no disease, and again, if everything turns
white, there will be white, but no black. Again, since the fact
that Socrates is ill is the contrary of the fact that Socrates is
well, and two contrary conditions cannot both obtain in one and
the same individual at the same time, both these contraries
could not exist at once: for if that Socrates was well was a fact,
then that Socrates was ill could not possibly be one.
40
It is plain that contrary attributes must needs be present in
subjects which belong to the same species or genus. Disease
and health require as their subject the body of an animal; white
and black require a body, without further qualification; justice
and injustice require as their subject the human soul.
Moreover, it is necessary that pairs of contraries should in all
cases either belong to the same genus or belong to contrary
genera or be themselves genera. White and black belong to the
same genus, colour; justice and injustice, to contrary genera,
virtue and vice; while good and evil do not belong to genera, but
are themselves actual genera, with terms under them.
12
There are four senses in which one thing can be said to be
'prior' to another. Primarily and most properly the term has
reference to time: in this sense the word is used to indicate that
one thing is older or more ancient than another, for the
expressions 'older' and 'more ancient' imply greater length of
time.
Secondly, one thing is said to be 'prior' to another when the
sequence of their being cannot be reversed. In this sense 'one' is
'prior' to 'two'. For if 'two' exists, it follows directly that 'one'
must exist, but if 'one' exists, it does not follow necessarily that
'two' exists: thus the sequence subsisting cannot be reversed. It
is agreed, then, that when the sequence of two things cannot be
reversed, then that one on which the other depends is called
'prior' to that other.
In the third place, the term 'prior' is used with reference to any
order, as in the case of science and of oratory. For in sciences
41
which use demonstration there is that which is prior and that
which is posterior in order; in geometry, the elements are prior
to the propositions; in reading and writing, the letters of the
alphabet are prior to the syllables. Similarly, in the case of
speeches, the exordium is prior in order to the narrative.
Besides these senses of the word, there is a fourth. That which
is better and more honourable is said to have a natural priority.
In common parlance men speak of those whom they honour
and love as 'coming first' with them. This sense of the word is
perhaps the most far-fetched.
Such, then, are the different senses in which the term 'prior' is
used.
Yet it would seem that besides those mentioned there is yet
another. For in those things, the being of each of which implies
that of the other, that which is in any way the cause may
reasonably be said to be by nature 'prior' to the effect. It is plain
that there are instances of this. The fact of the being of a man
carries with it the truth of the proposition that he is, and the
implication is reciprocal: for if a man is, the proposition
wherein we allege that he is true, and conversely, if the
proposition wherein we allege that he is true, then he is. The
true proposition, however, is in no way the cause of the being of
the man, but the fact of the man's being does seem somehow to
be the cause of the truth of the proposition, for the truth or
falsity of the proposition depends on the fact of the man's being
or not being.
Thus the word 'prior' may be used in five senses.
42
13
The term 'simultaneous' is primarily and most appropriately
applied to those things the genesis of the one of which is
simultaneous with that of the other; for in such cases neither is
prior or posterior to the other. Such things are said to be
simultaneous in point of time. Those things, again, are
'simultaneous' in point of nature, the being of each of which
involves that of the other, while at the same time neither is the
cause of the other's being. This is the case with regard to the
double and the half, for these are reciprocally dependent, since,
if there is a double, there is also a half, and if there is a half,
there is also a double, while at the same time neither is the
cause of the being of the other.
Again, those species which are distinguished one from another
and opposed one to another within the same genus are said to
be 'simultaneous' in nature. I mean those species which are
distinguished each from each by one and the same method of
division. Thus the 'winged' species is simultaneous with the
'terrestrial' and the 'water' species. These are distinguished
within the same genus, and are opposed each to each, for the
genus 'animal' has the 'winged', the 'terrestrial', and the 'water'
species, and no one of these is prior or posterior to another; on
the contrary, all such things appear to be 'simultaneous' in
nature. Each of these also, the terrestrial, the winged, and the
water species, can be divided again into subspecies. Those
species, then, also will be 'simultaneous' point of nature, which,
belonging to the same genus, are distinguished each from each
by one and the same method of differentiation.
But genera are prior to species, for the sequence of their being
cannot be reversed. If there is the species 'water-animal', there
will be the genus 'animal', but granted the being of the genus
43
'animal', it does not follow necessarily that there will be the
species 'water-animal'.
Those things, therefore, are said to be 'simultaneous' in nature,
the being of each of which involves that of the other, while at
the same time neither is in any way the cause of the other's
being; those species, also, which are distinguished each from
each and opposed within the same genus. Those things,
moreover, are 'simultaneous' in the unqualified sense of the
word which come into being at the same time.
14
There are six sorts of movement: generation, destruction,
increase, diminution, alteration, and change of place.
It is evident in all but one case that all these sorts of movement
are distinct each from each. Generation is distinct from
destruction, increase and change of place from diminution, and
so on. But in the case of alteration it may be argued that the
process necessarily implies one or other of the other five sorts
of motion. This is not true, for we may say that all affections, or
nearly all, produce in us an alteration which is distinct from all
other sorts of motion, for that which is affected need not suffer
either increase or diminution or any of the other sorts of
motion. Thus alteration is a distinct sort of motion; for, if it were
not, the thing altered would not only be altered, but would
forthwith necessarily suffer increase or diminution or some one
of the other sorts of motion in addition; which as a matter of
fact is not the case. Similarly that which was undergoing the
process of increase or was subject to some other sort of motion
would, if alteration were not a distinct form of motion,
necessarily be subject to alteration also. But there are some
44
things which undergo increase but yet not alteration. The
square, for instance, if a gnomon is applied to it, undergoes
increase but not alteration, and so it is with all other figures of
this sort. Alteration and increase, therefore, are distinct.
Speaking generally, rest is the contrary of motion. But the
different forms of motion have their own contraries in other
forms; thus destruction is the contrary of generation,
diminution of increase, rest in a place, of change of place. As for
this last, change in the reverse direction would seem to be most
truly its contrary; thus motion upwards is the contrary of
motion downwards and vice versa.
In the case of that sort of motion which yet remains, of those
that have been enumerated, it is not easy to state what is its
contrary. It appears to have no contrary, unless one should
define the contrary here also either as 'rest in its quality' or as
'change in the direction of the contrary quality', just as we
defined the contrary of change of place either as rest in a place
or as change in the reverse direction. For a thing is altered when
change of quality takes place; therefore either rest in its quality
or change in the direction of the contrary may be called the
contrary of this qualitative form of motion. In this way
becoming white is the contrary of becoming black; there is
alteration in the contrary direction, since a change of a
qualitative nature takes place.
15
The term 'to have' is used in various senses. In the first place it
is used with reference to habit or disposition or any other
quality, for we are said to 'have' a piece of knowledge or a virtue.
Then, again, it has reference to quantity, as, for instance, in the
45
case of a man's height; for he is said to 'have' a height of three
or four cubits. It is used, moreover, with regard to apparel, a
man being said to 'have' a coat or tunic; or in respect of
something which we have on a part of ourselves, as a ring on
the hand: or in respect of something which is a part of us, as
hand or foot. The term refers also to content, as in the case of a
vessel and wheat, or of a jar and wine; a jar is said to 'have'
wine, and a corn-measure wheat. The expression in such cases
has reference to content. Or it refers to that which has been
acquired; we are said to 'have' a house or a field. A man is also
said to 'have' a wife, and a wife a husband, and this appears to
be the most remote meaning of the term, for by the use of it we
mean simply that the husband lives with the wife.
Other senses of the word might perhaps be found, but the most
ordinary ones have all been enumerated.
46
Aristotle - On Interpretation
[Translated by E. M. Edghill]
First we must define the terms 'noun' and 'verb', then the terms
'denial' and 'affirmation', then 'proposition' and 'sentence.'
Spoken words are the symbols of mental experience and
written words are the symbols of spoken words. Just as all men
have not the same writing, so all men have not the same
speech sounds, but the mental experiences, which these
directly symbolize, are the same for all, as also are those things
of which our experiences are the images. This matter has,
however, been discussed in my treatise about the soul, for it
belongs to an investigation distinct from that which lies before
us.
As there are in the mind thoughts which do not involve truth or
falsity, and also those which must be either true or false, so it is
in speech. For truth and falsity imply combination and
separation. Nouns and verbs, provided nothing is added, are
like thoughts without combination or separation; 'man' and
'white', as isolated terms, are not yet either true or false. In
proof of this, consider the word 'goat-stag.' It has significance,
but there is no truth or falsity about it, unless 'is' or 'is not' is
added, either in the present or in some other tense.
47
By a noun we mean a sound significant by convention, which
has no reference to time, and of which no part is significant
apart from the rest. In the noun 'Fairsteed,' the part 'steed' has
no significance in and by itself, as in the phrase 'fair steed.' Yet
there is a difference between simple and composite nouns; for
in the former the part is in no way significant, in the latter it
contributes to the meaning of the whole, although it has not an
independent meaning. Thus in the word 'pirate-boat' the word
'boat' has no meaning except as part of the whole word.
The limitation 'by convention' was introduced because nothing
is by nature a noun or name - it is only so when it becomes a
symbol; inarticulate sounds, such as those which brutes
produce, are significant, yet none of these constitutes a noun.
The expression 'not-man' is not a noun. There is indeed no
recognized term by which we may denote such an expression,
for it is not a sentence or a denial. Let it then be called an
indefinite noun.
The expressions 'of Philo', 'to Philo', and so on, constitute not
nouns, but cases of a noun. The definition of these cases of a
noun is in other respects the same as that of the noun proper,
but, when coupled with 'is', 'was', or will be', they do not, as
they are, form a proposition either true or false, and this the
noun proper always does, under these conditions. Take the
words 'of Philo is' or 'of or 'of Philo is not'; these words do not,
as they stand, form either a true or a false proposition.
48
A verb is that which, in addition to its proper meaning, carries
with it the notion of time. No part of it has any independent
meaning, and it is a sign of something said of something else.
I will explain what I mean by saying that it carries with it the
notion of time. 'Health' is a noun, but 'is healthy' is a verb; for
besides its proper meaning it indicates the present existence of
the state in question.
Moreover, a verb is always a sign of something said of
something else, i.e. of something either predicable of or present
in some other thing.
Such expressions as 'is not-healthy', 'is not, ill', I do not
describe as verbs; for though they carry the additional note of
time, and always form a predicate, there is no specified name
for this variety; but let them be called indefinite verbs, since
they apply equally well to that which exists and to that which
does not.
Similarly 'he was healthy', 'he will be healthy', are not verbs,
but tenses of a verb; the difference lies in the fact that the verb
indicates present time, while the tenses of the verb indicate
those times which lie outside the present.
Verbs in and by themselves are substantival and have
significance, for he who uses such expressions arrests the
hearer's mind, and fixes his attention; but they do not, as they
stand, express any judgement, either positive or negative. For
neither are 'to be' and 'not to be' the participle 'being'
significant of any fact, unless something is added; for they do
not themselves indicate anything, but imply a copulation, of
which we cannot form a conception apart from the things
coupled.
49
A sentence is a significant portion of speech, some parts of
which have an independent meaning, that is to say, as an
utterance, though not as the expression of any positive
judgement. Let me explain. The word 'human' has meaning,
but does not constitute a proposition, either positive or
negative. It is only when other words are added that the whole
will form an affirmation or denial. But if we separate one
syllable of the word 'human' from the other, it has no meaning;
similarly in the word 'mouse', the part 'ouse' has no meaning in
itself, but is merely a sound. In composite words, indeed, the
parts contribute to the meaning of the whole; yet, as has been
pointed out, they have not an independent meaning.
Every sentence has meaning, not as being the natural means by
which a physical faculty is realized, but, as we have said, by
convention. Yet every sentence is not a proposition; only such
are propositions as have in them either truth or falsity. Thus a
prayer is a sentence, but is neither true nor false.
Let us therefore dismiss all other types of sentence but the
proposition, for this last concerns our present inquiry, whereas
the investigation of the others belongs rather to the study of
rhetoric or of poetry.
50
The first class of simple propositions is the simple affirmation,
the next, the simple denial; all others are only one by
conjunction.
Every proposition must contain a verb or the tense of a verb.
The phrase which defines the species 'man', if no verb in
present, past, or future time be added, is not a proposition. It
may be asked how the expression 'a footed animal with two
feet' can be called single; for it is not the circumstance that the
words follow in unbroken succession that effects the unity. This
inquiry, however, finds its place in an investigation foreign to
that before us.
We call those propositions single which indicate a single fact, or
the conjunction of the parts of which results in unity: those
propositions, on the other hand, are separate and many in
number, which indicate many facts, or whose parts have no
conjunction.
Let us, moreover, consent to call a noun or a verb an expression
only, and not a proposition, since it is not possible for a man to
speak in this way when he is expressing something, in such a
way as to make a statement, whether his utterance is an
answer to a question or an act of his own initiation.
To return: of propositions one kind is simple, i.e. that which
asserts or denies something of something, the other composite,
i.e. that which is compounded of simple propositions. A simple
proposition is a statement, with meaning, as to the presence of
something in a subject or its absence, in the present, past, or
future, according to the divisions of time.
51
An affirmation is a positive assertion of something about
something, a denial a negative assertion.
Now it is possible both to affirm and to deny the presence of
something which is present or of something which is not, and
since these same affirmations and denials are possible with
reference to those times which lie outside the present, it would
be possible to contradict any affirmation or denial. Thus it is
plain that every affirmation has an opposite denial, and
similarly every denial an opposite affirmation.
We will call such a pair of propositions a pair of contradictories.
Those positive and negative propositions are said to be
contradictory which have the same subject and predicate. The
identity of subject and of predicate must not be 'equivocal'.
Indeed there are definitive qualifications besides this, which we
make to meet the casuistries of sophists.
Some things are universal, others individual. By the term
'universal' I mean that which is of such a nature as to be
predicated of many subjects, by 'individual' that which is not
thus predicated. Thus 'man' is a universal, 'Callias' an
individual.
Our propositions necessarily sometimes concern a universal
subject, sometimes an individual.
If, then, a man states a positive and a negative proposition of
universal character with regard to a universal, these two
propositions are 'contrary'. By the expression 'a proposition of
52
universal character with regard to a universal', such
propositions as 'every man is white', 'no man is white' are
meant. When, on the other hand, the positive and negative
propositions, though they have regard to a universal, are yet
not of universal character, they will not be contrary, albeit the
meaning intended is sometimes contrary. As instances of
propositions made with regard to a universal, but not of
universal character, we may take the 'propositions 'man is
white', 'man is not white'. 'Man' is a universal, but the
proposition is not made as of universal character; for the word
'every' does not make the subject a universal, but rather gives
the proposition a universal character. If, however, both
predicate and subject are distributed, the proposition thus
constituted is contrary to truth; no affirmation will, under such
circumstances, be true. The proposition 'every man is every
animal' is an example of this type.
An affirmation is opposed to a denial in the sense which I
denote by the term 'contradictory', when, while the subject
remains the same, the affirmation is of universal character and
the denial is not. The affirmation 'every man is white' is the
contradictory of the denial 'not every man is white', or again,
the proposition 'no man is white' is the contradictory of the
proposition 'some men are white'. But propositions are opposed
as contraries when both the affirmation and the denial are
universal, as in the sentences 'every man is white', 'no man is
white', 'every man is just', 'no man is just'.
We see that in a pair of this sort both propositions cannot be
true, but the contradictories of a pair of contraries can
sometimes both be true with reference to the same subject; for
instance 'not every man is white' and some men are white' are
both true. Of such corresponding positive and negative
propositions as refer to universals and have a universal
character, one must be true and the other false. This is the case
53
also when the reference is to individuals, as in the propositions
'Socrates is white', 'Socrates is not white'.
When, on the other hand, the reference is to universals, but the
propositions are not universal, it is not always the case that one
is true and the other false, for it is possible to state truly that
man is white and that man is not white and that man is
beautiful and that man is not beautiful; for if a man is deformed
he is the reverse of beautiful, also if he is progressing towards
beauty he is not yet beautiful.
This statement might seem at first sight to carry with it a
contradiction, owing to the fact that the proposition 'man is not
white' appears to be equivalent to the proposition 'no man is
white'. This, however, is not the case, nor are they necessarily
at the same time true or false.
It is evident also that the denial corresponding to a single
affirmation is itself single; for the denial must deny just that
which the affirmation affirms concerning the same subject, and
must correspond with the affirmation both in the universal or
particular character of the subject and in the distributed or
undistributed sense in which it is understood.
For instance, the affirmation 'Socrates is white' has its proper
denial in the proposition 'Socrates is not white'. If anything else
be negatively predicated of the subject or if anything else be the
subject though the predicate remain the same, the denial will
not be the denial proper to that affirmation, but on that is
distinct.
The denial proper to the affirmation 'every man is white' is 'not
every man is white'; that proper to the affirmation 'some men
are white' is 'no man is white', while that proper to the
affirmation 'man is white' is 'man is not white'.
54
We have shown further that a single denial is contradictorily
opposite to a single affirmation and we have explained which
these are; we have also stated that contrary are distinct from
contradictory propositions and which the contrary are; also that
with regard to a pair of opposite propositions it is not always
the case that one is true and the other false. We have pointed
out, moreover, what the reason of this is and under what
circumstances the truth of the one involves the falsity of the
other.
8
An affirmation or denial is single, if it indicates some one fact
about some one subject; it matters not whether the subject is
universal and whether the statement has a universal character,
or whether this is not so. Such single propositions are: 'every
man is white', 'not every man is white';'man is white', 'man is
not white'; 'no man is white', 'some men are white'; provided
the word 'white' has one meaning. If, on the other hand, one
word has two meanings which do not combine to form one, the
affirmation is not single. For instance, if a man should establish
the symbol 'garment' as significant both of a horse and of a
man, the proposition 'garment is white' would not be a single
affirmation, nor its opposite a single denial. For it is equivalent
to the proposition 'horse and man are white', which, again, is
equivalent to the two propositions 'horse is white', 'man is
white'. If, then, these two propositions have more than a single
significance, and do not form a single proposition, it is plain
that the first proposition either has more than one significance
or else has none; for a particular man is not a horse.
55
This, then, is another instance of those propositions of which
both the positive and the negative forms may be true or false
simultaneously.
In the case of that which is or which has taken place,
propositions, whether positive or negative, must be true or
false. Again, in the case of a pair of contradictories, either when
the subject is universal and the propositions are of a universal
character, or when it is individual, as has been said,' one of the
two must be true and the other false; whereas when the subject
is universal, but the propositions are not of a universal
character, there is no such necessity. We have discussed this
type also in a previous chapter.
When the subject, however, is individual, and that which is
predicated of it relates to the future, the case is altered. For if all
propositions whether positive or negative are either true or
false, then any given predicate must either belong to the subject
or not, so that if one man affirms that an event of a given
character will take place and another denies it, it is plain that
the statement of the one will correspond with reality and that
of the other will not. For the predicate cannot both belong and
not belong to the subject at one and the same time with regard
to the future.
Thus, if it is true to say that a thing is white, it must necessarily
be white; if the reverse proposition is true, it will of necessity
not be white. Again, if it is white, the proposition stating that it
is white was true; if it is not white, the proposition to the
opposite effect was true. And if it is not white, the man who
states that it is making a false statement; and if the man who
56
states that it is white is making a false statement, it follows that
it is not white. It may therefore be argued that it is necessary
that affirmations or denials must be either true or false.
Now if this be so, nothing is or takes place fortuitously, either in
the present or in the future, and there are no real alternatives;
everything takes place of necessity and is fixed. For either he
that affirms that it will take place or he that denies this is in
correspondence with fact, whereas if things did not take place
of necessity, an event might just as easily not happen as
happen; for the meaning of the word 'fortuitous' with regard to
present or future events is that reality is so constituted that it
may issue in either of two opposite directions. Again, if a thing
is white now, it was true before to say that it would be white, so
that of anything that has taken place it was always true to say
'it is' or 'it will be'. But if it was always true to say that a thing is
or will be, it is not possible that it should not be or not be about
to be, and when a thing cannot not come to be, it is impossible
that it should not come to be, and when it is impossible that it
should not come to be, it must come to be. All, then, that is
about to be must of necessity take place. It results from this
that nothing is uncertain or fortuitous, for if it were fortuitous it
would not be necessary.
Again, to say that neither the affirmation nor the denial is true,
maintaining, let us say, that an event neither will take place nor
will not take place, is to take up a position impossible to defend.
In the first place, though facts should prove the one proposition
false, the opposite would still be untrue. Secondly, if it was true
to say that a thing was both white and large, both these
qualities must necessarily belong to it; and if they will belong to
it the next day, they must necessarily belong to it the next day.
But if an event is neither to take place nor not to take place the
next day, the element of chance will be eliminated. For
57
example, it would be necessary that a sea-fight should neither
take place nor fail to take place on the next day.
These awkward results and others of the same kind follow, if it
is an irrefragable law that of every pair of contradictory
propositions, whether they have regard to universals and are
stated as universally applicable, or whether they have regard to
individuals, one must be true and the other false, and that there
are no real alternatives, but that all that is or takes place is the
outcome of necessity. There would be no need to deliberate or
to take trouble, on the supposition that if we should adopt a
certain course, a certain result would follow, while, if we did
not, the result would not follow. For a man may predict an
event ten thousand years beforehand, and another may predict
the reverse; that which was truly predicted at the moment in
the past will of necessity take place in the fullness of time.
Further, it makes no difference whether people have or have
not actually made the contradictory statements. For it is
manifest that the circumstances are not influenced by the fact
of an affirmation or denial on the part of anyone. For events
will not take place or fail to take place because it was stated
that they would or would not take place, nor is this any more
the case if the prediction dates back ten thousand years or any
other space of time. Wherefore, if through all time the nature of
things was so constituted that a prediction about an event was
true, then through all time it was necessary that that should
find fulfillment; and with regard to all events, circumstances
have always been such that their occurrence is a matter of
necessity. For that of which someone has said truly that it will
be, cannot fail to take place; and of that which takes place, it
was always true to say that it would be.
Yet this view leads to an impossible conclusion; for we see that
both deliberation and action are causative with regard to the
58
future, and that, to speak more generally, in those things which
are not continuously actual there is potentiality in either
direction. Such things may either be or not be; events also
therefore may either take place or not take place. There are
many obvious instances of this. It is possible that this coat may
be cut in half, and yet it may not be cut in half, but wear out
first. In the same way, it is possible that it should not be cut in
half; unless this were so, it would not be possible that it should
wear out first. So it is therefore with all other events which
possess this kind of potentiality. It is therefore plain that it is
not of necessity that everything is or takes place; but in some
instances there are real alternatives, in which case the
affirmation is no more true and no more false than the denial;
while some exhibit a predisposition and general tendency in
one direction or the other, and yet can issue in the opposite
direction by exception.
Now that which is must needs be when it is, and that which is
not must needs not be when it is not. Yet it cannot be said
without qualification that all existence and non-existence is the
outcome of necessity. For there is a difference between saying
that that which is, when it is, must needs be, and simply saying
that all that is must needs be, and similarly in the case of that
which is not. In the case, also, of two contradictory propositions
this holds good. Everything must either be or not be, whether in
the present or in the future, but it is not always possible to
distinguish and state determinately which of these alternatives
must necessarily come about.
Let me illustrate. A sea-fight must either take place to-morrow
or not, but it is not necessary that it should take place to-
morrow, neither is it necessary that it should not take place, yet
it is necessary that it either should or should not take place to-
morrow. Since propositions correspond with facts, it is evident
that when in future events there is a real alternative, and a
59
potentiality in contrary directions, the corresponding
affirmation and denial have the same character.
This is the case with regard to that which is not always existent
or not always nonexistent. One of the two propositions in such
instances must be true and the other false, but we cannot say
determinately that this or that is false, but must leave the
alternative undecided. One may indeed be more likely to be true
than the other, but it cannot be either actually true or actually
false. It is therefore plain that it is not necessary that of an
affirmation and a denial one should be true and the other false.
For in the case of that which exists potentially, but not actually,
the rule which applies to that which exists actually does not
hold good. The case is rather as we have indicated.
10
An affirmation is the statement of a fact with regard to a
subject, and this subject is either a noun or that which has no
name; the subject and predicate in an affirmation must each
denote a single thing. I have already explained' what is meant
by a noun and by that which has no name; for I stated that the
expression 'not-man' was not a noun, in the proper sense of the
word, but an indefinite noun, denoting as it does in a certain
sense a single thing. Similarly the expression 'does not enjoy
health' is not a verb proper, but an indefinite verb. Every
affirmation, then, and every denial, will consist of a noun and a
verb, either definite or indefinite.
There can be no affirmation or denial without a verb; for the
expressions 'is', 'will be', 'was', 'is coming to be', and the like
are verbs according to our definition, since besides their specific
meaning they convey the notion of time. Thus the primary
60
affirmation and denial are 'as follows: 'man is', 'man is not'.
Next to these, there are the propositions: 'not-man is', 'not-man
is not'. Again we have the propositions: 'every man is, 'every
man is not', 'all that is not-man is', 'all that is not-man is not'.
The same classification holds good with regard to such periods
of time as lie outside the present.
When the verb 'is' is used as a third element in the sentence,
there can be positive and negative propositions of two sorts.
Thus in the sentence 'man is just' the verb 'is' is used as a third
element, call it verb or noun, which you will. Four propositions,
therefore, instead of two can be formed with these materials.
Two of the four, as regards their affirmation and denial,
correspond in their logical sequence with the propositions
which deal with a condition of privation; the other two do not
correspond with these.
I mean that the verb 'is' is added either to the term 'just' or to
the term 'not-just', and two negative propositions are formed in
the same way. Thus we have the four propositions. Reference to
the subjoined table will make matters clear:
A. Affirmation
B. Denial
Man is just
Man is not just
D. Denial
C. Affirmation
Man is not not-just Man is not-just
Here 'is' and 'is not' are added either to 'just' or to 'not-just'
61
This then is the proper scheme for these propositions, as has
been said in the Analytics. The same rule holds good, if the
subject is distributed. Thus we have the table:
A'. Affirmation
Every man is just
B\ Denial
Not every man
is just
D\ Denial
Not every man is
not-just
C. Affirmation
Every man is
not-just
Yet here it is not possible, in the same way as in the former
case, that the propositions joined in the table by a diagonal line
should both be true; though under certain circumstances this is
the case.
We have thus set out two pairs of opposite propositions; there
are moreover two other pairs, if a term be conjoined with 'not-
man', the latter forming a kind of subject. Thus:
A". Not-man is just
B". Not-man is not
just
D". Not-man is not
not-just
C". Not-man is not-
just
62
This is an exhaustive enumeration of all the pairs of opposite
propositions that can possibly be framed. This last group should
remain distinct from those which preceded it, since it employs
as its subject the expression 'not-man'.
When the verb 'is' does not fit the structure of the sentence (for
instance, when the verbs 'walks', 'enjoys health' are used), that
scheme applies, which applied when the word 'is' was added.
Thus we have the propositions: 'every man enjoys health',
'every man does-not-enjoy-health', 'all that is not-man enjoys
health', 'all that is not-man does-not-enjoy-health'. We must
not in these propositions use the expression 'not every man'.
The negative must be attached to the word 'man', for the word
'every' does not give to the subject a universal significance, but
implies that, as a subject, it is distributed. This is plain from the
following pairs: 'man enjoys health', 'man does not enjoy
health'; 'not-man enjoys health', 'not man does not enjoy
health'. These propositions differ from the former in being
indefinite and not universal in character. Thus the adjectives
'every' and no additional significance except that the subject,
whether in a positive or in a negative sentence, is distributed.
The rest of the sentence, therefore, will in each case be the
same.
Since the contrary of the proposition 'every animal is just' is 'no
animal is just', it is plain that these two propositions will never
both be true at the same time or with reference to the same
subject. Sometimes, however, the contradictories of these
contraries will both be true, as in the instance before us: the
propositions 'not every animal is just' and 'some animals are
just' are both true.
63
Further, the proposition 'no man is just' follows from the
proposition 'every man is not just' and the proposition 'not
every man is not just', which is the opposite of 'every man is
not-just', follows from the proposition 'some men are just'; for
if this be true, there must be some just men.
It is evident, also, that when the subject is individual, if a
question is asked and the negative answer is the true one, a
certain positive proposition is also true. Thus, if the question
were asked Socrates wise?' and the negative answer were the
true one, the positive inference 'Then Socrates is unwise' is
correct. But no such inference is correct in the case of
universals, but rather a negative proposition. For instance, if to
the question 'Is every man wise?' the answer is 'no', the
inference 'Then every man is unwise' is false. But under these
circumstances the inference 'Not every man is wise' is correct.
This last is the contradictory, the former the contrary. Negative
expressions, which consist of an indefinite noun or predicate,
such as 'not-man' or 'not-just', may seem to be denials
containing neither noun nor verb in the proper sense of the
words. But they are not. For a denial must always be either true
or false, and he that uses the expression 'not man', if nothing
more be added, is not nearer but rather further from making a
true or a false statement than he who uses the expression
'man'.
The propositions 'everything that is not man is just', and the
contradictory of this, are not equivalent to any of the other
propositions; on the other hand, the proposition 'everything
that is not man is not just' is equivalent to the proposition
'nothing that is not man is just'.
The conversion of the position of subject and predicate in a
sentence involves no difference in its meaning. Thus we say
'man is white' and 'white is man'. If these were not equivalent,
64
there would be more than one contradictory to the same
proposition, whereas it has been demonstrated' that each
proposition has one proper contradictory and one only. For of
the proposition 'man is white' the appropriate contradictory is
'man is not white', and of the proposition 'white is man', if its
meaning be different, the contradictory will either be 'white is
not not-man' or 'white is not man'. Now the former of these is
the contradictory of the proposition 'white is not-man', and the
latter of these is the contradictory of the proposition 'man is
white'; thus there will be two contradictories to one
proposition.
It is evident, therefore, that the inversion of the relative
position of subject and predicate does not affect the sense of
affirmations and denials.
11
There is no unity about an affirmation or denial which, either
positively or negatively, predicates one thing of many subjects,
or many things of the same subject, unless that which is
indicated by the many is really some one thing, do not apply
this word 'one' to those things which, though they have a single
recognized name, yet do not combine to form a unity. Thus,
man may be an animal, and biped, and domesticated, but these
three predicates combine to form a unity. On the other hand,
the predicates 'white', 'man', and 'walking' do not thus
combine. Neither, therefore, if these three form the subject of
an affirmation, nor if they form its predicate, is there any unity
about that affirmation. In both cases the unity is linguistic, but
not real.
65
If therefore the dialectical question is a request for an answer,
i.e. either for the admission of a premiss or for the admission of
one of two contradictories - and the premiss is itself always one
of two contradictories - the answer to such a question as
contains the above predicates cannot be a single proposition.
For as I have explained in the Topics, question is not a single
one, even if the answer asked for is true.
At the same time it is plain that a question of the form 'what is
it?' is not a dialectical question, for a dialectical questioner
must by the form of his question give his opponent the chance
of announcing one of two alternatives, whichever he wishes. He
must therefore put the question into a more definite form, and
inquire, e.g.. whether man has such and such a characteristic or
not.
Some combinations of predicates are such that the separate
predicates unite to form a single predicate. Let us consider
under what conditions this is and is not possible. We may
either state in two separate propositions that man is an animal
and that man is a biped, or we may combine the two, and state
that man is an animal with two feet. Similarly we may use
'man' and 'white' as separate predicates, or unite them into
one. Yet if a man is a shoemaker and is also good, we cannot
construct a composite proposition and say that he is a good
shoemaker. For if, whenever two separate predicates truly
belong to a subject, it follows that the predicate resulting from
their combination also truly belongs to the subject, many
absurd results ensue. For instance, a man is man and white.
Therefore, if predicates may always be combined, he is a white
man. Again, if the predicate 'white' belongs to him, then the
combination of that predicate with the former composite
predicate will be permissible. Thus it will be right to say that he
is a white man so on indefinitely. Or, again, we may combine
the predicates 'musical', 'white', and 'walking', and these may
66
be combined many times. Similarly we may say that Socrates is
Socrates and a man, and that therefore he is the man Socrates,
or that Socrates is a man and a biped, and that therefore he is a
two-footed man. Thus it is manifest that if man states
unconditionally that predicates can always be combined, many
absurd consequences ensue.
We will now explain what ought to be laid down.
Those predicates, and terms forming the subject of predication,
which are accidental either to the same subject or to one
another, do not combine to form a unity. Take the proposition
'man is white of complexion and musical'. Whiteness and being
musical do not coalesce to form a unity, for they belong only
accidentally to the same subject. Nor yet, if it were true to say
that that which is white is musical, would the terms 'musical'
and 'white' form a unity, for it is only incidentally that that
which is musical is white; the combination of the two will,
therefore, not form a unity.
Thus, again, whereas, if a man is both good and a shoemaker,
we cannot combine the two propositions and say simply that he
is a good shoemaker, we are, at the same time, able to combine
the predicates 'animal' and 'biped' and say that a man is an
animal with two feet, for these predicates are not accidental.
Those predicates, again, cannot form a unity, of which the one
is implicit in the other: thus we cannot combine the predicate
'white' again and again with that which already contains the
notion 'white', nor is it right to call a man an animal-man or a
two-footed man; for the notions 'animal' and 'biped' are
implicit in the word 'man'. On the other hand, it is possible to
predicate a term simply of any one instance, and to say that
some one particular man is a man or that some one white man
is a white man.
67
Yet this is not always possible: indeed, when in the adjunct
there is some opposite which involves a contradiction, the
predication of the simple term is impossible. Thus it is not right
to call a dead man a man. When, however, this is not the case,
it is not impossible.
Yet the facts of the case might rather be stated thus: when
some such opposite elements are present, resolution is never
possible, but when they are not present, resolution is
nevertheless not always possible. Take the proposition 'Homer
is so-and-so', say 'a poet'; does it follow that Homer is, or does
it not? The verb 'is' is here used of Homer only incidentally, the
proposition being that Homer is a poet, not that he is, in the
independent sense of the word.
Thus, in the case of those predications which have within them
no contradiction when the nouns are expanded into definitions,
and wherein the predicates belong to the subject in their own
proper sense and not in any indirect way, the individual may be
the subject of the simple propositions as well as of the
composite. But in the case of that which is not, it is not true to
say that because it is the object of opinion, it is; for the opinion
held about it is that it is not, not that it is.
12
As these distinctions have been made, we must consider the
mutual relation of those affirmations and denials which assert
or deny possibility or contingency, impossibility or necessity:
for the subject is not without difficulty.
We admit that of composite expressions those are contradictory
each to each which have the verb 'to be' its positive and
68
negative form respectively. Thus the contradictory of the
proposition 'man is' is 'man is not', not 'not-man is', and the
contradictory of 'man is white' is 'man is not white', not 'man is
not-white'. For otherwise, since either the positive or the
negative proposition is true of any subject, it will turn out true
to say that a piece of wood is a man that is not white.
Now if this is the case, in those propositions which do not
contain the verb 'to be' the verb which takes its place will
exercise the same function. Thus the contradictory of 'man
walks' is 'man does not walk', not 'not-man walks'; for to say
'man walks' merely equivalent to saying 'man is walking'.
If then this rule is universal, the contradictory of 'it may be' is
may not be', not 'it cannot be'.
Now it appears that the same thing both may and may not be;
for instance, everything that may be cut or may walk may also
escape cutting and refrain from walking; and the reason is that
those things that have potentiality in this sense are not always
actual. In such cases, both the positive and the negative
propositions will be true; for that which is capable of walking or
of being seen has also a potentiality in the opposite direction.
But since it is impossible that contradictory propositions should
both be true of the same subject, it follows that' it may not be'
is not the contradictory of 'it may be'. For it is a logical
consequence of what we have said, either that the same
predicate can be both applicable and inapplicable to one and
the same subject at the same time, or that it is not by the
addition of the verbs 'be' and 'not be', respectively, that positive
and negative propositions are formed. If the former of these
alternatives must be rejected, we must choose the latter.
The contradictory, then, of 'it may be' is 'it cannot be'. The
same rule applies to the proposition 'it is contingent that it
69
should be'; the contradictory of this is 'it is not contingent that
it should be'. The similar propositions, such as 'it is necessary'
and 'it is impossible', may be dealt with in the same manner.
For it comes about that just as in the former instances the verbs
'is' and 'is not' were added to the subject-matter of the
sentence 'white' and 'man', so here 'that it should be' and 'that
it should not be' are the subject-matter and 'is possible', 'is
contingent', are added. These indicate that a certain thing is or
is not possible, just as in the former instances 'is' and 'is not'
indicated that certain things were or were not the case.
The contradictory, then, of 'it may not be' is not 'it cannot be',
but 'it cannot not be', and the contradictory of 'it may be' is not
'it may not be', but cannot be'. Thus the propositions 'it may be'
and 'it may not be' appear each to imply the other: for, since
these two propositions are not contradictory, the same thing
both may and may not be. But the propositions 'it may be' and
'it cannot be' can never be true of the same subject at the same
time, for they are contradictory. Nor can the propositions 'it
may not be' and 'it cannot not be' be at once true of the same
subject.
The propositions which have to do with necessity are governed
by the same principle. The contradictory of 'it is necessary that
it should be', is not 'it is necessary that it should not be,' but 'it
is not necessary that it should be', and the contradictory of 'it is
necessary that it should not be' is 'it is not necessary that it
should not be'.
Again, the contradictory of 'it is impossible that it should be' is
not 'it is impossible that it should not be' but 'it is not
impossible that it should be', and the contradictory of 'it is
impossible that it should not be' is 'it is not impossible that it
should not be'.
70
To generalize, we must, as has been stated, define the clauses
'that it should be' and 'that it should not be' as the subject-
matter of the propositions, and in making these terms into
affirmations and denials we must combine them with 'that it
should be' and 'that it should not be' respectively.
We must consider the following pairs as contradictory
propositions:
It may be. It cannot be.
It is contingent.lt is not contingent.
It is impossible.lt is not impossible.
It is necessary.lt is not necessary.
It is true. It is not true.
13
Logical sequences follow in due course when we have arranged
the propositions thus. From the proposition 'it may be' it
follows that it is contingent, and the relation is reciprocal. It
follows also that it is not impossible and not necessary.
From the proposition 'it may not be' or 'it is contingent that it
should not be' it follows that it is not necessary that it should
not be and that it is not impossible that it should not be. From
the proposition 'it cannot be' or 'it is not contingent' it follows
that it is necessary that it should not be and that it is
impossible that it should be. From the proposition 'it cannot not
be' or 'it is not contingent that it should not be' it follows that it
71
is necessary that it should be and that it is impossible that it
should not be.
Let us consider these statements by the help of a table:
A. B.
It may be. It cannot be.
It is contingent. It is not contingent.
It is not impossible that it It is impossible that it should
should be. be.
It is not necessary that it It is necessary that it should
should be. not be.
C. D.
It may not be. It cannot not be.
It is contingent that it should It is not contingent that it
not be. should not be.
It is not impossible that it It is impossible that it should
should not be. not be.
It is not necessary that it It is necessary that it should
should not be. be.
Now the propositions 'it is impossible that it should be' and 'it
is not impossible that it should be' are consequent upon the
propositions 'it may be', 'it is contingent', and 'it cannot be', 'it
is not contingent', the contradictories upon the contradictories.
72
But there is inversion. The negative of the proposition 'it is
impossible' is consequent upon the proposition 'it may be' and
the corresponding positive in the first case upon the negative in
the second. For 'it is impossible' is a positive proposition and 'it
is not impossible' is negative.
We must investigate the relation subsisting between these
propositions and those which predicate necessity. That there is
a distinction is clear. In this case, contrary propositions follow
respectively from contradictory propositions, and the
contradictory propositions belong to separate sequences. For
the proposition 'it is not necessary that it should be' is not the
negative of 'it is necessary that it should not be', for both these
propositions may be true of the same subject; for when it is
necessary that a thing should not be, it is not necessary that it
should be. The reason why the propositions predicating
necessity do not follow in the same kind of sequence as the
rest, lies in the fact that the proposition 'it is impossible' is
equivalent, when used with a contrary subject, to the
proposition 'it is necessary'. For when it is impossible that a
thing should be, it is necessary, not that it should be, but that it
should not be, and when it is impossible that a thing should not
be, it is necessary that it should be. Thus, if the propositions
predicating impossibility or non-impossibility follow without
change of subject from those predicating possibility or non-
possibility, those predicating necessity must follow with the
contrary subject; for the propositions 'it is impossible' and 'it is
necessary' are not equivalent, but, as has been said, inversely
connected.
Yet perhaps it is impossible that the contradictory propositions
predicating necessity should be thus arranged. For when it is
necessary that a thing should be, it is possible that it should be.
(For if not, the opposite follows, since one or the other must
follow; so, if it is not possible, it is impossible, and it is thus
73
impossible that a thing should be, which must necessarily be;
which is absurd.)
Yet from the proposition 'it may be' it follows that it is not
impossible, and from that it follows that it is not necessary; it
comes about therefore that the thing which must necessarily be
need not be; which is absurd. But again, the proposition 'it is
necessary that it should be' does not follow from the
proposition 'it may be', nor does the proposition 'it is necessary
that it should not be'. For the proposition 'it may be' implies a
twofold possibility, while, if either of the two former
propositions is true, the twofold possibility vanishes. For if a
thing may be, it may also not be, but if it is necessary that it
should be or that it should not be, one of the two alternatives
will be excluded. It remains, therefore, that the proposition 'it is
not necessary that it should not be' follows from the
proposition 'it may be'. For this is true also of that which must
necessarily be.
Moreover the proposition 'it is not necessary that it should not
be' is the contradictory of that which follows from the
proposition 'it cannot be'; for 'it cannot be' is followed by 'it is
impossible that it should be' and by 'it is necessary that it
should not be', and the contradictory of this is the proposition
'it is not necessary that it should not be'. Thus in this case also
contradictory propositions follow contradictory in the way
indicated, and no logical impossibilities occur when they are
thus arranged.
It may be questioned whether the proposition 'it may be'
follows from the proposition 'it is necessary that it should be'. If
not, the contradictory must follow, namely that it cannot be, or,
if a man should maintain that this is not the contradictory, then
the proposition 'it may not be'.
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Now both of these are false of that which necessarily is. At the
same time, it is thought that if a thing may be cut it may also
not be cut, if a thing may be it may also not be, and thus it
would follow that a thing which must necessarily be may
possibly not be; which is false. It is evident, then, that it is not
always the case that that which may be or may walk possesses
also a potentiality in the other direction. There are exceptions.
In the first place we must except those things which possess a
potentiality not in accordance with a rational principle, as fire
possesses the potentiality of giving out heat, that is, an
irrational capacity. Those potentialities which involve a rational
principle are potentialities of more than one result, that is, of
contrary results; those that are irrational are not always thus
constituted. As I have said, fire cannot both heat and not heat,
neither has anything that is always actual any twofold
potentiality. Yet some even of those potentialities which are
irrational admit of opposite results. However, thus much has
been said to emphasize the truth that it is not every potentiality
which admits of opposite results, even where the word is used
always in the same sense.
But in some cases the word is used equivocally. For the term
'possible' is ambiguous, being used in the one case with
reference to facts, to that which is actualized, as when a man is
said to find walking possible because he is actually walking,
and generally when a capacity is predicated because it is
actually realized; in the other case, with reference to a state in
which realization is conditionally practicable, as when a man is
said to find walking possible because under certain conditions
he would walk. This last sort of potentiality belongs only to that
which can be in motion, the former can exist also in the case of
that which has not this power. Both of that which is walking
and is actual, and of that which has the capacity though not
necessarily realized, it is true to say that it is not impossible
that it should walk (or, in the other case, that it should be), but
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while we cannot predicate this latter kind of potentiality of that
which is necessary in the unqualified sense of the word, we can
predicate the former.
Our conclusion, then, is this: that since the universal is
consequent upon the particular, that which is necessary is also
possible, though not in every sense in which the word may be
used.
We may perhaps state that necessity and its absence are the
initial principles of existence and non-existence, and that all
else must be regarded as posterior to these.
It is plain from what has been said that that which is of
necessity is actual. Thus, if that which is eternal is prior,
actuality also is prior to potentiality. Some things are actualities
without potentiality, namely, the primary substances; a second
class consists of those things which are actual but also
potential, whose actuality is in nature prior to their potentiality,
though posterior in time; a third class comprises those things
which are never actualized, but are pure potentialities.
14
The question arises whether an affirmation finds its contrary in
a denial or in another affirmation; whether the proposition
'every man is just' finds its contrary in the proposition 'no man
is just', or in the proposition 'every man is unjust'. Take the
propositions 'Callias is just', 'Callias is not just', 'Callias is
unjust'; we have to discover which of these form contraries.
Now if the spoken word corresponds with the judgement of the
mind, and if, in thought, that judgement is the contrary of
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another, which pronounces a contrary fact, in the way, for
instance, in which the judgement 'every man is just'
pronounces a contrary to that pronounced by the judgement
'every man is unjust', the same must needs hold good with
regard to spoken affirmations.
But if, in thought, it is not the judgement which pronounces a
contrary fact that is the contrary of another, then one
affirmation will not find its contrary in another, but rather in
the corresponding denial. We must therefore consider which
true judgement is the contrary of the false, that which forms
the denial of the false judgement or that which affirms the
contrary fact.
Let me illustrate. There is a true judgement concerning that
which is good, that it is good; another, a false judgement, that it
is not good; and a third, which is distinct, that it is bad. Which
of these two is contrary to the true? And if they are one and the
same, which mode of expression forms the contrary?
It is an error to suppose that judgements are to be defined as
contrary in virtue of the fact that they have contrary subjects;
for the judgement concerning a good thing, that it is good, and
that concerning a bad thing, that it is bad, may be one and the
same, and whether they are so or not, they both represent the
truth. Yet the subjects here are contrary. But judgements are
not contrary because they have contrary subjects, but because
they are to the contrary effect.
Now if we take the judgement that that which is good is good,
and another that it is not good, and if there are at the same
time other attributes, which do not and cannot belong to the
good, we must nevertheless refuse to treat as the contraries of
the true judgement those which opine that some other attribute
subsists which does not subsist, as also those that opine that
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some other attribute does not subsist which does subsist, for
both these classes of judgement are of unlimited content.
Those judgements must rather be termed contrary to the true
judgements, in which error is present. Now these judgements
are those which are concerned with the starting points of
generation, and generation is the passing from one extreme to
its opposite; therefore error is a like transition.
Now that which is good is both good and not bad. The first
quality is part of its essence, the second accidental; for it is by
accident that it is not bad. But if that true judgement is most
really true, which concerns the subject's intrinsic nature, then
that false judgement likewise is most really false, which
concerns its intrinsic nature. Now the judgement that that is
good is not good is a false judgement concerning its intrinsic
nature, the judgement that it is bad is one concerning that
which is accidental. Thus the judgement which denies the true
judgement is more really false than that which positively
asserts the presence of the contrary quality. But it is the man
who forms that judgement which is contrary to the true who is
most thoroughly deceived, for contraries are among the things
which differ most widely within the same class. If then of the
two judgements one is contrary to the true judgement, but that
which is contradictory is the more truly contrary, then the
latter, it seems, is the real contrary. The judgement that that
which is good is bad is composite. For presumably the man who
forms that judgement must at the same time understand that
that which is good is not good.
Further, the contradictory is either always the contrary or
never; therefore, if it must necessarily be so in all other cases,
our conclusion in the case just dealt with would seem to be
correct. Now where terms have no contrary, that judgement is
false, which forms the negative of the true; for instance, he who
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thinks a man is not a man forms a false judgement. If then in
these cases the negative is the contrary, then the principle is
universal in its application.
Again, the judgement that that which is not good is not good is
parallel with the judgement that that which is good is good.
Besides these there is the judgement that that which is good is
not good, parallel with the judgement that that that is not good
is good. Let us consider, therefore, what would form the
contrary of the true judgement that that which is not good is
not good. The judgement that it is bad would, of course, fail to
meet the case, since two true judgements are never contrary
and this judgement might be true at the same time as that with
which it is connected. For since some things which are not good
are bad, both judgements may be true. Nor is the judgement
that it is not bad the contrary, for this too might be true, since
both qualities might be predicated of the same subject. It
remains, therefore, that of the judgement concerning that
which is not good, that it is not good, the contrary judgement is
that it is good; for this is false. In the same way, moreover, the
judgement concerning that which is good, that it is not good, is
the contrary of the judgement that it is good.
It is evident that it will make no difference if we universalize
the positive judgement, for the universal negative judgement
will form the contrary. For instance, the contrary of the
judgement that everything that is good is good is that nothing
that is good is good. For the judgement that that which is good
is good, if the subject be understood in a universal sense, is
equivalent to the judgement that whatever is good is good, and
this is identical with the judgement that everything that is good
is good. We may deal similarly with judgements concerning
that which is not good.
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If therefore this is the rule with judgements, and if spoken
affirmations and denials are judgements expressed in words, it
is plain that the universal denial is the contrary of the
affirmation about the same subject. Thus the propositions
'everything good is good', 'every man is good', have for their
contraries the propositions 'nothing good is good', 'no man is
good'. The contradictory propositions, on the other hand, are
'not everything good is good', 'not every man is good'.
It is evident, also, that neither true judgements nor true
propositions can be contrary the one to the other. For whereas,
when two propositions are true, a man may state both at the
same time without inconsistency, contrary propositions are
those which state contrary conditions, and contrary conditions
cannot subsist at one and the same time in the same subject.
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Aristotle - Prior Analytics
[Translated by A. J. Jenkinson]
Book I
We must first state the subject of our inquiry and the faculty to
which it belongs: its subject is demonstration and the faculty
that carries it out demonstrative science. We must next define a
premiss, a term, and a syllogism, and the nature of a perfect
and of an imperfect syllogism; and after that, the inclusion or
noninclusion of one term in another as in a whole, and what we
mean by predicating one term of all, or none, of another.
A premiss then is a sentence affirming or denying one thing of
another. This is either universal or particular or indefinite. By
universal I mean the statement that something belongs to all or
none of something else; by particular that it belongs to some or
not to some or not to all; by indefinite that it does or does not
belong, without any mark to show whether it is universal or
particular, e.g. 'contraries are subjects of the same science', or
'pleasure is not good'. The demonstrative premiss differs from
the dialectical, because the demonstrative premiss is the
assertion of one of two contradictory statements (the
demonstrator does not ask for his premiss, but lays it down),
whereas the dialectical premiss depends on the adversary's
choice between two contradictories. But this will make no
difference to the production of a syllogism in either case; for
both the demonstrator and the dialectician argue syllogistically
after stating that something does or does not belong to
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something else. Therefore a syllogistic premiss without
qualification will be an affirmation or denial of something
concerning something else in the way we have described; it will
be demonstrative, if it is true and obtained through the first
principles of its science; while a dialectical premiss is the giving
of a choice between two contradictories, when a man is
proceeding by question, but when he is syllogizing it is the
assertion of that which is apparent and generally admitted, as
has been said in the Topics. The nature then of a premiss and
the difference between syllogistic, demonstrative, and
dialectical premisses, may be taken as sufficiently defined by us
in relation to our present need, but will be stated accurately in
the sequel.
I call that a term into which the premiss is resolved, i.e. both the
predicate and that of which it is predicated, 'being' being added
and 'not being' removed, or vice versa.
A syllogism is discourse in which, certain things being stated,
something other than what is stated follows of necessity from
their being so. I mean by the last phrase that they produce the
consequence, and by this, that no further term is required from
without in order to make the consequence necessary.
I call that a perfect syllogism which needs nothing other than
what has been stated to make plain what necessarily follows; a
syllogism is imperfect, if it needs either one or more
propositions, which are indeed the necessary consequences of
the terms set down, but have not been expressly stated as
premisses.
That one term should be included in another as in a whole is
the same as for the other to be predicated of all of the first. And
we say that one term is predicated of all of another, whenever
no instance of the subject can be found of which the other term
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cannot be asserted: 'to be predicated of none' must be
understood in the same way.
Every premiss states that something either is or must be or may
be the attribute of something else; of premisses of these three
kinds some are affirmative, others negative, in respect of each
of the three modes of attribution; again some affirmative and
negative premisses are universal, others particular, others
indefinite. It is necessary then that in universal attribution the
terms of the negative premiss should be convertible, e.g. if no
pleasure is good, then no good will be pleasure; the terms of the
affirmative must be convertible, not however, universally, but in
part, e.g. if every pleasure, is good, some good must be pleasure;
the particular affirmative must convert in part (for if some
pleasure is good, then some good will be pleasure); but the
particular negative need not convert, for if some animal is not
man, it does not follow that some man is not animal.
First then take a universal negative with the terms A and B. If no
B is A, neither can any A be B. For if some A (say C) were B, it
would not be true that no B is A; for C is a B. But if every B is A
then some A is B. For if no A were B, then no B could be A. But
we assumed that every B is A. Similarly too, if the premiss is
particular. For if some B is A, then some of the As must be B. For
if none were, then no B would be A. But if some B is not A, there
is no necessity that some of the As should not be B; e.g. let B
stand for animal and A for man. Not every animal is a man; but
every man is an animal.
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The same manner of conversion will hold good also in respect
of necessary premisses. The universal negative converts
universally; each of the affirmatives converts into a particular. If
it is necessary that no B is A, it is necessary also that no A is B.
For if it is possible that some A is B, it would be possible also
that some B is A. If all or some B is A of necessity, it is necessary
also that some A is B: for if there were no necessity, neither
would some of the Bs be A necessarily. But the particular
negative does not convert, for the same reason which we have
already stated.
In respect of possible premisses, since possibility is used in
several senses (for we say that what is necessary and what is
not necessary and what is potential is possible), affirmative
statements will all convert in a manner similar to those
described. For if it is possible that all or some B is A, it will be
possible that some A is B. For if that were not possible, then no
B could possibly be A. This has been already proved. But in
negative statements the case is different. Whatever is said to be
possible, either because B necessarily is A, or because B is not
necessarily A, admits of conversion like other negative
statements, e.g. if one should say, it is possible that man is not
horse, or that no garment is white. For in the former case the
one term necessarily does not belong to the other; in the latter
there is no necessity that it should: and the premiss converts
like other negative statements. For if it is possible for no man to
be a horse, it is also admissible for no horse to be a man; and if
it is admissible for no garment to be white, it is also admissible
for nothing white to be a garment. For if any white thing must
be a garment, then some garment will necessarily be white. This
has been already proved. The particular negative also must be
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treated like those dealt with above. But if anything is said to be
possible because it is the general rule and natural (and it is in
this way we define the possible), the negative premisses can no
longer be converted like the simple negatives; the universal
negative premiss does not convert, and the particular does. This
will be plain when we speak about the possible. At present we
may take this much as clear in addition to what has been said:
the statement that it is possible that no B is A or some B is not A
is affirmative in form: for the expression 'is possible' ranks
along with 'is', and 'is' makes an affirmation always and in
every case, whatever the terms to which it is added, in
predication, e.g. 'it is not-good' or 'it is not-white' or in a word 'it
is not-this'. But this also will be proved in the sequel. In
conversion these premisses will behave like the other
affirmative propositions.
After these distinctions we now state by what means, when,
and how every syllogism is produced; subsequently we must
speak of demonstration. Syllogism should be discussed before
demonstration because syllogism is the general: the
demonstration is a sort of syllogism, but not every syllogism is a
demonstration.
Whenever three terms are so related to one another that the
last is contained in the middle as in a whole, and the middle is
either contained in, or excluded from, the first as in or from a
whole, the extremes must be related by a perfect syllogism. I
call that term middle which is itself contained in another and
contains another in itself: in position also this comes in the
middle. By extremes I mean both that term which is itself
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contained in another and that in which another is contained. If
A is predicated of all B, and B of all C, A must be predicated of
all C: we have already explained what we mean by 'predicated
of all'. Similarly also, if A is predicated of no B, and B of all C, it
is necessary that no C will be A.
But if the first term belongs to all the middle, but the middle to
none of the last term, there will be no syllogism in respect of
the extremes; for nothing necessary follows from the terms
being so related; for it is possible that the first should belong
either to all or to none of the last, so that neither a particular
nor a universal conclusion is necessary. But if there is no
necessary consequence, there cannot be a syllogism by means
of these premisses. As an example of a universal affirmative
relation between the extremes we may take the terms animal,
man, horse; of a universal negative relation, the terms animal,
man, stone. Nor again can syllogism be formed when neither
the first term belongs to any of the middle, nor the middle to
any of the last. As an example of a positive relation between the
extremes take the terms science, line, medicine: of a negative
relation science, line, unit.
If then the terms are universally related, it is clear in this figure
when a syllogism will be possible and when not, and that if a
syllogism is possible the terms must be related as described,
and if they are so related there will be a syllogism.
But if one term is related universally, the other in part only, to
its subject, there must be a perfect syllogism whenever
universality is posited with reference to the major term either
affirmatively or negatively, and particularity with reference to
the minor term affirmatively: but whenever the universality is
posited in relation to the minor term, or the terms are related in
any other way, a syllogism is impossible. I call that term the
major in which the middle is contained and that term the
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minor which comes under the middle. Let all B be A and some C
be B. Then if 'predicated of all' means what was said above, it is
necessary that some C is A. And if no B is A but some C is B, it is
necessary that some C is not A. The meaning of 'predicated of
none' has also been defined. So there will be a perfect syllogism.
This holds good also if the premiss BC should be indefinite,
provided that it is affirmative: for we shall have the same
syllogism whether the premiss is indefinite or particular.
But if the universality is posited with respect to the minor term
either affirmatively or negatively, a syllogism will not be
possible, whether the major premiss is positive or negative,
indefinite or particular: e.g. if some B is or is not A, and all C is
B. As an example of a positive relation between the extremes
take the terms good, state, wisdom: of a negative relation, good,
state, ignorance. Again if no C is B, but some B is or is not A or
not every B is A, there cannot be a syllogism. Take the terms
white, horse, swan: white, horse, raven. The same terms may be
taken also if the premiss BA is indefinite.
Nor when the major premiss is universal, whether affirmative
or negative, and the minor premiss is negative and particular,
can there be a syllogism, whether the minor premiss be
indefinite or particular: e.g. if all B is A and some C is not B, or if
not all C is B. For the major term may be predicable both of all
and of none of the minor, to some of which the middle term
cannot be attributed. Suppose the terms are animal, man,
white: next take some of the white things of which man is not
predicated - swan and snow: animal is predicated of all of the
one, but of none of the other. Consequently there cannot be a
syllogism. Again let no B be A, but let some C not be B. Take the
terms inanimate, man, white: then take some white things of
which man is not predicated - swan and snow: the term
inanimate is predicated of all of the one, of none of the other.
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Further since it is indefinite to say some C is not B, and it is true
that some C is not B, whether no C is B, or not all C is B, and
since if terms are assumed such that no C is B, no syllogism
follows (this has already been stated) it is clear that this
arrangement of terms will not afford a syllogism: otherwise one
would have been possible with a universal negative minor
premiss. A similar proof may also be given if the universal
premiss is negative.
Nor can there in any way be a syllogism if both the relations of
subject and predicate are particular, either positively or
negatively, or the one negative and the other affirmative, or one
indefinite and the other definite, or both indefinite. Terms
common to all the above are animal, white, horse: animal,
white, stone.
It is clear then from what has been said that if there is a
syllogism in this figure with a particular conclusion, the terms
must be related as we have stated: if they are related otherwise,
no syllogism is possible anyhow. It is evident also that all the
syllogisms in this figure are perfect (for they are all completed
by means of the premisses originally taken) and that all
conclusions are proved by this figure, viz. universal and
particular, affirmative and negative. Such a figure I call the first.
Whenever the same thing belongs to all of one subject, and to
none of another, or to all of each subject or to none of either, I
call such a figure the second; by middle term in it I mean that
which is predicated of both subjects, by extremes the terms of
which this is said, by major extreme that which lies near the
middle, by minor that which is further away from the middle.
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The middle term stands outside the extremes, and is first in
position. A syllogism cannot be perfect anyhow in this figure,
but it may be valid whether the terms are related universally or
not.
If then the terms are related universally a syllogism will be
possible, whenever the middle belongs to all of one subject and
to none of another (it does not matter which has the negative
relation), but in no other way. Let M be predicated of no N, but of
all 0. Since, then, the negative relation is convertible, N will
belong to no M: but M was assumed to belong to all 0:
consequently N will belong to no 0. This has already been
proved. Again if M belongs to all N, but to no 0, then N will
belong to no 0. For if M belongs to no 0, belongs to no M: but
M (as was said) belongs to all N: then will belong to no N: for
the first figure has again been formed. But since the negative
relation is convertible, N will belong to no 0. Thus it will be the
same syllogism that proves both conclusions.
It is possible to prove these results also by reductio ad
impossibile.
It is clear then that a syllogism is formed when the terms are so
related, but not a perfect syllogism; for necessity is not perfectly
established merely from the original premisses; others also are
needed.
But if M is predicated of every N and 0, there cannot be a
syllogism. Terms to illustrate a positive relation between the
extremes are substance, animal, man; a negative relation,
substance, animal, number - substance being the middle term.
Nor is a syllogism possible when M is predicated neither of any
N nor of any 0. Terms to illustrate a positive relation are line,
animal, man: a negative relation, line, animal, stone.
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It is clear then that if a syllogism is formed when the terms are
universally related, the terms must be related as we stated at
the outset: for if they are otherwise related no necessary
consequence follows.
If the middle term is related universally to one of the extremes,
a particular negative syllogism must result whenever the
middle term is related universally to the major whether
positively or negatively, and particularly to the minor and in a
manner opposite to that of the universal statement: by 'an
opposite manner' I mean, if the universal statement is negative,
the particular is affirmative: if the universal is affirmative, the
particular is negative. For if M belongs to no N, but to some 0, it
is necessary that N does not belong to some 0. For since the
negative statement is convertible, N will belong to no M: but M
was admitted to belong to some 0: therefore N will not belong
to some 0: for the result is reached by means of the first figure.
Again if M belongs to all N, but not to some 0, it is necessary
that N does not belong to some 0: for if N belongs to all 0, and
M is predicated also of all N, M must belong to all 0: but we
assumed that M does not belong to some 0. And if M belongs to
all N but not to all 0, we shall conclude that N does not belong
to all 0: the proof is the same as the above. But if M is
predicated of all 0, but not of all N, there will be no syllogism.
Take the terms animal, substance, raven; animal, white, raven.
Nor will there be a conclusion when M is predicated of no 0, but
of some N. Terms to illustrate a positive relation between the
extremes are animal, substance, unit: a negative relation,
animal, substance, science.
If then the universal statement is opposed to the particular, we
have stated when a syllogism will be possible and when not:
but if the premisses are similar in form, I mean both negative or
both affirmative, a syllogism will not be possible anyhow. First
let them be negative, and let the major premiss be universal, e.g.
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let M belong to no N, and not to some 0. It is possible then for N
to belong either to all or to no 0. Terms to illustrate the
negative relation are black, snow, animal. But it is not possible
to find terms of which the extremes are related positively and
universally, if M belongs to some 0, and does not belong to
some 0. For if N belonged to all 0, but M to no N, then M would
belong to no 0: but we assumed that it belongs to some 0. In
this way then it is not admissible to take terms: our point must
be proved from the indefinite nature of the particular
statement. For since it is true that M does not belong to some 0,
even if it belongs to no 0, and since if it belongs to no a
syllogism is (as we have seen) not possible, clearly it will not be
possible now either.
Again let the premisses be affirmative, and let the major
premiss as before be universal, e.g. let M belong to all N and to
some 0. It is possible then for N to belong to all or to no 0.
Terms to illustrate the negative relation are white, swan, stone.
But it is not possible to take terms to illustrate the universal
affirmative relation, for the reason already stated: the point
must be proved from the indefinite nature of the particular
statement. But if the minor premiss is universal, and M belongs
to no 0, and not to some N, it is possible for N to belong either
to all or to no 0. Terms for the positive relation are white,
animal, raven: for the negative relation, white, stone, raven. If
the premisses are affirmative, terms for the negative relation
are white, animal, snow; for the positive relation, white, animal,
swan. Evidently then, whenever the premisses are similar in
form, and one is universal, the other particular, a syllogism can,
not be formed anyhow. Nor is one possible if the middle term
belongs to some of each of the extremes, or does not belong to
some of either, or belongs to some of the one, not to some of the
other, or belongs to neither universally, or is related to them
indefinitely. Common terms for all the above are white, animal,
man: white, animal, inanimate. It is clear then from what has
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been said that if the terms are related to one another in the way
stated, a syllogism results of necessity; and if there is a
syllogism, the terms must be so related. But it is evident also
that all the syllogisms in this figure are imperfect: for all are
made perfect by certain supplementary statements, which
either are contained in the terms of necessity or are assumed as
hypotheses, i.e. when we prove per impossibile. And it is evident
that an affirmative conclusion is not attained by means of this
figure, but all are negative, whether universal or particular.
But if one term belongs to all, and another to none, of a third, or
if both belong to all, or to none, of it, I call such a figure the
third; by middle term in it I mean that of which both the
predicates are predicated, by extremes I mean the predicates, by
the major extreme that which is further from the middle, by the
minor that which is nearer to it. The middle term stands outside
the extremes, and is last in position. A syllogism cannot be
perfect in this figure either, but it may be valid whether the
terms are related universally or not to the middle term.
If they are universal, whenever both P and R belong to S, it
follows that P will necessarily belong to some R. For, since the
affirmative statement is convertible, S will belong to some R:
consequently since P belongs to all S, and S to some R, P must
belong to some R: for a syllogism in the first figure is produced.
It is possible to demonstrate this also per impossibile and by
exposition. For if both P and R belong to all S, should one of the
Ss, e.g. N, be taken, both P and R will belong to this, and thus P
will belong to some R.
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If R belongs to all S, and P to no S, there will be a syllogism to
prove that P will necessarily not belong to some R. This may be
demonstrated in the same way as before by converting the
premiss RS. It might be proved also per impossibile, as in the
former cases. But if R belongs to no S, P to all S, there will be no
syllogism. Terms for the positive relation are animal, horse,
man: for the negative relation animal, inanimate, man.
Nor can there be a syllogism when both terms are asserted of
no S. Terms for the positive relation are animal, horse,
inanimate; for the negative relation man, horse, inanimate -
inanimate being the middle term.
It is clear then in this figure also when a syllogism will be
possible and when not, if the terms are related universally. For
whenever both the terms are affirmative, there will be a
syllogism to prove that one extreme belongs to some of the
other; but when they are negative, no syllogism will be possible.
But when one is negative, the other affirmative, if the major is
negative, the minor affirmative, there will be a syllogism to
prove that the one extreme does not belong to some of the
other: but if the relation is reversed, no syllogism will be
possible. If one term is related universally to the middle, the
other in part only, when both are affirmative there must be a
syllogism, no matter which of the premisses is universal. For if
R belongs to all S, P to some S, P must belong to some R. For
since the affirmative statement is convertible S will belong to
some P: consequently since R belongs to all S, and S to some P, R
must also belong to some P: therefore P must belong to some R.
Again if R belongs to some S, and P to all S, P must belong to
some R. This may be demonstrated in the same way as the
preceding. And it is possible to demonstrate it also per
impossibile and by exposition, as in the former cases. But if one
term is affirmative, the other negative, and if the affirmative is
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universal, a syllogism will be possible whenever the minor term
is affirmative. For if R belongs to all S, but P does not belong to
some S, it is necessary that P does not belong to some R. For if P
belongs to all R, and R belongs to all S, then P will belong to all
S: but we assumed that it did not. Proof is possible also without
reduction ad impossibile, if one of the Ss be taken to which P
does not belong.
But whenever the major is affirmative, no syllogism will be
possible, e.g. if P belongs to all S and R does not belong to some
S. Terms for the universal affirmative relation are animate, man,
animal. For the universal negative relation it is not possible to
get terms, if R belongs to some S, and does not belong to some
S. For if P belongs to all S, and R to some S, then P will belong to
some R: but we assumed that it belongs to no R. We must put
the matter as before.' Since the expression 'it does not belong to
some' is indefinite, it may be used truly of that also which
belongs to none. But if R belongs to no S, no syllogism is
possible, as has been shown. Clearly then no syllogism will be
possible here.
But if the negative term is universal, whenever the major is
negative and the minor affirmative there will be a syllogism. For
if P belongs to no S, and R belongs to some S, P will not belong
to some R: for we shall have the first figure again, if the premiss
RS is converted.
But when the minor is negative, there will be no syllogism.
Terms for the positive relation are animal, man, wild: for the
negative relation, animal, science, wild - the middle in both
being the term wild.
Nor is a syllogism possible when both are stated in the negative,
but one is universal, the other particular. When the minor is
related universally to the middle, take the terms animal,
science, wild; animal, man, wild. When the major is related
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universally to the middle, take as terms for a negative relation
raven, snow, white. For a positive relation terms cannot be
found, if R belongs to some S, and does not belong to some S.
For if P belongs to all R, and R to some S, then P belongs to some
S: but we assumed that it belongs to no S. Our point, then, must
be proved from the indefinite nature of the particular
statement.
Nor is a syllogism possible anyhow, if each of the extremes
belongs to some of the middle or does not belong, or one
belongs and the other does not to some of the middle, or one
belongs to some of the middle, the other not to all, or if the
premisses are indefinite. Common terms for all are animal,
man, white: animal, inanimate, white.
It is clear then in this figure also when a syllogism will be
possible, and when not; and that if the terms are as stated, a
syllogism results of necessity, and if there is a syllogism, the
terms must be so related. It is clear also that all the syllogisms
in this figure are imperfect (for all are made perfect by certain
supplementary assumptions), and that it will not be possible to
reach a universal conclusion by means of this figure, whether
negative or affirmative.
It is evident also that in all the figures, whenever a proper
syllogism does not result, if both the terms are affirmative or
negative nothing necessary follows at all, but if one is
affirmative, the other negative, and if the negative is stated
universally, a syllogism always results relating the minor to the
major term, e.g. if A belongs to all or some B, and B belongs to
no C: for if the premisses are converted it is necessary that C
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does not belong to some A. Similarly also in the other figures: a
syllogism always results by means of conversion. It is evident
also that the substitution of an indefinite for a particular
affirmative will effect the same syllogism in all the figures.
It is clear too that all the imperfect syllogisms are made perfect
by means of the first figure. For all are brought to a conclusion
either ostensively or per impossibile. In both ways the first
figure is formed: if they are made perfect ostensively, because
(as we saw) all are brought to a conclusion by means of
conversion, and conversion produces the first figure: if they are
proved per impossibile, because on the assumption of the false
statement the syllogism comes about by means of the first
figure, e.g. in the last figure, if A and B belong to all C, it follows
that A belongs to some B: for if A belonged to no B, and B
belongs to all C, A would belong to no C: but (as we stated) it
belongs to all C. Similarly also with the rest.
It is possible also to reduce all syllogisms to the universal
syllogisms in the first figure. Those in the second figure are
clearly made perfect by these, though not all in the same way;
the universal syllogisms are made perfect by converting the
negative premiss, each of the particular syllogisms by reductio
ad impossibile. In the first figure particular syllogisms are
indeed made perfect by themselves, but it is possible also to
prove them by means of the second figure, reducing them ad
impossibile, e.g. if A belongs to all B, and B to some C, it follows
that A belongs to some C. For if it belonged to no C, and belongs
to all B, then B will belong to no C: this we know by means of
the second figure. Similarly also demonstration will be possible
in the case of the negative. For if A belongs to no B, and B
belongs to some C, A will not belong to some C: for if it belonged
to all C, and belongs to no B, then B will belong to no C: and this
(as we saw) is the middle figure. Consequently, since all
syllogisms in the middle figure can be reduced to universal
96
syllogisms in the first figure, and since particular syllogisms in
the first figure can be reduced to syllogisms in the middle
figure, it is clear that particular syllogisms can be reduced to
universal syllogisms in the first figure. Syllogisms in the third
figure, if the terms are universal, are directly made perfect by
means of those syllogisms; but, when one of the premisses is
particular, by means of the particular syllogisms in the first
figure: and these (we have seen) may be reduced to the
universal syllogisms in the first figure: consequently also the
particular syllogisms in the third figure may be so reduced. It is
clear then that all syllogisms may be reduced to the universal
syllogisms in the first figure.
We have stated then how syllogisms which prove that
something belongs or does not belong to something else are
constituted, both how syllogisms of the same figure are
constituted in themselves, and how syllogisms of different
figures are related to one another.
8
Since there is a difference according as something belongs,
necessarily belongs, or may belong to something else (for many
things belong indeed, but not necessarily, others neither
necessarily nor indeed at all, but it is possible for them to
belong), it is clear that there will be different syllogisms to prove
each of these relations, and syllogisms with differently related
terms, one syllogism concluding from what is necessary,
another from what is, a third from what is possible.
There is hardly any difference between syllogisms from
necessary premisses and syllogisms from premisses which
merely assert. When the terms are put in the same way, then,
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whether something belongs or necessarily belongs (or does not
belong) to something else, a syllogism will or will not result
alike in both cases, the only difference being the addition of the
expression 'necessarily' to the terms. For the negative statement
is convertible alike in both cases, and we should give the same
account of the expressions 'to be contained in something as in a
whole' and 'to be predicated of all of something'. With the
exceptions to be made below, the conclusion will be proved to
be necessary by means of conversion, in the same manner as in
the case of simple predication. But in the middle figure when
the universal statement is affirmative, and the particular
negative, and again in the third figure when the universal is
affirmative and the particular negative, the demonstration will
not take the same form, but it is necessary by the 'exposition' of
a part of the subject of the particular negative proposition, to
which the predicate does not belong, to make the syllogism in
reference to this: with terms so chosen the conclusion will
necessarily follow. But if the relation is necessary in respect of
the part taken, it must hold of some of that term in which this
part is included: for the part taken is just some of that. And
each of the resulting syllogisms is in the appropriate figure.
It happens sometimes also that when one premiss is necessary
the conclusion is necessary, not however when either premiss is
necessary, but only when the major is, e.g. if A is taken as
necessarily belonging or not belonging to B, but B is taken as
simply belonging to C: for if the premisses are taken in this way,
A will necessarily belong or not belong to C. For since
necessarily belongs, or does not belong, to every B, and since C
is one of the Bs, it is clear that for C also the positive or the
98
negative relation to A will hold necessarily. But if the major
premiss is not necessary, but the minor is necessary, the
conclusion will not be necessary. For if it were, it would result
both through the first figure and through the third that A
belongs necessarily to some B. But this is false; for B may be
such that it is possible that A should belong to none of it.
Further, an example also makes it clear that the conclusion not
be necessary, e.g. if A were movement, B animal, C man: man is
an animal necessarily, but an animal does not move necessarily,
nor does man. Similarly also if the major premiss is negative;
for the proof is the same.
In particular syllogisms, if the universal premiss is necessary,
then the conclusion will be necessary; but if the particular, the
conclusion will not be necessary, whether the universal premiss
is negative or affirmative. First let the universal be necessary,
and let A belong to all B necessarily, but let B simply belong to
some C: it is necessary then that A belongs to some C
necessarily: for C falls under B, and A was assumed to belong
necessarily to all B. Similarly also if the syllogism should be
negative: for the proof will be the same. But if the particular
premiss is necessary, the conclusion will not be necessary: for
from the denial of such a conclusion nothing impossible results,
just as it does not in the universal syllogisms. The same is true
of negative syllogisms. Try the terms movement, animal, white.
10
In the second figure, if the negative premiss is necessary, then
the conclusion will be necessary, but if the affirmative, not
necessary. First let the negative be necessary; let A be possible
of no B, and simply belong to C. Since then the negative
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statement is convertible, B is possible of no A. But A belongs to
all C; consequently B is possible of no C. For C falls under A. The
same result would be obtained if the minor premiss were
negative: for if A is possible be of no C, C is possible of no A: but
A belongs to all B, consequently C is possible of none of the Bs:
for again we have obtained the first figure. Neither then is B
possible of C: for conversion is possible without modifying the
relation.
But if the affirmative premiss is necessary, the conclusion will
not be necessary. Let A belong to all B necessarily, but to no C
simply. If then the negative premiss is converted, the first figure
results. But it has been proved in the case of the first figure that
if the negative major premiss is not necessary the conclusion
will not be necessary either. Therefore the same result will
obtain here. Further, if the conclusion is necessary, it follows
that C necessarily does not belong to some A. For if B
necessarily belongs to no C, C will necessarily belong to no B.
But B at any rate must belong to some A, if it is true (as was
assumed) that A necessarily belongs to all B. Consequently it is
necessary that C does not belong to some A. But nothing
prevents such an A being taken that it is possible for C to belong
to all of it. Further one might show by an exposition of terms
that the conclusion is not necessary without qualification,
though it is a necessary conclusion from the premisses. For
example let A be animal, B man, C white, and let the premisses
be assumed to correspond to what we had before: it is possible
that animal should belong to nothing white. Man then will not
belong to anything white, but not necessarily: for it is possible
for man to be born white, not however so long as animal
belongs to nothing white. Consequently under these conditions
the conclusion will be necessary, but it is not necessary without
qualification.
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Similar results will obtain also in particular syllogisms. For
whenever the negative premiss is both universal and necessary,
then the conclusion will be necessary: but whenever the
affirmative premiss is universal, the negative particular, the
conclusion will not be necessary. First then let the negative
premiss be both universal and necessary: let it be possible for
no B that A should belong to it, and let A simply belong to some
C. Since the negative statement is convertible, it will be possible
for no A that B should belong to it: but A belongs to some C;
consequently B necessarily does not belong to some of the Cs.
Again let the affirmative premiss be both universal and
necessary, and let the major premiss be affirmative. If then A
necessarily belongs to all B, but does not belong to some C, it is
clear that B will not belong to some C, but not necessarily. For
the same terms can be used to demonstrate the point, which
were used in the universal syllogisms. Nor again, if the negative
statement is necessary but particular, will the conclusion be
necessary. The point can be demonstrated by means of the
same terms.
11
In the last figure when the terms are related universally to the
middle, and both premisses are affirmative, if one of the two is
necessary, then the conclusion will be necessary. But if one is
negative, the other affirmative, whenever the negative is
necessary the conclusion also will be necessary, but whenever
the affirmative is necessary the conclusion will not be
necessary. First let both the premisses be affirmative, and let A
and B belong to all C, and let AC be necessary. Since then B
belongs to all C, C also will belong to some B, because the
universal is convertible into the particular: consequently if A
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belongs necessarily to all C, and C belongs to some B, it is
necessary that A should belong to some B also. For B is under C.
The first figure then is formed. A similar proof will be given also
if BC is necessary. For C is convertible with some A:
consequently if B belongs necessarily to all C, it will belong
necessarily also to some A.
Again let AC be negative, BC affirmative, and let the negative
premiss be necessary. Since then C is convertible with some B,
but A necessarily belongs to no C, A will necessarily not belong
to some B either: for B is under C. But if the affirmative is
necessary, the conclusion will not be necessary. For suppose BC
is affirmative and necessary, while AC is negative and not
necessary. Since then the affirmative is convertible, C also will
belong to some B necessarily: consequently if A belongs to none
of the Cs, while C belongs to some of the Bs, A will not belong to
some of the Bs - but not of necessity; for it has been proved, in
the case of the first figure, that if the negative premiss is not
necessary, neither will the conclusion be necessary. Further, the
point may be made clear by considering the terms. Let the term
A be 'good', let that which B signifies be 'animal', let the term C
be 'horse'. It is possible then that the term good should belong
to no horse, and it is necessary that the term animal should
belong to every horse: but it is not necessary that some animal
should not be good, since it is possible for every animal to be
good. Or if that is not possible, take as the term 'awake' or
'asleep': for every animal can accept these.
If, then, the premisses are universal, we have stated when the
conclusion will be necessary. But if one premiss is universal, the
other particular, and if both are affirmative, whenever the
universal is necessary the conclusion also must be necessary.
The demonstration is the same as before; for the particular
affirmative also is convertible. If then it is necessary that B
should belong to all C, and A falls under C, it is necessary that B
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should belong to some A. But if B must belong to some A, then A
must belong to some B: for conversion is possible. Similarly also
if AC should be necessary and universal: for B falls under C. But
if the particular premiss is necessary, the conclusion will not be
necessary. Let the premiss BC be both particular and necessary,
and let A belong to all C, not however necessarily. If the
proposition BC is converted the first figure is formed, and the
universal premiss is not necessary, but the particular is
necessary. But when the premisses were thus, the conclusion
(as we proved was not necessary: consequently it is not here
either. Further, the point is clear if we look at the terms. Let A be
waking, B biped, and C animal. It is necessary that B should
belong to some C, but it is possible for A to belong to C, and that
A should belong to B is not necessary. For there is no necessity
that some biped should be asleep or awake. Similarly and by
means of the same terms proof can be made, should the
proposition AC be both particular and necessary.
But if one premiss is affirmative, the other negative, whenever
the universal is both negative and necessary the conclusion also
will be necessary. For if it is not possible that A should belong to
any C, but B belongs to some C, it is necessary that A should not
belong to some B. But whenever the affirmative proposition is
necessary, whether universal or particular, or the negative is
particular, the conclusion will not be necessary. The proof of
this by reduction will be the same as before; but if terms are
wanted, when the universal affirmative is necessary, take the
terms 'waking' - 'animal' - 'man', 'man' being middle, and when
the affirmative is particular and necessary, take the terms
'waking' - 'animal' - 'white': for it is necessary that animal
should belong to some white thing, but it is possible that
waking should belong to none, and it is not necessary that
waking should not belong to some animal. But when the
negative proposition being particular is necessary, take the
terms 'biped', 'moving', 'animal', 'animal' being middle.
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12
It is clear then that a simple conclusion is not reached unless
both premisses are simple assertions, but a necessary-
conclusion is possible although one only of the premisses is
necessary. But in both cases, whether the syllogisms are
affirmative or negative, it is necessary that one premiss should
be similar to the conclusion. I mean by 'similar', if the
conclusion is a simple assertion, the premiss must be simple; if
the conclusion is necessary, the premiss must be necessary.
Consequently this also is clear, that the conclusion will be
neither necessary nor simple unless a necessary or simple
premiss is assumed.
13
Perhaps enough has been said about the proof of necessity, how
it comes about and how it differs from the proof of a simple
statement. We proceed to discuss that which is possible, when
and how and by what means it can be proved. I use the terms
'to be possible' and 'the possible' of that which is not necessary
but, being assumed, results in nothing impossible. We say
indeed ambiguously of the necessary that it is possible. But that
my definition of the possible is correct is clear from the phrases
by which we deny or on the contrary affirm possibility. For the
expressions 'it is not possible to belong', 'it is impossible to
belong', and 'it is necessary not to belong' are either identical or
follow from one another; consequently their opposites also, 'it is
possible to belong', 'it is not impossible to belong', and 'it is not
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necessary not to belong', will either be identical or follow from
one another. For of everything the affirmation or the denial
holds good. That which is possible then will be not necessary
and that which is not necessary will be possible. It results that
all premisses in the mode of possibility are convertible into one
another. I mean not that the affirmative are convertible into the
negative, but that those which are affirmative in form admit of
conversion by opposition, e.g. 'it is possible to belong' may be
converted into 'it is possible not to belong', and 'it is possible for
A to belong to all B' into 'it is possible for A to belong to no B' or
'not to all B', and 'it is possible for A to belong to some B' into 'it
is possible for A not to belong to some B'. And similarly the
other propositions in this mode can be converted. For since that
which is possible is not necessary, and that which is not
necessary may possibly not belong, it is clear that if it is
possible that A should belong to B, it is possible also that it
should not belong to B: and if it is possible that it should belong
to all, it is also possible that it should not belong to all. The
same holds good in the case of particular affirmations: for the
proof is identical. And such premisses are affirmative and not
negative; for 'to be possible' is in the same rank as 'to be', as
was said above.
Having made these distinctions we next point out that the
expression 'to be possible' is used in two ways. In one it means
to happen generally and fall short of necessity, e.g. man's
turning grey or growing or decaying, or generally what naturally
belongs to a thing (for this has not its necessity unbroken, since
man's existence is not continuous for ever, although if a man
does exist, it comes about either necessarily or generally). In
another sense the expression means the indefinite, which can
be both thus and not thus, e.g. an animal's walking or an
earthquake's taking place while it is walking, or generally what
happens by chance: for none of these inclines by nature in the
one way more than in the opposite.
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That which is possible in each of its two senses is convertible
into its opposite, not however in the same way: but what is
natural is convertible because it does not necessarily belong (for
in this sense it is possible that a man should not grow grey) and
what is indefinite is convertible because it inclines this way no
more than that. Science and demonstrative syllogism are not
concerned with things which are indefinite, because the middle
term is uncertain; but they are concerned with things that are
natural, and as a rule arguments and inquiries are made about
things which are possible in this sense. Syllogisms indeed can
be made about the former, but it is unusual at any rate to
inquire about them.
These matters will be treated more definitely in the sequel; our
business at present is to state the moods and nature of the
syllogism made from possible premisses. The expression 'it is
possible for this to belong to that' may be understood in two
senses: 'that' may mean either that to which 'that' belongs or
that to which it may belong; for the expression 'A is possible of
the subject of B' means that it is possible either of that of which
B is stated or of that of which B may possibly be stated. It makes
no difference whether we say, A is possible of the subject of B, or
all B admits of A. It is clear then that the expression 'A may
possibly belong to all B' might be used in two senses. First then
we must state the nature and characteristics of the syllogism
which arises if B is possible of the subject of C, and A is possible
of the subject of B. For thus both premisses are assumed in the
mode of possibility; but whenever A is possible of that of which
B is true, one premiss is a simple assertion, the other a
problematic. Consequently we must start from premisses which
are similar in form, as in the other cases.
106
14
Whenever A may possibly belong to all B, and B to all C, there
will be a perfect syllogism to prove that A may possibly belong
to all C. This is clear from the definition: for it was in this way
that we explained 'to be possible for one term to belong to all of
another'. Similarly if it is possible for A to belong no B, and for B
to belong to all C, then it is possible for A to belong to no C. For
the statement that it is possible for A not to belong to that of
which B may be true means (as we saw) that none of those
things which can possibly fall under the term B is left out of
account. But whenever A may belong to all B, and B may belong
to no C, then indeed no syllogism results from the premisses
assumed, but if the premiss BC is converted after the manner of
problematic propositions, the same syllogism results as before.
For since it is possible that B should belong to no C, it is possible
also that it should belong to all C. This has been stated above.
Consequently if B is possible for all C, and A is possible for all B,
the same syllogism again results. Similarly if in both the
premisses the negative is joined with 'it is possible': e.g. if A
may belong to none of the Bs, and B to none of the Cs. No
syllogism results from the assumed premisses, but if they are
converted we shall have the same syllogism as before. It is clear
then that if the minor premiss is negative, or if both premisses
are negative, either no syllogism results, or if one it is not
perfect. For the necessity results from the conversion.
But if one of the premisses is universal, the other particular,
when the major premiss is universal there will be a perfect
syllogism. For if A is possible for all B, and B for some C, then A
is possible for some C. This is clear from the definition of being
possible. Again if A may belong to no B, and B may belong to
some of the Cs, it is necessary that A may possibly not belong to
some of the Cs. The proof is the same as above. But if the
particular premiss is negative, and the universal is affirmative,
107
the major still being universal and the minor particular, e.g. A is
possible for all B, B may possibly not belong to some C, then a
clear syllogism does not result from the assumed premisses, but
if the particular premiss is converted and it is laid down that B
possibly may belong to some C, we shall have the same
conclusion as before, as in the cases given at the beginning.
But if the major premiss is the minor universal, whether both
are affirmative, or negative, or different in quality, or if both are
indefinite or particular, in no way will a syllogism be possible.
For nothing prevents B from reaching beyond A, so that as
predicates cover unequal areas. Let C be that by which B
extends beyond A. To C it is not possible that A should belong -
either to all or to none or to some or not to some, since
premisses in the mode of possibility are convertible and it is
possible for B to belong to more things than A can. Further, this
is obvious if we take terms; for if the premisses are as assumed,
the major term is both possible for none of the minor and must
belong to all of it. Take as terms common to all the cases under
consideration 'animal' - 'white' - 'man', where the major
belongs necessarily to the minor; 'animal' - 'white' - 'garment',
where it is not possible that the major should belong to the
minor. It is clear then that if the terms are related in this
manner, no syllogism results. For every syllogism proves that
something belongs either simply or necessarily or possibly. It is
clear that there is no proof of the first or of the second. For the
affirmative is destroyed by the negative, and the negative by the
affirmative. There remains the proof of possibility. But this is
impossible. For it has been proved that if the terms are related
in this manner it is both necessary that the major should
belong to all the minor and not possible that it should belong to
any. Consequently there cannot be a syllogism to prove the
possibility; for the necessary (as we stated) is not possible.
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It is clear that if the terms are universal in possible premisses a
syllogism always results in the first figure, whether they are
affirmative or negative, only a perfect syllogism results in the
first case, an imperfect in the second. But possibility must be
understood according to the definition laid down, not as
covering necessity. This is sometimes forgotten.
15
If one premiss is a simple proposition, the other a problematic,
whenever the major premiss indicates possibility all the
syllogisms will be perfect and establish possibility in the sense
defined; but whenever the minor premiss indicates possibility
all the syllogisms will be imperfect, and those which are
negative will establish not possibility according to the
definition, but that the major does not necessarily belong to
any, or to all, of the minor. For if this is so, we say it is possible
that it should belong to none or not to all. Let A be possible for
all B, and let B belong to all C. Since C falls under B, and A is
possible for all B, clearly it is possible for all C also. So a perfect
syllogism results. Likewise if the premiss AB is negative, and the
premiss BC is affirmative, the former stating possible, the latter
simple attribution, a perfect syllogism results proving that A
possibly belongs to no C.
It is clear that perfect syllogisms result if the minor premiss
states simple belonging: but that syllogisms will result if the
modality of the premisses is reversed, must be proved per
impossibile. At the same time it will be evident that they are
imperfect: for the proof proceeds not from the premisses
assumed. First we must state that if B's being follows
necessarily from As being, B's possibility will follow necessarily
109
from A's possibility. Suppose, the terms being so related, that A
is possible, and B is impossible. If then that which is possible,
when it is possible for it to be, might happen, and if that which
is impossible, when it is impossible, could not happen, and if at
the same time A is possible and B impossible, it would be
possible for A to happen without B, and if to happen, then to be.
For that which has happened, when it has happened, is. But we
must take the impossible and the possible not only in the
sphere of becoming, but also in the spheres of truth and
predicability, and the various other spheres in which we speak
of the possible: for it will be alike in all. Further we must
understand the statement that B's being depends on A's being,
not as meaning that if some single thing A is, B will be: for
nothing follows of necessity from the being of some one thing,
but from two at least, i.e. when the premisses are related in the
manner stated to be that of the syllogism. For if C is predicated
of D, and D of F, then G is necessarily predicated of F. And if each
is possible, the conclusion also is possible. If then, for example,
one should indicate the premisses by A, and the conclusion by
B, it would not only result that if A is necessary B is necessary,
but also that if A is possible, B is possible.
Since this is proved it is evident that if a false and not
impossible assumption is made, the consequence of the
assumption will also be false and not impossible: e.g. if A is
false, but not impossible, and if B is the consequence of A, B also
will be false but not impossible. For since it has been proved
that if B's being is the consequence of A's being, then B's
possibility will follow from A's possibility (and A is assumed to
be possible), consequently B will be possible: for if it were
impossible, the same thing would at the same time be possible
and impossible.
Since we have defined these points, let A belong to all B, and B
be possible for all C: it is necessary then that should be a
no
possible attribute for all C. Suppose that it is not possible, but
assume that B belongs to all C: this is false but not impossible. If
then A is not possible for C but B belongs to all C, then A is not
possible for all B: for a syllogism is formed in the third degree.
But it was assumed that A is a possible attribute for all B. It is
necessary then that A is possible for all C. For though the
assumption we made is false and not impossible, the
conclusion is impossible. It is possible also in the first figure to
bring about the impossibility, by assuming that B belongs to C.
For if B belongs to all C, and A is possible for all B, then A would
be possible for all C. But the assumption was made that A is not
possible for all C.
We must understand 'that which belongs to all' with no
limitation in respect of time, e.g. to the present or to a particular
period, but simply without qualification. For it is by the help of
such premisses that we make syllogisms, since if the premiss is
understood with reference to the present moment, there cannot
be a syllogism. For nothing perhaps prevents 'man' belonging at
a particular time to everything that is moving, i.e. if nothing else
were moving: but 'moving' is possible for every horse; yet 'man'
is possible for no horse. Further let the major term be 'animal',
the middle 'moving', the the minor 'man'. The premisses then
will be as before, but the conclusion necessary, not possible. For
man is necessarily animal. It is clear then that the universal
must be understood simply, without limitation in respect of
time.
Again let the premiss AB be universal and negative, and assume
that A belongs to no B, but B possibly belongs to all C. These
propositions being laid down, it is necessary that A possibly
belongs to no C. Suppose that it cannot belong, and that B
belongs to C, as above. It is necessary then that A belongs to
some B: for we have a syllogism in the third figure: but this is
impossible. Thus it will be possible for A to belong to no C; for if
111
at is supposed false, the consequence is an impossible one. This
syllogism then does not establish that which is possible
according to the definition, but that which does not necessarily
belong to any part of the subject (for this is the contradictory of
the assumption which was made: for it was supposed that A
necessarily belongs to some C, but the syllogism per impossibile
establishes the contradictory which is opposed to this). Further,
it is clear also from an example that the conclusion will not
establish possibility. Let A be 'raven', B 'intelligent', and C 'man'.
A then belongs to no B: for no intelligent thing is a raven. But B
is possible for all C: for every man may possibly be intelligent.
But A necessarily belongs to no C: so the conclusion does not
establish possibility. But neither is it always necessary. Let A be
'moving', B 'science', C 'man'. A then will belong to no B; but B is
possible for all C. And the conclusion will not be necessary. For
it is not necessary that no man should move; rather it is not
necessary that any man should move. Clearly then the
conclusion establishes that one term does not necessarily
belong to any instance of another term. But we must take our
terms better.
If the minor premiss is negative and indicates possibility, from
the actual premisses taken there can be no syllogism, but if the
problematic premiss is converted, a syllogism will be possible,
as before. Let A belong to all B, and let B possibly belong to no C.
If the terms are arranged thus, nothing necessarily follows: but
if the proposition BC is converted and it is assumed that B is
possible for all C, a syllogism results as before: for the terms are
in the same relative positions. Likewise if both the relations are
negative, if the major premiss states that A does not belong to B,
and the minor premiss indicates that B may possibly belong to
no C. Through the premisses actually taken nothing necessary
results in any way; but if the problematic premiss is converted,
we shall have a syllogism. Suppose that A belongs to no B, and B
may possibly belong to no C. Through these comes nothing
112
necessary. But if B is assumed to be possible for all C (and this is
true) and if the premiss AB remains as before, we shall again
have the same syllogism. But if it be assumed that B does not
belong to any C, instead of possibly not belonging, there cannot
be a syllogism anyhow, whether the premiss AB is negative or
affirmative. As common instances of a necessary and positive
relation we may take the terms white - animal - snow: of a
necessary and negative relation, white - animal - pitch. Clearly
then if the terms are universal, and one of the premisses is
assertoric, the other problematic, whenever the minor premiss
is problematic a syllogism always results, only sometimes it
results from the premisses that are taken, sometimes it requires
the conversion of one premiss. We have stated when each of
these happens and the reason why. But if one of the relations is
universal, the other particular, then whenever the major
premiss is universal and problematic, whether affirmative or
negative, and the particular is affirmative and assertoric, there
will be a perfect syllogism, just as when the terms are universal.
The demonstration is the same as before. But whenever the
major premiss is universal, but assertoric, not problematic, and
the minor is particular and problematic, whether both
premisses are negative or affirmative, or one is negative, the
other affirmative, in all cases there will be an imperfect
syllogism. Only some of them will be proved per impossibile,
others by the conversion of the problematic premiss, as has
been shown above. And a syllogism will be possible by means of
conversion when the major premiss is universal and assertoric,
whether positive or negative, and the minor particular, negative,
and problematic, e.g. if A belongs to all B or to no B, and B may
possibly not belong to some C. For if the premiss BC is
converted in respect of possibility, a syllogism results. But
whenever the particular premiss is assertoric and negative,
there cannot be a syllogism. As instances of the positive relation
we may take the terms white - animal - snow; of the negative,
113
white - animal - pitch. For the demonstration must be made
through the indefinite nature of the particular premiss. But if
the minor premiss is universal, and the major particular,
whether either premiss is negative or affirmative, problematic
or assertoric, nohow is a syllogism possible. Nor is a syllogism
possible when the premisses are particular or indefinite,
whether problematic or assertoric, or the one problematic, the
other assertoric. The demonstration is the same as above. As
instances of the necessary and positive relation we may take
the terms animal - white - man; of the necessary and negative
relation, animal - white - garment. It is evident then that if the
major premiss is universal, a syllogism always results, but if the
minor is universal nothing at all can ever be proved.
16
Whenever one premiss is necessary, the other problematic,
there will be a syllogism when the terms are related as before;
and a perfect syllogism when the minor premiss is necessary. If
the premisses are affirmative the conclusion will be
problematic, not assertoric, whether the premisses are universal
or not: but if one is affirmative, the other negative, when the
affirmative is necessary the conclusion will be problematic, not
negative assertoric; but when the negative is necessary the
conclusion will be problematic negative, and assertoric negative,
whether the premisses are universal or not. Possibility in the
conclusion must be understood in the same manner as before.
There cannot be an inference to the necessary negative
proposition: for 'not necessarily to belong' is different from
'necessarily not to belong'.
114
If the premisses are affirmative, clearly the conclusion which
follows is not necessary. Suppose A necessarily belongs to all B,
and let B be possible for all C. We shall have an imperfect
syllogism to prove that A may belong to all C. That it is
imperfect is clear from the proof: for it will be proved in the
same manner as above. Again, let A be possible for all B, and let
B necessarily belong to all C. We shall then have a syllogism to
prove that A may belong to all C, not that A does belong to all C:
and it is perfect, not imperfect: for it is completed directly
through the original premisses.
But if the premisses are not similar in quality, suppose first that
the negative premiss is necessary, and let necessarily A not be
possible for any B, but let B be possible for all C. It is necessary
then that A belongs to no C. For suppose A to belong to all C or
to some C. Now we assumed that A is not possible for any B.
Since then the negative proposition is convertible, B is not
possible for any A. But A is supposed to belong to all C or to
some C. Consequently B will not be possible for any C or for all
C. But it was originally laid down that B is possible for all C. And
it is clear that the possibility of belonging can be inferred, since
the fact of not belonging is inferred. Again, let the affirmative
premiss be necessary, and let A possibly not belong to any B,
and let B necessarily belong to all C. The syllogism will be
perfect, but it will establish a problematic negative, not an
assertoric negative. For the major premiss was problematic, and
further it is not possible to prove the assertoric conclusion per
impossibile. For if it were supposed that A belongs to some C,
and it is laid down that A possibly does not belong to any B, no
impossible relation between B and C follows from these
premisses. But if the minor premiss is negative, when it is
problematic a syllogism is possible by conversion, as above; but
when it is necessary no syllogism can be formed. Nor again
when both premisses are negative, and the minor is necessary.
The same terms as before serve both for the positive relation -
115
white-animal-snow, and for the negative relation - white-
animal-pitch.
The same relation will obtain in particular syllogisms.
Whenever the negative proposition is necessary, the conclusion
will be negative assertoric: e.g. if it is not possible that A should
belong to any B, but B may belong to some of the Cs, it is
necessary that A should not belong to some of the Cs. For if A
belongs to all C, but cannot belong to any B, neither can B
belong to any A. So if A belongs to all C, to none of the Cs can B
belong. But it was laid down that B may belong to some C. But
when the particular affirmative in the negative syllogism, e.g.
BC the minor premiss, or the universal proposition in the
affirmative syllogism, e.g. AB the major premiss, is necessary,
there will not be an assertoric conclusion. The demonstration is
the same as before. But if the minor premiss is universal, and
problematic, whether affirmative or negative, and the major
premiss is particular and necessary, there cannot be a syllogism.
Premisses of this kind are possible both where the relation is
positive and necessary, e.g. animal-white-man, and where it is
necessary and negative, e.g. animal-white-garment. But when
the universal is necessary, the particular problematic, if the
universal is negative we may take the terms animal-white-
raven to illustrate the positive relation, or animal-white-pitch to
illustrate the negative; and if the universal is affirmative we
may take the terms animal-white-swan to illustrate the positive
relation, and animal-white-snow to illustrate the negative and
necessary relation. Nor again is a syllogism possible when the
premisses are indefinite, or both particular. Terms applicable in
either case to illustrate the positive relation are animal-white-
man: to illustrate the negative, animal-white-inanimate. For the
relation of animal to some white, and of white to some
inanimate, is both necessary and positive and necessary and
negative. Similarly if the relation is problematic: so the terms
may be used for all cases.
116
Clearly then from what has been said a syllogism results or not
from similar relations of the terms whether we are dealing with
simple existence or necessity, with this exception, that if the
negative premiss is assertoric the conclusion is problematic, but
if the negative premiss is necessary the conclusion is both
problematic and negative assertoric. [It is clear also that all the
syllogisms are imperfect and are perfected by means of the
figures above mentioned.]
17
In the second figure whenever both premisses are problematic,
no syllogism is possible, whether the premisses are affirmative
or negative, universal or particular. But when one premiss is
assertoric, the other problematic, if the affirmative is assertoric
no syllogism is possible, but if the universal negative is
assertoric a conclusion can always be drawn. Similarly when
one premiss is necessary, the other problematic. Here also we
must understand the term 'possible' in the conclusion, in the
same sense as before.
First we must point out that the negative problematic
proposition is not convertible, e.g. if A may belong to no B, it
does not follow that B may belong to no A. For suppose it to
follow and assume that B may belong to no A. Since then
problematic affirmations are convertible with negations,
whether they are contraries or contradictories, and since B may
belong to no A, it is clear that B may belong to all A. But this is
false: for if all this can be that, it does not follow that all that
can be this: consequently the negative proposition is not
convertible. Further, these propositions are not incompatible, 'A
may belong to no B', 'B necessarily does not belong to some of
117
the As'; e.g. it is possible that no man should be white (for it is
also possible that every man should be white), but it is not true
to say that it is possible that no white thing should be a man:
for many white things are necessarily not men, and the
necessary (as we saw) other than the possible.
Moreover it is not possible to prove the convertibility of these
propositions by a reductio ad absurdum, i.e. by claiming assent
to the following argument: 'since it is false that B may belong to
no A, it is true that it cannot belong to no A, for the one
statement is the contradictory of the other. But if this is so, it is
true that B necessarily belongs to some of the As: consequently
A necessarily belongs to some of the Bs. But this is impossible.'
The argument cannot be admitted, for it does not follow that
some A is necessarily B, if it is not possible that no A should be
B. For the latter expression is used in two senses, one if A some
is necessarily B, another if some A is necessarily not B. For it is
not true to say that that which necessarily does not belong to
some of the As may possibly not belong to any A, just as it is not
true to say that what necessarily belongs to some A may
possibly belong to all A. If any one then should claim that
because it is not possible for C to belong to all D, it necessarily
does not belong to some D, he would make a false assumption:
for it does belong to all D, but because in some cases it belongs
necessarily, therefore we say that it is not possible for it to
belong to all. Hence both the propositions 'A necessarily belongs
to some B' and A necessarily does not belong to some B' are
opposed to the proposition A belongs to all B'. Similarly also
they are opposed to the proposition A may belong to no B'. It is
clear then that in relation to what is possible and not possible,
in the sense originally defined, we must assume, not that A
necessarily belongs to some B, but that A necessarily does not
belong to some B. But if this is assumed, no absurdity results:
consequently no syllogism. It is clear from what has been said
that the negative proposition is not convertible.
118
This being proved, suppose it possible that A may belong to no B
and to all C. By means of conversion no syllogism will result: for
the major premiss, as has been said, is not convertible. Nor can
a proof be obtained by a reductio ad absurdum: for if it is
assumed that B can belong to all C, no false consequence
results: for A may belong both to all C and to no C. In general, if
there is a syllogism, it is clear that its conclusion will be
problematic because neither of the premisses is assertoric; and
this must be either affirmative or negative. But neither is
possible. Suppose the conclusion is affirmative: it will be proved
by an example that the predicate cannot belong to the subject.
Suppose the conclusion is negative: it will be proved that it is
not problematic but necessary. Let A be white, B man, C horse. It
is possible then for A to belong to all of the one and to none of
the other. But it is not possible for B to belong nor not to belong
to C. That it is not possible for it to belong, is clear. For no horse
is a man. Neither is it possible for it not to belong. For it is
necessary that no horse should be a man, but the necessary we
found to be different from the possible. No syllogism then
results. A similar proof can be given if the major premiss is
negative, the minor affirmative, or if both are affirmative or
negative. The demonstration can be made by means of the same
terms. And whenever one premiss is universal, the other
particular, or both are particular or indefinite, or in whatever
other way the premisses can be altered, the proof will always
proceed through the same terms. Clearly then, if both the
premisses are problematic, no syllogism results.
18
But if one premiss is assertoric, the other problematic, if the
affirmative is assertoric and the negative problematic no
119
syllogism will be possible, whether the premisses are universal
or particular. The proof is the same as above, and by means of
the same terms. But when the affirmative premiss is
problematic, and the negative assertoric, we shall have a
syllogism. Suppose A belongs to no B, but can belong to all C. If
the negative proposition is converted, B will belong to no A. But
ex hypothesi can belong to all C: so a syllogism is made, proving
by means of the first figure that B may belong to no C. Similarly
also if the minor premiss is negative. But if both premisses are
negative, one being assertoric, the other problematic, nothing
follows necessarily from these premisses as they stand, but if
the problematic premiss is converted into its complementary
affirmative a syllogism is formed to prove that B may belong to
no C, as before: for we shall again have the first figure. But if
both premisses are affirmative, no syllogism will be possible.
This arrangement of terms is possible both when the relation is
positive, e.g. health, animal, man, and when it is negative, e.g.
health, horse, man.
The same will hold good if the syllogisms are particular.
Whenever the affirmative proposition is assertoric, whether
universal or particular, no syllogism is possible (this is proved
similarly and by the same examples as above), but when the
negative proposition is assertoric, a conclusion can be drawn by
means of conversion, as before. Again if both the relations are
negative, and the assertoric proposition is universal, although
no conclusion follows from the actual premisses, a syllogism
can be obtained by converting the problematic premiss into its
complementary affirmative as before. But if the negative
proposition is assertoric, but particular, no syllogism is possible,
whether the other premiss is affirmative or negative. Nor can a
conclusion be drawn when both premisses are indefinite,
whether affirmative or negative, or particular. The proof is the
same and by the same terms.
120
19
If one of the premisses is necessary, the other problematic, then
if the negative is necessary a syllogistic conclusion can be
drawn, not merely a negative problematic but also a negative
assertoric conclusion; but if the affirmative premiss is
necessary, no conclusion is possible. Suppose that A necessarily
belongs to no B, but may belong to all C. If the negative premiss
is converted B will belong to no A: but A ex hypothesi is capable
of belonging to all C: so once more a conclusion is drawn by the
first figure that B may belong to no C. But at the same time it is
clear that B will not belong to any C. For assume that it does:
then if A cannot belong to any B, and B belongs to some of the
Cs, A cannot belong to some of the Cs: but ex hypothesi it may
belong to all. A similar proof can be given if the minor premiss
is negative. Again let the affirmative proposition be necessary,
and the other problematic; i.e. suppose that A may belong to no
B, but necessarily belongs to all C. When the terms are arranged
in this way, no syllogism is possible. For (1) it sometimes turns
out that B necessarily does not belong to C. Let A be white, B
man, C swan. White then necessarily belongs to swan, but may
belong to no man; and man necessarily belongs to no swan;
Clearly then we cannot draw a problematic conclusion; for that
which is necessary is admittedly distinct from that which is
possible. (2) Nor again can we draw a necessary conclusion: for
that presupposes that both premisses are necessary, or at any
rate the negative premiss. (3) Further it is possible also, when
the terms are so arranged, that B should belong to C: for
nothing prevents C falling under B, A being possible for all B,
and necessarily belonging to C; e.g. if C stands for 'awake', B for
'animal', A for 'motion'. For motion necessarily belongs to what
121
is awake, and is possible for every animal: and everything that is
awake is animal. Clearly then the conclusion cannot be the
negative assertion, if the relation must be positive when the
terms are related as above. Nor can the opposite affirmations be
established: consequently no syllogism is possible. A similar
proof is possible if the major premiss is affirmative.
But if the premisses are similar in quality, when they are
negative a syllogism can always be formed by converting the
problematic premiss into its complementary affirmative as
before. Suppose A necessarily does not belong to B, and possibly
may not belong to C: if the premisses are converted B belongs to
no A, and A may possibly belong to all C: thus we have the first
figure. Similarly if the minor premiss is negative. But if the
premisses are affirmative there cannot be a syllogism. Clearly
the conclusion cannot be a negative assertoric or a negative
necessary proposition because no negative premiss has been
laid down either in the assertoric or in the necessary mode. Nor
can the conclusion be a problematic negative proposition. For if
the terms are so related, there are cases in which B necessarily
will not belong to C; e.g. suppose that A is white, B swan, C man.
Nor can the opposite affirmations be established, since we have
shown a case in which B necessarily does not belong to C. A
syllogism then is not possible at all.
Similar relations will obtain in particular syllogisms. For
whenever the negative proposition is universal and necessary, a
syllogism will always be possible to prove both a problematic
and a negative assertoric proposition (the proof proceeds by
conversion); but when the affirmative proposition is universal
and necessary, no syllogistic conclusion can be drawn. This can
be proved in the same way as for universal propositions, and by
the same terms. Nor is a syllogistic conclusion possible when
both premisses are affirmative: this also may be proved as
above. But when both premisses are negative, and the premiss
122
that definitely disconnects two terms is universal and
necessary, though nothing follows necessarily from the
premisses as they are stated, a conclusion can be drawn as
above if the problematic premiss is converted into its
complementary affirmative. But if both are indefinite or
particular, no syllogism can be formed. The same proof will
serve, and the same terms.
It is clear then from what has been said that if the universal and
negative premiss is necessary, a syllogism is always possible,
proving not merely a negative problematic, but also a negative
assertoric proposition; but if the affirmative premiss is
necessary no conclusion can be drawn. It is clear too that a
syllogism is possible or not under the same conditions whether
the mode of the premisses is assertoric or necessary. And it is
clear that all the syllogisms are imperfect, and are completed by
means of the figures mentioned.
20
In the last figure a syllogism is possible whether both or only
one of the premisses is problematic. When the premisses are
problematic the conclusion will be problematic; and also when
one premiss is problematic, the other assertoric. But when the
other premiss is necessary, if it is affirmative the conclusion will
be neither necessary or assertoric; but if it is negative the
syllogism will result in a negative assertoric proposition, as
above. In these also we must understand the expression
'possible' in the conclusion in the same way as before.
First let the premisses be problematic and suppose that both A
and B may possibly belong to every C. Since then the affirmative
proposition is convertible into a particular, and B may possibly
123
belong to every C, it follows that C may possibly belong to some
B. So, if A is possible for every C, and C is possible for some of
the Bs, then A is possible for some of the Bs. For we have got the
first figure. And A if may possibly belong to no C, but B may
possibly belong to all C, it follows that A may possibly not
belong to some B: for we shall have the first figure again by
conversion. But if both premisses should be negative no
necessary consequence will follow from them as they are
stated, but if the premisses are converted into their
corresponding affirmatives there will be a syllogism as before.
For if A and B may possibly not belong to C, if 'may possibly
belong' is substituted we shall again have the first figure by
means of conversion. But if one of the premisses is universal,
the other particular, a syllogism will be possible, or not, under
the arrangement of the terms as in the case of assertoric
propositions. Suppose that A may possibly belong to all C, and B
to some C. We shall have the first figure again if the particular
premiss is converted. For if A is possible for all C, and C for
some of the Bs, then A is possible for some of the Bs. Similarly if
the proposition BC is universal. Likewise also if the proposition
AC is negative, and the proposition BC affirmative: for we shall
again have the first figure by conversion. But if both premisses
should be negative - the one universal and the other particular
- although no syllogistic conclusion will follow from the
premisses as they are put, it will follow if they are converted, as
above. But when both premisses are indefinite or particular, no
syllogism can be formed: for A must belong sometimes to all B
and sometimes to no B. To illustrate the affirmative relation
take the terms animal-man-white; to illustrate the negative,
take the terms horse-man-white - white being the middle term.
124
21
If one premiss is pure, the other problematic, the conclusion
will be problematic, not pure; and a syllogism will be possible
under the same arrangement of the terms as before. First let the
premisses be affirmative: suppose that A belongs to all C, and B
may possibly belong to all C. If the proposition BC is converted,
we shall have the first figure, and the conclusion that A may
possibly belong to some of the Bs. For when one of the
premisses in the first figure is problematic, the conclusion also
(as we saw) is problematic. Similarly if the proposition BC is
pure, AC problematic; or if AC is negative, BC affirmative, no
matter which of the two is pure; in both cases the conclusion
will be problematic: for the first figure is obtained once more,
and it has been proved that if one premiss is problematic in that
figure the conclusion also will be problematic. But if the minor
premiss BC is negative, or if both premisses are negative, no
syllogistic conclusion can be drawn from the premisses as they
stand, but if they are converted a syllogism is obtained as
before.
If one of the premisses is universal, the other particular, then
when both are affirmative, or when the universal is negative,
the particular affirmative, we shall have the same sort of
syllogisms: for all are completed by means of the first figure. So
it is clear that we shall have not a pure but a problematic
syllogistic conclusion. But if the affirmative premiss is
universal, the negative particular, the proof will proceed by a
reductio ad impossibile. Suppose that B belongs to all C, and A
may possibly not belong to some C: it follows that may possibly
not belong to some B. For if A necessarily belongs to all B, and B
(as has been assumed) belongs to all C, A will necessarily belong
to all C: for this has been proved before. But it was assumed at
the outset that A may possibly not belong to some C.
125
Whenever both premisses are indefinite or particular, no
syllogism will be possible. The demonstration is the same as
was given in the case of universal premisses, and proceeds by
means of the same terms.
22
If one of the premisses is necessary, the other problematic,
when the premisses are affirmative a problematic affirmative
conclusion can always be drawn; when one proposition is
affirmative, the other negative, if the affirmative is necessary a
problematic negative can be inferred; but if the negative
proposition is necessary both a problematic and a pure negative
conclusion are possible. But a necessary negative conclusion
will not be possible, any more than in the other figures. Suppose
first that the premisses are affirmative, i.e. that A necessarily
belongs to all C, and B may possibly belong to all C. Since then A
must belong to all C, and C may belong to some B, it follows that
A may (not does) belong to some B: for so it resulted in the first
figure. A similar proof may be given if the proposition BC is
necessary, and AC is problematic. Again suppose one
proposition is affirmative, the other negative, the affirmative
being necessary: i.e. suppose A may possibly belong to no C, but
B necessarily belongs to all C. We shall have the first figure once
more: and - since the negative premiss is problematic - it is
clear that the conclusion will be problematic: for when the
premisses stand thus in the first figure, the conclusion (as we
found) is problematic. But if the negative premiss is necessary,
the conclusion will be not only that A may possibly not belong
to some B but also that it does not belong to some B. For
suppose that A necessarily does not belong to C, but B may
belong to all C. If the affirmative proposition BC is converted, we
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shall have the first figure, and the negative premiss is necessary.
But when the premisses stood thus, it resulted that A might
possibly not belong to some C, and that it did not belong to
some C; consequently here it follows that A does not belong to
some B. But when the minor premiss is negative, if it is
problematic we shall have a syllogism by altering the premiss
into its complementary affirmative, as before; but if it is
necessary no syllogism can be formed. For A sometimes
necessarily belongs to all B, and sometimes cannot possibly
belong to any B. To illustrate the former take the terms sleep-
sleeping horse-man; to illustrate the latter take the terms sleep-
waking horse-man.
Similar results will obtain if one of the terms is related
universally to the middle, the other in part. If both premisses
are affirmative, the conclusion will be problematic, not pure;
and also when one premiss is negative, the other affirmative,
the latter being necessary. But when the negative premiss is
necessary, the conclusion also will be a pure negative
proposition; for the same kind of proof can be given whether
the terms are universal or not. For the syllogisms must be made
perfect by means of the first figure, so that a result which
follows in the first figure follows also in the third. But when the
minor premiss is negative and universal, if it is problematic a
syllogism can be formed by means of conversion; but if it is
necessary a syllogism is not possible. The proof will follow the
same course as where the premisses are universal; and the
same terms may be used.
It is clear then in this figure also when and how a syllogism can
be formed, and when the conclusion is problematic, and when
it is pure. It is evident also that all syllogisms in this figure are
imperfect, and that they are made perfect by means of the first
figure.
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23
It is clear from what has been said that the syllogisms in these
figures are made perfect by means of universal syllogisms in
the first figure and are reduced to them. That every syllogism
without qualification can be so treated, will be clear presently,
when it has been proved that every syllogism is formed through
one or other of these figures.
It is necessary that every demonstration and every syllogism
should prove either that something belongs or that it does not,
and this either universally or in part, and further either
ostensively or hypothetically. One sort of hypothetical proof is
the reductio ad impossibile. Let us speak first of ostensive
syllogisms: for after these have been pointed out the truth of
our contention will be clear with regard to those which are
proved per impossibile, and in general hypothetically.
If then one wants to prove syllogistically A of B, either as an
attribute of it or as not an attribute of it, one must assert
something of something else. If now A should be asserted of B,
the proposition originally in question will have been assumed.
But if A should be asserted of C, but C should not be asserted of
anything, nor anything of it, nor anything else of A, no syllogism
will be possible. For nothing necessarily follows from the
assertion of some one thing concerning some other single thing.
Thus we must take another premiss as well. If then A be
asserted of something else, or something else of A, or
something different of C, nothing prevents a syllogism being
formed, but it will not be in relation to B through the premisses
taken. Nor when C belongs to something else, and that to
something else and so on, no connexion however being made
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with B, will a syllogism be possible concerning A in its relation
to B. For in general we stated that no syllogism can establish the
attribution of one thing to another, unless some middle term is
taken, which is somehow related to each by way of predication.
For the syllogism in general is made out of premisses, and a
syllogism referring to this out of premisses with the same
reference, and a syllogism relating this to that proceeds through
premisses which relate this to that. But it is impossible to take a
premiss in reference to B, if we neither affirm nor deny
anything of it; or again to take a premiss relating A to B, if we
take nothing common, but affirm or deny peculiar attributes of
each. So we must take something midway between the two,
which will connect the predications, if we are to have a
syllogism relating this to that. If then we must take something
common in relation to both, and this is possible in three ways
(either by predicating A of C, and C of B, or C of both, or both of
C), and these are the figures of which we have spoken, it is clear
that every syllogism must be made in one or other of these
figures. The argument is the same if several middle terms
should be necessary to establish the relation to B; for the figure
will be the same whether there is one middle term or many.
It is clear then that the ostensive syllogisms are effected by
means of the aforesaid figures; these considerations will show
that reductiones ad also are effected in the same way. For all
who effect an argument per impossibile infer syllogistically
what is false, and prove the original conclusion hypothetically
when something impossible results from the assumption of its
contradictory; e.g. that the diagonal of the square is
incommensurate with the side, because odd numbers are equal
to evens if it is supposed to be commensurate. One infers
syllogistically that odd numbers come out equal to evens, and
one proves hypothetically the incommensurability of the
diagonal, since a falsehood results through contradicting this.
For this we found to be reasoning per impossibile, viz. proving
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something impossible by means of an hypothesis conceded at
the beginning. Consequently, since the falsehood is established
in reductions ad impossibile by an ostensive syllogism, and the
original conclusion is proved hypothetically, and we have
already stated that ostensive syllogisms are effected by means
of these figures, it is evident that syllogisms per impossibile
also will be made through these figures. Likewise all the other
hypothetical syllogisms: for in every case the syllogism leads up
to the proposition that is substituted for the original thesis; but
the original thesis is reached by means of a concession or some
other hypothesis. But if this is true, every demonstration and
every syllogism must be formed by means of the three figures
mentioned above. But when this has been shown it is clear that
every syllogism is perfected by means of the first figure and is
reducible to the universal syllogisms in this figure.
24
Further in every syllogism one of the premisses must be
affirmative, and universality must be present: unless one of the
premisses is universal either a syllogism will not be possible, or
it will not refer to the subject proposed, or the original position
will be begged. Suppose we have to prove that pleasure in music
is good. If one should claim as a premiss that pleasure is good
without adding 'all', no syllogism will be possible; if one should
claim that some pleasure is good, then if it is different from
pleasure in music, it is not relevant to the subject proposed; if it
is this very pleasure, one is assuming that which was proposed
at the outset to be proved. This is more obvious in geometrical
proofs, e.g. that the angles at the base of an isosceles triangle
are equal. Suppose the lines A and B have been drawn to the
centre. If then one should assume that the angle AC is equal to
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the angle BD, without claiming generally that angles of
semicircles are equal; and again if one should assume that the
angle C is equal to the angle D, without the additional
assumption that every angle of a segment is equal to every
other angle of the same segment; and further if one should
assume that when equal angles are taken from the whole
angles, which are themselves equal, the remainders E and F are
equal, he will beg the thing to be proved, unless he also states
that when equals are taken from equals the remainders are
equal.
It is clear then that in every syllogism there must be a universal
premiss, and that a universal statement is proved only when all
the premisses are universal, while a particular statement is
proved both from two universal premisses and from one only:
consequently if the conclusion is universal, the premisses also
must be universal, but if the premisses are universal it is
possible that the conclusion may not be universal. And it is
clear also that in every syllogism either both or one of the
premisses must be like the conclusion. I mean not only in being
affirmative or negative, but also in being necessary, pure,
problematic. We must consider also the other forms of
predication.
It is clear also when a syllogism in general can be made and
when it cannot; and when a valid, when a perfect syllogism can
be formed; and that if a syllogism is formed the terms must be
arranged in one of the ways that have been mentioned.
25
It is clear too that every demonstration will proceed through
three terms and no more, unless the same conclusion is
131
established by different pairs of propositions; e.g. the
conclusion E may be established through the propositions A and
B, and through the propositions C and D, or through the
propositions A and B, or A and C, or B and C. For nothing
prevents there being several middles for the same terms. But in
that case there is not one but several syllogisms. Or again when
each of the propositions A and B is obtained by syllogistic
inference, e.g. by means of D and E, and again B by means of F
and G. Or one may be obtained by syllogistic, the other by
inductive inference. But thus also the syllogisms are many; for
the conclusions are many, e.g. A and B and C. But if this can be
called one syllogism, not many, the same conclusion may be
reached by more than three terms in this way, but it cannot be
reached as C is established by means of A and B. Suppose that
the proposition E is inferred from the premisses A, B, C, and D. It
is necessary then that of these one should be related to another
as whole to part: for it has already been proved that if a
syllogism is formed some of its terms must be related in this
way. Suppose then that A stands in this relation to B. Some
conclusion then follows from them. It must either be E or one or
other of C and D, or something other than these.
(1) If it is E the syllogism will have A and B for its sole premisses.
But if C and D are so related that one is whole, the other part,
some conclusion will follow from them also; and it must be
either E, or one or other of the propositions A and B, or
something other than these. And if it is (i) E, or (ii) A or B, either
(i) the syllogisms will be more than one, or (ii) the same thing
happens to be inferred by means of several terms only in the
sense which we saw to be possible. But if (iii) the conclusion is
other than E or A or B, the syllogisms will be many, and
unconnected with one another. But if C is not so related to D as
to make a syllogism, the propositions will have been assumed
to no purpose, unless for the sake of induction or of obscuring
the argument or something of the sort.
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(2) But if from the propositions A and B there follows not E but
some other conclusion, and if from C and D either A or B follows
or something else, then there are several syllogisms, and they
do not establish the conclusion proposed: for we assumed that
the syllogism proved E. And if no conclusion follows from C and
D, it turns out that these propositions have been assumed to no
purpose, and the syllogism does not prove the original
proposition.
So it is clear that every demonstration and every syllogism will
proceed through three terms only.
This being evident, it is clear that a syllogistic conclusion
follows from two premisses and not from more than two. For
the three terms make two premisses, unless a new premiss is
assumed, as was said at the beginning, to perfect the
syllogisms. It is clear therefore that in whatever syllogistic
argument the premisses through which the main conclusion
follows (for some of the preceding conclusions must be
premisses) are not even in number, this argument either has
not been drawn syllogistically or it has assumed more than was
necessary to establish its thesis.
If then syllogisms are taken with respect to their main
premisses, every syllogism will consist of an even number of
premisses and an odd number of terms (for the terms exceed
the premisses by one), and the conclusions will be half the
number of the premisses. But whenever a conclusion is reached
by means of prosyllogisms or by means of several continuous
middle terms, e.g. the proposition AB by means of the middle
terms C and D, the number of the terms will similarly exceed
that of the premisses by one (for the extra term must either be
added outside or inserted: but in either case it follows that the
relations of predication are one fewer than the terms related),
and the premisses will be equal in number to the relations of
133
predication. The premisses however will not always be even, the
terms odd; but they will alternate - when the premisses are
even, the terms must be odd; when the terms are even, the
premisses must be odd: for along with one term one premiss is
added, if a term is added from any quarter. Consequently since
the premisses were (as we saw) even, and the terms odd, we
must make them alternately even and odd at each addition. But
the conclusions will not follow the same arrangement either in
respect to the terms or to the premisses. For if one term is
added, conclusions will be added less by one than the pre-
existing terms: for the conclusion is drawn not in relation to the
single term last added, but in relation to all the rest, e.g. if to
ABC the term D is added, two conclusions are thereby added,
one in relation to A, the other in relation to B. Similarly with any
further additions. And similarly too if the term is inserted in the
middle: for in relation to one term only, a syllogism will not be
constructed. Consequently the conclusions will be much more
numerous than the terms or the premisses.
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.
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, through the
first in one mood, through the second in two. The particular
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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, but
once in the first, in two moods in the second, in three moods in
the third. 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, 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. 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.
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.
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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, 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, 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, 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. We shall explain in another place 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, 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. But those to which it
cannot belong need not be selected, because the negative
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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, 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. 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, and 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, 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, e.g. take as
subjects of the predicate 'animal' what are really subjects of the
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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, 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: for no syllogism can be made out of such premisses.
The reason why this is so will be clear in the sequel.
28
If men wish to establish something about some whole, 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. 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. 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: or conversely to the
attributes which cannot possibly be present in the subject, and
to the consequents of the predicate. If any members of these
groups are identical, one of the terms in question cannot
possibly belong to any of the other. For sometimes a syllogism
138
in the first figure results, 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. If any members of these two groups are identical, 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, the antecedents of E by G,
and attributes which cannot belong to E by H. If then one of the
Cs should be identical with one of the Fs, 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 Es:
for A follows C, and E follows all G. If F and D are identical, A
will belong to none of the Es by a prosyllogism: for since the
negative proposition is convertible, and F is identical with D, A
will belong to none of the Fs, but F belongs to all E. Again, if B
and H are identical, A will belong to none of the Es: for B will
belong to all A, but to no E: for it was assumed to be identical
with H, and H belonged to none of the Es. If D and G are
identical, A will not belong to some of the Es: 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 Es. 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.
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
139
look for those which are primary and most universal, 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. 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, 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 Cs and Fs.
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, 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, and we must not select consequents of all the terms,
because no syllogism is produced from them. For (as we saw) 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, e.g. if the
consequents of the terms in question are identical, or if the
antecedents of A are identical with those attributes which
140
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, 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, 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, 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. For if these
are taken, a syllogism will be formed to prove that A belongs to
none of the Es, 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 Hs. Again, if B
and G cannot belong to the same thing, it follows that A will not
belong to some of the Es: for then too we shall have the middle
figure: for B will belong to all A and to no G. Consequently B
must be identical with some of the Hs. 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 Hs: for that includes
everything which cannot belong to E.
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 Hs, and the syllogism results through
these terms. It turns out then that those who inquire in this
141
manner are looking gratuitously for some other way than the
necessary way because they have failed to observe the identity
of the Bs with the Hs.
29
Syllogisms which lead to impossible conclusions are similar to
ostensive syllogisms; they also are formed by means of the
consequents and antecedents of the terms in question. In both
cases the same inquiry is involved. For what is proved
ostensively may also be concluded syllogistically per
impossibile by means of the same terms; and what is proved
per impossibile may also be proved ostensively, e.g. that A
belongs to none of the Es. For suppose A to belong to some E:
then since B belongs to all A and A to some of the Es, B will
belong to some of the Es: but it was assumed that it belongs to
none. Again we may prove that A belongs to some E: for if A
belonged to none of the Es, and E belongs to all G, A will belong
to none of the Gs: but it was assumed to belong to all. Similarly
with the other propositions requiring proof. The proof per
impossibile will always and in all cases be from the
consequents and antecedents of the terms in question.
Whatever the problem the same inquiry is necessary whether
one wishes to use an ostensive syllogism or a reduction to
impossibility. For both the demonstrations start from the same
terms, e.g. suppose it has been proved that A belongs to no E,
because it turns out that otherwise B belongs to some of the Es
and this is impossible - if now it is assumed that B belongs to
no E and to all A, it is clear that A will belong to no E. Again if it
has been proved by an ostensive syllogism that A belongs to no
E, assume that A belongs to some E and it will be proved per
impossibile to belong to no E. Similarly with the rest. In all cases
142
it is necessary to find some common term other than the
subjects of inquiry, to which the syllogism establishing the false
conclusion may relate, so that if this premiss is converted, and
the other remains as it is, the syllogism will be ostensive by
means of the same terms. For the ostensive syllogism differs
from the reductio ad impossibile in this: in the ostensive
syllogism both remisses are laid down in accordance with the
truth, in the reductio ad impossibile one of the premisses is
assumed falsely
These points will be made clearer by the sequel, when we
discuss the reduction to impossibility: at present this much
must be clear, that we must look to terms of the kinds
mentioned whether we wish to use an ostensive syllogism or a
reduction to impossibility In the other hypothetical syllogisms,
I mean those which proceed by substitution, or by positing a
certain quality, the inquiry will be directed to the terms of the
problem to be proved - not the terms of the original problem,
but the new terms introduced; and the method of the inquiry
will be the same as before. But we must consider and determine
in how many ways hypothetical syllogisms are possible.
Each of the problems then can be proved in the manner
described; but it is possible to establish some of them
syllogistically in another way, e.g. universal problems by the
inquiry which leads up to a particular conclusion, with the
addition of an hypothesis. For if the Cs and the Gs should be
identical, but E should be assumed to belong to the Gs only,
then A would belong to every E: and again if the Ds and the Gs
should be identical, but E should be predicated of the Gs only, it
follows that A will belong to none of the Es. Clearly then we
must consider the matter in this way also. The method is the
same whether the relation is necessary or possible. For the
inquiry will be the same, and the syllogism will proceed through
terms arranged in the same order whether a possible or a pure
143
proposition is proved. We must find in the case of possible
relations, as well as terms that belong, terms which can belong
though they actually do not: for we have proved that the
syllogism which establishes a possible relation proceeds
through these terms as well. Similarly also with the other
modes of predication.
It is clear then from what has been said not only that all
syllogisms can be formed in this way, but also that they cannot
be formed in any other. For every syllogism has been proved to
be formed through one of the aforementioned figures, and
these cannot be composed through other terms than the
consequents and antecedents of the terms in question: for from
these we obtain the premisses and find the middle term.
Consequently a syllogism cannot be formed by means of other
terms.
30
The method is the same in all cases, in philosophy, in any art or
study. We must look for the attributes and the subjects of both
our terms, and we must supply ourselves with as many of these
as possible, and consider them by means of the three terms,
refuting statements in one way, confirming them in another, in
the pursuit of truth starting from premisses in which the
arrangement of the terms is in accordance with truth, while if
we look for dialectical syllogisms we must start from probable
premisses. The principles of syllogisms have been stated in
general terms, both how they are characterized and how we
must hunt for them, so as not to look to everything that is said
about the terms of the problem or to the same points whether
we are confirming or refuting, or again whether we are
144
confirming of all or of some, and whether we are refuting of all
or some, we must look to fewer points and they must be
definite. We have also stated how we must select with reference
to everything that is, e.g. about good or knowledge. But in each
science the principles which are peculiar are the most
numerous. Consequently it is the business of experience to give
the principles which belong to each subject. I mean for example
that astronomical experience supplies the principles of
astronomical science: for once the phenomena were adequately
apprehended, the demonstrations of astronomy were
discovered. Similarly with any other art or science.
Consequently, if the attributes of the thing are apprehended,
our business will then be to exhibit readily the demonstrations.
For if none of the true attributes of things had been omitted in
the historical survey, we should be able to discover the proof
and demonstrate everything which admitted of proof, and to
make that clear, whose nature does not admit of proof.
In general then we have explained fairly well how we must
select premisses: we have discussed the matter accurately in
the treatise concerning dialectic.
31
It is easy to see that division into classes is a small part of the
method we have described: for division is, so to speak, a weak
syllogism; for what it ought to prove, it begs, and it always
establishes something more general than the attribute in
question. First, this very point had escaped all those who used
the method of division; and they attempted to persuade men
that it was possible to make a demonstration of substance and
essence. Consequently they did not understand what it is
145
possible to prove syllogistically by division, nor did they
understand that it was possible to prove syllogistically in the
manner we have described. In demonstrations, when there is a
need to prove a positive statement, the middle term through
which the syllogism is formed must always be inferior to and
not comprehend the first of the extremes. But division has a
contrary intention: for it takes the universal as middle. Let
animal be the term signified by A, mortal by B, and immortal by
C, and let man, whose definition is to be got, be signified by D.
The man who divides assumes that every animal is either
mortal or immortal: i.e. whatever is A is all either B or C. Again,
always dividing, he lays it down that man is an animal, so he
assumes A of D as belonging to it. Now the true conclusion is
that every D is either B or C, consequently 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
146
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
147
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 being laid down, it is necessary
that any part of substance is 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
148
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.
149
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 Aristomenes 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
150
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
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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
152
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.
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'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, G 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
154
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 not have had a
syllogism proving that there is knowledge of the good, that it is
good, but that it is; e.g. let A stand for knowledge that it is, B for
being, C for good. Clearly then in syllogisms which are thus
limited we must take the terms in the way stated.
39
We ought also to exchange terms which have the same value,
word for word, and phrase for phrase, and word and phrase, and
155
always take a word in preference to a phrase: for thus the
setting out of the terms will be easier. For example if it makes
no difference whether we say that the supposable is not the
genus of the opinable or that the opinable is not identical with a
particular kind of supposable (for what is meant is the same in
both statements), it is better to take as the terms the
supposable and the opinable in preference to the phrase
suggested.
40
Since the expressions 'pleasure is good' and 'pleasure is the
good' are not identical, we must not set out the terms in the
same way; but if the syllogism is to prove that pleasure is the
good, the term must be 'the good', but if the object is to prove
that pleasure is good, the term will be 'good'. Similarly in all
other cases.
41
It is not the same, either in fact or in speech, that A belongs to
all of that to which B belongs, and that A belongs to all of that to
all of which B belongs: for nothing prevents B from belonging to
C, though not to all C: e.g. let B stand for beautiful, and C for
white. If beauty belongs to something white, it is true to say
that beauty belongs to that which is white; but not perhaps to
everything that is white. If then A belongs to B, but not to
everything of which B is predicated, then whether B belongs to
all C or merely belongs to C, it is not necessary that A should
156
belong, I do not say to all C, but even to C at all. But if A belongs
to everything of which B is truly stated, it will follow that A can
be said of all of that of all of which B is said. If however A is said
of that of all of which B may be said, nothing prevents B
belonging to C, and yet A not belonging to all C or to any C at all.
If then we take three terms it is clear that the expression A is
said of all of which B is said' means this, A is said of all the
things of which B is said'. And if B is said of all of a third term,
so also is A: but if B is not said of all of the third term, there is
no necessity that A should be said of all of it.
We must not suppose that something absurd results through
setting out the terms: for we do not use the existence of this
particular thing, but imitate the geometrician who says that
'this line a foot long' or 'this straight line' or 'this line without
breadth' exists although it does not, but does not use the
diagrams in the sense that he reasons from them. For in
general, if two things are not related as whole to part and part
to whole, the prover does not prove from them, and so no
syllogism a is formed. We (I mean the learner) use the process
of setting out terms like perception by sense, not as though it
were impossible to demonstrate without these illustrative
terms, as it is to demonstrate without the premisses of the
syllogism.
42
We should not forget that in the same syllogism not all
conclusions are reached through one figure, but one through
one figure, another through another. Clearly then we must
analyse arguments in accordance with this. Since not every
problem is proved in every figure, but certain problems in each
157
figure, it is clear from the conclusion in what figure the
premisses should be sought.
43
In reference to those arguments aiming at a definition which
have been directed to prove some part of the definition, we
must take as a term the point to which the argument has been
directed, not the whole definition: for so we shall be less likely
to be disturbed by the length of the term: e.g. if a man proves
that water is a drinkable liquid, we must take as terms
drinkable and water.
44
Further we must not try to reduce hypothetical syllogisms; for
with the given premisses it is not possible to reduce them. For
they have not been proved by syllogism, but assented to by
agreement. For instance if a man should suppose that unless
there is one faculty of contraries, there cannot be one science,
and should then argue that not every faculty is of contraries, e.g.
of what is healthy and what is sickly: for the same thing will
then be at the same time healthy and sickly. He has shown that
there is not one faculty of all contraries, but he has not proved
that there is not a science. And yet one must agree. But the
agreement does not come from a syllogism, but from an
hypothesis. This argument cannot be reduced: but the proof
that there is not a single faculty can. The latter argument
perhaps was a syllogism: but the former was an hypothesis.
158
The same holds good of arguments which are brought to a
conclusion per impossibile. These cannot be analysed either;
but the reduction to what is impossible can be analysed since it
is proved by syllogism, though the rest of the argument cannot,
because the conclusion is reached from an hypothesis. But
these differ from the previous arguments: for in the former a
preliminary agreement must be reached if one is to accept the
conclusion; e.g. an agreement that if there is proved to be one
faculty of contraries, then contraries fall under the same
science; whereas in the latter, even if no preliminary agreement
has been made, men still accept the reasoning, because the
falsity is patent, e.g. the falsity of what follows from the
assumption that the diagonal is commensurate, viz. that then
odd numbers are equal to evens.
Many other arguments are brought to a conclusion by the help
of an hypothesis; these we ought to consider and mark out
clearly. We shall describe in the sequel their differences, and the
various ways in which hypothetical arguments are formed: but
at present this much must be clear, that it is not possible to
resolve such arguments into the figures. And we have explained
the reason.
45
Whatever problems are proved in more than one figure, if they
have been established in one figure by syllogism, can be
reduced to another figure, e.g. a negative syllogism in the first
figure can be reduced to the second, and a syllogism in the
middle figure to the first, not all however but some only. The
point will be clear in the sequel. If A belongs to no B, and B to all
C, then A belongs to no C. Thus the first figure; but if the
159
negative statement is converted, we shall have the middle
figure. For B belongs to no A, and to all C. Similarly if the
syllogism is not universal but particular, e.g. if A belongs to no B,
and B to some C. Convert the negative statement and you will
have the middle figure.
The universal syllogisms in the second figure can be reduced to
the first, but only one of the two particular syllogisms. Let A
belong to no B and to all C. Convert the negative statement, and
you will have the first figure. For B will belong to no A and A to
all C. But if the affirmative statement concerns B, and the
negative C, C must be made first term. For C belongs to no A,
and A to all B: therefore C belongs to no B. B then belongs to no
C: for the negative statement is convertible.
But if the syllogism is particular, whenever the negative
statement concerns the major extreme, reduction to the first
figure will be possible, e.g. if A belongs to no B and to some C:
convert the negative statement and you will have the first
figure. For B will belong to no A and A to some C. But when the
affirmative statement concerns the major extreme, no
resolution will be possible, e.g. if A belongs to all B, but not to all
C: for the statement AB does not admit of conversion, nor would
there be a syllogism if it did.
Again syllogisms in the third figure cannot all be resolved into
the first, though all syllogisms in the first figure can be resolved
into the third. Let A belong to all B and B to some C. Since the
particular affirmative is convertible, C will belong to some B: but
A belonged to all B: so that the third figure is formed. Similarly
if the syllogism is negative: for the particular affirmative is
convertible: therefore A will belong to no B, and to some C.
Of the syllogisms in the last figure one only cannot be resolved
into the first, viz. when the negative statement is not universal:
all the rest can be resolved. Let A and B be affirmed of all C:
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then C can be converted partially with either A or B: C then
belongs to some B. Consequently we shall get the first figure, if
A belongs to all C, and C to some of the Bs. If A belongs to all C
and B to some C, the argument is the same: for B is convertible
in reference to C. But if B belongs to all C and A to some C, the
first term must be B: for B belongs to all C, and C to some A,
therefore B belongs to some A. But since the particular
statement is convertible, A will belong to some B. If the
syllogism is negative, when the terms are universal we must
take them in a similar way. Let B belong to all C, and A to no C:
then C will belong to some B, and A to no C; and so C will be
middle term. Similarly if the negative statement is universal,
the affirmative particular: for A will belong to no C, and C to
some of the Bs. But if the negative statement is particular, no
resolution will be possible, e.g. if B belongs to all C, and A not
belong to some C: convert the statement BC and both premisses
will be particular.
It is clear that in order to resolve the figures into one another
the premiss which concerns the minor extreme must be
converted in both the figures: for when this premiss is altered,
the transition to the other figure is made.
One of the syllogisms in the middle figure can, the other
cannot, be resolved into the third figure. Whenever the
universal statement is negative, resolution is possible. For if A
belongs to no B and to some C, both B and C alike are
convertible in relation to A, so that B belongs to no A and C to
some A. A therefore is middle term. But when A belongs to all B,
and not to some C, resolution will not be possible: for neither of
the premisses is universal after conversion.
Syllogisms in the third figure can be resolved into the middle
figure, whenever the negative statement is universal, e.g. if A
belongs to no C, and B to some or all C. For C then will belong to
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no A and to some B. But if the negative statement is particular,
no resolution will be possible: for the particular negative does
not admit of conversion.
It is clear then that the same syllogisms cannot be resolved in
these figures which could not be resolved into the first figure,
and that when syllogisms are reduced to the first figure these
alone are confirmed by reduction to what is impossible.
It is clear from what we have said how we ought to reduce
syllogisms, and that the figures may be resolved into one
another.
46
In establishing or refuting, it makes some difference whether
we suppose the expressions 'not to be this' and 'to be not-this'
are identical or different in meaning, e.g. 'not to be white' and
'to be not-white'. For they do not mean the same thing, nor is
'to be not-white' the negation of 'to be white', but 'not to be
white'. The reason for this is as follows. The relation of 'he can
walk' to 'he can not-walk' is similar to the relation of 'it is
white' to 'it is not-white'; so is that of 'he knows what is good'
to 'he knows what is not-good'. For there is no difference
between the expressions 'he knows what is good' and 'he is
knowing what is good', or 'he can walk' and 'he is able to walk':
therefore there is no difference between their contraries 'he
cannot walk'-'he is not able to walk'. If then 'he is not able to
walk' means the same as 'he is able not to walk', capacity to
walk and incapacity to walk will belong at the same time to the
same person (for the same man can both walk and not-walk,
and is possessed of knowledge of what is good and of what is
not-good), but an affirmation and a denial which are opposed to
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one another do not belong at the same time to the same thing.
As then 'not to know what is good' is not the same as 'to know
what is not good', so 'to be not-good' is not the same as 'not to
be good'. For when two pairs correspond, if the one pair are
different from one another, the other pair also must be
different. Nor is 'to be not-equal' the same as 'not to be equal':
for there is something underlying the one, viz. that which is
not-equal, and this is the unequal, but there is nothing
underlying the other. Wherefore not everything is either equal
or unequal, but everything is equal or is not equal. Further the
expressions 'it is a not-white log' and 'it is not a white log' do
not imply one another's truth. For if 'it is a not-white log', it
must be a log: but that which is not a white log need not be a
log at all. Therefore it is clear that 'it is not-good' is not the
denial of 'it is good'. If then every single statement may truly be
said to be either an affirmation or a negation, if it is not a
negation clearly it must in a sense be an affirmation. But every
affirmation has a corresponding negation. The negation then of
'it is not-good' is 'it is not not-good'. The relation of these
statements to one another is as follows. Let A stand for 'to be
good', B for 'not to be good', let C stand for 'to be not-good' and
be placed under B, and let D stand for not to be not-good' and
be placed under A. Then either A or B will belong to everything,
but they will never belong to the same thing; and either C or D
will belong to everything, but they will never belong to the same
thing. And B must belong to everything to which C belongs. For
if it is true to say 'it is a not-white', it is true also to say 'it is not
white': for it is impossible that a thing should simultaneously
be white and be not-white, or be a not-white log and be a white
log; consequently if the affirmation does not belong, the denial
must belong. But C does not always belong to B: for what is not
a log at all, cannot be a not-white log either. On the other hand
D belongs to everything to which A belongs. For either C or D
belongs to everything to which A belongs. But since a thing
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cannot be simultaneously not-white and white, D must belong
to everything to which A belongs. For of that which is white it is
true to say that it is not not-white. But A is not true of all D. For
of that which is not a log at all it is not true to say A, viz. that it
is a white log. Consequently D is true, but A is not true, i.e. that
it is a white log. It is clear also that A and C cannot together
belong to the same thing, and that B and D may possibly belong
to the same thing.
Privative terms are similarly related positive ter terms respect of
this arrangement. Let A stand for 'equal', B for 'not equal', C for
'unequal', D for 'not unequal'.
In many things also, to some of which something belongs which
does not belong to others, the negation may be true in a similar
way, viz. that all are not white or that each is not white, while
that each is not-white or all are not-white is false. Similarly also
'every animal is not-white' is not the negation of 'every animal
is white' (for both are false): the proper negation is 'every
animal is not white'. Since it is clear that 'it is not-white' and 'it
is not white' mean different things, and one is an affirmation,
the other a denial, it is evident that the method of proving each
cannot be the same, e.g. that whatever is an animal is not white
or may not be white, and that it is true to call it not-white; for
this means that it is not-white. But we may prove that it is true
to call it white or not-white in the same way for both are proved
constructively by means of the first figure. For the expression 'it
is true' stands on a similar footing to 'it is'. For the negation of
'it is true to call it white' is not 'it is true to call it not-white' but
'it is not true to call it white'. If then it is to be true to say that
whatever is a man is musical or is not-musical, we must
assume that whatever is an animal either is musical or is not-
musical; and the proof has been made. That whatever is a man
is not musical is proved destructively in the three ways
mentioned.
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In general whenever A and B are such that they cannot belong
at the same time to the same thing, and one of the two
necessarily belongs to everything, and again C and D are related
in the same way, and A follows C but the relation cannot be
reversed, then D must follow B and the relation cannot be
reversed. And A and D may belong to the same thing, but B and
C cannot. First it is clear from the following consideration that D
follows B. For since either C or D necessarily belongs to
everything; and since C cannot belong to that to which B
belongs, because it carries A along with it and A and B cannot
belong to the same thing; it is clear that D must follow B. Again
since C does not reciprocate with but A, but C or D belongs to
everything, it is possible that A and D should belong to the same
thing. But B and C cannot belong to the same thing, because A
follows C; and so something impossible results. It is clear then
that B does not reciprocate with D either, since it is possible that
D and A should belong at the same time to the same thing.
It results sometimes even in such an arrangement of terms that
one is deceived through not apprehending the opposites rightly,
one of which must belong to everything, e.g. we may reason
that 'if A and B cannot belong at the same time to the same
thing, but it is necessary that one of them should belong to
whatever the other does not belong to: and again C and D are
related in the same way, and follows everything which C
follows: it will result that B belongs necessarily to everything to
which D belongs': but this is false. Assume that F stands for the
negation of A and B, and again that H stands for the negation of
C and D. It is necessary then that either A or F should belong to
everything: for either the affirmation or the denial must belong.
And again either C or H must belong to everything: for they are
related as affirmation and denial. And ex hypothesi A belongs to
everything ever thing to which C belongs. Therefore H belongs
to everything to which F belongs. Again since either F or B
belongs to everything, and similarly either H or D, and since H
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follows F, B must follow D: for we know this. If then A follows C,
B must follow D'. But this is false: for as we proved the sequence
is reversed in terms so constituted. The fallacy arises because
perhaps it is not necessary that A or F should belong to
everything, or that F or B should belong to everything: for F is
not the denial of A. For not good is the negation of good: and
not-good is not identical with 'neither good nor not-good'.
Similarly also with C and D. For two negations have been
assumed in respect to one term.
Book II
We have already explained the number of the figures, the
character and number of the premisses, when and how a
syllogism is formed; further what we must look for when a
refuting and establishing propositions, and how we should
investigate a given problem in any branch of inquiry, also by
what means we shall obtain principles appropriate to each
subject. Since some syllogisms are universal, others particular,
all the universal syllogisms give more than one result, and of
particular syllogisms the affirmative yield more than one, the
negative yield only the stated conclusion. For all propositions
are convertible save only the particular negative: and the
conclusion states one definite thing about another definite
thing. Consequently all syllogisms save the particular negative
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yield more than one conclusion, e.g. if A has been proved to to
all or to some B, then B must belong to some A: and if A has
been proved to belong to no B, then B belongs to no A. This is a
different conclusion from the former. But if A does not belong to
some B, it is not necessary that B should not belong to some A:
for it may possibly belong to all A.
This then is the reason common to all syllogisms whether
universal or particular. But it is possible to give another reason
concerning those which are universal. For all the things that are
subordinate to the middle term or to the conclusion may be
proved by the same syllogism, if the former are placed in the
middle, the latter in the conclusion; e.g. if the conclusion AB is
proved through C, whatever is subordinate to B or C must accept
the predicate A: for if D is included in B as in a whole, and B is
included in A, then D will be included in A. Again if E is included
in C as in a whole, and C is included in A, then E will be
included in A. Similarly if the syllogism is negative. In the
second figure it will be possible to infer only that which is
subordinate to the conclusion, e.g. if A belongs to no B and to all
C; we conclude that B belongs to no C. If then D is subordinate
to C, clearly B does not belong to it. But that B does not belong
to what is subordinate to A is not clear by means of the
syllogism. And yet B does not belong to E, if E is subordinate to
A. But while it has been proved through the syllogism that B
belongs to no C, it has been assumed without proof that B does
not belong to A, consequently it does not result through the
syllogism that B does not belong to E.
But in particular syllogisms there will be no necessity of
inferring what is subordinate to the conclusion (for a syllogism
does not result when this premiss is particular), but whatever is
subordinate to the middle term may be inferred, not however
through the syllogism, e.g. if A belongs to all B and B to some C.
Nothing can be inferred about that which is subordinate to C;
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something can be inferred about that which is subordinate to B,
but not through the preceding syllogism. Similarly in the other
figures. That which is subordinate to the conclusion cannot be
proved; the other subordinate can be proved, only not through
the syllogism, just as in the universal syllogisms what is
subordinate to the middle term is proved (as we saw) from a
premiss which is not demonstrated: consequently either a
conclusion is not possible in the case of universal syllogisms or
else it is possible also in the case of particular syllogisms.
It is possible for the premisses of the syllogism to be true, or to
be false, or to be the one true, the other false. The conclusion is
either true or false necessarily. From true premisses it is not
possible to draw a false conclusion, but a true conclusion may
be drawn from false premisses, true however only in respect to
the fact, not to the reason. The reason cannot be established
from false premisses: why this is so will be explained in the
sequel.
First then that it is not possible to draw a false conclusion from
true premisses, is made clear by this consideration. If it is
necessary that B should be when A is, it is necessary that A
should not be when B is not. If then A is true, B must be true:
otherwise it will turn out that the same thing both is and is not
at the same time. But this is impossible. Let it not, because A is
laid down as a single term, be supposed that it is possible, when
a single fact is given, that something should necessarily result.
For that is not possible. For what results necessarily is the
conclusion, and the means by which this comes about are at the
least three terms, and two relations of subject and predicate or
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premisses. If then it is true that A belongs to all that to which B
belongs, and that B belongs to all that to which C belongs, it is
necessary that A should belong to all that to which C belongs,
and this cannot be false: for then the same thing will belong
and not belong at the same time. So A is posited as one thing,
being two premisses taken together. The same holds good of
negative syllogisms: it is not possible to prove a false conclusion
from true premisses.
But from what is false a true conclusion may be drawn, whether
both the premisses are false or only one, provided that this is
not either of the premisses indifferently, if it is taken as wholly
false: but if the premiss is not taken as wholly false, it does not
matter which of the two is false. (1) Let A belong to the whole of
C, but to none of the Bs, neither let B belong to C. This is
possible, e.g. animal belongs to no stone, nor stone to any man.
If then A is taken to belong to all B and B to all C, A will belong
to all C; consequently though both the premisses are false the
conclusion is true: for every man is an animal. Similarly with
the negative. For it is possible that neither A nor B should
belong to any C, although A belongs to all B, e.g. if the same
terms are taken and man is put as middle: for neither animal
nor man belongs to any stone, but animal belongs to every man.
Consequently if one term is taken to belong to none of that to
which it does belong, and the other term is taken to belong to
all of that to which it does not belong, though both the
premisses are false the conclusion will be true. (2) A similar
proof may be given if each premiss is partially false.
(3) But if one only of the premisses is false, when the first
premiss is wholly false, e.g. AB, the conclusion will not be true,
but if the premiss BC is wholly false, a true conclusion will be
possible. I mean by 'wholly false' the contrary of the truth, e.g. if
what belongs to none is assumed to belong to all, or if what
belongs to all is assumed to belong to none. Let A belong to no
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B, and B to all C. If then the premiss BC which I take is true, and
the premiss AB is wholly false, viz. that A belongs to all B, it is
impossible that the conclusion should be true: for A belonged to
none of the Cs, since A belonged to nothing to which B
belonged, and B belonged to all C. Similarly there cannot be a
true conclusion if A belongs to all B, and B to all C, but while the
true premiss BC is assumed, the wholly false premiss AB is also
assumed, viz. that A belongs to nothing to which B belongs:
here the conclusion must be false. For A will belong to all C,
since A belongs to everything to which B belongs, and B to all C.
It is clear then that when the first premiss is wholly false,
whether affirmative or negative, and the other premiss is true,
the conclusion cannot be true.
(4) But if the premiss is not wholly false, a true conclusion is
possible. For if A belongs to all C and to some B, and if B belongs
to all C, e.g. animal to every swan and to some white thing, and
white to every swan, then if we take as premisses that A
belongs to all B, and B to all C, A will belong to all C truly: for
every swan is an animal. Similarly if the statement AB is
negative. For it is possible that A should belong to some B and to
no C, and that B should belong to all C, e.g. animal to some
white thing, but to no snow, and white to all snow. If then one
should assume that A belongs to no B, and B to all C, then will
belong to no C.
(5) But if the premiss AB, which is assumed, is wholly true, and
the premiss BC is wholly false, a true syllogism will be possible:
for nothing prevents A belonging to all B and to all C, though B
belongs to no C, e.g. these being species of the same genus
which are not subordinate one to the other: for animal belongs
both to horse and to man, but horse to no man. If then it is
assumed that A belongs to all B and B to all C, the conclusion
will be true, although the premiss BC is wholly false. Similarly if
the premiss AB is negative. For it is possible that A should
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belong neither to any B nor to any C, and that B should not
belong to any C, e.g. a genus to species of another genus: for
animal belongs neither to music nor to the art of healing, nor
does music belong to the art of healing. If then it is assumed
that A belongs to no B, and B to all C, the conclusion will be true.
(6) And if the premiss BC is not wholly false but in part only,
even so the conclusion may be true. For nothing prevents A
belonging to the whole of B and of C, while B belongs to some C,
e.g. a genus to its species and difference: for animal belongs to
every man and to every footed thing, and man to some footed
things though not to all. If then it is assumed that A belongs to
all B, and B to all C, A will belong to all C: and this ex hypothesi
is true. Similarly if the premiss AB is negative. For it is possible
that A should neither belong to any B nor to any C, though B
belongs to some C, e.g. a genus to the species of another genus
and its difference: for animal neither belongs to any wisdom
nor to any instance of 'speculative', but wisdom belongs to
some instance of 'speculative'. If then it should be assumed that
A belongs to no B, and B to all C, will belong to no C: and this ex
hypothesi is true.
In particular syllogisms it is possible when the first premiss is
wholly false, and the other true, that the conclusion should be
true; also when the first premiss is false in part, and the other
true; and when the first is true, and the particular is false; and
when both are false. (7) For nothing prevents A belonging to no
B, but to some C, and B to some C, e.g. animal belongs to no
snow, but to some white thing, and snow to some white thing. If
then snow is taken as middle, and animal as first term, and it is
assumed that A belongs to the whole of B, and B to some C, then
the premiss BC is wholly false, the premiss BC true, and the
conclusion true. Similarly if the premiss AB is negative: for it is
possible that A should belong to the whole of B, but not to some
C, although B belongs to some C, e.g. animal belongs to every
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man, but does not follow some white, but man belongs to some
white; consequently if man be taken as middle term and it is
assumed that A belongs to no B but B belongs to some C, the
conclusion will be true although the premiss AB is wholly false.
(If the premiss AB is false in part, the conclusion may be true.
For nothing prevents A belonging both to B and to some C, and
B belonging to some C, e.g. animal to something beautiful and
to something great, and beautiful belonging to something great.
If then A is assumed to belong to all B, and B to some C, the a
premiss AB will be partially false, the premiss BC will be true,
and the conclusion true. Similarly if the premiss AB is negative.
For the same terms will serve, and in the same positions, to
prove the point.
(9) Again if the premiss AB is true, and the premiss BC is false,
the conclusion may be true. For nothing prevents A belonging to
the whole of B and to some C, while B belongs to no C, e.g.
animal to every swan and to some black things, though swan
belongs to no black thing. Consequently if it should be assumed
that A belongs to all B, and B to some C, the conclusion will be
true, although the statement BC is false. Similarly if the premiss
AB is negative. For it is possible that A should belong to no B,
and not to some C, while B belongs to no C, e.g. a genus to the
species of another genus and to the accident of its own species:
for animal belongs to no number and not to some white things,
and number belongs to nothing white. If then number is taken
as middle, and it is assumed that A belongs to no B, and B to
some C, then A will not belong to some C, which ex hypothesi is
true. And the premiss AB is true, the premiss BC false.
(10) Also if the premiss AB is partially false, and the premiss BC
is false too, the conclusion may be true. For nothing prevents A
belonging to some B and to some C, though B belongs to no C,
e.g. if B is the contrary of C, and both are accidents of the same
genus: for animal belongs to some white things and to some
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black things, but white belongs to no black thing. If then it is
assumed that A belongs to all B, and B to some C, the conclusion
will be true. Similarly if the premiss AB is negative: for the same
terms arranged in the same way will serve for the proof.
(11) Also though both premisses are false the conclusion may be
true. For it is possible that A may belong to no B and to some C,
while B belongs to no C, e.g. a genus in relation to the species of
another genus, and to the accident of its own species: for
animal belongs to no number, but to some white things, and
number to nothing white. If then it is assumed that A belongs to
all B and B to some C, the conclusion will be true, though both
premisses are false. Similarly also if the premiss AB is negative.
For nothing prevents A belonging to the whole of B, and not to
some C, while B belongs to no C, e.g. animal belongs to every
swan, and not to some black things, and swan belongs to
nothing black. Consequently if it is assumed that A belongs to
no B, and B to some C, then A does not belong to some C. The
conclusion then is true, but the premisses arc false.
In the middle figure it is possible in every way to reach a true
conclusion through false premisses, whether the syllogisms are
universal or particular, viz. when both premisses are wholly
false; when each is partially false; when one is true, the other
wholly false (it does not matter which of the two premisses is
false); if both premisses are partially false; if one is quite true,
the other partially false; if one is wholly false, the other partially
true. For (1) if A belongs to no B and to all C, e.g. animal to no
stone and to every horse, then if the premisses are stated
contrariwise and it is assumed that A belongs to all B and to no
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C, though the premisses are wholly false they will yield a true
conclusion. Similarly if A belongs to all B and to no C: for we
shall have the same syllogism.
(2) Again if one premiss is wholly false, the other wholly true:
for nothing prevents A belonging to all B and to all C, though B
belongs to no C, e.g. a genus to its co-ordinate species. For
animal belongs to every horse and man, and no man is a horse.
If then it is assumed that animal belongs to all of the one, and
none of the other, the one premiss will be wholly false, the
other wholly true, and the conclusion will be true whichever
term the negative statement concerns.
(3) Also if one premiss is partially false, the other wholly true.
For it is possible that A should belong to some B and to all C,
though B belongs to no C, e.g. animal to some white things and
to every raven, though white belongs to no raven. If then it is
assumed that A belongs to no B, but to the whole of C, the
premiss AB is partially false, the premiss AC wholly true, and
the conclusion true. Similarly if the negative statement is
transposed: the proof can be made by means of the same terms.
Also if the affirmative premiss is partially false, the negative
wholly true, a true conclusion is possible. For nothing prevents
A belonging to some B, but not to C as a whole, while B belongs
to no C, e.g. animal belongs to some white things, but to no
pitch, and white belongs to no pitch. Consequently if it is
assumed that A belongs to the whole of B, but to no C, the
premiss AB is partially false, the premiss AC is wholly true, and
the conclusion is true.
(4) And if both the premisses are partially false, the conclusion
may be true. For it is possible that A should belong to some B
and to some C, and B to no C, e.g. animal to some white things
and to some black things, though white belongs to nothing
black. If then it is assumed that A belongs to all B and to no C,
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both premisses are partially false, but the conclusion is true.
Similarly, if the negative premiss is transposed, the proof can be
made by means of the same terms.
It is clear also that our thesis holds in particular syllogisms. For
(5) nothing prevents A belonging to all B and to some C, though
B does not belong to some C, e.g. animal to every man and to
some white things, though man will not belong to some white
things. If then it is stated that A belongs to no B and to some C,
the universal premiss is wholly false, the particular premiss is
true, and the conclusion is true. Similarly if the premiss AB is
affirmative: for it is possible that A should belong to no B, and
not to some C, though B does not belong to some C, e.g. animal
belongs to nothing lifeless, and does not belong to some white
things, and lifeless will not belong to some white things. If then
it is stated that A belongs to all B and not to some C, the
premiss AB which is universal is wholly false, the premiss AC is
true, and the conclusion is true. Also a true conclusion is
possible when the universal premiss is true, and the particular
is false. For nothing prevents A following neither B nor C at all,
while B does not belong to some C, e.g. animal belongs to no
number nor to anything lifeless, and number does not follow
some lifeless things. If then it is stated that A belongs to no B
and to some C, the conclusion will be true, and the universal
premiss true, but the particular false. Similarly if the premiss
which is stated universally is affirmative. For it is possible that
should A belong both to B and to G as wholes, though B does not
follow some C, e.g. a genus in relation to its species and
difference: for animal follows every man and footed things as a
whole, but man does not follow every footed thing.
Consequently if it is assumed that A belongs to the whole of B,
but does not belong to some C, the universal premiss is true, the
particular false, and the conclusion true.
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(6) It is clear too that though both premisses are false they may
yield a true conclusion, since it is possible that A should belong
both to B and to C as wholes, though B does not follow some C.
For if it is assumed that A belongs to no B and to some C, the
premisses are both false, but the conclusion is true. Similarly if
the universal premiss is affirmative and the particular negative.
For it is possible that A should follow no B and all C, though B
does not belong to some C, e.g. animal follows no science but
every man, though science does not follow every man. If then A
is assumed to belong to the whole of B, and not to follow some
C, the premisses are false but the conclusion is true.
In the last figure a true conclusion may come through what is
false, alike when both premisses are wholly false, when each is
partly false, when one premiss is wholly true, the other false,
when one premiss is partly false, the other wholly true, and vice
versa, and in every other way in which it is possible to alter the
premisses. For (1) nothing prevents neither A nor B from
belonging to any C, while A belongs to some B, e.g. neither man
nor footed follows anything lifeless, though man belongs to
some footed things. If then it is assumed that A and B belong to
all C, the premisses will be wholly false, but the conclusion true.
Similarly if one premiss is negative, the other affirmative. For it
is possible that B should belong to no C, but A to all C, and that
should not belong to some B, e.g. black belongs to no swan,
animal to every swan, and animal not to everything black.
Consequently if it is assumed that B belongs to all C, and A to
no C, A will not belong to some B: and the conclusion is true,
though the premisses are false.
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(2) Also if each premiss is partly false, the conclusion may be
true. For nothing prevents both A and B from belonging to some
C while A belongs to some B, e.g. white and beautiful belong to
some animals, and white to some beautiful things. If then it is
stated that A and B belong to all C, the premisses are partially
false, but the conclusion is true. Similarly if the premiss AC is
stated as negative. For nothing prevents A from not belonging,
and B from belonging, to some C, while A does not belong to all
B, e.g. white does not belong to some animals, beautiful belongs
to some animals, and white does not belong to everything
beautiful. Consequently if it is assumed that A belongs to no C,
and B to all C, both premisses are partly false, but the
conclusion is true.
(3) Similarly if one of the premisses assumed is wholly false, the
other wholly true. For it is possible that both A and B should
follow all C, though A does not belong to some B, e.g. animal
and white follow every swan, though animal does not belong to
everything white. Taking these then as terms, if one assumes
that B belongs to the whole of C, but A does not belong to C at
all, the premiss BC will be wholly true, the premiss AC wholly
false, and the conclusion true. Similarly if the statement BC is
false, the statement AC true, the conclusion may be true. The
same terms will serve for the proof. Also if both the premisses
assumed are affirmative, the conclusion may be true. For
nothing prevents B from following all C, and A from not
belonging to C at all, though A belongs to some B, e.g. animal
belongs to every swan, black to no swan, and black to some
animals. Consequently if it is assumed that A and B belong to
every C, the premiss BC is wholly true, the premiss AC is wholly
false, and the conclusion is true. Similarly if the premiss AC
which is assumed is true: the proof can be made through the
same terms.
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(4) Again if one premiss is wholly true, the other partly false, the
conclusion may be true. For it is possible that B should belong to
all C, and A to some C, while A belongs to some B, e.g. biped
belongs to every man, beautiful not to every man, and beautiful
to some bipeds. If then it is assumed that both A and B belong
to the whole of C, the premiss BC is wholly true, the premiss AC
partly false, the conclusion true. Similarly if of the premisses
assumed AC is true and BC partly false, a true conclusion is
possible: this can be proved, if the same terms as before are
transposed. Also the conclusion may be true if one premiss is
negative, the other affirmative. For since it is possible that B
should belong to the whole of C, and A to some C, and, when
they are so, that A should not belong to all B, therefore it is
assumed that B belongs to the whole of C, and A to no C, the
negative premiss is partly false, the other premiss wholly true,
and the conclusion is true. Again since it has been proved that if
A belongs to no C and B to some C, it is possible that A should
not belong to some C, it is clear that if the premiss AC is wholly
true, and the premiss BC partly false, it is possible that the
conclusion should be true. For if it is assumed that A belongs to
no C, and B to all C, the premiss AC is wholly true, and the
premiss BC is partly false.
(5) It is clear also in the case of particular syllogisms that a true
conclusion may come through what is false, in every possible
way. For the same terms must be taken as have been taken
when the premisses are universal, positive terms in positive
syllogisms, negative terms in negative. For it makes no
difference to the setting out of the terms, whether one assumes
that what belongs to none belongs to all or that what belongs to
some belongs to all. The same applies to negative statements.
It is clear then that if the conclusion is false, the premisses of
the argument must be false, either all or some of them; but
when the conclusion is true, it is not necessary that the
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premisses should be true, either one or all, yet it is possible,
though no part of the syllogism is true, that the conclusion may
none the less be true; but it is not necessitated. The reason is
that when two things are so related to one another, that if the
one is, the other necessarily is, then if the latter is not, the
former will not be either, but if the latter is, it is not necessary
that the former should be. But it is impossible that the same
thing should be necessitated by the being and by the not-being
of the same thing. I mean, for example, that it is impossible that
B should necessarily be great since A is white and that B should
necessarily be great since A is not white. For whenever since
this, A, is white it is necessary that that, B, should be great, and
since B is great that C should not be white, then it is necessary
if is white that C should not be white. And whenever it is
necessary, since one of two things is, that the other should be, it
is necessary, if the latter is not, that the former (viz. A) should
not be. If then B is not great A cannot be white. But if, when A is
not white, it is necessary that B should be great, it necessarily
results that if B is not great, B itself is great. (But this is
impossible.) For if B is not great, A will necessarily not be white.
If then when this is not white B must be great, it results that if B
is not great, it is great, just as if it were proved through three
terms.
Circular and reciprocal proof means proof by means of the
conclusion, i.e. by converting one of the premisses simply and
inferring the premiss which was assumed in the original
syllogism: e.g. suppose it has been necessary to prove that A
belongs to all C, and it has been proved through B; suppose that
A should now be proved to belong to B by assuming that A
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belongs to C, and C to B - so A belongs to B: but in the first
syllogism the converse was assumed, viz. that B belongs to C. Or
suppose it is necessary to prove that B belongs to C, and A is
assumed to belong to C, which was the conclusion of the first
syllogism, and B to belong to A but the converse was assumed
in the earlier syllogism, viz. that A belongs to B. In no other way
is reciprocal proof possible. If another term is taken as middle,
the proof is not circular: for neither of the propositions assumed
is the same as before: if one of the accepted terms is taken as
middle, only one of the premisses of the first syllogism can be
assumed in the second: for if both of them are taken the same
conclusion as before will result: but it must be different. If the
terms are not convertible, one of the premisses from which the
syllogism results must be undemonstrated: for it is not possible
to demonstrate through these terms that the third belongs to
the middle or the middle to the first. If the terms are
convertible, it is possible to demonstrate everything reciprocally,
e.g. if A and B and C are convertible with one another. Suppose
the proposition AC has been demonstrated through B as middle
term, and again the proposition AB through the conclusion and
the premiss BC converted, and similarly the proposition BC
through the conclusion and the premiss AB converted. But it is
necessary to prove both the premiss CB, and the premiss BA: for
we have used these alone without demonstrating them. If then
it is assumed that B belongs to all C, and C to all A, we shall
have a syllogism relating B to A. Again if it is assumed that C
belongs to all A, and A to all B, C must belong to all B. In both
these syllogisms the premiss CA has been assumed without
being demonstrated: the other premisses had ex hypothesi been
proved. Consequently if we succeed in demonstrating this
premiss, all the premisses will have been proved reciprocally. If
then it is assumed that C belongs to all B, and B to all A, both
the premisses assumed have been proved, and C must belong to
A. It is clear then that only if the terms are convertible is
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circular and reciprocal demonstration possible (if the terms are
not convertible, the matter stands as we said above). But it turns
out in these also that we use for the demonstration the very
thing that is being proved: for C is proved of B, and B of by
assuming that C is said of and C is proved of A through these
premisses, so that we use the conclusion for the demonstration.
In negative syllogisms reciprocal proof is as follows. Let B
belong to all C, and A to none of the Bs: we conclude that A
belongs to none of the Cs. If again it is necessary to prove that A
belongs to none of the Bs (which was previously assumed) A
must belong to no C, and C to all B: thus the previous premiss is
reversed. If it is necessary to prove that B belongs to C, the
proposition AB must no longer be converted as before: for the
premiss 'B belongs to no A' is identical with the premiss 'A
belongs to no B'. But we must assume that B belongs to all of
that to none of which longs. Let A belong to none of the Cs
(which was the previous conclusion) and assume that B belongs
to all of that to none of which A belongs. It is necessary then
that B should belong to all C. Consequently each of the three
propositions has been made a conclusion, and this is circular
demonstration, to assume the conclusion and the converse of
one of the premisses, and deduce the remaining premiss.
In particular syllogisms it is not possible to demonstrate the
universal premiss through the other propositions, but the
particular premiss can be demonstrated. Clearly it is impossible
to demonstrate the universal premiss: for what is universal is
proved through propositions which are universal, but the
conclusion is not universal, and the proof must start from the
conclusion and the other premiss. Further a syllogism cannot
be made at all if the other premiss is converted: for the result is
that both premisses are particular. But the particular premiss
may be proved. Suppose that A has been proved of some C
through B. If then it is assumed that B belongs to all A and the
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conclusion is retained, B will belong to some C: for we obtain
the first figure and A is middle. But if the syllogism is negative,
it is not possible to prove the universal premiss, for the reason
given above. But it is possible to prove the particular premiss, if
the proposition AB is converted as in the universal syllogism, i.e
'B belongs to some of that to some of which A does not belong':
otherwise no syllogism results because the particular premiss is
negative.
In the second figure it is not possible to prove an affirmative
proposition in this way, but a negative proposition may be
proved. An affirmative proposition is not proved because both
premisses of the new syllogism are not affirmative (for the
conclusion is negative) but an affirmative proposition is (as we
saw) proved from premisses which are both affirmative. The
negative is proved as follows. Let A belong to all B, and to no C:
we conclude that B belongs to no C. If then it is assumed that B
belongs to all A, it is necessary that A should belong to no C: for
we get the second figure, with B as middle. But if the premiss AB
was negative, and the other affirmative, we shall have the first
figure. For C belongs to all A and B to no C, consequently B
belongs to no A: neither then does A belong to B. Through the
conclusion, therefore, and one premiss, we get no syllogism, but
if another premiss is assumed in addition, a syllogism will be
possible. But if the syllogism not universal, the universal
premiss cannot be proved, for the same reason as we gave
above, but the particular premiss can be proved whenever the
universal statement is affirmative. Let A belong to all B, and not
to all C: the conclusion is BC. If then it is assumed that B
belongs to all A, but not to all C, A will not belong to some C, B
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being middle. But if the universal premiss is negative, the
premiss AC will not be demonstrated by the conversion of AB:
for it turns out that either both or one of the premisses is
negative; consequently a syllogism will not be possible. But the
proof will proceed as in the universal syllogisms, if it is
assumed that A belongs to some of that to some of which B
does not belong.
In the third figure, when both premisses are taken universally, it
is not possible to prove them reciprocally: for that which is
universal is proved through statements which are universal, but
the conclusion in this figure is always particular, so that it is
clear that it is not possible at all to prove through this figure the
universal premiss. But if one premiss is universal, the other
particular, proof of the latter will sometimes be possible,
sometimes not. When both the premisses assumed are
affirmative, and the universal concerns the minor extreme,
proof will be possible, but when it concerns the other extreme,
impossible. Let A belong to all C and B to some C: the conclusion
is the statement AB. If then it is assumed that C belongs to all A,
it has been proved that C belongs to some B, but that B belongs
to some C has not been proved. And yet it is necessary, if C
belongs to some B, that B should belong to some C. But it is not
the same that this should belong to that, and that to this: but
we must assume besides that if this belongs to some of that,
that belongs to some of this. But if this is assumed the
syllogism no longer results from the conclusion and the other
premiss. But if B belongs to all C, and A to some C, it will be
possible to prove the proposition AC, when it is assumed that C
belongs to all B, and A to some B. For if C belongs to all B and A
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to some B, it is necessary that A should belong to some C, B
being middle. And whenever one premiss is affirmative the
other negative, and the affirmative is universal, the other
premiss can be proved. Let B belong to all C, and A not to some
C: the conclusion is that A does not belong to some B. If then it
is assumed further that C belongs to all B, it is necessary that A
should not belong to some C, B being middle. But when the
negative premiss is universal, the other premiss is not except as
before, viz. if it is assumed that that belongs to some of that, to
some of which this does not belong, e.g. if A belongs to no C,
and B to some C: the conclusion is that A does not belong to
some B. If then it is assumed that C belongs to some of that to
some of which does not belong, it is necessary that C should
belong to some of the Bs. In no other way is it possible by
converting the universal premiss to prove the other: for in no
other way can a syllogism be formed.
It is clear then that in the first figure reciprocal proof is made
both through the third and through the first figure - if the
conclusion is affirmative through the first; if the conclusion is
negative through the last. For it is assumed that that belongs to
all of that to none of which this belongs. In the middle figure,
when the syllogism is universal, proof is possible through the
second figure and through the first, but when particular
through the second and the last. In the third figure all proofs
are made through itself. It is clear also that in the third figure
and in the middle figure those syllogisms which are not made
through those figures themselves either are not of the nature of
circular proof or are imperfect.
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8
To convert a syllogism means to alter the conclusion and make
another syllogism to prove that either the extreme cannot
belong to the middle or the middle to the last term. For it is
necessary, if the conclusion has been changed into its opposite
and one of the premisses stands, that the other premiss should
be destroyed. For if it should stand, the conclusion also must
stand. It makes a difference whether the conclusion is
converted into its contradictory or into its contrary. For the
same syllogism does not result whichever form the conversion
takes. This will be made clear by the sequel. By contradictory
opposition I mean the opposition of 'to all' to 'not to all', and of
'to some' to 'to none'; by contrary opposition I mean the
opposition of 'to all' to 'to none', and of 'to some' to 'not to
some'. Suppose that A been proved of C, through B as middle
term. If then it should be assumed that A belongs to no C, but to
all B, B will belong to no C. And if A belongs to no C, and B to all
C, A will belong, not to no B at all, but not to all B. For (as we
saw) the universal is not proved through the last figure. In a
word it is not possible to refute universally by conversion the
premiss which concerns the major extreme: for the refutation
always proceeds through the third since it is necessary to take
both premisses in reference to the minor extreme. Similarly if
the syllogism is negative. Suppose it has been proved that A
belongs to no C through B. Then if it is assumed that A belongs
to all C, and to no B, B will belong to none of the Cs. And if A and
B belong to all C, A will belong to some B: but in the original
premiss it belonged to no B.
If the conclusion is converted into its contradictory, the
syllogisms will be contradictory and not universal. For one
premiss is particular, so that the conclusion also will be
particular. Let the syllogism be affirmative, and let it be
converted as stated. Then if A belongs not to all C, but to all B, B
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will belong not to all C. And if A belongs not to all C, but B
belongs to all C, A will belong not to all B. Similarly if the
syllogism is negative. For if A belongs to some C, and to no B, B
will belong, not to no C at all, but - not to some C. And if A
belongs to some C, and B to all C, as was originally assumed, A
will belong to some B.
In particular syllogisms when the conclusion is converted into
its contradictory, both premisses may be refuted, but when it is
converted into its contrary, neither. For the result is no longer,
as in the universal syllogisms, refutation in which the
conclusion reached by 0, conversion lacks universality, but no
refutation at all. Suppose that A has been proved of some C. If
then it is assumed that A belongs to no C, and B to some C, A
will not belong to some B: and if A belongs to no C, but to all B, B
will belong to no C.Thus both premisses are refuted. But neither
can be refuted if the conclusion is converted into its contrary.
For if A does not belong to some C, but to all B, then B will not
belong to some C. But the original premiss is not yet refuted: for
it is possible that B should belong to some C, and should not
belong to some C. The universal premiss AB cannot be affected
by a syllogism at all: for if A does not belong to some of the Cs,
but B belongs to some of the Cs, neither of the premisses is
universal. Similarly if the syllogism is negative: for if it should
be assumed that A belongs to all C, both premisses are refuted:
but if the assumption is that A belongs to some C, neither
premiss is refuted. The proof is the same as before.
In the second figure it is not possible to refute the premiss
which concerns the major extreme by establishing something
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contrary to it, whichever form the conversion of the conclusion
may take. For the conclusion of the refutation will always be in
the third figure, and in this figure (as we saw) there is no
universal syllogism. The other premiss can be refuted in a
manner similar to the conversion: I mean, if the conclusion of
the first syllogism is converted into its contrary, the conclusion
of the refutation will be the contrary of the minor premiss of
the first, if into its contradictory, the contradictory. Let A belong
to all B and to no C: conclusion BC. If then it is assumed that B
belongs to all C, and the proposition AB stands, A will belong to
all C, since the first figure is produced. If B belongs to all C, and
A to no C, then A belongs not to all B: the figure is the last. But if
the conclusion BC is converted into its contradictory, the
premiss AB will be refuted as before, the premiss, AC by its
contradictory. For if B belongs to some C, and A to no C, then A
will not belong to some B. Again if B belongs to some C, and A to
all B, A will belong to some C, so that the syllogism results in
the contradictory of the minor premiss. A similar proof can be
given if the premisses are transposed in respect of their quality.
If the syllogism is particular, when the conclusion is converted
into its contrary neither premiss can be refuted, as also
happened in the first figure,' if the conclusion is converted into
its contradictory, both premisses can be refuted. Suppose that A
belongs to no B, and to some C: the conclusion is BC. If then it is
assumed that B belongs to some C, and the statement AB
stands, the conclusion will be that A does not belong to some C.
But the original statement has not been refuted: for it is
possible that A should belong to some C and also not to some C.
Again if B belongs to some C and A to some C, no syllogism will
be possible: for neither of the premisses taken is universal.
Consequently the proposition AB is not refuted. But if the
conclusion is converted into its contradictory, both premisses
can be refuted. For if B belongs to all C, and A to no B, A will
belong to no C: but it was assumed to belong to some C. Again if
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B belongs to all C and A to some C, A will belong to some B. The
same proof can be given if the universal statement is
affirmative.
10
In the third figure when the conclusion is converted into its
contrary, neither of the premisses can be refuted in any of the
syllogisms, but when the conclusion is converted into its
contradictory, both premisses may be refuted and in all the
moods. Suppose it has been proved that A belongs to some B, C
being taken as middle, and the premisses being universal. If
then it is assumed that A does not belong to some B, but B
belongs to all C, no syllogism is formed about A and C. Nor if A
does not belong to some B, but belongs to all C, will a syllogism
be possible about B and C. A similar proof can be given if the
premisses are not universal. For either both premisses arrived at
by the conversion must be particular, or the universal premiss
must refer to the minor extreme. But we found that no
syllogism is possible thus either in the first or in the middle
figure. But if the conclusion is converted into its contradictory,
both the premisses can be refuted. For if A belongs to no B, and
B to all C, then A belongs to no C: again if A belongs to no B, and
to all C, B belongs to no C. And similarly if one of the premisses
is not universal. For if A belongs to no B, and B to some C, A will
not belong to some C: if A belongs to no B, and to C, B will
belong to no C.
Similarly if the original syllogism is negative. Suppose it has
been proved that A does not belong to some B, BC being
affirmative, AC being negative: for it was thus that, as we saw, a
syllogism could be made. Whenever then the contrary of the
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conclusion is assumed a syllogism will not be possible. For if A
belongs to some B, and B to all C, no syllogism is possible (as we
saw) about A and C. Nor, if A belongs to some B, and to no C,
was a syllogism possible concerning B and C. Therefore the
premisses are not refuted. But when the contradictory of the
conclusion is assumed, they are refuted. For if A belongs to all B,
and B to C, A belongs to all C: but A was supposed originally to
belong to no C. Again if A belongs to all B, and to no C, then B
belongs to no C: but it was supposed to belong to all C. A similar
proof is possible if the premisses are not universal. For AC
becomes universal and negative, the other premiss particular
and affirmative. If then A belongs to all B, and B to some C, it
results that A belongs to some C: but it was supposed to belong
to no C. Again if A belongs to all B, and to no C, then B belongs
to no C: but it was assumed to belong to some C. If A belongs to
some B and B to some C, no syllogism results: nor yet if A
belongs to some B, and to no C. Thus in one way the premisses
are refuted, in the other way they are not.
From what has been said it is clear how a syllogism results in
each figure when the conclusion is converted; when a result
contrary to the premiss, and when a result contradictory to the
premiss, is obtained. It is clear that in the first figure the
syllogisms are formed through the middle and the last figures,
and the premiss which concerns the minor extreme is alway
refuted through the middle figure, the premiss which concerns
the major through the last figure. In the second figure
syllogisms proceed through the first and the last figures, and
the premiss which concerns the minor extreme is always
refuted through the first figure, the premiss which concerns the
major extreme through the last. In the third figure the
refutation proceeds through the first and the middle figures; the
premiss which concerns the major is always refuted through
the first figure, the premiss which concerns the minor through
the middle figure.
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11
It is clear then what conversion is, how it is effected in each
figure, and what syllogism results. The syllogism per
impossibile is proved when the contradictory of the conclusion
stated and another premiss is assumed; it can be made in all
the figures. For it resembles conversion, differing only in this:
conversion takes place after a syllogism has been formed and
both the premisses have been taken, but a reduction to the
impossible takes place not because the contradictory has been
agreed to already, but because it is clear that it is true. The
terms are alike in both, and the premisses of both are taken in
the same way. For example if A belongs to all B, C being middle,
then if it is supposed that A does not belong to all B or belongs
to no B, but to all C (which was admitted to be true), it follows
that C belongs to no B or not to all B. But this is impossible:
consequently the supposition is false: its contradictory then is
true. Similarly in the other figures: for whatever moods admit of
conversion admit also of the reduction per impossibile.
All the problems can be proved per impossibile in all the figures,
excepting the universal affirmative, which is proved in the
middle and third figures, but not in the first. Suppose that A
belongs not to all B, or to no B, and take besides another
premiss concerning either of the terms, viz. that C belongs to all
A, or that B belongs to all D; thus we get the first figure. If then
it is supposed that A does not belong to all B, no syllogism
results whichever term the assumed premiss concerns; but if it
is supposed that A belongs to no B, when the premiss BD is
assumed as well we shall prove syllogistically what is false, but
not the problem proposed. For if A belongs to no B, and B
belongs to all D, A belongs to no D. Let this be impossible: it is
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false then A belongs to no B. But the universal affirmative is not
necessarily true if the universal negative is false. But if the
premiss CA is assumed as well, no syllogism results, nor does it
do so when it is supposed that A does not belong to all B.
Consequently it is clear that the universal affirmative cannot be
proved in the first figure per impossibile.
But the particular affirmative and the universal and particular
negatives can all be proved. Suppose that A belongs to no B, and
let it have been assumed that B belongs to all or to some C.
Then it is necessary that A should belong to no C or not to all C.
But this is impossible (for let it be true and clear that A belongs
to all C): consequently if this is false, it is necessary that A
should belong to some B. But if the other premiss assumed
relates to A, no syllogism will be possible. Nor can a conclusion
be drawn when the contrary of the conclusion is supposed, e.g.
that A does not belong to some B. Clearly then we must suppose
the contradictory.
Again suppose that A belongs to some B, and let it have been
assumed that C belongs to all A. It is necessary then that C
should belong to some B. But let this be impossible, so that the
supposition is false: in that case it is true that A belongs to no B.
We may proceed in the same way if the proposition CA has been
taken as negative. But if the premiss assumed concerns B, no
syllogism will be possible. If the contrary is supposed, we shall
have a syllogism and an impossible conclusion, but the problem
in hand is not proved. Suppose that A belongs to all B, and let it
have been assumed that C belongs to all A. It is necessary then
that C should belong to all B. But this is impossible, so that it is
false that A belongs to all B. But we have not yet shown it to be
necessary that A belongs to no B, if it does not belong to all B.
Similarly if the other premiss taken concerns B; we shall have a
syllogism and a conclusion which is impossible, but the
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hypothesis is not refuted. Therefore it is the contradictory that
we must suppose.
To prove that A does not belong to all B, we must suppose that it
belongs to all B: for if A belongs to all B, and C to all A, then C
belongs to all B; so that if this is impossible, the hypothesis is
false. Similarly if the other premiss assumed concerns B. The
same results if the original proposition CA was negative: for
thus also we get a syllogism. But if the negative proposition
concerns B, nothing is proved. If the hypothesis is that A
belongs not to all but to some B, it is not proved that A belongs
not to all B, but that it belongs to no B. For if A belongs to some
B, and C to all A, then C will belong to some B. If then this is
impossible, it is false that A belongs to some B; consequently it
is true that A belongs to no B. But if this is proved, the truth is
refuted as well; for the original conclusion was that A belongs to
some B, and does not belong to some B. Further the impossible
does not result from the hypothesis: for then the hypothesis
would be false, since it is impossible to draw a false conclusion
from true premisses: but in fact it is true: for A belongs to some
B. Consequently we must not suppose that A belongs to some B,
but that it belongs to all B. Similarly if we should be proving that
A does not belong to some B: for if 'not to belong to some' and
'to belong not to all' have the same meaning, the demonstration
of both will be identical.
It is clear then that not the contrary but the contradictory ought
to be supposed in all the syllogisms. For thus we shall have
necessity of inference, and the claim we make is one that will
be generally accepted. For if of everything one or other of two
contradictory statements holds good, then if it is proved that
the negation does not hold, the affirmation must be true. Again
if it is not admitted that the affirmation is true, the claim that
the negation is true will be generally accepted. But in neither
way does it suit to maintain the contrary: for it is not necessary
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that if the universal negative is false, the universal affirmative
should be true, nor is it generally accepted that if the one is
false the other is true.
12
It is clear then that in the first figure all problems except the
universal affirmative are proved per impossibile. But in the
middle and the last figures this also is proved. Suppose that A
does not belong to all B, and let it have been assumed that A
belongs to all C. If then A belongs not to all B, but to all C, C will
not belong to all B. But this is impossible (for suppose it to be
clear that C belongs to all B): consequently the hypothesis is
false. It is true then that A belongs to all B. But if the contrary is
supposed, we shall have a syllogism and a result which is
impossible: but the problem in hand is not proved. For if A
belongs to no B, and to all C, C will belong to no B. This is
impossible; so that it is false that A belongs to no B. But though
this is false, it does not follow that it is true that A belongs to all
B.
When A belongs to some B, suppose that A belongs to no B, and
let A belong to all C. It is necessary then that C should belong to
no B. Consequently, if this is impossible, A must belong to some
B. But if it is supposed that A does not belong to some B, we
shall have the same results as in the first figure.
Again suppose that A belongs to some B, and let A belong to no
C. It is necessary then that C should not belong to some B. But
originally it belonged to all B, consequently the hypothesis is
false: A then will belong to no B.
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When A does not belong to an B, suppose it does belong to all B,
and to no C. It is necessary then that C should belong to no B.
But this is impossible: so that it is true that A does not belong to
all B. It is clear then that all the syllogisms can be formed in the
middle figure.
13
Similarly they can all be formed in the last figure. Suppose that
A does not belong to some B, but C belongs to all B: then A does
not belong to some C. If then this is impossible, it is false that A
does not belong to some B; so that it is true that A belongs to all
B. But if it is supposed that A belongs to no B, we shall have a
syllogism and a conclusion which is impossible: but the
problem in hand is not proved: for if the contrary is supposed,
we shall have the same results as before.
But to prove that A belongs to some B, this hypothesis must be
made. If A belongs to no B, and C to some B, A will belong not to
all C. If then this is false, it is true that A belongs to some B.
When A belongs to no B, suppose A belongs to some B, and let it
have been assumed that C belongs to all B. Then it is necessary
that A should belong to some C. But ex hypothesi it belongs to
no C, so that it is false that A belongs to some B. But if it is
supposed that A belongs to all B, the problem is not proved.
But this hypothesis must be made if we are prove that A belongs
not to all B. For if A belongs to all B and C to some B, then A
belongs to some C. But this we assumed not to be so, so it is
false that A belongs to all B. But in that case it is true that A
belongs not to all B. If however it is assumed that A belongs to
some B, we shall have the same result as before.
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It is clear then that in all the syllogisms which proceed per
impossibile the contradictory must be assumed. And it is plain
that in the middle figure an affirmative conclusion, and in the
last figure a universal conclusion, are proved in a way.
14
Demonstration per impossibile differs from ostensive proof in
that it posits what it wishes to refute by reduction to a
statement admitted to be false; whereas ostensive proof starts
from admitted positions. Both, indeed, take two premisses that
are admitted, but the latter takes the premisses from which the
syllogism starts, the former takes one of these, along with the
contradictory of the original conclusion. Also in the ostensive
proof it is not necessary that the conclusion should be known,
nor that one should suppose beforehand that it is true or not: in
the other it is necessary to suppose beforehand that it is not
true. It makes no difference whether the conclusion is
affirmative or negative; the method is the same in both cases.
Everything which is concluded ostensively can be proved per
impossibile, and that which is proved per impossibile can be
proved ostensively, through the same terms. Whenever the
syllogism is formed in the first figure, the truth will be found in
the middle or the last figure, if negative in the middle, if
affirmative in the last. Whenever the syllogism is formed in the
middle figure, the truth will be found in the first, whatever the
problem may be. Whenever the syllogism is formed in the last
figure, the truth will be found in the first and middle figures, if
affirmative in first, if negative in the middle. Suppose that A has
been proved to belong to no B, or not to all B, through the first
figure. Then the hypothesis must have been that A belongs to
some B, and the original premisses that C belongs to all A and to
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no B. For thus the syllogism was made and the impossible
conclusion reached. But this is the middle figure, if C belongs to
all A and to no B. And it is clear from these premisses that A
belongs to no B. Similarly if has been proved not to belong to all
B. For the hypothesis is that A belongs to all B; and the original
premisses are that C belongs to all A but not to all B. Similarly
too, if the premiss CA should be negative: for thus also we have
the middle figure. Again suppose it has been proved that A
belongs to some B. The hypothesis here is that is that A belongs
to no B; and the original premisses that B belongs to all C, and A
either to all or to some C: for in this way we shall get what is
impossible. But if A and B belong to all C, we have the last
figure. And it is clear from these premisses that A must belong
to some B. Similarly if B or A should be assumed to belong to
some C.
Again suppose it has been proved in the middle figure that A
belongs to all B. Then the hypothesis must have been that A
belongs not to all B, and the original premisses that A belongs to
all C, and C to all B: for thus we shall get what is impossible. But
if A belongs to all C, and C to all B, we have the first figure.
Similarly if it has been proved that A belongs to some B: for the
hypothesis then must have been that A belongs to no B, and the
original premisses that A belongs to all C, and C to some B. If
the syllogism is negative, the hypothesis must have been that A
belongs to some B, and the original premisses that A belongs to
no C, and C to all B, so that the first figure results. If the
syllogism is not universal, but proof has been given that A does
not belong to some B, we may infer in the same way. The
hypothesis is that A belongs to all B, the original premisses that
A belongs to no C, and C belongs to some B: for thus we get the
first figure.
Again suppose it has been proved in the third figure that A
belongs to all B. Then the hypothesis must have been that A
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belongs not to all B, and the original premisses that C belongs to
all B, and A belongs to all C; for thus we shall get what is
impossible. And the original premisses form the first figure.
Similarly if the demonstration establishes a particular
proposition: the hypothesis then must have been that A belongs
to no B, and the original premisses that C belongs to some B,
and A to all C. If the syllogism is negative, the hypothesis must
have been that A belongs to some B, and the original premisses
that C belongs to no A and to all B, and this is the middle figure.
Similarly if the demonstration is not universal. The hypothesis
will then be that A belongs to all B, the premisses that C belongs
to no A and to some B: and this is the middle figure.
It is clear then that it is possible through the same terms to
prove each of the problems ostensively as well. Similarly it will
be possible if the syllogisms are ostensive to reduce them ad
impossibile in the terms which have been taken, whenever the
contradictory of the conclusion of the ostensive syllogism is
taken as a premiss. For the syllogisms become identical with
those which are obtained by means of conversion, so that we
obtain immediately the figures through which each problem
will be solved. It is clear then that every thesis can be proved in
both ways, i.e. per impossibile and ostensively, and it is not
possible to separate one method from the other.
15
In what figure it is possible to draw a conclusion from
premisses which are opposed, and in what figure this is not
possible, will be made clear in this way. Verbally four kinds of
opposition are possible, viz. universal affirmative to universal
negative, universal affirmative to particular negative, particular
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affirmative to universal negative, and particular affirmative to
particular negative: but really there are only three: for the
particular affirmative is only verbally opposed to the particular
negative. Of the genuine opposites I call those which are
universal contraries, the universal affirmative and the universal
negative, e.g. 'every science is good', 'no science is good'; the
others I call contradictories.
In the first figure no syllogism whether affirmative or negative
can be made out of opposed premisses: no affirmative syllogism
is possible because both premisses must be affirmative, but
opposites are, the one affirmative, the other negative: no
negative syllogism is possible because opposites affirm and
deny the same predicate of the same subject, and the middle
term in the first figure is not predicated of both extremes, but
one thing is denied of it, and it is affirmed of something else:
but such premisses are not opposed.
In the middle figure a syllogism can be made both
oLcontradictories and of contraries. Let A stand for good, let B
and C stand for science. If then one assumes that every science
is good, and no science is good, A belongs to all B and to no C, so
that B belongs to no C: no science then is a science. Similarly if
after taking 'every science is good' one took 'the science of
medicine is not good'; for A belongs to all B but to no C, so that
a particular science will not be a science. Again, a particular
science will not be a science if A belongs to all C but to no B, and
B is science, C medicine, and A supposition: for after taking 'no
science is supposition', one has assumed that a particular
science is supposition. This syllogism differs from the preceding
because the relations between the terms are reversed: before,
the affirmative statement concerned B, now it concerns C.
Similarly if one premiss is not universal: for the middle term is
always that which is stated negatively of one extreme, and
affirmatively of the other. Consequently it is possible that
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contradictories may lead to a conclusion, though not always or
in every mood, but only if the terms subordinate to the middle
are such that they are either identical or related as whole to
part. Otherwise it is impossible: for the premisses cannot
anyhow be either contraries or contradictories.
In the third figure an affirmative syllogism can never be made
out of opposite premisses, for the reason given in reference to
the first figure; but a negative syllogism is possible whether the
terms are universal or not. Let B and C stand for science, A for
medicine. If then one should assume that all medicine is
science and that no medicine is science, he has assumed that B
belongs to all A and C to no A, so that a particular science will
not be a science. Similarly if the premiss BA is not assumed
universally. For if some medicine is science and again no
medicine is science, it results that some science is not science,
The premisses are contrary if the terms are taken universally; if
one is particular, they are contradictory.
We must recognize that it is possible to take opposites in the
way we said, viz. 'all science is good' and 'no science is good' or
'some science is not good'. This does not usually escape notice.
But it is possible to establish one part of a contradiction through
other premisses, or to assume it in the way suggested in the
Topics. Since there are three oppositions to affirmative
statements, it follows that opposite statements may be
assumed as premisses in six ways; we may have either
universal affirmative and negative, or universal affirmative and
particular negative, or particular affirmative and universal
negative, and the relations between the terms may be reversed;
e.g. A may belong to all B and to no C, or to all C and to no B, or
to all of the one, not to all of the other; here too the relation
between the terms may be reversed. Similarly in the third
figure. So it is clear in how many ways and in what figures a
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syllogism can be made by means of premisses which are
opposed.
It is clear too that from false premisses it is possible to draw a
true conclusion, as has been said before, but it is not possible if
the premisses are opposed. For the syllogism is always contrary
to the fact, e.g. if a thing is good, it is proved that it is not good,
if an animal, that it is not an animal because the syllogism
springs out of a contradiction and the terms presupposed are
either identical or related as whole and part. It is evident also
that in fallacious reasonings nothing prevents a contradiction to
the hypothesis from resulting, e.g. if something is odd, it is not
odd. For the syllogism owed its contrariety to its contradictory
premisses; if we assume such premisses we shall get a result
that contradicts our hypothesis. But we must recognize that
contraries cannot be inferred from a single syllogism in such a
way that we conclude that what is not good is good, or anything
of that sort unless a self-contradictory premiss is at once
assumed, e.g. 'every animal is white and not white', and we
proceed 'man is an animal'. Either we must introduce the
contradiction by an additional assumption, assuming, e.g., that
every science is supposition, and then assuming 'Medicine is a
science, but none of it is supposition' (which is the mode in
which refutations are made), or we must argue from two
syllogisms. In no other way than this, as was said before, is it
possible that the premisses should be really contrary.
16
To beg and assume the original question is a species of failure
to demonstrate the problem proposed; but this happens in
many ways. A man may not reason syllogistically at all, or he
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may argue from premisses which are less known or equally
unknown, or he may establish the antecedent by means of its
consequents; for demonstration proceeds from what is more
certain and is prior. Now begging the question is none of these:
but since we get to know some things naturally through
themselves, and other things by means of something else (the
first principles through themselves, what is subordinate to
them through something else), whenever a man tries to prove
what is not self-evident by means of itself, then he begs the
original question. This may be done by assuming what is in
question at once; it is also possible to make a transition to other
things which would naturally be proved through the thesis
proposed, and demonstrate it through them, e.g. if A should be
proved through B, and B through C, though it was natural that C
should be proved through A: for it turns out that those who
reason thus are proving A by means of itself. This is what those
persons do who suppose that they are constructing parallel
straight lines: for they fail to see that they are assuming facts
which it is impossible to demonstrate unless the parallels exist.
So it turns out that those who reason thus merely say a
particular thing is, if it is: in this way everything will be self-
evident. But that is impossible.
If then it is uncertain whether A belongs to C, and also whether
A belongs to B, and if one should assume that A does belong to
B, it is not yet clear whether he begs the original question, but it
is evident that he is not demonstrating: for what is as uncertain
as the question to be answered cannot be a principle of a
demonstration. If however B is so related to C that they are
identical, or if they are plainly convertible, or the one belongs to
the other, the original question is begged. For one might equally
well prove that A belongs to B through those terms if they are
convertible. But if they are not convertible, it is the fact that they
are not that prevents such a demonstration, not the method of
demonstrating. But if one were to make the conversion, then he
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would be doing what we have described and effecting a
reciprocal proof with three propositions.
Similarly if he should assume that B belongs to C, this being as
uncertain as the question whether A belongs to C, the question
is not yet begged, but no demonstration is made. If however A
and B are identical either because they are convertible or
because A follows B, then the question is begged for the same
reason as before. For we have explained the meaning of begging
the question, viz. proving that which is not self-evident by
means of itself.
If then begging the question is proving what is not self-evident
by means of itself, in other words failing to prove when the
failure is due to the thesis to be proved and the premiss through
which it is proved being equally uncertain, either because
predicates which are identical belong to the same subject, or
because the same predicate belongs to subjects which are
identical, the question may be begged in the middle and third
figures in both ways, though, if the syllogism is affirmative, only
in the third and first figures. If the syllogism is negative, the
question is begged when identical predicates are denied of the
same subject; and both premisses do not beg the question
indifferently (in a similar way the question may be begged in
the middle figure), because the terms in negative syllogisms are
not convertible. In scientific demonstrations the question is
begged when the terms are really related in the manner
described, in dialectical arguments when they are according to
common opinion so related.
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17
The objection that 'this is not the reason why the result is false',
which we frequently make in argument, is made primarily in
the case of a reductio ad impossibile, to rebut the proposition
which was being proved by the reduction. For unless a man has
contradicted this proposition he will not say, 'False cause', but
urge that something false has been assumed in the earlier parts
of the argument; nor will he use the formula in the case of an
ostensive proof; for here what one denies is not assumed as a
premiss. Further when anything is refuted ostensively by the
terms ABC, it cannot be objected that the syllogism does not
depend on the assumption laid down. For we use the expression
'false cause', when the syllogism is concluded in spite of the
refutation of this position; but that is not possible in ostensive
proofs: since if an assumption is refuted, a syllogism can no
longer be drawn in reference to it. It is clear then that the
expression 'false cause' can only be used in the case of a
reductio ad impossibile, and when the original hypothesis is so
related to the impossible conclusion, that the conclusion results
indifferently whether the hypothesis is made or not. The most
obvious case of the irrelevance of an assumption to a
conclusion which is false is when a syllogism drawn from
middle terms to an impossible conclusion is independent of the
hypothesis, as we have explained in the Topics. For to put that
which is not the cause as the cause, is just this: e.g. if a man,
wishing to prove that the diagonal of the square is
incommensurate with the side, should try to prove Zeno's
theorem that motion is impossible, and so establish a reductio
ad impossibile: for Zeno's false theorem has no connexion at all
with the original assumption. Another case is where the
impossible conclusion is connected with the hypothesis, but
does not result from it. This may happen whether one traces the
connexion upwards or downwards, e.g. if it is laid down that A
belongs to B, B to C, and C to D, and it should be false that B
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belongs to D: for if we eliminated A and assumed all the same
that B belongs to C and C to D, the false conclusion would not
depend on the original hypothesis. Or again trace the connexion
upwards; e.g. suppose that A belongs to B, E to A and F to E, it
being false that F belongs to A. In this way too the impossible
conclusion would result, though the original hypothesis were
eliminated. But the impossible conclusion ought to be
connected with the original terms: in this way it will depend on
the hypothesis, e.g. when one traces the connexion downwards,
the impossible conclusion must be connected with that term
which is predicate in the hypothesis: for if it is impossible that
A should belong to D, the false conclusion will no longer result
after A has been eliminated. If one traces the connexion
upwards, the impossible conclusion must be connected with
that term which is subject in the hypothesis: for if it is
impossible that F should belong to B, the impossible conclusion
will disappear if B is eliminated. Similarly when the syllogisms
are negative.
It is clear then that when the impossibility is not related to the
original terms, the false conclusion does not result on account
of the assumption. Or perhaps even so it may sometimes be
independent. For if it were laid down that A belongs not to B but
to K, and that K belongs to C and C to D, the impossible
conclusion would still stand. Similarly if one takes the terms in
an ascending series. Consequently since the impossibility
results whether the first assumption is suppressed or not, it
would appear to be independent of that assumption. Or perhaps
we ought not to understand the statement that the false
conclusion results independently of the assumption, in the
sense that if something else were supposed the impossibility
would result; but rather we mean that when the first
assumption is eliminated, the same impossibility results
through the remaining premisses; since it is not perhaps absurd
that the same false result should follow from several
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hypotheses, e.g. that parallels meet, both on the assumption
that the interior angle is greater than the exterior and on the
assumption that a triangle contains more than two right angles.
18
A false argument depends on the first false statement in it.
Every syllogism is made out of two or more premisses. If then
the false conclusion is drawn from two premisses, one or both
of them must be false: for (as we proved) a false syllogism
cannot be drawn from two premisses. But if the premisses are
more than two, e.g. if C is established through A and B, and
these through D, E, F, and G, one of these higher propositions
must be false, and on this the argument depends: for A and B
are inferred by means of D, E, F, and G. Therefore the conclusion
and the error results from one of them.
19
In order to avoid having a syllogism drawn against us we must
take care, whenever an opponent asks us to admit the reason
without the conclusions, not to grant him the same term twice
over in his premisses, since we know that a syllogism cannot be
drawn without a middle term, and that term which is stated
more than once is the middle. How we ought to watch the
middle in reference to each conclusion, is evident from our
knowing what kind of thesis is proved in each figure. This will
not escape us since we know how we are maintaining the
argument.
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That which we urge men to beware of in their admissions, they
ought in attack to try to conceal. This will be possible first, if,
instead of drawing the conclusions of preliminary syllogisms,
they take the necessary premisses and leave the conclusions in
the dark; secondly if instead of inviting assent to propositions
which are closely connected they take as far as possible those
that are not connected by middle terms. For example suppose
that A is to be inferred to be true of F, B, C, D, and E being middle
terms. One ought then to ask whether A belongs to B, and next
whether D belongs to E, instead of asking whether B belongs to
C; after that he may ask whether B belongs to C, and so on. If
the syllogism is drawn through one middle term, he ought to
begin with that: in this way he will most likely deceive his
opponent.
20
Since we know when a syllogism can be formed and how its
terms must be related, it is clear when refutation will be
possible and when impossible. A refutation is possible whether
everything is conceded, or the answers alternate (one, I mean,
being affirmative, the other negative). For as has been shown a
syllogism is possible whether the terms are related in
affirmative propositions or one proposition is affirmative, the
other negative: consequently, if what is laid down is contrary to
the conclusion, a refutation must take place: for a refutation is a
syllogism which establishes the contradictory. But if nothing is
conceded, a refutation is impossible: for no syllogism is possible
(as we saw) when all the terms are negative: therefore 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
206
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
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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
208
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.
209
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 G 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 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
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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
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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
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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.
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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.
214
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
taken a new term, being so far without knowledge that A
belongs to C. Or again suppose that the terms intermediate
between B and C are few: for thus too we are nearer knowledge.
For example let D stand for squaring, E for rectilinear figure, F
for circle. If there were only one term intermediate between E
and F (viz. that the circle is made equal to a rectilinear figure by
the help of lunules), we should be near to knowledge. But when
BC is not more probable than AC, and the intermediate terms
are not few, I do not call this reduction: nor again when the
statement BC is immediate: for such a statement is knowledge.
26
An objection is a premiss contrary to a premiss. It differs from a
premiss, because it may be particular, but a premiss either
cannot be particular at all or not in universal syllogisms. An
objection is brought in two ways and through two figures; in
two ways because every objection is either universal or
particular, by two figures because objections are brought in
215
opposition to the premiss, and opposites can be proved only in
the first and third figures. If a man maintains a universal
affirmative, we reply with a universal or a particular negative;
the former is proved from the first figure, the latter from the
third. For example let stand for there being a single science, B
for contraries. If a man premises that contraries are subjects of
a single science, the objection may be either that opposites are
never subjects of a single science, and contraries are opposites,
so that we get the first figure, or that the knowable and the
unknowable are not subjects of a single science: this proof is in
the third figure: for it is true of C (the knowable and the
unknowable) that they are contraries, and it is false that they
are the subjects of a single science.
Similarly if the premiss objected to is negative. For if a man
maintains that contraries are not subjects of a single science,
we reply either that all opposites or that certain contraries, e.g.
what is healthy and what is sickly, are subjects of the same
science: the former argument issues from the first, the latter
from the third figure.
In general if a man urges a universal objection he must frame
his contradiction with reference to the universal of the terms
taken by his opponent, e.g. if a man maintains that contraries
are not subjects of the same science, his opponent must reply
that there is a single science of all opposites. Thus we must
have the first figure: for the term which embraces the original
subject becomes the middle term.
If the objection is particular, the objector must frame his
contradiction with reference to a term relatively to which the
subject of his opponent's premiss is universal, e.g. he will point
out that the knowable and the unknowable are not subjects of
the same science: 'contraries' is universal relatively to these.
And we have the third figure: for the particular term assumed is
216
middle, e.g. the knowable and the unknowable. Premisses from
which it is possible to draw the contrary conclusion are what we
start from when we try to make objections. Consequently we
bring objections in these figures only: for in them only are
opposite syllogisms possible, since the second figure cannot
produce an affirmative conclusion.
Besides, an objection in the middle figure would require a fuller
argument, e.g. if it should not be granted that A belongs to B,
because C does not follow B. This can be made clear only by
other premisses. But an objection ought not to turn off into
other things, but have its new premiss quite clear immediately.
For this reason also this is the only figure from which proof by
signs cannot be obtained.
We must consider later the other kinds of objection, namely the
objection from contraries, from similars, and from common
opinion, and inquire whether a particular objection cannot be
elicited from the first figure or a negative objection from the
second.
27
A probability and a sign are not identical, but a probability is a
generally approved proposition: what men know to happen or
not to happen, to be or not to be, for the most part thus and
thus, is a probability, e.g. 'the envious hate', 'the beloved show
affection'. A sign means a demonstrative proposition necessary
or generally approved: for anything such that when it is another
thing is, or when it has come into being the other has come into
being before or after, is a sign of the other's being or having
come into being. Now an enthymeme is a syllogism starting
from probabilities or signs, and a sign may be taken in three
217
ways, corresponding to the position of the middle term in the
figures. For it may be taken as in the first figure or the second or
the third. For example the proof that a woman is with child
because she has milk is in the first figure: for to have milk is the
middle term. Let A represent to be with child, B to have milk, C
woman. The proof that wise men are good, since Pittacus is
good, comes through the last figure. Let A stand for good, B for
wise men, C for Pittacus. It is true then to affirm both A and B of
C: only men do not say the latter, because they know it, though
they state the former. The proof that a woman is with child
because she is pale is meant to come through the middle figure:
for since paleness follows women with child and is a
concomitant of this woman, people suppose it has been proved
that she is with child. Let A stand for paleness, B for being with
child, C for woman. Now if the one proposition is stated, we
have only a sign, but if the other is stated as well, a syllogism,
e.g. 'Pittacus is generous, since ambitious men are generous and
Pittacus is ambitious.' Or again 'Wise men are good, since
Pittacus is not only good but wise.' In this way then syllogisms
are formed, only that which proceeds through the first figure is
irrefutable if it is true (for it is universal), that which proceeds
through the last figure is refutable even if the conclusion is true,
since the syllogism is not universal nor correlative to the matter
in question: for though Pittacus is good, it is not therefore
necessary that all other wise men should be good. But the
syllogism which proceeds through the middle figure is always
refutable in any case: for a syllogism can never be formed when
the terms are related in this way: for though a woman with
child is pale, and this woman also is pale, it is not necessary
that she should be with child. Truth then may be found in signs
whatever their kind, but they have the differences we have
stated.
We must either divide signs in the way stated, and among them
designate the middle term as the index (for people call that the
218
index which makes us know, and the middle term above all has
this character), or else we must call the arguments derived from
the extremes signs, that derived from the middle term the
index: for that which is proved through the first figure is most
generally accepted and most true.
It is possible to infer character from features, if it is granted that
the body and the soul are changed together by the natural
affections: I say 'natural', for though perhaps by learning music
a man has made some change in his soul, this is not one of
those affections which are natural to us; rather I refer to
passions and desires when I speak of natural emotions. If then
this were granted and also that for each change there is a
corresponding sign, and we could state the affection and sign
proper to each kind of animal, we shall be able to infer
character from features. For if there is an affection which
belongs properly to an individual kind, e.g. courage to lions, it is
necessary that there should be a sign of it: for ex hypothesi
body and soul are affected together. Suppose this sign is the
possession of large extremities: this may belong to other kinds
also though not universally. For the sign is proper in the sense
stated, because the affection is proper to the whole kind,
though not proper to it alone, according to our usual manner of
speaking. The same thing then will be found in another kind,
and man may be brave, and some other kinds of animal as well.
They will then have the sign: for ex hypothesi there is one sign
corresponding to each affection. If then this is so, and we can
collect signs of this sort in these animals which have only one
affection proper to them - but each affection has its sign, since
it is necessary that it should have a single sign - we shall then
be able to infer character from features. But if the kind as a
whole has two properties, e.g. if the lion is both brave and
generous, how shall we know which of the signs which are its
proper concomitants is the sign of a particular affection?
Perhaps if both belong to some other kind though not to the
219
whole of it, and if, in those kinds in which each is found though
not in the whole of their members, some members possess one
of the affections and not the other: e.g. if a man is brave but not
generous, but possesses, of the two signs, large extremities, it is
clear that this is the sign of courage in the lion also. To judge
character from features, then, is possible in the first figure if the
middle term is convertible with the first extreme, but is wider
than the third term and not convertible with it: e.g. let A stand
for courage, B for large extremities, and C for lion. B then
belongs to everything to which C belongs, but also to others. But
A belongs to everything to which B belongs, and to nothing
besides, but is convertible with B: otherwise, there would not be
a single sign correlative with each affection.
220
Aristotle - Posterior Analytics
[Translated by G. R. G. Mure]
Book I
All instruction given or received by way of argument proceeds
from pre-existent knowledge. This becomes evident upon a
survey of all the species of such instruction. The mathematical
sciences and all other speculative disciplines are acquired in
this way, and so are the two forms of dialectical reasoning,
syllogistic and inductive; for each of these latter make use of
old knowledge to impart new, the syllogism assuming an
audience that accepts its premisses, induction exhibiting the
universal as implicit in the clearly known particular. Again, the
persuasion exerted by rhetorical arguments is in principle the
same, since they use either example, a kind of induction, or
enthymeme, a form of syllogism.
The pre-existent knowledge required is of two kinds. In some
cases admission of the fact must be assumed, in others
comprehension of the meaning of the term used, and
sometimes both assumptions are essential. Thus, we assume
that every predicate can be either truly affirmed or truly denied
of any subject, and that 'triangle' means so and so; as regards
'unit' we have to make the double assumption of the meaning
of the word and the existence of the thing. The reason is that
these several objects are not equally obvious to us. Recognition
of a truth may in some cases contain as factors both previous
knowledge and also knowledge acquired simultaneously with
221
that recognition - knowledge, this latter, of the particulars
actually falling under the universal and therein already virtually
known. For example, the student knew beforehand that the
angles of every triangle are equal to two right angles; but it was
only at the actual moment at which he was being led on to
recognize this as true in the instance before him that he came
to know 'this figure inscribed in the semicircle' to be a triangle.
For some things (viz. the singulars finally reached which are not
predicable of anything else as subject) are only learnt in this
way, i.e. there is here no recognition through a middle of a
minor term as subject to a major. Before he was led on to
recognition or before he actually drew a conclusion, we should
perhaps say that in a manner he knew, in a manner not.
If he did not in an unqualified sense of the term know the
existence of this triangle, how could he know without
qualification that its angles were equal to two right angles? No:
clearly he knows not without qualification but only in the sense
that he knows universally. If this distinction is not drawn, we
are faced with the dilemma in the Meno: either a man will learn
nothing or what he already knows; for we cannot accept the
solution which some people offer. A man is asked, 'Do you, or do
you not, know that every pair is even?' He says he does know it.
The questioner then produces a particular pair, of the existence,
and so a fortiori of the evenness, of which he was unaware. The
solution which some people offer is to assert that they do not
know that every pair is even, but only that everything which
they know to be a pair is even: yet what they know to be even is
that of which they have demonstrated evenness, i.e. what they
made the subject of their premiss, viz. not merely every triangle
or number which they know to be such, but any and every
number or triangle without reservation. For no premiss is ever
couched in the form 'every number which you know to be such',
or 'every rectilinear figure which you know to be such': the
predicate is always construed as applicable to any and every
222
instance of the thing. On the other hand, I imagine there is
nothing to prevent a man in one sense knowing what he is
learning, in another not knowing it. The strange thing would be,
not if in some sense he knew what he was learning, but if he
were to know it in that precise sense and manner in which he
was learning it.
We suppose ourselves to possess unqualified scientific
knowledge of a thing, as opposed to knowing it in the accidental
way in which the sophist knows, when we think that we know
the cause on which the fact depends, as the cause of that fact
and of no other, and, further, that the fact could not be other
than it is. Now that scientific knowing is something of this sort
is evident - witness both those who falsely claim it and those
who actually possess it, since the former merely imagine
themselves to be, while the latter are also actually, in the
condition described. Consequently the proper object of
unqualified scientific knowledge is something which cannot be
other than it is.
There may be another manner of knowing as well - that will be
discussed later. What I now assert is that at all events we do
know by demonstration. By demonstration I mean a syllogism
productive of scientific knowledge, a syllogism, that is, the grasp
of which is eo ipso such knowledge. Assuming then that my
thesis as to the nature of scientific knowing is correct, the
premisses of demonstrated knowledge must be true, primary,
immediate, better known than and prior to the conclusion,
which is further related to them as effect to cause. Unless these
conditions are satisfied, the basic truths will not be
223
'appropriate' to the conclusion. Syllogism there may indeed be
without these conditions, but such syllogism, not being
productive of scientific knowledge, will not be demonstration.
The premisses must be true: for that which is non-existent
cannot be known - we cannot know, e.g. that the diagonal of a
square is commensurate with its side. The premisses must be
primary and indemonstrable; otherwise they will require
demonstration in order to be known, since to have knowledge, if
it be not accidental knowledge, of things which are
demonstrable, means precisely to have a demonstration of
them. The premisses must be the causes of the conclusion,
better known than it, and prior to it; its causes, since we possess
scientific knowledge of a thing only when we know its cause;
prior, in order to be causes; antecedently known, this
antecedent knowledge being not our mere understanding of the
meaning, but knowledge of the fact as well. Now 'prior' and
'better known' are ambiguous terms, for there is a difference
between what is prior and better known in the order of being
and what is prior and better known to man. I mean that objects
nearer to sense are prior and better known to man; objects
without qualification prior and better known are those further
from sense. Now the most universal causes are furthest from
sense and particular causes are nearest to sense, and they are
thus exactly opposed to one another. In saying that the
premisses of demonstrated knowledge must be primary, I mean
that they must be the 'appropriate' basic truths, for I identify
primary premiss and basic truth. A 'basic truth' in a
demonstration is an immediate proposition. An immediate
proposition is one which has no other proposition prior to it. A
proposition is either part of an enunciation, i.e. it predicates a
single attribute of a single subject. If a proposition is dialectical,
it assumes either part indifferently; if it is demonstrative, it lays
down one part to the definite exclusion of the other because
that part is true. The term 'enunciation' denotes either part of a
224
contradiction indifferently. A contradiction is an opposition
which of its own nature excludes a middle. The part of a
contradiction which conjoins a predicate with a subject is an
affirmation; the part disjoining them is a negation. I call an
immediate basic truth of syllogism a 'thesis' when, though it is
not susceptible of proof by the teacher, yet ignorance of it does
not constitute a total bar to progress on the part of the pupil:
one which the pupil must know if he is to learn anything
whatever is an axiom. I call it an axiom because there are such
truths and we give them the name of axioms par excellence. If a
thesis assumes one part or the other of an enunciation, i.e.
asserts either the existence or the non-existence of a subject, it
is a hypothesis; if it does not so assert, it is a definition.
Definition is a 'thesis' or a 'laying something down', since the
arithmetician lays it down that to be a unit is to be
quantitatively indivisible; but it is not a hypothesis, for to define
what a unit is is not the same as to affirm its existence.
Now since the required ground of our knowledge - i.e. of our
conviction - of a fact is the possession of such a syllogism as we
call demonstration, and the ground of the syllogism is the facts
constituting its premisses, we must not only know the primary
premisses - some if not all of them - beforehand, but know
them better than the conclusion: for the cause of an attribute's
inherence in a subject always itself inheres in the subject more
firmly than that attribute; e.g. the cause of our loving anything
is dearer to us than the object of our love. So since the primary
premisses are the cause of our knowledge - i.e. of our conviction
- it follows that we know them better - that is, are more
convinced of them - than their consequences, precisely because
of our knowledge of the latter is the effect of our knowledge of
the premisses. Now a man cannot believe in anything more
than in the things he knows, unless he has either actual
knowledge of it or something better than actual knowledge. But
we are faced with this paradox if a student whose belief rests
225
on demonstration has not prior knowledge; a man must believe
in some, if not in all, of the basic truths more than in the
conclusion. Moreover, if a man sets out to acquire the scientific
knowledge that comes through demonstration, he must not
only have a better knowledge of the basic truths and a firmer
conviction of them than of the connexion which is being
demonstrated: more than this, nothing must be more certain or
better known to him than these basic truths in their character
as contradicting the fundamental premisses which lead to the
opposed and erroneous conclusion. For indeed the conviction of
pure science must be unshakable.
Some hold that, owing to the necessity of knowing the primary
premisses, there is no scientific knowledge. Others think there
is, but that all truths are demonstrable. Neither doctrine is
either true or a necessary deduction from the premisses. The
first school, assuming that there is no way of knowing other
than by demonstration, maintain that an infinite regress is
involved, on the ground that if behind the prior stands no
primary, we could not know the posterior through the prior
(wherein they are right, for one cannot traverse an infinite
series): if on the other hand - they say - the series terminates
and there are primary premisses, yet these are unknowable
because incapable of demonstration, which according to them
is the only form of knowledge. And since thus one cannot know
the primary premisses, knowledge of the conclusions which
follow from them is not pure scientific knowledge nor properly
knowing at all, but rests on the mere supposition that the
premisses are true. The other party agree with them as regards
knowing, holding that it is only possible by demonstration, but
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they see no difficulty in holding that all truths are
demonstrated, on the ground that demonstration may be
circular and reciprocal.
Our own doctrine is that not all knowledge is demonstrative: on
the contrary, knowledge of the immediate premisses is
independent of demonstration. (The necessity of this is obvious;
for since we must know the prior premisses from which the
demonstration is drawn, and since the regress must end in
immediate truths, those truths must be indemonstrable.) Such,
then, is our doctrine, and in addition we maintain that besides
scientific knowledge there is its originative source which
enables us to recognize the definitions.
Now demonstration must be based on premisses prior to and
better known than the conclusion; and the same things cannot
simultaneously be both prior and posterior to one another: so
circular demonstration is clearly not possible in the unqualified
sense of 'demonstration', but only possible if 'demonstration' be
extended to include that other method of argument which rests
on a distinction between truths prior to us and truths without
qualification prior, i.e. the method by which induction produces
knowledge. But if we accept this extension of its meaning, our
definition of unqualified knowledge will prove faulty; for there
seem to be two kinds of it. Perhaps, however, the second form of
demonstration, that which proceeds from truths better known
to us, is not demonstration in the unqualified sense of the term.
The advocates of circular demonstration are not only faced with
the difficulty we have just stated: in addition their theory
reduces to the mere statement that if a thing exists, then it does
exist - an easy way of proving anything. That this is so can be
clearly shown by taking three terms, for to constitute the circle
it makes no difference whether many terms or few or even only
two are taken. Thus by direct proof, if A is, B must be; if B is, C
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must be; therefore if A is, C must be. Since then - by the circular
proof - if A is, B must be, and if B is, A must be, A may be
substituted for C above. Then 'if B is, A must be'='if B is, C must
be', which above gave the conclusion 'if A is, C must be': but C
and A have been identified. Consequently the upholders of
circular demonstration are in the position of saying that if A is,
A must be - a simple way of proving anything. Moreover, even
such circular demonstration is impossible except in the case of
attributes that imply one another, viz. 'peculiar' properties.
Now, it has been shown that the positing of one thing - be it one
term or one premiss - never involves a necessary consequent:
two premisses constitute the first and smallest foundation for
drawing a conclusion at all and therefore a fortiori for the
demonstrative syllogism of science. If, then, A is implied in B
and C, and B and C are reciprocally implied in one another and
in A, it is possible, as has been shown in my writings on the
syllogism, to prove all the assumptions on which the original
conclusion rested, by circular demonstration in the first figure.
But it has also been shown that in the other figures either no
conclusion is possible, or at least none which proves both the
original premisses. Propositions the terms of which are not
convertible cannot be circularly demonstrated at all, and since
convertible terms occur rarely in actual demonstrations, it is
clearly frivolous and impossible to say that demonstration is
reciprocal and that therefore everything can be demonstrated.
Since the object of pure scientific knowledge cannot be other
than it is, the truth obtained by demonstrative knowledge will
be necessary. And since demonstrative knowledge is only
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present when we have a demonstration, it follows that
demonstration is an inference from necessary premisses. So we
must consider what are the premisses of demonstration - i.e.
what is their character: and as a preliminary, let us define what
we mean by an attribute 'true in every instance of its subject',
an 'essential' attribute, and a 'commensurate and universal'
attribute. I call 'true in every instance' what is truly predicable
of all instances - not of one to the exclusion of others - and at
all times, not at this or that time only; e.g. if animal is truly
predicable of every instance of man, then if it be true to say 'this
is a man', 'this is an animal' is also true, and if the one be true
now the other is true now. A corresponding account holds if
point is in every instance predicable as contained in line. There
is evidence for this in the fact that the objection we raise
against a proposition put to us as true in every instance is either
an instance in which, or an occasion on which, it is not true.
Essential attributes are (1) such as belong to their subject as
elements in its essential nature (e.g. line thus belongs to
triangle, point to line; for the very being or 'substance' of
triangle and line is composed of these elements, which are
contained in the formulae defining triangle and line): (2) such
that, while they belong to certain subjects, the subjects to which
they belong are contained in the attribute's own defining
formula. Thus straight and curved belong to line, odd and even,
prime and compound, square and oblong, to number; and also
the formula defining any one of these attributes contains its
subject - e.g. line or number as the case may be.
Extending this classification to all other attributes, I distinguish
those that answer the above description as belonging
essentially to their respective subjects; whereas attributes
related in neither of these two ways to their subjects I call
accidents or 'coincidents'; e.g. musical or white is a 'coincident'
of animal.
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Further (a) that is essential which is not predicated of a subject
other than itself: e.g. 'the walking [thing]' walks and is white in
virtue of being something else besides; whereas substance, in
the sense of whatever signifies a 'this somewhat', is not what it
is in virtue of being something else besides. Things, then, not
predicated of a subject I call essential; things predicated of a
subject I call accidental or 'coincidental'.
In another sense again (b) a thing consequentially connected
with anything is essential; one not so connected is
'coincidental'. An example of the latter is 'While he was walking
it lightened': the lightning was not due to his walking; it was,
we should say, a coincidence. If, on the other hand, there is a
consequential connexion, the predication is essential; e.g. if a
beast dies when its throat is being cut, then its death is also
essentially connected with the cutting, because the cutting was
the cause of death, not death a 'coincident' of the cutting.
So far then as concerns the sphere of connexions scientifically
known in the unqualified sense of that term, all attributes
which (within that sphere) are essential either in the sense that
their subjects are contained in them, or in the sense that they
are contained in their subjects, are necessary as well as
consequentially connected with their subjects. For it is
impossible for them not to inhere in their subjects either simply
or in the qualified sense that one or other of a pair of opposites
must inhere in the subject; e.g. in line must be either
straightness or curvature, in number either oddness or
evenness. For within a single identical genus the contrary of a
given attribute is either its privative or its contradictory; e.g.
within number what is not odd is even, inasmuch as within this
sphere even is a necessary consequent of not-odd. So, since any
given predicate must be either affirmed or denied of any
subject, essential attributes must inhere in their subjects of
necessity.
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Thus, then, we have established the distinction between the
attribute which is 'true in every instance' and the 'essential'
attribute.
I term 'commensurately universal' an attribute which belongs to
every instance of its subject, and to every instance essentially
and as such; from which it clearly follows that all
commensurate universals inhere necessarily in their subjects.
The essential attribute, and the attribute that belongs to its
subject as such, are identical. E.g. point and straight belong to
line essentially, for they belong to line as such; and triangle as
such has two right angles, for it is essentially equal to two right
angles.
An attribute belongs commensurately and universally to a
subject when it can be shown to belong to any random instance
of that subject and when the subject is the first thing to which
it can be shown to belong. Thus, e.g. (1) the equality of its angles
to two right angles is not a commensurately universal attribute
of figure. For though it is possible to show that a figure has its
angles equal to two right angles, this attribute cannot be
demonstrated of any figure selected at haphazard, nor in
demonstrating does one take a figure at random - a square is a
figure but its angles are not equal to two right angles. On the
other hand, any isosceles triangle has its angles equal to two
right angles, yet isosceles triangle is not the primary subject of
this attribute but triangle is prior. So whatever can be shown to
have its angles equal to two right angles, or to possess any other
attribute, in any random instance of itself and primarily - that is
the first subject to which the predicate in question belongs
commensurately and universally, and the demonstration, in the
essential sense, of any predicate is the proof of it as belonging
to this first subject commensurately and universally: while the
proof of it as belonging to the other subjects to which it
attaches is demonstration only in a secondary and unessential
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sense. Nor again (2) is equality to two right angles a
commensurately universal attribute of isosceles; it is of wider
application.
We must not fail to observe that we often fall into error because
our conclusion is not in fact primary and commensurately
universal in the sense in which we think we prove it so. We
make this mistake (1) when the subject is an individual or
individuals above which there is no universal to be found: (2)
when the subjects belong to different species and there is a
higher universal, but it has no name: (3) when the subject which
the demonstrator takes as a whole is really only a part of a
larger whole; for then the demonstration will be true of the
individual instances within the part and will hold in every
instance of it, yet the demonstration will not be true of this
subject primarily and commensurately and universally. When a
demonstration is true of a subject primarily and
commensurately and universally, that is to be taken to mean
that it is true of a given subject primarily and as such. Case (3)
may be thus exemplified. If a proof were given that
perpendiculars to the same line are parallel, it might be
supposed that lines thus perpendicular were the proper subject
of the demonstration because being parallel is true of every
instance of them. But it is not so, for the parallelism depends
not on these angles being equal to one another because each is
a right angle, but simply on their being equal to one another. An
example of (1) would be as follows: if isosceles were the only
triangle, it would be thought to have its angles equal to two
right angles qua isosceles. An instance of (2) would be the law
that proportionals alternate. Alternation used to be
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demonstrated separately of numbers, lines, solids, and
durations, though it could have been proved of them all by a
single demonstration. Because there was no single name to
denote that in which numbers, lengths, durations, and solids
are identical, and because they differed specifically from one
another, this property was proved of each of them separately.
To-day, however, the proof is commensurately universal, for
they do not possess this attribute qua lines or qua numbers, but
qua manifesting this generic character which they are
postulated as possessing universally. Hence, even if one prove of
each kind of triangle that its angles are equal to two right
angles, whether by means of the same or different proofs; still,
as long as one treats separately equilateral, scalene, and
isosceles, one does not yet know, except sophistically, that
triangle has its angles equal to two right angles, nor does one
yet know that triangle has this property commensurately and
universally, even if there is no other species of triangle but
these. For one does not know that triangle as such has this
property, nor even that 'all' triangles have it - unless 'all' means
'each taken singly': if 'all' means 'as a whole class', then, though
there be none in which one does not recognize this property,
one does not know it of 'all triangles'.
When, then, does our knowledge fail of commensurate
universality, and when it is unqualified knowledge? If triangle
be identical in essence with equilateral, i.e. with each or all
equilaterals, then clearly we have unqualified knowledge: if on
the other hand it be not, and the attribute belongs to equilateral
qua triangle; then our knowledge fails of commensurate
universality. 'But', it will be asked, 'does this attribute belong to
the subject of which it has been demonstrated qua triangle or
qua isosceles? What is the point at which the subject, to which
it belongs is primary? (i.e. to what subject can it be
demonstrated as belonging commensurately and universally?)'
Clearly this point is the first term in which it is found to inhere
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as the elimination of inferior differentiae proceeds. Thus the
angles of a brazen isosceles triangle are equal to two right
angles: but eliminate brazen and isosceles and the attribute
remains. 'But' - you may say - 'eliminate figure or limit, and the
attribute vanishes.' True, but figure and limit are not the first
differentiae whose elimination destroys the attribute. 'Then
what is the first?' If it is triangle, it will be in virtue of triangle
that the attribute belongs to all the other subjects of which it is
predicable, and triangle is the subject to which it can be
demonstrated as belonging commensurately and universally.
Demonstrative knowledge must rest on necessary basic truths;
for the object of scientific knowledge cannot be other than it is.
Now attributes attaching essentially to their subjects attach
necessarily to them: for essential attributes are either elements
in the essential nature of their subjects, or contain their
subjects as elements in their own essential nature. (The pairs of
opposites which the latter class includes are necessary because
one member or the other necessarily inheres.) It follows from
this that premisses of the demonstrative syllogism must be
connexions essential in the sense explained: for all attributes
must inhere essentially or else be accidental, and accidental
attributes are not necessary to their subjects.
We must either state the case thus, or else premise that the
conclusion of demonstration is necessary and that a
demonstrated conclusion cannot be other than it is, and then
infer that the conclusion must be developed from necessary
premisses. For though you may reason from true premisses
without demonstrating, yet if your premisses are necessary you
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will assuredly demonstrate - in such necessity you have at once
a distinctive character of demonstration. That demonstration
proceeds from necessary premisses is also indicated by the fact
that the objection we raise against a professed demonstration is
that a premiss of it is not a necessary truth - whether we think
it altogether devoid of necessity, or at any rate so far as our
opponent's previous argument goes. This shows how naive it is
to suppose one's basic truths rightly chosen if one starts with a
proposition which is (1) popularly accepted and (2) true, such as
the sophists' assumption that to know is the same as to possess
knowledge. For (1) popular acceptance or rejection is no
criterion of a basic truth, which can only be the primary law of
the genus constituting the subject matter of the demonstration;
and (2) not all truth is 'appropriate'.
A further proof that the conclusion must be the development of
necessary premisses is as follows. Where demonstration is
possible, one who can give no account which includes the cause
has no scientific knowledge. If, then, we suppose a syllogism in
which, though A necessarily inheres in G, yet B, the middle term
of the demonstration, is not necessarily connected with A and
C, then the man who argues thus has no reasoned knowledge of
the conclusion, since this conclusion does not owe its necessity
to the middle term; for though the conclusion is necessary, the
mediating link is a contingent fact. Or again, if a man is without
knowledge now, though he still retains the steps of the
argument, though there is no change in himself or in the fact
and no lapse of memory on his part; then neither had he
knowledge previously. But the mediating link, not being
necessary, may have perished in the interval; and if so, though
there be no change in him nor in the fact, and though he will
still retain the steps of the argument, yet he has not knowledge,
and therefore had not knowledge before. Even if the link has not
actually perished but is liable to perish, this situation is possible
and might occur. But such a condition cannot be knowledge.
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When the conclusion is necessary, the middle through which it
was proved may yet quite easily be non-necessary. You can in
fact infer the necessary even from a non-necessary premiss,
just as you can infer the true from the not true. On the other
hand, when the middle is necessary the conclusion must be
necessary; just as true premisses always give a true conclusion.
Thus, if A is necessarily predicated of B and B of C, then A is
necessarily predicated of C. But when the conclusion is
nonnecessary the middle cannot be necessary either. Thus: let A
be predicated non-necessarily of G but necessarily of B, and let B
be a necessary predicate of C; then A too will be a necessary
predicate of C, which by hypothesis it is not.
To sum up, then: demonstrative knowledge must be knowledge
of a necessary nexus, and therefore must clearly be obtained
through a necessary middle term; otherwise its possessor will
know neither the cause nor the fact that his conclusion is a
necessary connexion. Either he will mistake the non-necessary
for the necessary and believe the necessity of the conclusion
without knowing it, or else he will not even believe it - in which
case he will be equally ignorant, whether he actually infers the
mere fact through middle terms or the reasoned fact and from
immediate premisses.
Of accidents that are not essential according to our definition of
essential there is no demonstrative knowledge; for since an
accident, in the sense in which I here speak of it, may also not
inhere, it is impossible to prove its inherence as a necessary
conclusion. A difficulty, however, might be raised as to why in
dialectic, if the conclusion is not a necessary connexion, such
and such determinate premisses should be proposed in order to
deal with such and such determinate problems. Would not the
result be the same if one asked any questions whatever and
then merely stated one's conclusion? The solution is that
determinate questions have to be put, not because the replies to
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them affirm facts which necessitate facts affirmed by the
conclusion, but because these answers are propositions which if
the answerer affirm, he must affirm the conclusion and affirm
it with truth if they are true.
Since it is just those attributes within every genus which are
essential and possessed by their respective subjects as such
that are necessary it is clear that both the conclusions and the
premisses of demonstrations which produce scientific
knowledge are essential. For accidents are not necessary: and,
further, since accidents are not necessary one does not
necessarily have reasoned knowledge of a conclusion drawn
from them (this is so even if the accidental premisses are
invariable but not essential, as in proofs through signs; for
though the conclusion be actually essential, one will not know
it as essential nor know its reason); but to have reasoned
knowledge of a conclusion is to know it through its cause. We
may conclude that the middle must be consequentially
connected with the minor, and the major with the middle.
It follows that we cannot in demonstrating pass from one genus
to another. We cannot, for instance, prove geometrical truths by
arithmetic. For there are three elements in demonstration: (1)
what is proved, the conclusion - an attribute inhering
essentially in a genus; (2) the axioms, i.e. axioms which are
premisses of demonstration; (3) the subject - genus whose
attributes, i.e. essential properties, are revealed by the
demonstration. The axioms which are premisses of
demonstration may be identical in two or more sciences: but in
the case of two different genera such as arithmetic and
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geometry you cannot apply arithmetical demonstration to the
properties of magnitudes unless the magnitudes in question are
numbers. How in certain cases transference is possible I will
explain later.
Arithmetical demonstration and the other sciences likewise
possess, each of them, their own genera; so that if the
demonstration is to pass from one sphere to another, the genus
must be either absolutely or to some extent the same. If this is
not so, transference is clearly impossible, because the extreme
and the middle terms must be drawn from the same genus:
otherwise, as predicated, they will not be essential and will thus
be accidents. That is why it cannot be proved by geometry that
opposites fall under one science, nor even that the product of
two cubes is a cube. Nor can the theorem of any one science be
demonstrated by means of another science, unless these
theorems are related as subordinate to superior (e.g. as optical
theorems to geometry or harmonic theorems to arithmetic).
Geometry again cannot prove of lines any property which they
do not possess qua lines, i.e. in virtue of the fundamental truths
of their peculiar genus: it cannot show, for example, that the
straight line is the most beautiful of lines or the contrary of the
circle; for these qualities do not belong to lines in virtue of their
peculiar genus, but through some property which it shares with
other genera.
8
It is also clear that if the premisses from which the syllogism
proceeds are commensurately universal, the conclusion of such
i.e. in the unqualified sense - must also be eternal. Therefore no
attribute can be demonstrated nor known by strictly scientific
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knowledge to inhere in perishable things. The proof can only be
accidental, because the attribute's connexion with its perishable
subject is not commensurately universal but temporary and
special. If such a demonstration is made, one premiss must be
perishable and not commensurately universal (perishable
because only if it is perishable will the conclusion be perishable;
not commensurately universal, because the predicate will be
predicable of some instances of the subject and not of others);
so that the conclusion can only be that a fact is true at the
moment - not commensurately and universally. The same is
true of definitions, since a definition is either a primary premiss
or a conclusion of a demonstration, or else only differs from a
demonstration in the order of its terms. Demonstration and
science of merely frequent occurrences - e.g. of eclipse as
happening to the moon - are, as such, clearly eternal: whereas
so far as they are not eternal they are not fully commensurate.
Other subjects too have properties attaching to them in the
same way as eclipse attaches to the moon.
It is clear that if the conclusion is to show an attribute inhering
as such, nothing can be demonstrated except from its
'appropriate' basic truths. Consequently a proof even from true,
indemonstrable, and immediate premisses does not constitute
knowledge. Such proofs are like Bryson's method of squaring
the circle; for they operate by taking as their middle a common
character - a character, therefore, which the subject may share
with another - and consequently they apply equally to subjects
different in kind. They therefore afford knowledge of an
attribute only as inhering accidentally, not as belonging to its
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subject as such: otherwise they would not have been applicable
to another genus.
Our knowledge of any attribute's connexion with a subject is
accidental unless we know that connexion through the middle
term in virtue of which it inheres, and as an inference from
basic premisses essential and 'appropriate' to the subject -
unless we know, e.g. the property of possessing angles equal to
two right angles as belonging to that subject in which it inheres
essentially, and as inferred from basic premisses essential and
'appropriate' to that subject: so that if that middle term also
belongs essentially to the minor, the middle must belong to the
same kind as the major and minor terms. The only exceptions
to this rule are such cases as theorems in harmonics which are
demonstrable by arithmetic. Such theorems are proved by the
same middle terms as arithmetical properties, but with a
qualification - the fact falls under a separate science (for the
subject genus is separate), but the reasoned fact concerns the
superior science, to which the attributes essentially belong.
Thus, even these apparent exceptions show that no attribute is
strictly demonstrable except from its 'appropriate' basic truths,
which, however, in the case of these sciences have the requisite
identity of character.
It is no less evident that the peculiar basic truths of each
inhering attribute are indemonstrable; for basic truths from
which they might be deduced would be basic truths of all that
is, and the science to which they belonged would possess
universal sovereignty. This is so because he knows better whose
knowledge is deduced from higher causes, for his knowledge is
from prior premisses when it derives from causes themselves
uncaused: hence, if he knows better than others or best of all,
his knowledge would be science in a higher or the highest
degree. But, as things are, demonstration is not transferable to
another genus, with such exceptions as we have mentioned of
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the application of geometrical demonstrations to theorems in
mechanics or optics, or of arithmetical demonstrations to those
of harmonics.
It is hard to be sure whether one knows or not; for it is hard to
be sure whether one's knowledge is based on the basic truths
appropriate to each attribute - the differentia of true knowledge.
We think we have scientific knowledge if we have reasoned
from true and primary premisses. But that is not so: the
conclusion must be homogeneous with the basic facts of the
science.
10
I call the basic truths of every genus those elements in it the
existence of which cannot be proved. As regards both these
primary truths and the attributes dependent on them the
meaning of the name is assumed. The fact of their existence as
regards the primary truths must be assumed; but it has to be
proved of the remainder, the attributes. Thus we assume the
meaning alike of unity, straight, and triangular; but while as
regards unity and magnitude we assume also the fact of their
existence, in the case of the remainder proof is required.
Of the basic truths used in the demonstrative sciences some are
peculiar to each science, and some are common, but common
only in the sense of analogous, being of use only in so far as
they fall within the genus constituting the province of the
science in question.
Peculiar truths are, e.g. the definitions of line and straight;
common truths are such as 'take equals from equals and equals
remain'. Only so much of these common truths is required as
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falls within the genus in question: for a truth of this kind will
have the same force even if not used generally but applied by
the geometer only to magnitudes, or by the arithmetician only
to numbers. Also peculiar to a science are the subjects the
existence as well as the meaning of which it assumes, and the
essential attributes of which it investigates, e.g. in arithmetic
units, in geometry points and lines. Both the existence and the
meaning of the subjects are assumed by these sciences; but of
their essential attributes only the meaning is assumed. For
example arithmetic assumes the meaning of odd and even,
square and cube, geometry that of incommensurable, or of
deflection or verging of lines, whereas the existence of these
attributes is demonstrated by means of the axioms and from
previous conclusions as premisses. Astronomy too proceeds in
the same way. For indeed every demonstrative science has three
elements: (1) that which it posits, the subject genus whose
essential attributes it examines; (2) the so-called axioms, which
are primary premisses of its demonstration; (3) the attributes,
the meaning of which it assumes. Yet some sciences may very
well pass over some of these elements; e.g. we might not
expressly posit the existence of the genus if its existence were
obvious (for instance, the existence of hot and cold is more
evident than that of number); or we might omit to assume
expressly the meaning of the attributes if it were well
understood. In the way the meaning of axioms, such as 'Take
equals from equals and equals remain', is well known and so
not expressly assumed. Nevertheless in the nature of the case
the essential elements of demonstration are three: the subject,
the attributes, and the basic premisses.
That which expresses necessary self-grounded fact, and which
we must necessarily believe, is distinct both from the
hypotheses of a science and from illegitimate postulate - I say
'must believe', because all syllogism, and therefore a fortiori
demonstration, is addressed not to the spoken word, but to the
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discourse within the soul, and though we can always raise
objections to the spoken word, to the inward discourse we
cannot always object. That which is capable of proof but
assumed by the teacher without proof is, if the pupil believes
and accepts it, hypothesis, though only in a limited sense
hypothesis - that is, relatively to the pupil; if the pupil has no
opinion or a contrary opinion on the matter, the same
assumption is an illegitimate postulate. Therein lies the
distinction between hypothesis and illegitimate postulate: the
latter is the contrary of the pupil's opinion, demonstrable, but
assumed and used without demonstration.
The definition - viz. those which are not expressed as
statements that anything is or is not - are not hypotheses: but it
is in the premisses of a science that its hypotheses are
contained. Definitions require only to be understood, and this is
not hypothesis - unless it be contended that the pupil's hearing
is also an hypothesis required by the teacher. Hypotheses, on
the contrary, postulate facts on the being of which depends the
being of the fact inferred. Nor are the geometer's hypotheses
false, as some have held, urging that one must not employ
falsehood and that the geometer is uttering falsehood in stating
that the line which he draws is a foot long or straight, when it is
actually neither. The truth is that the geometer does not draw
any conclusion from the being of the particular line of which he
speaks, but from what his diagrams symbolize. A further
distinction is that all hypotheses and illegitimate postulates are
either universal or particular, whereas a definition is neither.
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11
So demonstration does not necessarily imply the being of Forms
nor a One beside a Many, but it does necessarily imply the
possibility of truly predicating one of many; since without this
possibility we cannot save the universal, and if the universal
goes, the middle term goes witb. it, and so demonstration
becomes impossible. We conclude, then, that there must be a
single identical term unequivocally predicable of a number of
individuals.
The law that it is impossible to affirm and deny simultaneously
the same predicate of the same subject is not expressly posited
by any demonstration except when the conclusion also has to
be expressed in that form; in which case the proof lays down as
its major premiss that the major is truly affirmed of the middle
but falsely denied. It makes no difference, however, if we add to
the middle, or again to the minor term, the corresponding
negative. For grant a minor term of which it is true to predicate
man - even if it be also true to predicate not-man of it - still
grant simply that man is animal and not not-animal, and the
conclusion follows: for it will still be true to say that Callias -
even if it be also true to say that not-Callias - is animal and not
not-animal. The reason is that the major term is predicable not
only of the middle, but of something other than the middle as
well, being of wider application; so that the conclusion is not
affected even if the middle is extended to cover the original
middle term and also what is not the original middle term.
The law that every predicate can be either truly affirmed or
truly denied of every subject is posited by such demonstration
as uses reductio ad impossibile, and then not always
universally, but so far as it is requisite; within the limits, that is,
of the genus - the genus, I mean (as I have already explained), to
which the man of science applies his demonstrations. In virtue
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of the common elements of demonstration - I mean the
common axioms which are used as premisses of
demonstration, not the subjects nor the attributes
demonstrated as belonging to them - all the sciences have
communion with one another, and in communion with them all
is dialectic and any science which might attempt a universal
proof of axioms such as the law of excluded middle, the law
that the subtraction of equals from equals leaves equal
remainders, or other axioms of the same kind. Dialectic has no
definite sphere of this kind, not being confined to a single
genus. Otherwise its method would not be interrogative; for the
interrogative method is barred to the demonstrator, who cannot
use the opposite facts to prove the same nexus. This was shown
in my work on the syllogism.
12
If a syllogistic question is equivalent to a proposition
embodying one of the two sides of a contradiction, and if each
science has its peculiar propositions from which its peculiar
conclusion is developed, then there is such a thing as a
distinctively scientific question, and it is the interrogative form
of the premisses from which the 'appropriate' conclusion of
each science is developed. Hence it is clear that not every
question will be relevant to geometry, nor to medicine, nor to
any other science: only those questions will be geometrical
which form premisses for the proof of the theorems of
geometry or of any other science, such as optics, which uses the
same basic truths as geometry. Of the other sciences the like is
true. Of these questions the geometer is bound to give his
account, using the basic truths of geometry in conjunction with
his previous conclusions; of the basic truths the geometer, as
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such, is not bound to give any account. The like is true of the
other sciences. There is a limit, then, to the questions which we
may put to each man of science; nor is each man of science
bound to answer all inquiries on each several subject, but only
such as fall within the defined field of his own science. If, then,
in controversy with a geometer qua geometer the disputant
confines himself to geometry and proves anything from
geometrical premisses, he is clearly to be applauded; if he goes
outside these he will be at fault, and obviously cannot even
refute the geometer except accidentally. One should therefore
not discuss geometry among those who are not geometers, for
in such a company an unsound argument will pass unnoticed.
This is correspondingly true in the other sciences.
Since there are 'geometrical' questions, does it follow that there
are also distinctively 'ungeometrical' questions? Further, in each
special science - geometry for instance - what kind of error is it
that may vitiate questions, and yet not exclude them from that
science? Again, is the erroneous conclusion one constructed
from premisses opposite to the true premisses, or is it formal
fallacy though drawn from geometrical premisses? Or, perhaps,
the erroneous conclusion is due to the drawing of premisses
from another science; e.g. in a geometrical controversy a
musical question is distinctively ungeometrical, whereas the
notion that parallels meet is in one sense geometrical, being
ungeometrical in a different fashion: the reason being that
'ungeometrical', like 'unrhythmical', is equivocal, meaning in
the one case not geometry at all, in the other bad geometry? It
is this error, i.e. error based on premisses of this kind - 'of the
science but false - that is the contrary of science. In
mathematics the formal fallacy is not so common, because it is
the middle term in which the ambiguity lies, since the major is
predicated of the whole of the middle and the middle of the
whole of the minor (the predicate of course never has the prefix
'all'); and in mathematics one can, so to speak, see these middle
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terms with an intellectual vision, while in dialectic the
ambiguity may escape detection. E.g. 'Is every circle a figure?' A
diagram shows that this is so, but the minor premiss 'Are epics
circles?' is shown by the diagram to be false.
If a proof has an inductive minor premiss, one should not bring
an 'objection' against it. For since every premiss must be
applicable to a number of cases (otherwise it will not be true in
every instance, which, since the syllogism proceeds from
universals, it must be), then assuredly the same is true of an
'objection'; since premisses and 'objections' are so far the same
that anything which can be validly advanced as an 'objection'
must be such that it could take the form of a premiss, either
demonstrative or dialectical. On the other hand, arguments
formally illogical do sometimes occur through taking as
middles mere attributes of the major and minor terms. An
instance of this is Caeneus' proof that fire increases in
geometrical proportion: 'Fire', he argues, 'increases rapidly, and
so does geometrical proportion'. There is no syllogism so, but
there is a syllogism if the most rapidly increasing proportion is
geometrical and the most rapidly increasing proportion is
attributable to fire in its motion. Sometimes, no doubt, it is
impossible to reason from premisses predicating mere
attributes: but sometimes it is possible, though the possibility is
overlooked. If false premisses could never give true conclusions
'resolution' would be easy, for premisses and conclusion would
in that case inevitably reciprocate. I might then argue thus: let A
be an existing fact; let the existence of A imply such and such
facts actually known to me to exist, which we may call B. I can
now, since they reciprocate, infer A from B.
Reciprocation of premisses and conclusion is more frequent in
mathematics, because mathematics takes definitions, but never
an accident, for its premisses - a second characteristic
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distinguishing mathematical reasoning from dialectical
disputations.
A science expands not by the interposition of fresh middle
terms, but by the apposition of fresh extreme terms. E.g. A is
predicated of B, B of C, C of D, and so indefinitely. Or the
expansion may be lateral: e.g. one major A, may be proved of
two minors, C and E. Thus let A represent number - a number or
number taken indeterminately; B determinate odd number; C
any particular odd number. We can then predicate A of C. Next
let D represent determinate even number, and E even number.
Then A is predicable of E.
13
Knowledge of the fact differs from knowledge of the reasoned
fact. To begin with, they differ within the same science and in
two ways: (1) when the premisses of the syllogism are not
immediate (for then the proximate cause is not contained in
them - a necessary condition of knowledge of the reasoned
fact): (2) when the premisses are immediate, but instead of the
cause the better known of the two reciprocals is taken as the
middle; for of two reciprocally predicable terms the one which
is not the cause may quite easily be the better known and so
become the middle term of the demonstration. Thus (2) (a) you
might prove as follows that the planets are near because they
do not twinkle: let C be the planets, B not twinkling, A
proximity. Then B is predicable of C; for the planets do not
twinkle. But A is also predicable of B, since that which does not
twinkle is near - we must take this truth as having been
reached by induction or sense-perception. Therefore A is a
necessary predicate of C; so that we have demonstrated that the
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planets are near. This syllogism, then, proves not the reasoned
fact but only the fact; since they are not near because they do
not twinkle, but, because they are near, do not twinkle. The
major and middle of the proof, however, may be reversed, and
then the demonstration will be of the reasoned fact. Thus: let C
be the planets, B proximity, A not twinkling. Then B is an
attribute of C, and A - not twinkling - of B. Consequently A is
predicable of C, and the syllogism proves the reasoned fact,
since its middle term is the proximate cause. Another example
is the inference that the moon is spherical from its manner of
waxing. Thus: since that which so waxes is spherical, and since
the moon so waxes, clearly the moon is spherical. Put in this
form, the syllogism turns out to be proof of the fact, but if the
middle and major be reversed it is proof of the reasoned fact;
since the moon is not spherical because it waxes in a certain
manner, but waxes in such a manner because it is spherical.
(Let C be the moon, B spherical, and A waxing.) Again (b), in
cases where the cause and the effect are not reciprocal and the
effect is the better known, the fact is demonstrated but not the
reasoned fact. This also occurs (1) when the middle falls outside
the major and minor, for here too the strict cause is not given,
and so the demonstration is of the fact, not of the reasoned fact.
For example, the question 'Why does not a wall breathe?' might
be answered, 'Because it is not an animal'; but that answer
would not give the strict cause, because if not being an animal
causes the absence of respiration, then being an animal should
be the cause of respiration, according to the rule that if the
negation of causes the non-inherence of y, the affirmation of x
causes the inherence of y; e.g. if the disproportion of the hot
and cold elements is the cause of ill health, their proportion is
the cause of health; and conversely, if the assertion of x causes
the inherence of y, the negation of x must cause y's non-
inherence. But in the case given this consequence does not
result; for not every animal breathes. A syllogism with this kind
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of cause takes place in the second figure. Thus: let A be animal,
B respiration, C wall. Then A is predicable of all B (for all that
breathes is animal), but of no C; and consequently B is
predicable of no C; that is, the wall does not breathe. Such
causes are like far-fetched explanations, which precisely consist
in making the cause too remote, as in Anacharsis' account of
why the Scythians have no flute-players; namely because they
have no vines.
Thus, then, do the syllogism of the fact and the syllogism of the
reasoned fact differ within one science and according to the
position of the middle terms. But there is another way too in
which the fact and the reasoned fact differ, and that is when
they are investigated respectively by different sciences. This
occurs in the case of problems related to one another as
subordinate and superior, as when optical problems are
subordinated to geometry, mechanical problems to stereometry,
harmonic problems to arithmetic, the data of observation to
astronomy. (Some of these sciences bear almost the same
name; e.g. mathematical and nautical astronomy, mathematical
and acoustical harmonics.) Here it is the business of the
empirical observers to know the fact, of the mathematicians to
know the reasoned fact; for the latter are in possession of the
demonstrations giving the causes, and are often ignorant of the
fact: just as we have often a clear insight into a universal, but
through lack of observation are ignorant of some of its
particular instances. These connexions have a perceptible
existence though they are manifestations of forms. For the
mathematical sciences concern forms: they do not demonstrate
properties of a substratum, since, even though the geometrical
subjects are predicable as properties of a perceptible
substratum, it is not as thus predicable that the mathematician
demonstrates properties of them. As optics is related to
geometry, so another science is related to optics, namely the
theory of the rainbow. Here knowledge of the fact is within the
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province of the natural philosopher, knowledge of the reasoned
fact within that of the optician, either qua optician or qua
mathematical optician. Many sciences not standing in this
mutual relation enter into it at points; e.g. medicine and
geometry: it is the physician's business to know that circular
wounds heal more slowly, the geometer's to know the reason
why.
14
Of all the figures the most scientific is the first. Thus, it is the
vehicle of the demonstrations of all the mathematical sciences,
such as arithmetic, geometry, and optics, and practically all of
all sciences that investigate causes: for the syllogism of the
reasoned fact is either exclusively or generally speaking and in
most cases in this figure - a second proof that this figure is the
most scientific; for grasp of a reasoned conclusion is the
primary condition of knowledge. Thirdly, the first is the only
figure which enables us to pursue knowledge of the essence of a
thing. In the second figure no affirmative conclusion is possible,
and knowledge of a thing's essence must be affirmative; while
in the third figure the conclusion can be affirmative, but cannot
be universal, and essence must have a universal character: e.g.
man is not two-footed animal in any 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.
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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 As 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 BEE.., 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
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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
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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.
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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 is an
attribute of no B will not be an attribute of all A either; for if it
be an attribute of all A, it will also be an attribute of all B, which
is contrary to supposition; but if C be nevertheless assumed to
be a universal attribute of A, but an attribute of no B, then the
premiss C-B is true but the major is false. The case is similar if
the major is made the negative premiss. For in fact what is an
attribute of no A will not be an attribute of any B either; and if it
be yet assumed that C is universally non-attributable to A, but a
universal attribute of B, the premiss C-A is true but the minor
wholly false. Again, in fact it is false to assume that that which
is an attribute of all B is an attribute of no A, for if it be an
attribute of all B, it must be an attribute of some A. If then C is
nevertheless assumed to be an attribute of all B but of no A, G-B
will be true but C-A false.
It is thus clear that in the case of atomic propositions erroneous
inference will be possible not only when both premisses are
false but also when only one is false.
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17
In the case of attributes not atomically connected with or
disconnected from their subjects, (a) (i) as long as the false
conclusion is inferred through the 'appropriate' middle, only the
major and not both premisses can be false. By 'appropriate
middle' I mean the middle term through which the
contradictory - i.e. the true-conclusion is inferrible. Thus, let A
be attributable to B through a middle term C: then, since to
produce a conclusion the premiss C-B must be taken
affirmatively, it is clear that this premiss must always be true,
for its quality is not changed. But the major A-C is false, for it is
by a change in the quality of A-C that the conclusion becomes
its contradictory - i.e. true. Similarly (ii) if the middle is taken
from another series of predication; e.g. suppose D to be not only
contained within A as a part within its whole but also
predicable of all B. Then the premiss D-B must remain
unchanged, but the quality of A-D must be changed; so that D-B
is always true, A-D always false. Such error is practically
identical with that which is inferred through the 'appropriate'
middle. On the other hand, (b) if the conclusion is not inferred
through the 'appropriate' middle - (i) when the middle is
subordinate to A but is predicable of no B, both premisses must
be false, because if there is to be a conclusion both must be
posited as asserting the contrary of what is actually the fact,
and so posited both become false: e.g. suppose that actually all
D is A but no B is D; then if these premisses are changed in
quality, a conclusion will follow and both of the new premisses
will be false. When, however, (ii) the middle D is not subordinate
to A, A-D will be true, D-B false - A-D true because A was not
subordinate to D, D-B false because if it had been true, the
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conclusion too would have been true; but it is ex hypothesi
false.
When the erroneous inference is in the second figure, both
premisses cannot be entirely false; since if B is subordinate to A,
there can be no middle predicable of all of one extreme and of
none of the other, as was stated before. One premiss, however,
may be false, and it may be either of them. Thus, if C is actually
an attribute of both A and B, but is assumed to be an attribute of
A only and not of B, C-A will be true, C-B false: or again if C be
assumed to be attributable to B but to no A, C-B will be true, C-A
false.
We have stated when and through what kinds of premisses
error will result in cases where the erroneous conclusion is
negative. If the conclusion is affirmative, (a) (i) it may be
inferred through the 'appropriate' middle term. In this case both
premisses cannot be false since, as we said before, C-B must
remain unchanged if there is to be a conclusion, and
consequently A-C, the quality of which is changed, will always
be false. This is equally true if (ii) the middle is taken from
another series of predication, as was stated to be the case also
with regard to negative error; for D-B must remain unchanged,
while the quality of A-D must be converted, and the type of
error is the same as before.
(b) The middle may be inappropriate. Then (i) if D is subordinate
to A, A-D will be true, but D-B false; since A may quite well be
predicable of several terms no one of which can be
subordinated to another. If, however, (ii) D is not subordinate to
A, obviously A-D, since it is affirmed, will always be false, while
D-B may be either true or false; for A may very well be an
attribute of no D, whereas all B is D, e.g. no science is animal, all
music is science. Equally well A may be an attribute of no D, and
D of no B. It emerges, then, that if the middle term is not
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subordinate to the major, not only both premisses but either
singly may be false.
Thus we have made it clear how many varieties of erroneous
inference are liable to happen and through what kinds of
premisses they occur, in the case both of immediate and of
demonstrable truths.
18
It is also clear that the loss of any one of the senses entails the
loss of a corresponding portion of knowledge, and that, since we
learn either by induction or by demonstration, this knowledge
cannot be acquired. Thus demonstration develops from
universals, induction from particulars; but since it is possible to
familiarize the pupil with even the so-called mathematical
abstractions only through induction - i.e. only because each
subject genus possesses, in virtue of a determinate
mathematical character, certain properties which can be treated
as separate even though they do not exist in isolation - it is
consequently impossible to come to grasp universals except
through induction. But induction is impossible for those who
have not sense-perception. For it is sense-perception alone
which is adequate for grasping the particulars: they cannot be
objects of scientific knowledge, because neither can universals
give us knowledge of them without induction, nor can we get it
through induction without sense-perception.
258
19
Every syllogism is effected by means of three terms. One kind of
syllogism serves to prove that A inheres in C by showing that A
inheres in B and B in C; the other is negative and one of its
premisses asserts one term of another, while the other denies
one term of another. It is clear, then, that these are the
fundamentals and so-called hypotheses of syllogism. Assume
them as they have been stated, and proof is bound to follow -
proof that A inheres in C through B, and again that A inheres in
B through some other middle term, and similarly that B inheres
in C. If our reasoning aims at gaining credence and so is merely
dialectical, it is obvious that we have only to see that our
inference is based on premisses as credible as possible: so that
if a middle term between A and B is credible though not real,
one can reason through it and complete a dialectical syllogism.
If, however, one is aiming at truth, one must be guided by the
real connexions of subjects and attributes. Thus: since there are
attributes which are predicated of a subject essentially or
naturally and not coincidentally - not, that is, in the sense in
which we say 'That white (thing) is a man', which is not the
same mode of predication as when we say 'The man is white':
the man is white not because he is something else but because
he is man, but the white is man because 'being white' coincides
with 'humanity' within one substratum - therefore there are
terms such as are naturally subjects of predicates. Suppose,
then, C such a term not itself attributable to anything else as to
a subject, but the proximate subject of the attribute B - i.e. so
that B-C is immediate; suppose further E related immediately to
F, and F to B. The first question is, must this series terminate, or
can it proceed to infinity? The second question is as follows:
Suppose nothing is essentially predicated of A, but A is
predicated primarily of H and of no intermediate prior term, and
suppose H similarly related to G and G to B; then must this
series also terminate, or can it too proceed to infinity? There is
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this much difference between the questions: the first is, is it
possible to start from that which is not itself attributable to
anything else but is the subject of attributes, and ascend to
infinity? The second is the problem whether one can start from
that which is a predicate but not itself a subject of predicates,
and descend to infinity? A third question is, if the extreme
terms are fixed, can there be an infinity of middles? I mean this:
suppose for example that A inheres in C and B is intermediate
between them, but between B and A there are other middles,
and between these again fresh middles; can these proceed to
infinity or can they not? This is the equivalent of inquiring, do
demonstrations proceed to infinity, i.e. is everything
demonstrable? Or do ultimate subject and primary attribute
limit one another?
I hold that the same questions arise with regard to negative
conclusions and premisses: viz. if A is attributable to no B, then
either this predication will be primary, or there will be an
intermediate term prior to B to which a is not attributable - G,
let us say, which is attributable to all B - and there may still be
another term H prior to G, which is attributable to all G. The
same questions arise, I say, because in these cases too either the
series of prior terms to which a is not attributable is infinite or it
terminates.
One cannot ask the same questions in the case of reciprocating
terms, since when subject and predicate are convertible there is
neither primary nor ultimate subject, seeing that all the
reciprocals qua subjects stand in the same relation to one
another, whether we say that the subject has an infinity of
attributes or that both subjects and attributes - and we raised
the question in both cases - are infinite in number. These
questions then cannot be asked - unless, indeed, the terms can
reciprocate by two different modes, by accidental predication in
one relation and natural predication in the other.
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20
Now, it is clear that if the predications terminate in both the
upward and the downward direction (by 'upward' I mean the
ascent to the more universal, by 'downward' the descent to the
more particular), the middle terms cannot be infinite in number.
For suppose that A is predicated of F, and that the intermediates
- call them B B' B"... - are infinite, then clearly you might
descend from and find one term predicated of another ad
infinitum, since you have an infinity of terms between you and
F; and equally, if you ascend from F, there are infinite terms
between you and A. It follows that if these processes are
impossible there cannot be an infinity of intermediates between
A and F. Nor is it of any effect to urge that some terms of the
series AB...F are contiguous so as to exclude intermediates,
while others cannot be taken into the argument at all:
whichever terms of the series B...I take, the number of
intermediates in the direction either of A or of F must be finite
or infinite: where the infinite series starts, whether from the
first term or from a later one, is of no moment, for the
succeeding terms in any case are infinite in number.
21
Further, if in affirmative demonstration the series terminates in
both directions, clearly it will terminate too in negative
demonstration. Let us assume that we cannot proceed to
infinity either by ascending from the ultimate term (by 'ultimate
term' I mean a term such as was, not itself attributable to a
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subject but itself the subject of attributes), or by descending
towards an ultimate from the primary term (by 'primary term' I
mean a term predicable of a subject but not itself a subject). If
this assumption is justified, the series will also terminate in the
case of negation. For a negative conclusion can be proved in all
three figures. In the first figure it is proved thus: no B is A, all C
is B. In packing the interval B-C we must reach immediate
propositions - as is always the case with the minor premiss -
since B-C is affirmative. As regards the other premiss it is plain
that if the major term is denied of a term D prior to B, D will
have to be predicable of all B, and if the major is denied of yet
another term prior to D, this term must be predicable of all D.
Consequently, since the ascending series is finite, the descent
will also terminate and there will be a subject of which A is
primarily non-predicable. In the second figure the syllogism is,
all A is B, no C is B,..no C is A. If proof of this is required, plainly
it may be shown either in the first figure as above, in the second
as here, or in the third. The first figure has been discussed, and
we will proceed to display the second, proof by which will be as
follows: all B is D, no C is D..., since it is required that B should
be a subject of which a predicate is affirmed. Next, since D is to
be proved not to belong to C, then D has a further predicate
which is denied of C. Therefore, since the succession of
predicates affirmed of an ever higher universal terminates, the
succession of predicates denied terminates too.
The third figure shows it as follows: all B is A, some B is not C.
Therefore some A is not C. This premiss, i.e. C-B, will be proved
either in the same figure or in one of the two figures discussed
above. In the first and second figures the series terminates. If
we use the third figure, we shall take as premisses, all E is B,
some E is not C, and this premiss again will be proved by a
similar prosyllogism. But since it is assumed that the series of
descending subjects also terminates, plainly the series of more
universal non-predicables will terminate also. Even supposing
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that the proof is not confined to one method, but employs them
all and is now in the first figure, now in the second or third -
even so the regress will terminate, for the methods are finite in
number, and if finite things are combined in a finite number of
ways, the result must be finite.
Thus it is plain that the regress of middles terminates in the
case of negative demonstration, if it does so also in the case of
affirmative demonstration. That in fact the regress terminates
in both these cases may be made clear by the following
dialectical considerations.
22
In the case of predicates constituting the essential nature of a
thing, it clearly terminates, seeing that if definition is possible,
or in other words, if essential form is knowable, and an infinite
series cannot be traversed, predicates constituting a thing's
essential nature must be finite in number. But as regards
predicates generally we have the following prefatory remarks to
make. (1) We can affirm without falsehood 'the white (thing) is
walking', and that big (thing) is a log'; or again, 'the log is big',
and 'the man walks'. But the affirmation differs in the two
cases. When I affirm 'the white is a log', I mean that something
which happens to be white is a log - not that white is the
substratum in which log inheres, for it was not qua white or qua
a species of white that the white (thing) came to be a log, and
the white (thing) is consequently not a log except incidentally.
On the other hand, when I affirm 'the log is white', I do not
mean that something else, which happens also to be a log, is
white (as I should if I said 'the musician is white,' which would
mean 'the man who happens also to be a musician is white'); on
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the contrary, log is here the substratum - the substratum which
actually came to be white, and did so qua wood or qua a species
of wood and qua nothing else.
If we must lay down a rule, let us entitle the latter kind of
statement predication, and the former not predication at all, or
not strict but accidental predication. 'White' and 'log' will thus
serve as types respectively of predicate and subject.
We shall assume, then, that the predicate is invariably
predicated strictly and not accidentally of the subject, for on
such predication demonstrations depend for their force. It
follows from this that when a single attribute is predicated of a
single subject, the predicate must affirm of the subject either
some element constituting its essential nature, or that it is in
some way qualified, quantified, essentially related, active,
passive, placed, or dated.
(2) Predicates which signify substance signify that the subject is
identical with the predicate or with a species of the predicate.
Predicates not signifying substance which are predicated of a
subject not identical with themselves or with a species of
themselves are accidental or coincidental; e.g. white is a
coincident of man, seeing that man is not identical with white
or a species of white, but rather with animal, since man is
identical with a species of animal. These predicates which do
not signify substance must be predicates of some other subject,
and nothing can be white which is not also other than white.
The Forms we can dispense with, for they are mere sound
without sense; and even if there are such things, they are not
relevant to our discussion, since demonstrations are concerned
with predicates such as we have defined.
(3) If A is a quality of B, B cannot be a quality of A - a quality of a
quality. Therefore A and B cannot be predicated reciprocally of
one another in strict predication: they can be affirmed without
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falsehood of one another, but not genuinely predicated of each
other. For one alternative is that they should be substantially
predicated of one another, i.e. B would become the genus or
differentia of A - the predicate now become subject. But it has
been shown that in these substantial predications neither the
ascending predicates nor the descending subjects form an
infinite series; e.g. neither the series, man is biped, biped is
animal, &c, nor the series predicating animal of man, man of
Callias, Callias of a further, subject as an element of its essential
nature, is infinite. For all such substance is definable, and an
infinite series cannot be traversed in thought: consequently
neither the ascent nor the descent is infinite, since a substance
whose predicates were infinite would not be definable. Hence
they will not be predicated each as the genus of the other; for
this would equate a genus with one of its own species. Nor (the
other alternative) can a quale be reciprocally predicated of a
quale, nor any term belonging to an adjectival category of
another such term, except by accidental predication; for all such
predicates are coincidents and are predicated of substances. On
the other hand - in proof of the impossibility of an infinite
ascending series - every predication displays the subject as
somehow qualified or quantified or as characterized under one
of the other adjectival categories, or else is an element in its
substantial nature: these latter are limited in number, and the
number of the widest kinds under which predications fall is
also limited, for every predication must exhibit its subject as
somehow qualified, quantified, essentially related, acting or
suffering, or in some place or at some time.
I assume first that predication implies a single subject and a
single attribute, and secondly that predicates which are not
substantial are not predicated of one another. We assume this
because such predicates are all coincidents, and though some
are essential coincidents, others of a different type, yet we
maintain that all of them alike are predicated of some
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substratum and that a coincident is never a substratum - since
we do not class as a coincident anything which does not owe its
designation to its being something other than itself, but always
hold that any coincident is predicated of some substratum
other than itself, and that another group of coincidents may
have a different substratum. Subject to these assumptions then,
neither the ascending nor the descending series of predication
in which a single attribute is predicated of a single subject is
infinite. For the subjects of which coincidents are predicated are
as many as the constitutive elements of each individual
substance, and these we have seen are not infinite in number,
while in the ascending series are contained those constitutive
elements with their coincidents - both of which are finite. We
conclude that there is a given subject (D) of which some
attribute (C) is primarily predicable; that there must be an
attribute (B) primarily predicable of the first attribute, and that
the series must end with a term (A) not predicable of any term
prior to the last subject of which it was predicated (B), and of
which no term prior to it is predicable.
The argument we have given is one of the so-called proofs; an
alternative proof follows. Predicates so related to their subjects
that there are other predicates prior to them predicable of those
subjects are demonstrable; but of demonstrable propositions
one cannot have something better than knowledge, nor can one
know them without demonstration. Secondly, if a consequent is
only known through an antecedent (viz. premisses prior to it)
and we neither know this antecedent nor have something
better than knowledge of it, then we shall not have scientific
knowledge of the consequent. Therefore, if it is possible through
demonstration to know anything without qualification and not
merely as dependent on the acceptance of certain premisses -
i.e. hypothetically - the series of intermediate predications must
terminate. If it does not terminate, and beyond any predicate
taken as higher than another there remains another still higher,
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then every predicate is demonstrable. Consequently, since these
demonstrable predicates are infinite in number and therefore
cannot be traversed, we shall not know them by demonstration.
If, therefore, we have not something better than knowledge of
them, we cannot through demonstration have unqualified but
only hypothetical science of anything.
As dialectical proofs of our contention these may carry
conviction, but an analytic process will show more briefly that
neither the ascent nor the descent of predication can be infinite
in the demonstrative sciences which are the object of our
investigation. Demonstration proves the inherence of essential
attributes in things. Now attributes may be essential for two
reasons: either because they are elements in the essential
nature of their subjects, or because their subjects are elements
in their essential nature. An example of the latter is odd as an
attribute of number - though it is number's attribute, yet
number itself is an element in the definition of odd; of the
former, multiplicity or the indivisible, which are elements in the
definition of number. In neither kind of attribution can the
terms be infinite. They are not infinite where each is related to
the term below it as odd is to number, for this would mean the
inherence in odd of another attribute of odd in whose nature
odd was an essential element: but then number will be an
ultimate subject of the whole infinite chain of attributes, and be
an element in the definition of each of them. Hence, since an
infinity of attributes such as contain their subject in their
definition cannot inhere in a single thing, the ascending series
is equally finite. Note, moreover, that all such attributes must so
inhere in the ultimate subject - e.g. its attributes in number and
number in them - as to be commensurate with the subject and
not of wider extent. Attributes which are essential elements in
the nature of their subjects are equally finite: otherwise
definition would be impossible. Hence, if all the attributes
predicated are essential and these cannot be infinite, the
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ascending series will terminate, and consequently the
descending series too.
If this is so, it follows that the intermediates between any two
terms are also always limited in number. An immediately
obvious consequence of this is that demonstrations necessarily
involve basic truths, and that the contention of some - referred
to at the outset - that all truths are demonstrable is mistaken.
For if there are basic truths, (a) not all truths are demonstrable,
and (b) an infinite regress is impossible; since if either (a) or (b)
were not a fact, it would mean that no interval was immediate
and indivisible, but that all intervals were divisible. This is true
because a conclusion is demonstrated by the interposition, not
the apposition, of a fresh term. If such interposition could
continue to infinity there might be an infinite number of terms
between any two terms; but this is impossible if both the
ascending and descending series of predication terminate; and
of this fact, which before was shown dialectically, analytic proof
has now been given.
23
It is an evident corollary of these conclusions that if the same
attribute A inheres in two terms C and D predicable either not at
all, or not of all instances, of one another, it does not always
belong to them in virtue of a common middle term. Isosceles
and scalene possess the attribute of having their angles equal to
two right angles in virtue of a common middle; for they possess
it in so far as they are both a certain kind of figure, and not in so
far as they differ from one another. But this is not always the
case: for, were it so, if we take B as the common middle in virtue
of which A inheres in C and D, clearly B would inhere in C and D
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through a second common middle, and this in turn would
inhere in C and D through a third, so that between two terms an
infinity of intermediates would fall - an impossibility. Thus it
need not always be in virtue of a common middle term that a
single attribute inheres in several subjects, since there must be
immediate intervals. Yet if the attribute to be proved common to
two subjects is to be one of their essential attributes, the middle
terms involved must be within one subject genus and be
derived from the same group of immediate premisses; for we
have seen that processes of proof cannot pass from one genus
to another.
It is also clear that when A inheres in B, this can be
demonstrated if there is a middle term. Further, the 'elements'
of such a conclusion are the premisses containing the middle in
question, and they are identical in number with the middle
terms, seeing that the immediate propositions - or at least such
immediate propositions as are universal - are the 'elements'. If,
on the other hand, there is no middle term, demonstration
ceases to be possible: we are on the way to the basic truths.
Similarly if A does not inhere in B, this can be demonstrated if
there is a middle term or a term prior to B in which A does not
inhere: otherwise there is no demonstration and a basic truth is
reached. There are, moreover, as many 'elements' of the
demonstrated conclusion as there are middle terms, since it is
propositions containing these middle terms that are the basic
premisses on which the demonstration rests; and as there are
some indemonstrable basic truths asserting that 'this is that' or
that 'this inheres in that', so there are others denying that 'this
is that' or that 'this inheres in that' - in fact some basic truths
will affirm and some will deny being.
When we are to prove a conclusion, we must take a primary
essential predicate - suppose it C - of the subject B, and then
suppose A similarly predicable of C. If we proceed in this
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manner, no proposition or attribute which falls beyond A is
admitted in the proof: the interval is constantly condensed until
subject and predicate become indivisible, i.e. one. We have our
unit when the premiss becomes immediate, since the
immediate premiss alone is a single premiss in the unqualified
sense of 'single'. And as in other spheres the basic element is
simple but not identical in all - in a system of weight it is the
mina, in music the quarter-tone, and so on - so in syllogism the
unit is an immediate premiss, and in the knowledge that
demonstration gives it is an intuition. In syllogisms, then, which
prove the inherence of an attribute, nothing falls outside the
major term. In the case of negative syllogisms on the other
hand, (1) in the first figure nothing falls outside the major term
whose inherence is in question; e.g. to prove through a middle C
that A does not inhere in B the premisses required are, all B is C,
no C is A. Then if it has to be proved that no C is A, a middle
must be found between and C; and this procedure will never
vary.
(2) If we have to show that E is not D by means of the premisses,
all D is C; no E, or not all E, is C; then the middle will never fall
beyond E, and E is the subject of which D is to be denied in the
conclusion.
(3) In the third figure the middle will never fall beyond the
limits of the subject and the attribute denied of it.
24
Since demonstrations may be either commensurately universal
or particular, and either affirmative or negative; the question
arises, which form is the better? And the same question may be
put in regard to so-called 'direct' demonstration and reductio ad
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impossibile. Let us first examine the commensurately universal
and the particular forms, and when we have cleared up this
problem proceed to discuss 'direct' demonstration and reductio
ad impossibile.
The following considerations might lead some minds to prefer
particular demonstration.
(1) The superior demonstration is the demonstration which
gives us greater knowledge (for this is the ideal of
demonstration), and we have greater knowledge of a particular
individual when we know it in itself than when we know it
through something else; e.g. we know Coriscus the musician
better when we know that Coriscus is musical than when we
know only that man is musical, and a like argument holds in all
other cases. But commensurately universal demonstration,
instead of proving that the subject itself actually is x, proves
only that something else is x - e.g. in attempting to prove that
isosceles is x, it proves not that isosceles but only that triangle
is x - whereas particular demonstration proves that the subject
itself is x. The demonstration, then, that a subject, as such,
possesses an attribute is superior. If this is so, and if the
particular rather than the commensurately universal forms
demonstrates, particular demonstration is superior.
(2) The universal has not a separate being over against groups of
singulars. Demonstration nevertheless creates the opinion that
its function is conditioned by something like this - some
separate entity belonging to the real world; that, for instance, of
triangle or of figure or number, over against particular triangles,
figures, and numbers. But demonstration which touches the
real and will not mislead is superior to that which moves
among unrealities and is delusory. Now commensurately
universal demonstration is of the latter kind: if we engage in it
we find ourselves reasoning after a fashion well illustrated by
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the argument that the proportionate is what answers to the
definition of some entity which is neither line, number, solid,
nor plane, but a proportionate apart from all these. Since, then,
such a proof is characteristically commensurate and universal,
and less touches reality than does particular demonstration,
and creates a false opinion, it will follow that commensurate
and universal is inferior to particular demonstration.
We may retort thus. (1) The first argument applies no more to
commensurate and universal than to particular demonstration.
If equality to two right angles is attributable to its subject not
qua isosceles but qua triangle, he who knows that isosceles
possesses that attribute knows the subject as qua itself
possessing the attribute, to a less degree than he who knows
that triangle has that attribute. To sum up the whole matter: if a
subject is proved to possess qua triangle an attribute which it
does not in fact possess qua triangle, that is not demonstration:
but if it does possess it qua triangle the rule applies that the
greater knowledge is his who knows the subject as possessing
its attribute qua that in virtue of which it actually does possess
it. Since, then, triangle is the wider term, and there is one
identical definition of triangle - i.e. the term is not equivocal -
and since equality to two right angles belongs to all triangles, it
is isosceles qua triangle and not triangle qua isosceles which
has its angles so related. It follows that he who knows a
connexion universally has greater knowledge of it as it in fact is
than he who knows the particular; and the inference is that
commensurate and universal is superior to particular
demonstration.
(2) If there is a single identical definition i.e. if the
commensurate universal is unequivocal - then the universal
will possess being not less but more than some of the
particulars, inasmuch as it is universals which comprise the
imperishable, particulars that tend to perish.
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(3) Because the universal has a single meaning, we are not
therefore compelled to suppose that in these examples it has
being as a substance apart from its particulars - any more than
we need make a similar supposition in the other cases of
unequivocal universal predication, viz. where the predicate
signifies not substance but quality, essential relatedness, or
action. If such a supposition is entertained, the blame rests not
with the demonstration but with the hearer.
(4) Demonstration is syllogism that proves the cause, i.e. the
reasoned fact, and it is rather the commensurate universal than
the particular which is causative (as may be shown thus: that
which possesses an attribute through its own essential nature is
itself the cause of the inherence, and the commensurate
universal is primary; hence the commensurate universal is the
cause). Consequently commensurately universal demonstration
is superior as more especially proving the cause, that is the
reasoned fact.
(5) Our search for the reason ceases, and we think that we know,
when the coming to be or existence of the fact before us is not
due to the coming to be or existence of some other fact, for the
last step of a search thus conducted is eo ipso the end and limit
of the problem. Thus: 'Why did he come?' 'To get the money -
wherewith to pay a debt - that he might thereby do what was
right.' When in this regress we can no longer find an efficient or
final cause, we regard the last step of it as the end of the coming
- or being or coming to be - and we regard ourselves as then
only having full knowledge of the reason why he came.
If, then, all causes and reasons are alike in this respect, and if
this is the means to full knowledge in the case of final causes
such as we have exemplified, it follows that in the case of the
other causes also full knowledge is attained when an attribute
no longer inheres because of something else. Thus, when we
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learn that exterior angles are equal to four right angles because
they are the exterior angles of an isosceles, there still remains
the question 'Why has isosceles this attribute?' and its answer
'Because it is a triangle, and a triangle has it because a triangle
is a rectilinear figure.' If rectilinear figure possesses the property
for no further reason, at this point we have full knowledge - but
at this point our knowledge has become commensurately
universal, and so we conclude that commensurately universal
demonstration is superior.
(6) The more demonstration becomes particular the more it
sinks into an indeterminate manifold, while universal
demonstration tends to the simple and determinate. But objects
so far as they are an indeterminate manifold are unintelligible,
so far as they are determinate, intelligible: they are therefore
intelligible rather in so far as they are universal than in so far as
they are particular. From this it follows that universals are more
demonstrable: but since relative and correlative increase
concomitantly, of the more demonstrable there will be fuller
demonstration. Hence the commensurate and universal form,
being more truly demonstration, is the superior.
(7) Demonstration which teaches two things is preferable to
demonstration which teaches only one. He who possesses
commensurately universal demonstration knows the particular
as well, but he who possesses particular demonstration does
not know the universal. So that this is an additional reason for
preferring commensurately universal demonstration. And there
is yet this further argument:
(8) Proof becomes more and more proof of the commensurate
universal as its middle term approaches nearer to the basic
truth, and nothing is so near as the immediate premiss which is
itself the basic truth. If, then, proof from the basic truth is more
accurate than proof not so derived, demonstration which
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depends more closely on it is more accurate than
demonstration which is less closely dependent. But
commensurately universal demonstration is characterized by
this closer dependence, and is therefore superior. Thus, if A had
to be proved to inhere in D, and the middles were B and C, B
being the higher term would render the demonstration which it
mediated the more universal.
Some of these arguments, however, are dialectical. The clearest
indication of the precedence of commensurately universal
demonstration is as follows: if of two propositions, a prior and a
posterior, we have a grasp of the prior, we have a kind of
knowledge - a potential grasp - of the posterior as well. For
example, if one knows that the angles of all triangles are equal
to two right angles, one knows in a sense - potentially - that the
isosceles' angles also are equal to two right angles, even if one
does not know that the isosceles is a triangle; but to grasp this
posterior proposition is by no means to know the
commensurate universal either potentially or actually.
Moreover, commensurately universal demonstration is through
and through intelligible; particular demonstration issues in
sense-perception.
25
The preceding arguments constitute our defence of the
superiority of commensurately universal to particular
demonstration. That affirmative demonstration excels negative
may be shown as follows.
(1) We may assume the superiority ceteris paribus of the
demonstration which derives from fewer postulates or
hypotheses - in short from fewer premisses; for, given that all
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these are equally well known, where they are fewer knowledge
will be more speedily acquired, and that is a desideratum. The
argument implied in our contention that demonstration from
fewer assumptions is superior may be set out in universal form
as follows. Assuming that in both cases alike the middle terms
are known, and that middles which are prior are better known
than such as are posterior, we may suppose two demonstrations
of the inherence of A in E, the one proving it through the
middles B, C and D, the other through F and G. Then A-D is
known to the same degree as A-E (in the second proof), but A-D
is better known than and prior to A-E (in the first proof); since
A-E is proved through A-D, and the ground is more certain than
the conclusion.
Hence demonstration by fewer premisses is ceteris paribus
superior. Now both affirmative and negative demonstration
operate through three terms and two premisses, but whereas
the former assumes only that something is, the latter assumes
both that something is and that something else is not, and thus
operating through more kinds of premiss is inferior.
(2) It has been proved that no conclusion follows if both
premisses are negative, but that one must be negative, the other
affirmative. So we are compelled to lay down the following
additional rule: as the demonstration expands, the affirmative
premisses must increase in number, but there cannot be more
than one negative premiss in each complete proof. Thus,
suppose no B is A, and all C is B. Then if both the premisses are
to be again expanded, a middle must be interposed. Let us
interpose D between A and B, and E between B and C. Then
clearly E is affirmatively related to B and C, while D is
affirmatively related to B but negatively to A; for all B is D, but
there must be no D which is A. Thus there proves to be a single
negative premiss, A-D. In the further prosyllogisms too it is the
same, because in the terms of an affirmative syllogism the
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middle is always related affirmatively to both extremes; in a
negative syllogism it must be negatively related only to one of
them, and so this negation comes to be a single negative
premiss, the other premisses being affirmative. If, then, that
through which a truth is proved is a better known and more
certain truth, and if the negative proposition is proved through
the affirmative and not vice versa, affirmative demonstration,
being prior and better known and more certain, will be superior.
(3) The basic truth of demonstrative syllogism is the universal
immediate premiss, and the universal premiss asserts in
affirmative demonstration and in negative denies: and the
affirmative proposition is prior to and better known than the
negative (since affirmation explains denial and is prior to
denial, just as being is prior to not-being). It follows that the
basic premiss of affirmative demonstration is superior to that of
negative demonstration, and the demonstration which uses
superior basic premisses is superior.
(4) Affirmative demonstration is more of the nature of a basic
form of proof, because it is a sine qua non of negative
demonstration.
26
Since affirmative demonstration is superior to negative, it is
clearly superior also to reductio ad impossibile. We must first
make certain what is the difference between negative
demonstration and reductio ad impossibile. Let us suppose that
no B is A, and that all C is B: the conclusion necessarily follows
that no C is A. If these premisses are assumed, therefore, the
negative demonstration that no C is A is direct. Reductio ad
impossibile, on the other hand, proceeds as follows. Supposing
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we are to prove that does not inhere in B, we have to assume
that it does inhere, and further that B inheres in C, with the
resulting inference that A inheres in C. This we have to suppose
a known and admitted impossibility; and we then infer that A
cannot inhere in B. Thus if the inherence of B in C is not
questioned, As inherence in B is impossible.
The order of the terms is the same in both proofs: they differ
according to which of the negative propositions is the better
known, the one denying A of B or the one denying A of C. When
the falsity of the conclusion is the better known, we use
reductio ad impossible; when the major premiss of the
syllogism is the more obvious, we use direct demonstration. All
the same the proposition denying A of B is, in the order of being,
prior to that denying A of C; for premisses are prior to the
conclusion which follows from them, and 'no C is A is the
conclusion, 'no B is A one of its premisses. For the destructive
result of reductio ad impossibile is not a proper conclusion, nor
are its antecedents proper premisses. On the contrary: the
constituents of syllogism are premisses related to one another
as whole to part or part to whole, whereas the premisses A-C
and A-B are not thus related to one another. Now the superior
demonstration is that which proceeds from better known and
prior premisses, and while both these forms depend for
credence on the not-being of something, yet the source of the
one is prior to that of the other. Therefore negative
demonstration will have an unqualified superiority to reductio
ad impossibile, and affirmative demonstration, being superior to
negative, will consequently be superior also to reductio ad
impossibile.
278
27
The science which is knowledge at once of the fact and of the
reasoned fact, not of the fact by itself without the reasoned fact,
is the more exact and the prior science.
A science such as arithmetic, which is not a science of
properties qua inhering in a substratum, is more exact than and
prior to a science like harmonics, which is a science of
properties inhering in a substratum; and similarly a science like
arithmetic, which is constituted of fewer basic elements, is
more exact than and prior to geometry, which requires
additional elements. What I mean by 'additional elements' is
this: a unit is substance without position, while a point is
substance with position; the latter contains an additional
element.
28
A single science is one whose domain is a single genus, viz. all
the subjects constituted out of the primary entities of the genus
- i.e. the parts of this total subject - and their essential
properties.
One science differs from another when their basic truths have
neither a common source nor are derived those of the one
science from those the other. This is verified when we reach the
indemonstrable premisses of a science, for they must be within
one genus with its conclusions: and this again is verified if the
conclusions proved by means of them fall within one genus -
i.e. are homogeneous.
279
29
One can have several demonstrations of the same connexion
not only by taking from the same series of predication middles
which are other than the immediately cohering term e.g. by
taking C, D, and F severally to prove A-B - but also by taking a
middle from another series. Thus let A be change, D alteration
of a property, B feeling pleasure, and G relaxation. We can then
without falsehood predicate D of B and A of D, for he who is
pleased suffers alteration of a property, and that which alters a
property changes. Again, we can predicate A of G without
falsehood, and G of B; for to feel pleasure is to relax, and to relax
is to change. So the conclusion can be drawn through middles
which are different, i.e. not in the same series - yet not so that
neither of these middles is predicable of the other, for they must
both be attributable to some one subject.
A further point worth investigating is how many ways of
proving the same conclusion can be obtained by varying the
figure.
30
There is no knowledge by demonstration of chance
conjunctions; for chance conjunctions exist neither by necessity
nor as general connexions but comprise what comes to be as
something distinct from these. Now demonstration is
concerned only with one or other of these two; for all reasoning
proceeds from necessary or general premisses, the conclusion
being necessary if the premisses are necessary and general if
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the premisses are general. Consequently, if chance conjunctions
are neither general nor necessary, they are not demonstrable.
31
Scientific knowledge is not possible through the act of
perception. Even if perception as a faculty is of 'the such' and
not merely of a 'this somewhat', yet one must at any rate
actually perceive a 'this somewhat', and at a definite present
place and time: but that which is commensurately universal
and true in all cases one cannot perceive, since it is not 'this'
and it is not 'now'; if it were, it would not be commensurately
universal - the term we apply to what is always and
everywhere. Seeing, therefore, that demonstrations are
commensurately universal and universals imperceptible, we
clearly cannot obtain scientific knowledge by the act of
perception: nay, it is obvious that even if it were possible to
perceive that a triangle has its angles equal to two right angles,
we should still be looking for a demonstration - we should not
(as some say) possess knowledge of it; for perception must be of
a particular, whereas scientific knowledge involves the
recognition of the commensurate universal. So if we were on
the moon, and saw the earth shutting out the sun's light, we
should not know the cause of the eclipse: we should perceive
the present fact of the eclipse, but not the reasoned fact at all,
since the act of perception is not of the commensurate
universal. I do not, of course, deny that by watching the
frequent recurrence of this event we might, after tracking the
commensurate universal, possess a demonstration, for the
commensurate universal is elicited from the several groups of
singulars.
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The commensurate universal is precious because it makes clear
the cause; so that in the case of facts like these which have a
cause other than themselves universal knowledge is more
precious than sense-perceptions and than intuition. (As regards
primary truths there is of course a different account to be
given.) Hence it is clear that knowledge of things demonstrable
cannot be acquired by perception, unless the term perception is
applied to the possession of scientific knowledge through
demonstration. Nevertheless certain points do arise with regard
to connexions to be proved which are referred for their
explanation to a failure in sense-perception: there are cases
when an act of vision would terminate our inquiry, not because
in seeing we should be knowing, but because we should have
elicited the universal from seeing; if, for example, we saw the
pores in the glass and the light passing through, the reason of
the kindling would be clear to us because we should at the
same time see it in each instance and intuit that it must be so
in all instances.
32
All syllogisms cannot have the same basic truths. This may be
shown first of all by the following dialectical considerations. (1)
Some syllogisms are true and some false: for though a true
inference is possible from false premisses, yet this occurs once
only - I mean if A for instance, is truly predicable of C, but B, the
middle, is false, both A-B and B-C being false; nevertheless, if
middles are taken to prove these premisses, they will be false
because every conclusion which is a falsehood has false
premisses, while true conclusions have true premisses, and
false and true differ in kind. Then again, (2) falsehoods are not
all derived from a single identical set of principles: there are
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falsehoods which are the contraries of one another and cannot
coexist, e.g. 'justice is injustice', and 'justice is cowardice'; 'man
is horse', and 'man is ox'; 'the equal is greater', and 'the equal is
less.' From established principles we may argue the case as
follows, confining ourselves therefore to true conclusions. Not
even all these are inferred from the same basic truths; many of
them in fact have basic truths which differ generically and are
not transferable; units, for instance, which are without position,
cannot take the place of points, which have position. The
transferred terms could only fit in as middle terms or as major
or minor terms, or else have some of the other terms between
them, others outside them.
Nor can any of the common axioms - such, I mean, as the law
of excluded middle - serve as premisses for the proof of all
conclusions. For the kinds of being are different, and some
attributes attach to quanta and some to qualia only; and proof
is achieved by means of the common axioms taken in
conjunction with these several kinds and their attributes.
Again, it is not true that the basic truths are much fewer than
the conclusions, for the basic truths are the premisses, and the
premisses are formed by the apposition of a fresh extreme term
or the interposition of a fresh middle. Moreover, the number of
conclusions is indefinite, though the number of middle terms is
finite; and lastly some of the basic truths are necessary, others
variable.
Looking at it in this way we see that, since the number of
conclusions is indefinite, the basic truths cannot be identical or
limited in number. If, on the other hand, identity is used in
another sense, and it is said, e.g. 'these and no other are the
fundamental truths of geometry, these the fundamentals of
calculation, these again of medicine'; would the statement
mean anything except that the sciences have basic truths? To
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call them identical because they are self-identical is absurd,
since everything can be identified with everything in that sense
of identity. Nor again can the contention that all conclusions
have the same basic truths mean that from the mass of all
possible premisses any conclusion may be drawn. That would
be exceedingly naive, for it is not the case in the clearly evident
mathematical sciences, nor is it possible in analysis, since it is
the immediate premisses which are the basic truths, and a
fresh conclusion is only formed by the addition of a new
immediate premiss: but if it be admitted that it is these primary
immediate premisses which are basic truths, each subject-
genus will provide one basic truth. If, however, it is not argued
that from the mass of all possible premisses any conclusion
may be proved, nor yet admitted that basic truths differ so as to
be generically different for each science, it remains to consider
the possibility that, while the basic truths of all knowledge are
within one genus, special premisses are required to prove
special conclusions. But that this cannot be the case has been
shown by our proof that the basic truths of things generically
different themselves differ generically. For fundamental truths
are of two kinds, those which are premisses of demonstration
and the subject-genus; and though the former are common, the
latter - number, for instance, and magnitude - are peculiar.
33
Scientific knowledge and its object differ from opinion and the
object of opinion in that scientific knowledge is
commensurately universal and proceeds by necessary
connexions, and that which is necessary cannot be otherwise.
So though there are things which are true and real and yet can
be otherwise, scientific knowledge clearly does not concern
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them: if it did, things which can be otherwise would be
incapable of being otherwise. Nor are they any concern of
rational intuition - by rational intuition I mean an originative
source of scientific knowledge - nor of indemonstrable
knowledge, which is the grasping of the immediate premiss.
Since then rational intuition, science, and opinion, and what is
revealed by these terms, are the only things that can be 'true', it
follows that it is opinion that is concerned with that which may
be true or false, and can be otherwise: opinion in fact is the
grasp of a premiss which is immediate but not necessary. This
view also fits the observed facts, for opinion is unstable, and so
is the kind of being we have described as its object. Besides,
when a man thinks a truth incapable of being otherwise he
always thinks that he knows it, never that he opines it. He
thinks that he opines when he thinks that a connexion, though
actually so, may quite easily be otherwise; for he believes that
such is the proper object of opinion, while the necessary is the
object of knowledge.
In what sense, then, can the same thing be the object of both
opinion and knowledge? And if any one chooses to maintain
that all that he knows he can also opine, why should not
opinion be knowledge? For he that knows and he that opines
will follow the same train of thought through the same middle
terms until the immediate premisses are reached; because it is
possible to opine not only the fact but also the reasoned fact,
and the reason is the middle term; so that, since the former
knows, he that opines also has knowledge.
The truth perhaps is that if a man grasp truths that cannot be
other than they are, in the way in which he grasps the
definitions through which demonstrations take place, he will
have not opinion but knowledge: if on the other hand he
apprehends these attributes as inhering in their subjects, but
not in virtue of the subjects' substance and essential nature
285
possesses opinion and not genuine knowledge; and his opinion,
if obtained through immediate premisses, will be both of the
fact and of the reasoned fact; if not so obtained, of the fact
alone. The object of opinion and knowledge is not quite
identical; it is only in a sense identical, just as the object of true
and false opinion is in a sense identical. The sense in which
some maintain that true and false opinion can have the same
object leads them to embrace many strange doctrines,
particularly the doctrine that what a man opines falsely he does
not opine at all. There are really many senses of 'identical', and
in one sense the object of true and false opinion can be the
same, in another it cannot. Thus, to have a true opinion that the
diagonal is commensurate with the side would be absurd: but
because the diagonal with which they are both concerned is the
same, the two opinions have objects so far the same: on the
other hand, as regards their essential definable nature these
objects differ. The identity of the objects of knowledge and
opinion is similar. Knowledge is the apprehension of, e.g. the
attribute 'animal' as incapable of being otherwise, opinion the
apprehension of 'animal' as capable of being otherwise - e.g. the
apprehension that animal is an element in the essential nature
of man is knowledge; the apprehension of animal as predicable
of man but not as an element in man's essential nature is
opinion: man is the subject in both judgements, but the mode
of inherence differs.
This also shows that one cannot opine and know the same
thing simultaneously; for then one would apprehend the same
thing as both capable and incapable of being otherwise - an
impossibility. Knowledge and opinion of the same thing can co-
exist in two different people in the sense we have explained,
but not simultaneously in the same person. That would involve
a man's simultaneously apprehending, e.g. (1) that man is
essentially animal - i.e. cannot be other than animal - and (2)
286
that man is not essentially animal, that is, we may assume, may
be other than animal.
Further consideration of modes of thinking and their
distribution under the heads of discursive thought, intuition,
science, art, practical wisdom, and metaphysical thinking,
belongs rather partly to natural science, partly to moral
philosophy.
34
Quick wit is a faculty of hitting upon the middle term
instantaneously. It would be exemplified by a man who saw
that the moon has her bright side always turned towards the
sun, and quickly grasped the cause of this, namely that she
borrows her light from him; or observed somebody in
conversation with a man of wealth and divined that he was
borrowing money, or that the friendship of these people sprang
from a common enmity. In all these instances he has seen the
major and minor terms and then grasped the causes, the
middle terms.
Let A represent 'bright side turned sunward', B 'lighted from the
sun', C the moon. Then B, 'lighted from the sun' is predicable of
C, the moon, and A, 'having her bright side towards the source
of her light', is predicable of B. So A is predicable of C through B.
287
Book II
The kinds of question we ask are as many as the kinds of things
which we know. They are in fact four: - (1) whether the
connexion of an attribute with a thing is a fact, (2) what is the
reason of the connexion, (3) whether a thing exists, (4) What is
the nature of the thing. Thus, when our question concerns a
complex of thing and attribute and we ask whether the thing is
thus or otherwise qualified - whether, e.g. the sun suffers
eclipse or not - then we are asking as to the fact of a connexion.
That our inquiry ceases with the discovery that the sun does
suffer eclipse is an indication of this; and if we know from the
start that the sun suffers eclipse, we do not inquire whether it
does so or not. On the other hand, when we know the fact we
ask the reason; as, for example, when we know that the sun is
being eclipsed and that an earthquake is in progress, it is the
reason of eclipse or earthquake into which we inquire.
Where a complex is concerned, then, those are the two
questions we ask; but for some objects of inquiry we have a
different kind of question to ask, such as whether there is or is
not a centaur or a God. (By 'is or is not' I mean 'is or is not,
without further qualification'; as opposed to 'is or is not [e.g.]
white'.) On the other hand, when we have ascertained the
thing's existence, we inquire as to its nature, asking, for
instance, 'what, then, is God?' or 'what is man?'.
288
These, then, are the four kinds of question we ask, and it is in
the answers to these questions that our knowledge consists.
Now when we ask whether a connexion is a fact, or whether a
thing without qualification is, we are really asking whether the
connexion or the thing has a 'middle'; and when we have
ascertained either that the connexion is a fact or that the thing
is - i.e. ascertained either the partial or the unqualified being of
the thing-and are proceeding to ask the reason of the connexion
or the nature of the thing, then we are asking what the 'middle'
is.
(By distinguishing the fact of the connexion and the existence
of the thing as respectively the partial and the unqualified being
of the thing, I mean that if we ask 'does the moon suffer
eclipse?', or 'does the moon wax?', the question concerns a part
of the thing's being; for what we are asking in such questions is
whether a thing is this or that, i.e. has or has not this or that
attribute: whereas, if we ask whether the moon or night exists,
the question concerns the unqualified being of a thing.)
We conclude that in all our inquiries we are asking either
whether there is a 'middle' or what the 'middle' is: for the
'middle' here is precisely the cause, and it is the cause that we
seek in all our inquiries. Thus, 'Does the moon suffer eclipse?'
means 'Is there or is there not a cause producing eclipse of the
moon?', and when we have learnt that there is, our next
question is, 'What, then, is this cause? for the cause through
which a thing is - not is this or that, i.e. has this or that
attribute, but without qualification is - and the cause through
which it is - not is without qualification, but is this or that as
having some essential attribute or some accident - are both
alike the middle'. By that which is without qualification I mean
the subject, e.g. moon or earth or sun or triangle; by that which
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a subject is (in the partial sense) I mean a property, e.g. eclipse,
equality or inequality, interposition or non-interposition. For in
all these examples it is clear that the nature of the thing and
the reason of the fact are identical: the question 'What is
eclipse?' and its answer 'The privation of the moon's light by the
interposition of the earth' are identical with the question 'What
is the reason of eclipse?' or 'Why does the moon suffer eclipse?'
and the reply 'Because of the failure of light through the earth's
shutting it out'. Again, for 'What is a concord? A commensurate
numerical ratio of a high and a low note', we may substitute
'What ratio makes a high and a low note concordant? Their
relation according to a commensurate numerical ratio.' 'Are the
high and the low note concordant?' is equivalent to 'Is their
ratio commensurate?'; and when we find that it is
commensurate, we ask 'What, then, is their ratio?'.
Cases in which the 'middle' is sensible show that the object of
our inquiry is always the 'middle': we inquire, because we have
not perceived it, whether there is or is not a 'middle' causing,
e.g. an eclipse. On the other hand, if we were on the moon we
should not be inquiring either as to the fact or the reason, but
both fact and reason would be obvious simultaneously. For the
act of perception would have enabled us to know the universal
too; since, the present fact of an eclipse being evident,
perception would then at the same time give us the present fact
of the earth's screening the sun's light, and from this would
arise the universal.
Thus, as we maintain, to know a thing's nature is to know the
reason why it is; and this is equally true of things in so far as
they are said without qualification to he as opposed to being
possessed of some attribute, and in so far as they are said to be
possessed of some attribute such as equal to right angles, or
greater or less.
290
It is clear, then, that all questions are a search for a 'middle'. Let
us now state how essential nature is revealed and in what way
it can be reduced to demonstration; what definition is, and
what things are definable. And let us first discuss certain
difficulties which these questions raise, beginning what we
have to say with a point most intimately connected with our
immediately preceding remarks, namely the doubt that might
be felt as to whether or not it is possible to know the same thing
in the same relation, both by definition and by demonstration. It
might, I mean, be urged that definition is held to concern
essential nature and is in every case universal and affirmative;
whereas, on the other hand, some conclusions are negative and
some are not universal; e.g. all in the second figure are negative,
none in the third are universal. And again, not even all
affirmative conclusions in the first figure are definable, e.g.
'every triangle has its angles equal to two right angles'. An
argument proving this difference between demonstration and
definition is that to have scientific knowledge of the
demonstrable is identical with possessing a demonstration of it:
hence if demonstration of such conclusions as these is possible,
there clearly cannot also be definition of them. If there could,
one might know such a conclusion also in virtue of its
definition without possessing the demonstration of it; for there
is nothing to stop our having the one without the other.
Induction too will sufficiently convince us of this difference; for
never yet by defining anything - essential attribute or accident -
did we get knowledge of it. Again, if to define is to acquire
knowledge of a substance, at any rate such attributes are not
substances.
291
It is evident, then, that not everything demonstrable can be
defined. What then? Can everything definable be demonstrated,
or not? There is one of our previous arguments which covers
this too. Of a single thing qua single there is a single scientific
knowledge. Hence, since to know the demonstrable
scientifically is to possess the demonstration of it, an
impossible consequence will follow: - possession of its
definition without its demonstration will give knowledge of the
demonstrable.
Moreover, the basic premisses of demonstrations are
definitions, and it has already been shown that these will be
found indemonstrable; either the basic premisses will be
demonstrable and will depend on prior premisses, and the
regress will be endless; or the primary truths will be
indemonstrable definitions.
But if the definable and the demonstrable are not wholly the
same, may they yet be partially the same? Or is that impossible,
because there can be no demonstration of the definable? There
can be none, because definition is of the essential nature or
being of something, and all demonstrations evidently posit and
assume the essential nature - mathematical demonstrations,
for example, the nature of unity and the odd, and all the other
sciences likewise. Moreover, every demonstration proves a
predicate of a subject as attaching or as not attaching to it, but
in definition one thing is not predicated of another; we do not,
e.g. predicate animal of biped nor biped of animal, nor yet figure
of plane - plane not being figure nor figure plane. Again, to
prove essential nature is not the same as to prove the fact of a
connexion. Now definition reveals essential nature,
demonstration reveals that a given attribute attaches or does
not attach to a given subject; but different things require
different demonstrations - unless the one demonstration is
related to the other as part to whole. I add this because if all
292
triangles have been proved to possess angles equal to two right
angles, then this attribute has been proved to attach to
isosceles; for isosceles is a part of which all triangles constitute
the whole. But in the case before us the fact and the essential
nature are not so related to one another, since the one is not a
part of the other.
So it emerges that not all the definable is demonstrable nor all
the demonstrable definable; and we may draw the general
conclusion that there is no identical object of which it is
possible to possess both a definition and a demonstration. It
follows obviously that definition and demonstration are neither
identical nor contained either within the other: if they were,
their objects would be related either as identical or as whole
and part.
So much, then, for the first stage of our problem. The next step
is to raise the question whether syllogism - i.e. demonstration -
of the definable nature is possible or, as our recent argument
assumed, impossible.
We might argue it impossible on the following grounds: - (a)
syllogism proves an attribute of a subject through the middle
term; on the other hand (b) its definable nature is both 'peculiar'
to a subject and predicated of it as belonging to its essence. But
in that case (1) the subject, its definition, and the middle term
connecting them must be reciprocally predicable of one
another; for if A is to C, obviously A is 'peculiar' to B and B to C -
in fact all three terms are 'peculiar' to one another: and further
(2) if A inheres in the essence of all B and B is predicated
293
universally of all C as belonging to C's essence, A also must be
predicated of C as belonging to its essence.
If one does not take this relation as thus duplicated - if, that is,
A is predicated as being of the essence of B, but B is not of the
essence of the subjects of which it is predicated - A will not
necessarily be predicated of C as belonging to its essence. So
both premisses will predicate essence, and consequently B also
will be predicated of C as its essence. Since, therefore, both
premisses do predicate essence - i.e. definable form - C's
definable form will appear in the middle term before the
conclusion is drawn.
We may generalize by supposing that it is possible to prove the
essential nature of man. Let C be man, A man's essential nature
- two-footed animal, or aught else it may be. Then, if we are to
syllogize, A must be predicated of all B. But this premiss will be
mediated by a fresh definition, which consequently will also be
the essential nature of man. Therefore the argument assumes
what it has to prove, since B too is the essential nature of man.
It is, however, the case in which there are only the two
premisses - i.e. in which the premisses are primary and
immediate - which we ought to investigate, because it best
illustrates the point under discussion.
Thus they who prove the essential nature of soul or man or
anything else through reciprocating terms beg the question. It
would be begging the question, for example, to contend that the
soul is that which causes its own life, and that what causes its
own life is a self-moving number; for one would have to
postulate that the soul is a self-moving number in the sense of
being identical with it. For if A is predicable as a mere
consequent of B and B of C, A will not on that account be the
definable form of C: A will merely be what it was true to say of
C. Even if A is predicated of all B inasmuch as B is identical with
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a species of A, still it will not follow: being an animal is
predicated of being a man - since it is true that in all instances
to be human is to be animal, just as it is also true that every
man is an animal - but not as identical with being man.
We conclude, then, that unless one takes both the premisses as
predicating essence, one cannot infer that A is the definable
form and essence of C: but if one does so take them, in
assuming B one will have assumed, before drawing the
conclusion, what the definable form of C is; so that there has
been no inference, for one has begged the question.
Nor, as was said in my formal logic, is the method of division a
process of inference at all, since at no point does the
characterization of the subject follow necessarily from the
premising of certain other facts: division demonstrates as little
as does induction. For in a genuine demonstration the
conclusion must not be put as a question nor depend on a
concession, but must follow necessarily from its premisses,
even if the respondent deny it. The definer asks 'Is man animal
or inanimate?' and then assumes - he has not inferred - that
man is animal. Next, when presented with an exhaustive
division of animal into terrestrial and aquatic, he assumes that
man is terrestrial. Moreover, that man is the complete formula,
terrestrial-animal, does not follow necessarily from the
premisses: this too is an assumption, and equally an
assumption whether the division comprises many differentiae
or few. (Indeed as this method of division is used by those who
proceed by it, even truths that can be inferred actually fail to
appear as such.) For why should not the whole of this formula
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be true of man, and yet not exhibit his essential nature or
definable form? Again, what guarantee is there against an
unessential addition, or against the omission of the final or of
an intermediate determinant of the substantial being?
The champion of division might here urge that though these
lapses do occur, yet we can solve that difficulty if all the
attributes we assume are constituents of the definable form,
and if, postulating the genus, we produce by division the
requisite uninterrupted sequence of terms, and omit nothing;
and that indeed we cannot fail to fulfil these conditions if what
is to be divided falls whole into the division at each stage, and
none of it is omitted; and that this - the dividendum - must
without further question be (ultimately) incapable of fresh
specific division. Nevertheless, we reply, division does not
involve inference; if it gives knowledge, it gives it in another
way. Nor is there any absurdity in this: induction, perhaps, is
not demonstration any more than is division, et it does make
evident some truth. Yet to state a definition reached by division
is not to state a conclusion: as, when conclusions are drawn
without their appropriate middles, the alleged necessity by
which the inference follows from the premisses is open to a
question as to the reason for it, so definitions reached by
division invite the same question.
Thus to the question 'What is the essential nature of man?' the
divider replies 'Animal, mortal, footed, biped, wingless'; and
when at each step he is asked 'Why?', he will say, and, as he
thinks, proves by division, that all animal is mortal or immortal:
but such a formula taken in its entirety is not definition; so that
even if division does demonstrate its formula, definition at any
rate does not turn out to be a conclusion of inference.
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Can we nevertheless actually demonstrate what a thing
essentially and substantially is, but hypothetically, i.e. by
premising (1) that its definable form is constituted by the
'peculiar' attributes of its essential nature; (2) that such and
such are the only attributes of its essential nature, and that the
complete synthesis of them is peculiar to the thing; and thus -
since in this synthesis consists the being of the thing -
obtaining our conclusion? Or is the truth that, since proof must
be through the middle term, the definable form is once more
assumed in this minor premiss too?
Further, just as in syllogizing we do not premise what syllogistic
inference is (since the premisses from which we conclude must
be related as whole and part), so the definable form must not
fall within the syllogism but remain outside the premisses
posited. It is only against a doubt as to its having been a
syllogistic inference at all that we have to defend our argument
as conforming to the definition of syllogism. It is only when
some one doubts whether the conclusion proved is the
definable form that we have to defend it as conforming to the
definition of definable form which we assumed. Hence
syllogistic inference must be possible even without the express
statement of what syllogism is or what definable form is.
The following type of hypothetical proof also begs the question.
If evil is definable as the divisible, and the definition of a thing's
contrary - if it has one the contrary of the thing's definition;
then, if good is the contrary of evil and the indivisible of the
divisible, we conclude that to be good is essentially to be
indivisible. The question is begged because definable form is
assumed as a premiss, and as a premiss which is to prove
definable form. 'But not the same definable form', you may
object. That I admit, for in demonstrations also we premise that
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'this' is predicable of 'that'; but in this premiss the term we
assert of the minor is neither the major itself nor a term
identical in definition, or convertible, with the major.
Again, both proof by division and the syllogism just described
are open to the question why man should be animal-biped-
terrestrial and not merely animal and terrestrial, since what
they premise does not ensure that the predicates shall
constitute a genuine unity and not merely belong to a single
subject as do musical and grammatical when predicated of the
same man.
How then by definition shall we prove substance or essential
nature? We cannot show it as a fresh fact necessarily following
from the assumption of premisses admitted to be facts - the
method of demonstration: we may not proceed as by induction
to establish a universal on the evidence of groups of particulars
which offer no exception, because induction proves not what
the essential nature of a thing is but that it has or has not some
attribute. Therefore, since presumably one cannot prove
essential nature by an appeal to sense perception or by pointing
with the finger, what other method remains?
To put it another way: how shall we by definition prove
essential nature? He who knows what human - or any other -
nature is, must know also that man exists; for no one knows the
nature of what does not exist - one can know the meaning of
the phrase or name 'goat-stag' but not what the essential
nature of a goat-stag is. But further, if definition can prove what
is the essential nature of a thing, can it also prove that it exists?
And how will it prove them both by the same process, since
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definition exhibits one single thing and demonstration another
single thing, and what human nature is and the fact that man
exists are not the same thing? Then too we hold that it is by
demonstration that the being of everything must be proved -
unless indeed to be were its essence; and, since being is not a
genus, it is not the essence of anything. Hence the being of
anything as fact is matter for demonstration; and this is the
actual procedure of the sciences, for the geometer assumes the
meaning of the word triangle, but that it is possessed of some
attribute he proves. What is it, then, that we shall prove in
defining essential nature? Triangle? In that case a man will
know by definition what a thing's nature is without knowing
whether it exists. But that is impossible.
Moreover it is clear, if we consider the methods of defining
actually in use, that definition does not prove that the thing
defined exists: since even if there does actually exist something
which is equidistant from a centre, yet why should the thing
named in the definition exist? Why, in other words, should this
be the formula defining circle? One might equally well call it the
definition of mountain copper. For definitions do not carry a
further guarantee that the thing defined can exist or that it is
what they claim to define: one can always ask why.
Since, therefore, to define is to prove either a thing's essential
nature or the meaning of its name, we may conclude that
definition, if it in no sense proves essential nature, is a set of
words signifying precisely what a name signifies. But that were
a strange consequence; for (1) both what is not substance and
what does not exist at all would be definable, since even non-
existents can be signified by a name: (2) all sets of words or
sentences would be definitions, since any kind of sentence
could be given a name; so that we should all be talking in
definitions, and even the Iliad would be a definition: (3) no
demonstration can prove that any particular name means any
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particular thing: neither, therefore, do definitions, in addition to
revealing the meaning of a name, also reveal that the name has
this meaning. It appears then from these considerations that
neither definition and syllogism nor their objects are identical,
and further that definition neither demonstrates nor proves
anything, and that knowledge of essential nature is not to be
obtained either by definition or by demonstration.
8
We must now start afresh and consider which of these
conclusions are sound and which are not, and what is the
nature of definition, and whether essential nature is in any
sense demonstrable and definable or in none.
Now to know its essential nature is, as we said, the same as to
know the cause of a thing's existence, and the proof of this
depends on the fact that a thing must have a cause. Moreover,
this cause is either identical with the essential nature of the
thing or distinct from it; and if its cause is distinct from it, the
essential nature of the thing is either demonstrable or
indemonstrable. Consequently, if the cause is distinct from the
thing's essential nature and demonstration is possible, the
cause must be the middle term, and, the conclusion proved
being universal and affirmative, the proof is in the first figure.
So the method just examined of proving it through another
essential nature would be one way of proving essential nature,
because a conclusion containing essential nature must be
inferred through a middle which is an essential nature just as a
'peculiar' property must be inferred through a middle which is a
'peculiar' property; so that of the two definable natures of a
single thing this method will prove one and not the other.
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Now it was said before that this method could not amount to
demonstration of essential nature - it is actually a dialectical
proof of it - so let us begin again and explain by what method it
can be demonstrated. When we are aware of a fact we seek its
reason, and though sometimes the fact and the reason dawn on
us simultaneously, yet we cannot apprehend the reason a
moment sooner than the fact; and clearly in just the same way
we cannot apprehend a thing's definable form without
apprehending that it exists, since while we are ignorant
whether it exists we cannot know its essential nature. Moreover
we are aware whether a thing exists or not sometimes through
apprehending an element in its character, and sometimes
accidentally, as, for example, when we are aware of thunder as a
noise in the clouds, of eclipse as a privation of light, or of man
as some species of animal, or of the soul as a self-moving thing.
As often as we have accidental knowledge that the thing exists,
we must be in a wholly negative state as regards awareness of
its essential nature; for we have not got genuine knowledge
even of its existence, and to search for a thing's essential nature
when we are unaware that it exists is to search for nothing. On
the other hand, whenever we apprehend an element in the
thing's character there is less difficulty. Thus it follows that the
degree of our knowledge of a thing's essential nature is
determined by the sense in which we are aware that it exists.
Let us then take the following as our first instance of being
aware of an element in the essential nature. Let A be eclipse, C
the moon, B the earth's acting as a screen. Now to ask whether
the moon is eclipsed or not is to ask whether or not B has
occurred. But that is precisely the same as asking whether A has
a defining condition; and if this condition actually exists, we
assert that A also actually exists. Or again we may ask which
side of a contradiction the defining condition necessitates: does
it make the angles of a triangle equal or not equal to two right
angles? When we have found the answer, if the premisses are
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immediate, we know fact and reason together; if they are not
immediate, we know the fact without the reason, as in the
following example: let C be the moon, A eclipse, B the fact that
the moon fails to produce shadows though she is full and
though no visible body intervenes between us and her. Then if
B, failure to produce shadows in spite of the absence of an
intervening body, is attributable A to C, and eclipse, is
attributable to B, it is clear that the moon is eclipsed, but the
reason why is not yet clear, and we know that eclipse exists, but
we do not know what its essential nature is. But when it is clear
that A is attributable to C and we proceed to ask the reason of
this fact, we are inquiring what is the nature of B: is it the
earth's acting as a screen, or the moon's rotation or her
extinction? But B is the definition of the other term, viz. in these
examples, of the major term A; for eclipse is constituted by the
earth acting as a screen. Thus, (1) 'What is thunder?' 'The
quenching of fire in cloud', and (2) 'Why does it thunder?'
'Because fire is quenched in the cloud', are equivalent. Let C be
cloud, A thunder, B the quenching of fire. Then B is attributable
to C, cloud, since fire is quenched in it; and A, noise, is
attributable to B; and B is assuredly the definition of the major
term A. If there be a further mediating cause of B, it will be one
of the remaining partial definitions of A.
We have stated then how essential nature is discovered and
becomes known, and we see that, while there is no syllogism -
i.e. no demonstrative syllogism - of essential nature, yet it is
through syllogism, viz. demonstrative syllogism, that essential
nature is exhibited. So we conclude that neither can the
essential nature of anything which has a cause distinct from
itself be known without demonstration, nor can it be
demonstrated; and this is what we contended in our
preliminary discussions.
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Now while some things have a cause distinct from themselves,
others have not. Hence it is evident that there are essential
natures which are immediate, that is are basic premisses; and
of these not only that they are but also what they are must be
assumed or revealed in some other way. This too is the actual
procedure of the arithmetician, who assumes both the nature
and the existence of unit. On the other hand, it is possible (in
the manner explained) to exhibit through demonstration the
essential nature of things which have a 'middle', i.e. a cause of
their substantial being other than that being itself; but we do
not thereby demonstrate it.
10
Since definition is said to be the statement of a thing's nature,
obviously one kind of definition will be a statement of the
meaning of the name, or of an equivalent nominal formula. A
definition in this sense tells you, e.g. the meaning of the phrase
'triangular character'. When we are aware that triangle exists,
we inquire the reason why it exists. But it is difficult thus to
learn the definition of things the existence of which we do not
genuinely know - the cause of this difficulty being, as we said
before, that we only know accidentally whether or not the thing
exists. Moreover, a statement may be a unity in either of two
ways, by conjunction, like the Iliad, or because it exhibits a
single predicate as inhering not accidentally in a single subject.
That then is one way of defining definition. Another kind of
definition is a formula exhibiting the cause of a thing's
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existence. Thus the former signifies without proving, but the
latter will clearly be a quasi-demonstration of essential nature,
differing from demonstration in the arrangement of its terms.
For there is a difference between stating why it thunders, and
stating what is the essential nature of thunder; since the first
statement will be 'Because fire is quenched in the clouds', while
the statement of what the nature of thunder is will be 'The
noise of fire being quenched in the clouds'. Thus the same
statement takes a different form: in one form it is continuous
demonstration, in the other definition. Again, thunder can be
defined as noise in the clouds, which is the conclusion of the
demonstration embodying essential nature. On the other hand
the definition of immediates is an indemonstrable positing of
essential nature.
We conclude then that definition is (a) an indemonstrable
statement of essential nature, or (b) a syllogism of essential
nature differing from demonstration in grammatical form, or (c)
the conclusion of a demonstration giving essential nature.
Our discussion has therefore made plain (1) in what sense and
of what things the essential nature is demonstrable, and in
what sense and of what things it is not; (2) what are the various
meanings of the term definition, and in what sense and of what
things it proves the essential nature, and in what sense and of
what things it does not; (3) what is the relation of definition to
demonstration, and how far the same thing is both definable
and demonstrable and how far it is not.
11
We think we have scientific knowledge when we know the
cause, and there are four causes: (1) the definable form, (2) an
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antecedent which necessitates a consequent, (3) the efficient
cause, (4) the final cause. Hence each of these can be the middle
term of a proof, for (a) though the inference from antecedent to
necessary consequent does not hold if only one premiss is
assumed - two is the minimum - still when there are two it
holds on condition that they have a single common middle
term. So it is from the assumption of this single middle term
that the conclusion follows necessarily. The following example
will also show this. Why is the angle in a semicircle a right
angle? - or from what assumption does it follow that it is a right
angle? Thus, let A be right angle, B the half of two right angles, C
the angle in a semicircle. Then B is the cause in virtue of which
A, right angle, is attributable to C, the angle in a semicircle,
since B=A and the other, viz. C,=B, for C is half of two right
angles. Therefore it is the assumption of B, the half of two right
angles, from which it follows that A is attributable to C, i.e. that
the angle in a semicircle is a right angle. Moreover, B is identical
with (b) the defining form of A, since it is what As definition
signifies. Moreover, the formal cause has already been shown to
be the middle, (c) 'Why did the Athenians become involved in
the Persian war?' means 'What cause originated the waging of
war against the Athenians?' and the answer is, 'Because they
raided Sardis with the Eretrians', since this originated the war.
Let A be war, B unprovoked raiding, C the Athenians. Then B,
unprovoked raiding, is true of C, the Athenians, and A is true of
B, since men make war on the unjust aggressor. So A, having
war waged upon them, is true of B, the initial aggressors, and B
is true of C, the Athenians, who were the aggressors. Hence here
too the cause - in this case the efficient cause - is the middle
term, (d) This is no less true where the cause is the final cause.
E.g. why does one take a walk after supper? For the sake of one's
health. Why does a house exist? For the preservation of one's
goods. The end in view is in the one case health, in the other
preservation. To ask the reason why one must walk after supper
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is precisely to ask to what end one must do it. Let C be walking
after supper, B the non-regurgitation of food, A health. Then let
walking after supper possess the property of preventing food
from rising to the orifice of the stomach, and let this condition
be healthy; since it seems that B, the non-regurgitation of food,
is attributable to C, taking a walk, and that A, health, is
attributable to B. What, then, is the cause through which A, the
final cause, inheres in C? It is B, the non-regurgitation of food;
but B is a kind of definition of A, for A will be explained by it.
Why is B the cause of A's belonging to C? Because to be in a
condition such as B is to be in health. The definitions must be
transposed, and then the detail will become clearer.
Incidentally, here the order of coming to be is the reverse of
what it is in proof through the efficient cause: in the efficient
order the middle term must come to be first, whereas in the
teleological order the minor, C, must first take place, and the
end in view comes last in time.
The same thing may exist for an end and be necessitated as
well. For example, light shines through a lantern (1) because
that which consists of relatively small particles necessarily
passes through pores larger than those particles - assuming
that light does issue by penetration - and (2) for an end, namely
to save us from stumbling. If then, a thing can exist through two
causes, can it come to be through two causes - as for instance if
thunder be a hiss and a roar necessarily produced by the
quenching of fire, and also designed, as the Pythagoreans say,
for a threat to terrify those that lie in Tartarus? Indeed, there are
very many such cases, mostly among the processes and
products of the natural world; for nature, in different senses of
the term 'nature', produces now for an end, now by necessity.
Necessity too is of two kinds. It may work in accordance with a
thing's natural tendency, or by constraint and in opposition to it;
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as, for instance, by necessity a stone is borne both upwards and
downwards, but not by the same necessity.
Of the products of man's intelligence some are never due to
chance or necessity but always to an end, as for example a
house or a statue; others, such as health or safety, may result
from chance as well.
It is mostly in cases where the issue is indeterminate (though
only where the production does not originate in chance, and the
end is consequently good), that a result is due to an end, and
this is true alike in nature or in art. By chance, on the other
hand, nothing comes to be for an end.
12
The effect may be still coming to be, or its occurrence may be
past or future, yet the cause will be the same as when it is
actually existent - for it is the middle which is the cause -
except that if the effect actually exists the cause is actually
existent, if it is coming to be so is the cause, if its occurrence is
past the cause is past, if future the cause is future. For example,
the moon was eclipsed because the earth intervened, is
becoming eclipsed because the earth is in process of
intervening, will be eclipsed because the earth will intervene, is
eclipsed because the earth intervenes.
To take a second example: assuming that the definition of ice is
solidified water, let C be water, A solidified, B the middle, which
is the cause, namely total failure of heat. Then B is attributed to
C, and A, solidification, to B: ice when B is occurring, has formed
when B has occurred, and will form when B shall occur.
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This sort of cause, then, and its effect come to be
simultaneously when they are in process of becoming, and exist
simultaneously when they actually exist; and the same holds
good when they are past and when they are future. But what of
cases where they are not simultaneous? Can causes and effects
different from one another form, as they seem to us to form, a
continuous succession, a past effect resulting from a past cause
different from itself, a future effect from a future cause different
from it, and an effect which is coming-to-be from a cause
different from and prior to it? Now on this theory it is from the
posterior event that we reason (and this though these later
events actually have their source of origin in previous events - a
fact which shows that also when the effect is coming-to-be we
still reason from the posterior event), and from the event we
cannot reason (we cannot argue that because an event A has
occurred, therefore an event B has occurred subsequently to A
but still in the past - and the same holds good if the occurrence
is future) - cannot reason because, be the time interval definite
or indefinite, it will never be possible to infer that because it is
true to say that A occurred, therefore it is true to say that B, the
subsequent event, occurred; for in the interval between the
events, though A has already occurred, the latter statement will
be false. And the same argument applies also to future events;
i.e. one cannot infer from an event which occurred in the past
that a future event will occur. The reason of this is that the
middle must be homogeneous, past when the extremes are
past, future when they are future, coming to be when they are
coming-to-be, actually existent when they are actually existent;
and there cannot be a middle term homogeneous with
extremes respectively past and future. And it is a further
difficulty in this theory that the time interval can be neither
indefinite nor definite, since during it the inference will be false.
We have also to inquire what it is that holds events together so
that the coming-to-be now occurring in actual things follows
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upon a past event. It is evident, we may suggest, that a past
event and a present process cannot be 'contiguous', for not even
two past events can be 'contiguous'. For past events are limits
and atomic; so just as points are not 'contiguous' neither are
past events, since both are indivisible. For the same reason a
past event and a present process cannot be 'contiguous', for the
process is divisible, the event indivisible. Thus the relation of
present process to past event is analogous to that of line to
point, since a process contains an infinity of past events. These
questions, however, must receive a more explicit treatment in
our general theory of change.
The following must suffice as an account of the manner in
which the middle would be identical with the cause on the
supposition that coming-to-be is a series of consecutive events:
for in the terms of such a series too the middle and major terms
must form an immediate premiss; e.g. we argue that, since C
has occurred, therefore A occurred: and C's occurrence was
posterior, A's prior; but C is the source of the inference because
it is nearer to the present moment, and the starting-point of
time is the present. We next argue that, since D has occurred,
therefore C occurred. Then we conclude that, since D has
occurred, therefore A must have occurred; and the cause is C,
for since D has occurred C must have occurred, and since C has
occurred A must previously have occurred.
If we get our middle term in this way, will the series terminate
in an immediate premiss, or since, as we said, no two events are
'contiguous', will a fresh middle term always intervene because
there is an infinity of middles? No: though no two events are
'contiguous', yet we must start from a premiss consisting of a
middle and the present event as major. The like is true of future
events too, since if it is true to say that D will exist, it must be a
prior truth to say that A will exist, and the cause of this
conclusion is C; for if D will exist, C will exist prior to D, and if C
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will exist, A will exist prior to it. And here too the same infinite
divisibility might be urged, since future events are not
'contiguous'. But here too an immediate basic premiss must be
assumed. And in the world of fact this is so: if a house has been
built, then blocks must have been quarried and shaped. The
reason is that a house having been built necessitates a
foundation having been laid, and if a foundation has been laid
blocks must have been shaped beforehand. Again, if a house
will be built, blocks will similarly be shaped beforehand; and
proof is through the middle in the same way, for the foundation
will exist before the house.
Now we observe in Nature a certain kind of circular process of
coming-to-be; and this is possible only if the middle and
extreme terms are reciprocal, since conversion is conditioned by
reciprocity in the terms of the proof. This - the convertibility of
conclusions and premisses - has been proved in our early
chapters, and the circular process is an instance of this. In
actual fact it is exemplified thus: when the earth had been
moistened an exhalation was bound to rise, and when an
exhalation had risen cloud was bound to form, and from the
formation of cloud rain necessarily resulted and by the fall of
rain the earth was necessarily moistened: but this was the
starting-point, so that a circle is completed; for posit any one of
the terms and another follows from it, and from that another,
and from that again the first.
Some occurrences are universal (for they are, or come-to-be
what they are, always and in ever case); others again are not
always what they are but only as a general rule: for instance,
not every man can grow a beard, but it is the general rule. In the
case of such connexions the middle term too must be a general
rule. For if A is predicated universally of B and B of C, A too must
be predicated always and in every instance of C, since to hold in
every instance and always is of the nature of the universal. But
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we have assumed a connexion which is a general rule;
consequently the middle term B must also be a general rule. So
connexions which embody a general rule - i.e. which exist or
come to be as a general rule - will also derive from immediate
basic premisses.
13
We have already explained how essential nature is set out in
the terms of a demonstration, and the sense in which it is or is
not demonstrable or definable; so let us now discuss the
method to be adopted in tracing the elements predicated as
constituting the definable form.
Now of the attributes which inhere always in each several thing
there are some which are wider in extent than it but not wider
than its genus (by attributes of wider extent mean all such as
are universal attributes of each several subject, but in their
application are not confined to that subject), while an attribute
may inhere in every triad, yet also in a subject not a triad - as
being inheres in triad but also in subjects not numbers at all -
odd on the other hand is an attribute inhering in every triad and
of wider application (inhering as it does also in pentad), but
which does not extend beyond the genus of triad; for pentad is a
number, but nothing outside number is odd. It is such attributes
which we have to select, up to the exact point at which they are
severally of wider extent than the subject but collectively
coextensive with it; for this synthesis must be the substance of
the thing. For example every triad possesses the attributes
number, odd, and prime in both senses, i.e. not only as
possessing no divisors, but also as not being a sum of numbers.
This, then, is precisely what triad is, viz. a number, odd, and
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prime in the former and also the latter sense of the term: for
these attributes taken severally apply, the first two to all odd
numbers, the last to the dyad also as well as to the triad, but,
taken collectively, to no other subject. Now since we have
shown above' that attributes predicated as belonging to the
essential nature are necessary and that universals are
necessary, and since the attributes which we select as inhering
in triad, or in any other subject whose attributes we select in
this way, are predicated as belonging to its essential nature,
triad will thus possess these attributes necessarily. Further, that
the synthesis of them constitutes the substance of triad is
shown by the following argument. If it is not identical with the
being of triad, it must be related to triad as a genus named or
nameless. It will then be of wider extent than triad - assuming
that wider potential extent is the character of a genus. If on the
other hand this synthesis is applicable to no subject other than
the individual triads, it will be identical with the being of triad,
because we make the further assumption that the substance of
each subject is the predication of elements in its essential
nature down to the last differentia characterizing the
individuals. It follows that any other synthesis thus exhibited
will likewise be identical with the being of the subject.
The author of a hand-book on a subject that is a generic whole
should divide the genus into its first infimae species - number
e.g. into triad and dyad - and then endeavour to seize their
definitions by the method we have described - the definition,
for example, of straight line or circle or right angle. After that,
having established what the category is to which the subaltern
genus belongs - quantity or quality, for instance - he should
examine the properties 'peculiar' to the species, working
through the proximate common differentiae. He should proceed
thus because the attributes of the genera compounded of the
infimae species will be clearly given by the definitions of the
species; since the basic element of them all is the definition, i.e.
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the simple infirma species, and the attributes inhere essentially
in the simple infimae species, in the genera only in virtue of
these.
Divisions according to differentiae are a useful accessory to this
method. What force they have as proofs we did, indeed, explain
above, but that merely towards collecting the essential nature
they may be of use we will proceed to show. They might, indeed,
seem to be of no use at all, but rather to assume everything at
the start and to be no better than an initial assumption made
without division. But, in fact, the order in which the attributes
are predicated does make a difference - it matters whether we
say animal-tame-biped, or biped-animal-tame. For if every
definable thing consists of two elements and 'animal-tame'
forms a unity, and again out of this and the further differentia
man (or whatever else is the unity under construction) is
constituted, then the elements we assume have necessarily
been reached by division. Again, division is the only possible
method of avoiding the omission of any element of the
essential nature. Thus, if the primary genus is assumed and we
then take one of the lower divisions, the dividendum will not
fall whole into this division: e.g. it is not all animal which is
either whole-winged or split-winged but all winged animal, for
it is winged animal to which this differentiation belongs. The
primary differentiation of animal is that within which all
animal falls. The like is true of every other genus, whether
outside animal or a subaltern genus of animal; e.g. the primary
differentiation of bird is that within which falls every bird, of
fish that within which falls every fish. So, if we proceed in this
way, we can be sure that nothing has been omitted: by any
other method one is bound to omit something without knowing
it.
To define and divide one need not know the whole of existence.
Yet some hold it impossible to know the differentiae
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distinguishing each thing from every single other thing without
knowing every single other thing; and one cannot, they say,
know each thing without knowing its differentiae, since
everything is identical with that from which it does not differ,
and other than that from which it differs. Now first of all this is
a fallacy: not every differentia precludes identity, since many
differentiae inhere in things specifically identical, though not in
the substance of these nor essentially Secondly, when one has
taken one's differing pair of opposites and assumed that the
two sides exhaust the genus, and that the subject one seeks to
define is present in one or other of them, and one has further
verified its presence in one of them; then it does not matter
whether or not one knows all the other subjects of which the
differentiae are also predicated. For it is obvious that when by
this process one reaches subjects incapable of further
differentiation one will possess the formula defining the
substance. Moreover, to postulate that the division exhausts the
genus is not illegitimate if the opposites exclude a middle; since
if it is the differentia of that genus, anything contained in the
genus must lie on one of the two sides.
In establishing a definition by division one should keep three
objects in view: (1) the admission only of elements in the
definable form, (2) the arrangement of these in the right order,
(3) the omission of no such elements. The first is feasible
because one can establish genus and differentia through the
topic of the genus, just as one can conclude the inherence of an
accident through the topic of the accident. The right order will
be achieved if the right term is assumed as primary, and this
will be ensured if the term selected is predicable of all the
others but not all they of it; since there must be one such term.
Having assumed this we at once proceed in the same way with
the lower terms; for our second term will be the first of the
remainder, our third the first of those which follow the second
in a 'contiguous' series, since when the higher term is excluded,
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that term of the remainder which is 'contiguous' to it will be
primary, and so on. Our procedure makes it clear that no
elements in the definable form have been omitted: we have
taken the differentia that comes first in the order of division,
pointing out that animal, e.g. is divisible exhaustively into A and
B, and that the subject accepts one of the two as its predicate.
Next we have taken the differentia of the whole thus reached,
and shown that the whole we finally reach is not further
divisible - i.e. that as soon as we have taken the last differentia
to form the concrete totality, this totality admits of no division
into species. For it is clear that there is no superfluous addition,
since all these terms we have selected are elements in the
definable form; and nothing lacking, since any omission would
have to be a genus or a differentia. Now the primary term is a
genus, and this term taken in conjunction with its differentiae
is a genus: moreover the differentiae are all included, because
there is now no further differentia; if there were, the final
concrete would admit of division into species, which, we said, is
not the case.
To resume our account of the right method of investigation: We
must start by observing a set of similar - i.e. specifically
identical - individuals, and consider what element they have in
common. We must then apply the same process to another set
of individuals which belong to one species and are generically
but not specifically identical with the former set. When we have
established what the common element is in all members of this
second species, and likewise in members of further species, we
should again consider whether the results established possess
any identity, and persevere until we reach a single formula,
since this will be the definition of the thing. But if we reach not
one formula but two or more, evidently the definiendum cannot
be one thing but must be more than one. I may illustrate my
meaning as follows. If we were inquiring what the essential
nature of pride is, we should examine instances of proud men
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we know of to see what, as such, they have in common; e.g. if
Alcibiades was proud, or Achilles and Ajax were proud, we
should find on inquiring what they all had in common, that it
was intolerance of insult; it was this which drove Alcibiades to
war, Achilles wrath, and Ajax to suicide. We should next
examine other cases, Lysander, for example, or Socrates, and
then if these have in common indifference alike to good and ill
fortune, I take these two results and inquire what common
element have equanimity amid the vicissitudes of life and
impatience of dishonour. If they have none, there will be two
genera of pride. Besides, every definition is always universal and
commensurate: the physician does not prescribe what is
healthy for a single eye, but for all eyes or for a determinate
species of eye. It is also easier by this method to define the
single species than the universal, and that is why our procedure
should be from the several species to the universal genera - this
for the further reason too that equivocation is less readily
detected in genera than in infimae species. Indeed, perspicuity
is essential in definitions, just as inferential movement is the
minimum required in demonstrations; and we shall attain
perspicuity if we can collect separately the definition of each
species through the group of singulars which we have
established e.g. the definition of similarity not unqualified but
restricted to colours and to figures; the definition of acuteness,
but only of sound - and so proceed to the common universal
with a careful avoidance of equivocation. We may add that if
dialectical disputation must not employ metaphors, clearly
metaphors and metaphorical expressions are precluded in
definition: otherwise dialectic would involve metaphors.
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14
In order to formulate the connexions we wish to prove we have
to select our analyses and divisions. The method of selection
consists in laying down the common genus of all our subjects of
investigation - if e.g. they are animals, we lay down what the
properties are which inhere in every animal. These established,
we next lay down the properties essentially connected with the
first of the remaining classes - e.g. if this first subgenus is bird,
the essential properties of every bird - and so on, always
characterizing the proximate subgenus. This will clearly at once
enable us to say in virtue of what character the subgenera -
man, e.g. or horse - possess their properties. Let A be animal, B
the properties of every animal, C D E various species of animal.
Then it is clear in virtue of what character B inheres in D -
namely A - and that it inheres in C and E for the same reason:
and throughout the remaining subgenera always the same rule
applies.
We are now taking our examples from the traditional class-
names, but we must not confine ourselves to considering these.
We must collect any other common character which we
observe, and then consider with what species it is connected
and what.properties belong to it. For example, as the common
properties of horned animals we collect the possession of a
third stomach and only one row of teeth. Then since it is clear
in virtue of what character they possess these attributes -
namely their horned character - the next question is, to what
species does the possession of horns attach?
Yet a further method of selection is by analogy: for we cannot
find a single identical name to give to a squid's pounce, a fish's
spine, and an animal's bone, although these too possess
common properties as if there were a single osseous nature.
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15
Some connexions that require proof are identical in that they
possess an identical 'middle' e.g. a whole group might be proved
through 'reciprocal replacement' - and of these one class are
identical in genus, namely all those whose difference consists
in their concerning different subjects or in their mode of
manifestation. This latter class may be exemplified by the
questions as to the causes respectively of echo, of reflection,
and of the rainbow: the connexions to be proved which these
questions embody are identical generically, because all three are
forms of repercussion; but specifically they are different.
Other connexions that require proof only differ in that the
'middle' of the one is subordinate to the 'middle' of the other.
For example: Why does the Nile rise towards the end of the
month? Because towards its close the month is more stormy.
Why is the month more stormy towards its close? Because the
moon is waning. Here the one cause is subordinate to the other.
16
The question might be raised with regard to cause and effect
whether when the effect is present the cause also is present;
whether, for instance, if a plant sheds its leaves or the moon is
eclipsed, there is present also the cause of the eclipse or of the
fall of the leaves - the possession of broad leaves, let us say, in
the latter case, in the former the earth's interposition. For, one
might argue, if this cause is not present, these phenomena will
have some other cause: if it is present, its effect will be at once
implied by it - the eclipse by the earth's interposition, the fall of
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the leaves by the possession of broad leaves; but if so, they will
be logically coincident and each capable of proof through the
other. Let me illustrate: Let A be deciduous character, B the
possession of broad leaves, C vine. Now if A inheres in B (for
every broad-leaved plant is deciduous), and B in C (every vine
possessing broad leaves); then A inheres in C (every vine is
deciduous), and the middle term B is the cause. But we can also
demonstrate that the vine has broad leaves because it is
deciduous. Thus, let D be broad-leaved, E deciduous, F vine.
Then E inheres in F (since every vine is deciduous), and D in E
(for every deciduous plant has broad leaves): therefore every
vine has broad leaves, and the cause is its deciduous character.
If, however, they cannot each be the cause of the other (for
cause is prior to effect, and the earth's interposition is the cause
of the moon's eclipse and not the eclipse of the interposition) -
if, then, demonstration through the cause is of the reasoned
fact and demonstration not through the cause is of the bare
fact, one who knows it through the eclipse knows the fact of the
earth's interposition but not the reasoned fact. Moreover, that
the eclipse is not the cause of the interposition, but the
interposition of the eclipse, is obvious because the interposition
is an element in the definition of eclipse, which shows that the
eclipse is known through the interposition and not vice versa.
On the other hand, can a single effect have more than one
cause? One might argue as follows: if the same attribute is
predicable of more than one thing as its primary subject, let B
be a primary subject in which A inheres, and C another primary
subject of A, and D and E primary subjects of B and C
respectively. A will then inhere in D and E, and B will be the
cause of As inherence in D, C of As inherence in E.The presence
of the cause thus necessitates that of the effect, but the
presence of the effect necessitates the presence not of all that
may cause it but only of a cause which yet need not be the
whole cause. We may, however, suggest that if the connexion to
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be proved is always universal and commensurate, not only will
the cause be a whole but also the effect will be universal and
commensurate. For instance, deciduous character will belong
exclusively to a subject which is a whole, and, if this whole has
species, universally and commensurately to those species - i.e.
either to all species of plant or to a single species. So in these
universal and commensurate connexions the 'middle' and its
effect must reciprocate, i.e. be convertible. Supposing, for
example, that the reason why trees are deciduous is the
coagulation of sap, then if a tree is deciduous, coagulation must
be present, and if coagulation is present - not in any subject but
in a tree - then that tree must be deciduous.
17
Can the cause of an identical effect be not identical in every
instance of the effect but different? Or is that impossible?
Perhaps it is impossible if the effect is demonstrated as
essential and not as inhering in virtue of a symptom or an
accident - because the middle is then the definition of the
major term - though possible if the demonstration is not
essential. Now it is possible to consider the effect and its subject
as an accidental conjunction, though such conjunctions would
not be regarded as connexions demanding scientific proof. But
if they are accepted as such, the middle will correspond to the
extremes, and be equivocal if they are equivocal, generically one
if they are generically one. Take the question why proportionals
alternate. The cause when they are lines, and when they are
numbers, is both different and identical; different in so far as
lines are lines and not numbers, identical as involving a given
determinate increment. In all proportionals this is so. Again, the
cause of likeness between colour and colour is other than that
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between figure and figure; for likeness here is equivocal,
meaning perhaps in the latter case equality of the ratios of the
sides and equality of the angles, in the case of colours identity
of the act of perceiving them, or something else of the sort.
Again, connexions requiring proof which are identical by
analogy middles also analogous.
The truth is that cause, effect, and subject are reciprocally
predicable in the following way. If the species are taken
severally, the effect is wider than the subject (e.g. the possession
of external angles equal to four right angles is an attribute
wider than triangle or are), but it is coextensive with the species
taken collectively (in this instance with all figures whose
external angles are equal to four right angles). And the middle
likewise reciprocates, for the middle is a definition of the major;
which is incidentally the reason why all the sciences are built
up through definition.
We may illustrate as follows. Deciduous is a universal attribute
of vine, and is at the same time of wider extent than vine; and
of fig, and is of wider extent than fig: but it is not wider than but
coextensive with the totality of the species. Then if you take the
middle which is proximate, it is a definition of deciduous. I say
that, because you will first reach a middle next the subject, and
a premiss asserting it of the whole subject, and after that a
middle - the coagulation of sap or something of the sort -
proving the connexion of the first middle with the major: but it
is the coagulation of sap at the junction of leaf-stalk and stem
which defines deciduous.
If an explanation in formal terms of the inter-relation of cause
and effect is demanded, we shall offer the following. Let A be an
attribute of all B, and B of every species of D, but so that both A
and B are wider than their respective subjects. Then B will be a
universal attribute of each species of D (since I call such an
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attribute universal even if it is not commensurate, and I call an
attribute primary universal if it is commensurate, not with each
species severally but with their totality), and it extends beyond
each of them taken separately.
Thus, B is the cause of A's inherence in the species of D:
consequently A must be of wider extent than B; otherwise why
should B be the cause of A's inherence in D any more than A the
cause of B's inherence in D? Now if A is an attribute of all the
species of E, all the species of E will be united by possessing
some common cause other than B: otherwise how shall we be
able to say that A is predicable of all of which E is predicable,
while E is not predicable of all of which A can be predicated? I
mean how can there fail to be some special cause of A's
inherence in E, as there was of A's inherence in all the species of
D? Then are the species of E, too, united by possessing some
common cause? This cause we must look for. Let us call it C.
We conclude, then, that the same effect may have more than
one cause, but not in subjects specifically identical. For
instance, the cause of longevity in quadrupeds is lack of bile, in
birds a dry constitution - or certainly something different.
18
If immediate premisses are not reached at once, and there is
not merely one middle but several middles, i.e. several causes; is
the cause of the property's inherence in the several species the
middle which is proximate to the primary universal, or the
middle which is proximate to the species? Clearly the cause is
that nearest to each species severally in which it is manifested,
for that is the cause of the subject's falling under the universal.
To illustrate formally: C is the cause of B's inherence in D; hence
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C is the cause of A's inherence in D, B of A's inherence in C,
while the cause of A's inherence in B is B itself.
19
As regards syllogism and demonstration, the definition of, and
the conditions required to produce each of them, are now clear,
and with that also the definition of, and the conditions required
to produce, demonstrative knowledge, since it is the same as
demonstration. As to the basic premisses, how they become
known and what is the developed state of knowledge of them is
made clear by raising some preliminary problems.
We have already said that scientific knowledge through
demonstration is impossible unless a man knows the primary
immediate premisses. But there are questions which might be
raised in respect of the apprehension of these immediate
premisses: one might not only ask whether it is of the same
kind as the apprehension of the conclusions, but also whether
there is or is not scientific knowledge of both; or scientific
knowledge of the latter, and of the former a different kind of
knowledge; and, further, whether the developed states of
knowledge are not innate but come to be in us, or are innate but
at first unnoticed. Now it is strange if we possess them from
birth; for it means that we possess apprehensions more
accurate than demonstration and fail to notice them. If on the
other hand we acquire them and do not previously possess
them, how could we apprehend and learn without a basis of
pre-existent knowledge? For that is impossible, as we used to
find in the case of demonstration. So it emerges that neither
can we possess them from birth, nor can they come to be in us
if we are without knowledge of them to the extent of having no
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such developed state at all. Therefore we must possess a
capacity of some sort, but not such as to rank higher in accuracy
than these developed states. And this at least is an obvious
characteristic of all animals, for they possess a congenital
discriminative capacity which is called sense-perception. But
though sense-perception is innate in all animals, in some the
sense-impression comes to persist, in others it does not. So
animals in which this persistence does not come to be have
either no knowledge at all outside the act of perceiving, or no
knowledge of objects of which no impression persists; animals
in which it does come into being have perception and can
continue to retain the sense-impression in the soul: and when
such persistence is frequently repeated a further distinction at
once arises between those which out of the persistence of such
sense-impressions develop a power of systematizing them and
those which do not. So out of sense-perception comes to be
what we call memory, and out of frequently repeated memories
of the same thing develops experience; for a number of
memories constitute a single experience. From experience again
- i.e. from the universal now stabilized in its entirety within the
soul, the one beside the many which is a single identity within
them all - originate the skill of the craftsman and the
knowledge of the man of science, skill in the sphere of coming
to be and science in the sphere of being.
We conclude that these states of knowledge are neither innate
in a determinate form, nor developed from other higher states
of knowledge, but from sense-perception. It is like a rout in
battle stopped by first one man making a stand and then
another, until the original formation has been restored. The soul
is so constituted as to be capable of this process.
Let us now restate the account given already, though with
insufficient clearness. When one of a number of logically
indiscriminable particulars has made a stand, the earliest
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universal is present in the soul: for though the act of sense-
perception is of the particular, its content is universal - is man,
for example, not the man Callias. A fresh stand is made among
these rudimentary universals, and the process does not cease
until the indivisible concepts, the true universals, are
established: e.g. such and such a species of animal is a step
towards the genus animal, which by the same process is a step
towards a further generalization.
Thus it is clear that we must get to know the primary premisses
by induction; for the method by which even sense-perception
implants the universal is inductive. Now of the thinking states
by which we grasp truth, some are unfailingly true, others admit
of error - opinion, for instance, and calculation, whereas
scientific knowing and intuition are always true: further, no
other kind of thought except intuition is more accurate than
scientific knowledge, whereas primary premisses are more
knowable than demonstrations, and all scientific knowledge is
discursive. From these considerations it follows that there will
be no scientific knowledge of the primary premisses, and since
except intuition nothing can be truer than scientific knowledge,
it will be intuition that apprehends the primary premisses - a
result which also follows from the fact that demonstration
cannot be the originative source of demonstration, nor,
consequently, scientific knowledge of scientific knowledge. If,
therefore, it is the only other kind of true thinking except
scientific knowing, intuition will be the originative source of
scientific knowledge. And the originative source of science
grasps the original basic premiss, while science as a whole is
similarly related as originative source to the whole body of fact.
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Aristotle - Topics
[Translated by W. A. Pickard-Cambridge]
Book I
Our treatise proposes to find a line of inquiry whereby we shall
be able to reason from opinions that are generally accepted
about every problem propounded to us, and also shall ourselves,
when standing up to an argument, avoid saying anything that
will obstruct us. First, then, we must say what reasoning is, and
what its varieties are, in order to grasp dialectical reasoning: for
this is the object of our search in the treatise before us.
Now reasoning is an argument in which, certain things being
laid down, something other than these necessarily comes about
through them, (a) It is a 'demonstration', when the premisses
from which the reasoning starts are true and primary, or are
such that our knowledge of them has originally come through
premisses which are primary and true: (b) reasoning, on the
other hand, is 'dialectical', if it reasons from opinions that are
generally accepted. Things are 'true' and 'primary' which are
believed on the strength not of anything else but of themselves:
for in regard to the first principles of science it is improper to
ask any further for the why and wherefore of them; each of the
first principles should command belief in and by itself. On the
other hand, those opinions are 'generally accepted' which are
accepted by every one or by the majority or by the philosophers
- i.e. by all, or by the majority, or by the most notable and
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illustrious of them. Again (c), reasoning is 'contentious' if it
starts from opinions that seem to be generally accepted, but are
not really such, or again if it merely seems to reason from
opinions that are or seem to be generally accepted. For not
every opinion that seems to be generally accepted actually is
generally accepted. For in none of the opinions which we call
generally accepted is the illusion entirely on the surface, as
happens in the case of the principles of contentious arguments;
for the nature of the fallacy in these is obvious immediately,
and as a rule even to persons with little power of
comprehension. So then, of the contentious reasonings
mentioned, the former really deserves to be called 'reasoning'
as well, but the other should be called 'contentious reasoning',
but not 'reasoning', since it appears to reason, but does not
really do so. Further (d), besides all the reasonings we have
mentioned there are the mis-reasonings that start from the
premisses peculiar to the special sciences, as happens (for
example) in the case of geometry and her sister sciences. For
this form of reasoning appears to differ from the reasonings
mentioned above; the man who draws a false figure reasons
from things that are neither true and primary, nor yet generally
accepted. For he does not fall within the definition; he does not
assume opinions that are received either by every one or by the
majority or by philosophers - that is to say, by all, or by most, or
by the most illustrious of them - but he conducts his reasoning
upon assumptions which, though appropriate to the science in
question, are not true; for he effects his mis-reasoning either by
describing the semicircles wrongly or by drawing certain lines in
a way in which they could not be drawn.
The foregoing must stand for an outline survey of the species of
reasoning. In general, in regard both to all that we have already
discussed and to those which we shall discuss later, we may
remark that that amount of distinction between them may
serve, because it is not our purpose to give the exact definition
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of any of them; we merely want to describe them in outline; we
consider it quite enough from the point of view of the line of
inquiry before us to be able to recognize each of them in some
sort of way.
Next in order after the foregoing, we must say for how many
and for what purposes the treatise is useful. They are three -
intellectual training, casual encounters, and the philosophical
sciences. That it is useful as a training is obvious on the face of
it. The possession of a plan of inquiry will enable us more easily
to argue about the subject proposed. For purposes of casual
encounters, it is useful because when we have counted up the
opinions held by most people, we shall meet them on the
ground not of other people's convictions but of their own, while
we shift the ground of any argument that they appear to us to
state unsoundly. For the study of the philosophical sciences it is
useful, because the ability to raise searching difficulties on both
sides of a subject will make us detect more easily the truth and
error about the several points that arise. It has a further use in
relation to the ultimate bases of the principles used in the
several sciences. For it is impossible to discuss them at all from
the principles proper to the particular science in hand, seeing
that the principles are the prius of everything else: it is through
the opinions generally held on the particular points that these
have to be discussed, and this task belongs properly, or most
appropriately, to dialectic: for dialectic is a process of criticism
wherein lies the path to the principles of all inquiries.
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We shall be in perfect possession of the way to proceed when
we are in a position like that which we occupy in regard to
rhetoric and medicine and faculties of that kind: this means the
doing of that which we choose with the materials that are
available. For it is not every method that the rhetorician will
employ to persuade, or the doctor to heal; still, if he omits none
of the available means, we shall say that his grasp of the science
is adequate.
First, then, we must see of what parts our inquiry consists. Now
if we were to grasp (a) with reference to how many, and what
kind of, things arguments take place, and with what materials
they start, and (b) how we are to become well supplied with
these, we should have sufficiently won our goal. Now the
materials with which arguments start are equal in number, and
are identical, with the subjects on which reasonings take place.
For arguments start with 'propositions', while the subjects on
which reasonings take place are 'problems'. Now every
proposition and every problem indicates either a genus or a
peculiarity or an accident - for the differentia too, applying as it
does to a class (or genus), should be ranked together with the
genus. Since, however, of what is peculiar to anything part
signifies its essence, while part does not, let us divide the
'peculiar' into both the aforesaid parts, and call that part which
indicates the essence a 'definition', while of the remainder let
us adopt the terminology which is generally current about these
things, and speak of it as a 'property'. What we have said, then,
makes it clear that according to our present division, the
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elements turn out to be four, all told, namely either property or
definition or genus or accident. Do not let any one suppose us
to mean that each of these enunciated by itself constitutes a
proposition or problem, but only that it is from these that both
problems and propositions are formed. The difference between
a problem and a proposition is a difference in the turn of the
phrase. For if it be put in this way, «'An animal that walks on
two feet» is the definition of man, is it not?' or '«Animal» is the
genus of man, is it not?' the result is a proposition: but if thus,
'Is «an animal that walks on two feet» a definition of man or
no?' [or 'Is «animal» his genus or no?'] the result is a problem.
Similarly too in other cases. Naturally, then, problems and
propositions are equal in number: for out of every proposition
you will make a problem if you change the turn of the phrase.
We must now say what are 'definition', 'property', 'genus', and
'accident'. A 'definition' is a phrase signifying a thing's essence.
It is rendered in the form either of a phrase in lieu of a term, or
of a phrase in lieu of another phrase; for it is sometimes
possible to define the meaning of a phrase as well. People
whose rendering consists of a term only, try it as they may,
clearly do not render the definition of the thing in question,
because a definition is always a phrase of a certain kind. One
may, however, use the word 'definitory' also of such a remark as
'The «becoming» is «beautiful»', and likewise also of the
question, 'Are sensation and knowledge the same or different?',
for argument about definitions is mostly concerned with
questions of sameness and difference. In a word we may call
'definitory' everything that falls under the same branch of
inquiry as definitions; and that all the above-mentioned
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examples are of this character is clear on the face of them. For if
we are able to argue that two things are the same or are
different, we shall be well supplied by the same turn of
argument with lines of attack upon their definitions as well: for
when we have shown that they are not the same we shall have
demolished the definition. Observe, please, that the converse of
this last statement does not hold: for to show that they are the
same is not enough to establish a definition. To show, however,
that they are not the same is enough of itself to overthrow it.
A 'property' is a predicate which does not indicate the essence
of a thing, but yet belongs to that thing alone, and is predicated
convertibly of it. Thus it is a property of man to-be-capable of
learning grammar: for if A be a man, then he is capable of
learning grammar, and if he be capable of learning grammar, he
is a man. For no one calls anything a 'property' which may
possibly belong to something else, e.g. 'sleep' in the case of
man, even though at a certain time it may happen to belong to
him alone. That is to say, if any such thing were actually to be
called a property, it will be called not a 'property' absolutely, but
a 'temporary' or a 'relative' property: for 'being on the right
hand side' is a temporary property, while 'two-footed' is in point
of fact ascribed as a property in certain relations; e.g. it is a
property of man relatively to a horse and a dog. That nothing
which may belong to anything else than A is a convertible
predicate of A is clear: for it does not necessarily follow that if
something is asleep it is a man.
A 'genus' is what is predicated in the category of essence of a
number of things exhibiting differences in kind. We should treat
as predicates in the category of essence all such things as it
would be appropriate to mention in reply to the question, 'What
is the object before you?'; as, for example, in the case of man, if
asked that question, it is appropriate to say 'He is an animal'.
The question, 'Is one thing in the same genus as another or in a
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different one?' is also a 'generic' question; for a question of that
kind as well falls under the same branch of inquiry as the
genus: for having argued that 'animal' is the genus of man, and
likewise also of ox, we shall have argued that they are in the
same genus; whereas if we show that it is the genus of the one
but not of the other, we shall have argued that these things are
not in the same genus.
An 'accident' is (i) something which, though it is none of the
foregoing - i.e. neither a definition nor a property nor a genus
yet belongs to the thing: (something which may possibly either
belong or not belong to any one and the self-same thing, as
(e.g.) the 'sitting posture' may belong or not belong to some self-
same thing. Likewise also 'whiteness', for there is nothing to
prevent the same thing being at one time white, and at another
not white. Of the definitions of accident the second is the
better: for if he adopts the first, any one is bound, if he is to
understand it, to know already what 'definition' and 'genus' and
'property' are, whereas the second is sufficient of itself to tell us
the essential meaning of the term in question. To Accident are
to be attached also all comparisons of things together, when
expressed in language that is drawn in any kind of way from
what happens (accidit) to be true of them; such as, for example,
the question, 'Is the honourable or the expedient preferable?'
and 'Is the life of virtue or the life of self-indulgence the
pleasanter?', and any other problem which may happen to be
phrased in terms like these. For in all such cases the question is
'to which of the two does the predicate in question happen
(accidit) to belong more closely?' It is clear on the face of it that
there is nothing to prevent an accident from becoming a
temporary or relative property. Thus the sitting posture is an
accident, but will be a temporary property, whenever a man is
the only person sitting, while if he be not the only one sitting, it
is still a property relatively to those who are not sitting. So then,
there is nothing to prevent an accident from becoming both a
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relative and a temporary property; but a property absolutely it
will never be.
We must not fail to observe that all remarks made in criticism
of a 'property' and 'genus' and 'accident' will be applicable to
'definitions' as well. For when we have shown that the attribute
in question fails to belong only to the term defined, as we do
also in the case of a property, or that the genus rendered in the
definition is not the true genus, or that any of the things
mentioned in the phrase used does not belong, as would be
remarked also in the case of an accident, we shall have
demolished the definition; so that, to use the phrase previously
employed,' all the points we have enumerated might in a
certain sense be called 'definitory'. But we must not on this
account expect to find a single line of inquiry which will apply
universally to them all: for this is not an easy thing to find, and,
even were one found, it would be very obscure indeed, and of
little service for the treatise before us. Rather, a special plan of
inquiry must be laid down for each of the classes we have
distinguished, and then, starting from the rules that are
appropriate in each case, it will probably be easier to make our
way right through the task before us. So then, as was said
before,' we must outline a division of our subject, and other
questions we must relegate each to the particular branch to
which it most naturally belongs, speaking of them as 'definitory'
and 'generic' questions. The questions I mean have practically
been already assigned to their several branches.
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First of all we must define the number of senses borne by the
term 'Sameness'. Sameness would be generally regarded as
falling, roughly speaking, into three divisions. We generally
apply the term numerically or specifically or generically -
numerically in cases where there is more than one name but
only one thing, e.g. 'doublet' and 'cloak'; specifically, where
there is more than one thing, but they present no differences in
respect of their species, as one man and another, or one horse
and another: for things like this that fall under the same species
are said to be 'specifically the same'. Similarly, too, those things
are called generically the same which fall under the same
genus, such as a horse and a man. It might appear that the
sense in which water from the same spring is called 'the same
water' is somehow different and unlike the senses mentioned
above: but really such a case as this ought to be ranked in the
same class with the things that in one way or another are called
'the same' in view of unity of species. For all such things seem
to be of one family and to resemble one another. For the reaon
why all water is said to be specifically the same as all other
water is because of a certain likeness it bears to it, and the only
difference in the case of water drawn from the same spring is
this, that the likeness is more emphatic: that is why we do not
distinguish it from the things that in one way or another are
called 'the same' in view of unity of species. It is generally
supposed that the term 'the same' is most used in a sense
agreed on by every one when applied to what is numerically
one. But even so, it is apt to be rendered in more than one
sense; its most literal and primary use is found whenever the
sameness is rendered in reference to an alternative name or
definition, as when a cloak is said to be the same as a doublet,
or an animal that walks on two feet is said to be the same as a
man: a second sense is when it is rendered in reference to a
property, as when what can acquire knowledge is called the
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same as a man, and what naturally travels upward the same as
fire: while a third use is found when it is rendered in reference
to some term drawn from Accident, as when the creature who is
sitting, or who is musical, is called the same as Socrates. For all
these uses mean to signify numerical unity. That what I have
just said is true may be best seen where one form of appellation
is substituted for another. For often when we give the order to
call one of the people who are sitting down, indicating him by
name, we change our description, whenever the person to
whom we give the order happens not to understand us; he will,
we think, understand better from some accidental feature; so
we bid him call to us 'the man who is sitting' or 'who is
conversing over there' - clearly supposing ourselves to be
indicating the same object by its name and by its accident.
8
Of 'sameness' then, as has been said,' three senses are to be
distinguished. Now one way to confirm that the elements
mentioned above are those out of which and through which and
to which arguments proceed, is by induction: for if any one were
to survey propositions and problems one by one, it would be
seen that each was formed either from the definition of
something or from its property or from its genus or from its
accident. Another way to confirm it is through reasoning. For
every predicate of a subject must of necessity be either
convertible with its subject or not: and if it is convertible, it
would be its definition or property, for if it signifies the essence,
it is the definition; if not, it is a property: for this was what a
property is, viz. what is predicated convertibly, but does not
signify the essence. If, on the other hand, it is not predicated
convertibly of the thing, it either is or is not one of the terms
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contained in the definition of the subject: and if it be one of
those terms, then it will be the genus or the differentia,
inasmuch as the definition consists of genus and differentiae;
whereas, if it be not one of those terms, clearly it would be an
accident, for accident was said' to be what belongs as an
attribute to a subject without being either its definition or its
genus or a property.
Next, then, we must distinguish between the classes of
predicates in which the four orders in question are found. These
are ten in number: Essence, Quantity, Quality, Relation, Place,
Time, Position, State, Activity, Passivity. For the accident and
genus and property and definition of anything will always be in
one of these categories: for all the propositions found through
these signify either something's essence or its quality or
quantity or some one of the other types of predicate. It is clear,
too, on the face of it that the man who signifies something's
essence signifies sometimes a substance, sometimes a quality,
sometimes some one of the other types of predicate. For when
man is set before him and he says that what is set there is 'a
man' or 'an animal', he states its essence and signifies a
substance; but when a white colour is set before him and he
says that what is set there is 'white' or is 'a colour', he states its
essence and signifies a quality. Likewise, also, if a magnitude of
a cubit be set before him and he says that what is set there is a
magnitude of a cubit, he will be describing its essence and
signifying a quantity. Likewise, also, in the other cases: for each
of these kinds of predicate, if either it be asserted of itself, or its
genus be asserted of it, signifies an essence: if, on the other
hand, one kind of predicate is asserted of another kind, it does
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not signify an essence, but a quantity or a quality or one of the
other kinds of predicate. Such, then, and so many, are the
subjects on which arguments take place, and the materials with
which they start. How we are to acquire them, and by what
means we are to become well supplied with them, falls next to
be told.
10
First, then, a definition must be given of a 'dialectical
proposition' and a 'dialectical problem'. For it is not every
proposition nor yet every problem that is to be set down as
dialectical: for no one in his senses would make a proposition of
what no one holds, nor yet make a problem of what is obvious
to everybody or to most people: for the latter admits of no
doubt, while to the former no one would assent. Now a
dialectical proposition consists in asking something that is held
by all men or by most men or by the philosophers, i.e. either by
all, or by most, or by the most notable of these, provided it be
not contrary to the general opinion; for a man would probably
assent to the view of the philosophers, if it be not contrary to
the opinions of most men. Dialectical propositions also include
views which are like those generally accepted; also propositions
which contradict the contraries of opinions that are taken to be
generally accepted, and also all opinions that are in accordance
with the recognized arts. Thus, supposing it to be a general
opinion that the knowledge of contraries is the same, it might
probably pass for a general opinion also that the perception of
contraries is the same: also, supposing it to be a general opinion
that there is but one single science of grammar, it might pass
for a general opinion that there is but one science of flute-
playing as well, whereas, if it be a general opinion that there is
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more than one science of grammar, it might pass for a general
opinion that there is more than one science of flute-playing as
well: for all these seem to be alike and akin. Likewise, also,
propositions contradicting the contraries of general opinions
will pass as general opinions: for if it be a general opinion that
one ought to do good to one's friends, it will also be a general
opinion that one ought not to do them harm. Here, that one
ought to do harm to one's friends is contrary to the general
view, and that one ought not to do them harm is the
contradictory of that contrary. Likewise also, if one ought to do
good to one's friends, one ought not to do good to one's
enemies: this too is the contradictory of the view contrary to the
general view; the contrary being that one ought to do good to
one's enemies. Likewise, also, in other cases. Also, on
comparison, it will look like a general opinion that the contrary
predicate belongs to the contrary subject: e.g. if one ought to do
good to one's friends, one ought also to do evil to one's enemies,
it might appear also as if doing good to one's friends were a
contrary to doing evil to one's enemies: but whether this is or is
not so in reality as well will be stated in the course of the
discussion upon contraries. Clearly also, all opinions that are in
accordance with the arts are dialectical propositions; for people
are likely to assent to the views held by those who have made a
study of these things, e.g. on a question of medicine they will
agree with the doctor, and on a question of geometry with the
geometrician; and likewise also in other cases.
11
A dialectical problem is a subject of inquiry that contributes
either to choice and avoidance, or to truth and knowledge, and
that either by itself, or as a help to the solution of some other
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such problem. It must, moreover, be something on which either
people hold no opinion either way, or the masses hold a
contrary opinion to the philosophers, or the philosophers to the
masses, or each of them among themselves. For some problems
it is useful to know with a view to choice or avoidance, e.g.
whether pleasure is to be chosen or not, while some it is useful
to know merely with a view to knowledge, e.g. whether the
universe is eternal or not: others, again, are not useful in and by
themselves for either of these purposes, but yet help us in
regard to some such problems; for there are many things which
we do not wish to know in and by themselves, but for the sake
of other things, in order that through them we may come to
know something else. Problems also include questions in regard
to which reasonings conflict (the difficulty then being whether
so - and so is so or not, there being convincing arguments for
both views); others also in regard to which we have no
argument because they are so vast, and we find it difficult to
give our reasons, e.g. the question whether the universe is
eternal or no: for into questions of that kind too it is possible to
inquire.
Problems, then, and propositions are to be defined as aforesaid.
A 'thesis' is a supposition of some eminent philosopher that
conflicts with the general opinion; e.g. the view that
contradiction is impossible, as Antisthenes said; or the view of
Heraclitus that all things are in motion; or that Being is one, as
Melissus says: for to take notice when any ordinary person
expresses views contrary to men's usual opinions would be silly.
Or it may be a view about which we have a reasoned theory
contrary to men's usual opinions, e.g. the view maintained by
the sophists that what is need not in every case either have
come to be or be eternal: for a musician who is a grammarian
'is' so without ever having 'come to be' so, or being so eternally.
For even if a man does not accept this view, he might do so on
the ground that it is reasonable.
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Now a 'thesis' also is a problem, though a problem is not always
a thesis, inasmuch as some problems are such that we have no
opinion about them either way. That a thesis, however, also
forms a problem, is clear: for it follows of necessity from what
has been said that either the mass of men disagree with the
philosophers about the thesis, or that the one or the other class
disagree among themselves, seeing that the thesis is a
supposition in conflict with general opinion. Practically all
dialectical problems indeed are now called 'theses'. But it
should make no difference whichever description is used; for
our object in thus distinguishing them has not been to create a
terminology, but to recognize what differences happen to be
found between them.
Not every problem, nor every thesis, should be examined, but
only one which might puzzle one of those who need argument,
not punishment or perception. For people who are puzzled to
know whether one ought to honour the gods and love one's
parents or not need punishment, while those who are puzzled
to know whether snow is white or not need perception. The
subjects should not border too closely upon the sphere of
demonstration, nor yet be too far removed from it: for the
former cases admit of no doubt, while the latter involve
difficulties too great for the art of the trainer.
12
Having drawn these definitions, we must distinguish how many
species there are of dialectical arguments. There is on the one
hand Induction, on the other Reasoning. Now what reasoning is
has been said before: induction is a passage from individuals to
universals, e.g. the argument that supposing the skilled pilot is
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the most effective, and likewise the skilled charioteer, then in
general the skilled man is the best at his particular task.
Induction is the more convincing and clear: it is more readily
learnt by the use of the senses, and is applicable generally to
the mass of men, though reasoning is more forcible and
effective against contradictious people.
13
The classes, then, of things about which, and of things out of
which, arguments are constructed, are to be distinguished in
the way we have said before. The means whereby we are to
become well supplied with reasonings are four: (1) the securing
of propositions; (2) the power to distinguish in how many
senses particular expression is used; (3) the discovery of the
differences of things; (4) the investigation of likeness. The last
three, as well, are in a certain sense propositions: for it is
possible to make a proposition corresponding to each of them,
e.g. (1) 'The desirable may mean either the honourable or the
pleasant or the expedient'; and (2) Sensation differs from
knowledge in that the latter may be recovered again after it has
been lost, while the former cannot'; and (3) The relation of the
healthy to health is like that of the vigorous to vigour'. The first
proposition depends upon the use of one term in several senses,
the second upon the differences of things, the third upon their
likenesses.
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14
Propositions should be selected in a number of ways
corresponding to the number of distinctions drawn in regard to
the proposition: thus one may first take in hand the opinions
held by all or by most men or by the philosophers, i.e. by all, or
most, or the most notable of them; or opinions contrary to those
that seem to be generally held; and, again, all opinions that are
in accordance with the arts. We must make propositions also of
the contradictories of opinions contrary to those that seem to
be generally held, as was laid down before. It is useful also to
make them by selecting not only those opinions that actually
are accepted, but also those that are like these, e.g. 'The
perception of contraries is the same' - the knowledge of them
being so - and 'we see by admission of something into
ourselves, not by an emission'; for so it is, too, in the case of the
other senses; for in hearing we admit something into ourselves;
we do not emit; and we taste in the same way. Likewise also in
the other cases. Moreover, all statements that seem to be true in
all or in most cases, should be taken as a principle or accepted
position; for they are posited by those who do not also see what
exception there may be. We should select also from the written
handbooks of argument, and should draw up sketch-lists of
them upon each several kind of subject, putting them down
under separate headings, e.g. 'On Good', or 'On Life' - and that
'On Good' should deal with every form of good, beginning with
the category of essence. In the margin, too, one should indicate
also the opinions of individual thinkers, e.g. 'Empedocles said
that the elements of bodies were four': for any one might assent
to the saying of some generally accepted authority.
Of propositions and problems there are - to comprehend the
matter in outline - three divisions: for some are ethical
propositions, some are on natural philosophy, while some are
logical. Propositions such as the following are ethical, e.g.
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'Ought one rather to obey one's parents or the laws, if they
disagree?'; such as this are logical, e.g. 'Is the knowledge of
opposites the same or not?'; while such as this are on natural
philosophy, e.g. 'Is the universe eternal or not?' Likewise also
with problems. The nature of each of the aforesaid kinds of
proposition is not easily rendered in a definition, but we have to
try to recognize each of them by means of the familiarity
attained through induction, examining them in the light of the
illustrations given above.
For purposes of philosophy we must treat of these things
according to their truth, but for dialectic only with an eye to
general opinion. All propositions should be taken in their most
universal form; then, the one should be made into many. E.g.
'The knowledge of opposites is the same'; next, 'The knowledge
of contraries is the same', and that 'of relative terms'. In the
same way these two should again be divided, as long as division
is possible, e.g. the knowledge of 'good and evil', of 'white and
black', or 'cold and hot'. Likewise also in other cases.
15
On the formation, then, of propositions, the above remarks are
enough. As regards the number of senses a term bears, we must
not only treat of those terms which bear different senses, but
we must also try to render their definitions; e.g. we must not
merely say that justice and courage are called 'good' in one
sense, and that what conduces to vigour and what conduces to
health are called so in another, but also that the former are so
called because of a certain intrinsic quality they themselves
have, the latter because they are productive of a certain result
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and not because of any intrinsic quality in themselves. Similarly
also in other cases.
Whether a term bears a number of specific meanings or one
only, may be considered by the following means. First, look and
see if its contrary bears a number of meanings, whether the
discrepancy between them be one of kind or one of names. For
in some cases a difference is at once displayed even in the
names; e.g. the contrary of 'sharp' in the case of a note is 'flat',
while in the case of a solid edge it is 'dull'. Clearly, then, the
contrary of 'sharp' bears several meanings, and if so, also does
'sharp'; for corresponding to each of the former terms the
meaning of its contrary will be different. For 'sharp' will not be
the same when contrary to 'dull' and to 'flat', though 'sharp' is
the contrary of each. Again Barhu ('flat', 'heavy') in the case of a
note has 'sharp' as its contrary, but in the case of a solid mass
'light', so that Barhu is used with a number of meanings,
inasmuch as its contrary also is so used. Likewise, also, 'fine' as
applied to a picture has 'ugly' as its contrary, but, as applied to a
house, 'ramshackle'; so that 'fine' is an ambiguous term.
In some cases there is no discrepancy of any sort in the names
used, but a difference of kind between the meanings is at once
obvious: e.g. in the case of 'clear' and 'obscure': for sound is
called 'clear' and 'obscure', just as 'colour' is too. As regards the
names, then, there is no discrepancy, but the difference in kind
between the meanings is at once obvious: for colour is not
called 'clear' in a like sense to sound. This is plain also through
sensation: for of things that are the same in kind we have the
same sensation, whereas we do not judge clearness by the same
sensation in the case of sound and of colour, but in the latter
case we judge by sight, in the former by hearing. Likewise also
with 'sharp' and 'dull' in regard to flavours and solid edges: here
in the latter case we judge by touch, but in the former by taste.
For here again there is no discrepancy in the names used, in the
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case either of the original terms or of their contraries: for the
contrary also of sharp in either sense is 'dull'.
Moreover, see if one sense of a term has a contrary, while
another has absolutely none; e.g. the pleasure of drinking has a
contrary in the pain of thirst, whereas the pleasure of seeing
that the diagonal is incommensurate with the side has none, so
that 'pleasure' is used in more than one sense. To 'love' also,
used of the frame of mind, has to 'hate' as its contrary, while as
used of the physical activity (kissing) it has none: clearly,
therefore, to 'love' is an ambiguous term. Further, see in regard
to their intermediates, if some meanings and their contraries
have an intermediate, others have none, or if both have one but
not the same one, e.g. 'clear' and 'obscure' in the case of colours
have 'grey' as an intermediate, whereas in the case of sound
they have none, or, if they have, it is 'harsh', as some people say
that a harsh sound is intermediate. 'Clear', then, is an
ambiguous term, and likewise also 'obscure'. See, moreover, if
some of them have more than one intermediate, while others
have but one, as is the case with 'clear' and 'obscure', for in the
case of colours there are numbers of intermediates, whereas in
regard to sound there is but one, viz. 'harsh'.
Again, in the case of the contradictory opposite, look and see if
it bears more than one meaning. For if this bears more than one
meaning, then the opposite of it also will be used in more than
one meaning; e.g. 'to fail to see' a phrase with more than one
meaning, viz. (1) to fail to possess the power of sight, (2) to fail
to put that power to active use. But if this has more than one
meaning, it follows necessarily that 'to see' also has more than
one meaning: for there will be an opposite to each sense of 'to
fail to see'; e.g. the opposite of 'not to possess the power of
sight' is to possess it, while of 'not to put the power of sight to
active use', the opposite is to put it to active use.
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Moreover, examine the case of terms that denote the privation
or presence of a certain state: for if the one term bears more
than one meaning, then so will the remaining term: e.g. if 'to
have sense' be used with more than one meaning, as applied to
the soul and to the body, then 'to be wanting in sense' too will
be used with more than one meaning, as applied to the soul and
to the body. That the opposition between the terms now in
question depends upon the privation or presence of a certain
state is clear, since animals naturally possess each kind of
'sense', both as applied to the soul and as applied to the body.
Moreover, examine the inflected forms. For if 'justly' has more
than one meaning, then 'just', also, will be used with more than
one meaning; for there will be a meaning of 'just' to each of the
meanings of 'justly'; e.g. if the word 'justly' be used of judging
according to one's own opinion, and also of judging as one
ought, then 'just' also will be used in like manner. In the same
way also, if 'healthy' has more than one meaning, then
'healthily' also will be used with more than one meaning: e.g. if
'healthy' describes both what produces health and what
preserves health and what betokens health, then 'healthily' also
will be used to mean 'in such a way as to produce' or 'preserve'
or 'betoken' health. Likewise also in other cases, whenever the
original term bears more than one meaning, the inflexion also
that is formed from it will be used with more than one
meaning, and vice versa.
Look also at the classes of the predicates signified by the term,
and see if they are the same in all cases. For if they are not the
same, then clearly the term is ambiguous: e.g. 'good' in the case
of food means 'productive of pleasure', and in the case of
medicine 'productive of health', whereas as applied to the soul
it means to be of a certain quality, e.g. temperate or courageous
or just: and likewise also, as applied to 'man'. Sometimes it
signifies what happens at a certain time, as (e.g.) the good that
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happens at the right time: for what happens at the right time is
called good. Often it signifies what is of certain quantity, e.g. as
applied to the proper amount: for the proper amount too is
called good. So then the term 'good' is ambiguous. In the same
way also 'clear', as applied to a body, signifies a colour, but in
regard to a note it denotes what is 'easy to hear'. 'Sharp', too, is
in a closely similar case: for the same term does not bear the
same meaning in all its applications: for a sharp note is a swift
note, as the mathematical theorists of harmony tell us, whereas
a sharp (acute) angle is one that is less than a right angle, while
a sharp dagger is one containing a sharp angle (point).
Look also at the genera of the objects denoted by the same
term, and see if they are different without being subaltern, as
(e.g.) 'donkey', which denotes both the animal and the engine.
For the definition of them that corresponds to the name is
different: for the one will be declared to be an animal of a
certain kind, and the other to be an engine of a certain kind. If,
however, the genera be subaltern, there is no necessity for the
definitions to be different. Thus (e.g.) 'animal' is the genus of
'raven', and so is 'bird'. Whenever therefore we say that the
raven is a bird, we also say that it is a certain kind of animal, so
that both the genera are predicated of it. Likewise also
whenever we call the raven a 'flying biped animal', we declare it
to be a bird: in this way, then, as well, both the genera are
predicated of raven, and also their definition. But in the case of
genera that are not subaltern this does not happen, for
whenever we call a thing an 'engine', we do not call it an
animal, nor vice versa.
Look also and see not only if the genera of the term before you
are different without being subaltern, but also in the case of its
contrary: for if its contrary bears several senses, clearly the term
before you does so as well.
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It is useful also to look at the definition that arises from the use
of the term in combination, e.g. of a 'clear (lit. white) body' of a
'clear note'. For then if what is peculiar in each case be
abstracted, the same expression ought to remain over. This does
not happen in the case of ambiguous terms, e.g. in the cases
just mentioned. For the former will be body possessing such
and such a colour', while the latter will be 'a note easy to hear'.
Abstract, then, 'a body 'and' a note', and the remainder in each
case is not the same. It should, however, have been had the
meaning of 'clear' in each case been synonymous.
Often in the actual definitions as well ambiguity creeps in
unawares, and for this reason the definitions also should be
examined. If (e.g.) any one describes what betokens and what
produces health as 'related commensurably to health', we must
not desist but go on to examine in what sense he has used the
term 'commensurably' in each case, e.g. if in the latter case it
means that 'it is of the right amount to produce health',
whereas in the for it means that 'it is such as to betoken what
kind of state prevails'.
Moreover, see if the terms cannot be compared as 'more or less'
or as 'in like manner', as is the case (e.g.) with a 'clear' (lit.
white) sound and a 'clear' garment, and a 'sharp' flavour and a
'sharp' note. For neither are these things said to be clear or
sharp 'in a like degree', nor yet is the one said to be clearer or
sharper than the other. 'Clear', then, and 'sharp' are ambiguous.
For synonyms are always comparable; for they will always be
used either in like manner, or else in a greater degree in one
case.
Now since of genera that are different without being subaltern
the differentiae also are different in kind, e.g. those of 'animal'
and 'knowledge' (for the differentiae of these are different), look
and see if the meanings comprised under the same term are
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differentiae of genera that are different without being subaltern,
as e.g. 'sharp' is of a 'note' and a 'solid'. For being 'sharp'
differentiates note from note, and likewise also one solid from
another. 'Sharp', then, is an ambiguous term: for it forms
differentiae of genera that are different without being subaltern.
Again, see if the actual meanings included under the same term
themselves have different differentiae, e.g. 'colour' in bodies
and 'colour' in tunes: for the differentiae of 'colour' in bodies are
'sight-piercing' and 'sight compressing', whereas 'colour' in
melodies has not the same differentiae. Colour, then, is an
ambiguous term; for things that are the same have the same
differentiae.
Moreover, since the species is never the differentia of anything,
look and see if one of the meanings included under the same
term be a species and another a differentia, as (e.g.) clear' (lit.
white) as applied to a body is a species of colour, whereas in the
case of a note it is a differentia; for one note is differentiated
from another by being 'clear'.
16
The presence, then, of a number of meanings in a term may be
investigated by these and like means. The differences which
things present to each other should be examined within the
same genera, e.g. 'Wherein does justice differ from courage, and
wisdom from temperance?' - for all these belong to the same
genus; and also from one genus to another, provided they be not
very much too far apart, e.g. 'Wherein does sensation differ
from knowledge?: for in the case of genera that are very far
apart, the differences are entirely obvious.
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17
Likeness should be studied, first, in the case of things belonging
to different genera, the formulae being 'A:B = C:D' (e.g. as
knowledge stands to the object of knowledge, so is sensation
related to the object of sensation), and 'As A is in B, so is C in D'
(e.g. as sight is in the eye, so is reason in the soul, and as is a
calm in the sea, so is windlessness in the air). Practice is more
especially needed in regard to terms that are far apart; for in the
case of the rest, we shall be more easily able to see in one
glance the points of likeness. We should also look at things
which belong to the same genus, to see if any identical attribute
belongs to them all, e.g. to a man and a horse and a dog; for in
so far as they have any identical attribute, in so far they are
alike.
18
It is useful to have examined the number of meanings of a term
both for clearness' sake (for a man is more likely to know what
it is he asserts, if it bas been made clear to him how many
meanings it may have), and also with a view to ensuring that
our reasonings shall be in accordance with the actual facts and
not addressed merely to the term used. For as long as it is not
clear in how many senses a term is used, it is possible that the
answerer and the questioner are not directing their minds upon
the same thing: whereas when once it has been made clear how
many meanings there are, and also upon which of them the
former directs his mind when he makes his assertion, the
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questioner would then look ridiculous if he failed to address his
argument to this. It helps us also both to avoid being misled and
to mislead by false reasoning: for if we know the number of
meanings of a term, we shall certainly never be misled by false
reasoning, but shall know if the questioner fails to address his
argument to the same point; and when we ourselves put the
questions we shall be able to mislead him, if our answerer
happens not to know the number of meanings of our terms.
This, however, is not possible in all cases, but only when of the
many senses some are true and others are false. This manner of
argument, however, does not belong properly to dialectic;
dialecticians should therefore by all means beware of this kind
of verbal discussion, unless any one is absolutely unable to
discuss the subject before him in any other way.
The discovery of the differences of things helps us both in
reasonings about sameness and difference, and also in
recognizing what any particular thing is. That it helps us in
reasoning about sameness and difference is clear: for when we
have discovered a difference of any kind whatever between the
objects before us, we shall already have shown that they are not
the same: while it helps us in recognizing what a thing is,
because we usually distinguish the expression that is proper to
the essence of each particular thing by means of the
differentiae that are proper to it.
The examination of likeness is useful with a view both to
inductive arguments and to hypothetical reasonings, and also
with a view to the rendering of definitions. It is useful for
inductive arguments, because it is by means of an induction of
individuals in cases that are alike that we claim to bring the
universal in evidence: for it is not easy to do this if we do not
know the points of likeness. It is useful for hypothetical
reasonings because it is a general opinion that among similars
what is true of one is true also of the rest. If, then, with regard
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to any of them we are well supplied with matter for a
discussion, we shall secure a preliminary admission that
however it is in these cases, so it is also in the case before us:
then when we have shown the former we shall have shown, on
the strength of the hypothesis, the matter before us as well: for
we have first made the hypothesis that however it is in these
cases, so it is also in the case before us, and have then proved
the point as regards these cases. It is useful for the rendering of
definitions because, if we are able to see in one glance what is
the same in each individual case of it, we shall be at no loss into
what genus we ought to put the object before us when we
define it: for of the common predicates that which is most
definitely in the category of essence is likely to be the genus.
Likewise, also, in the case of objects widely divergent, the
examination of likeness is useful for purposes of definition, e.g.
the sameness of a calm at sea, and windlessness in the air (each
being a form of rest), and of a point on a line and the unit in
number - each being a starting point. If, then, we render as the
genus what is common to all the cases, we shall get the credit
of defining not inappropriately. Definition-mongers too nearly
always render them in this way: they declare the unit to be the
startingpoint of number, and the point the startingpoint of a
line. It is clear, then, that they place them in that which is
common to both as their genus.
The means, then, whereby reasonings are effected, are these:
the commonplace rules, for the observance of which the
aforesaid means are useful, are as follows.
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Book II
Of problems some are universal, others particular. Universal
problems are such as 'Every pleasure is good' and 'No pleasure
is good'; particular problems are such as 'Some pleasure is good'
and 'Some pleasure is not good'. The methods of establishing
and overthrowing a view universally are common to both kinds
of problems; for when we have shown that a predicate belongs
in every case, we shall also have shown that it belongs in some
cases. Likewise, also, if we show that it does not belong in any
case, we shall also have shown that it does not belong in every
case. First, then, we must speak of the methods of overthrowing
a view universally, because such are common to both universal
and particular problems, and because people more usually
introduce theses asserting a predicate than denying it, while
those who argue with them overthrow it. The conversion of an
appropriate name which is drawn from the element 'accident' is
an extremely precarious thing; for in the case of accidents and
in no other it is possible for something to be true conditionally
and not universally. Names drawn from the elements
'definition' and 'property' and 'genus' are bound to be
convertible; e.g. if 'to be an animal that walks on two feet is an
attribute of S', then it will be true by conversion to say that 'S is
an animal that walks on two feet'. Likewise, also, if drawn from
the genus; for if 'to be an animal is an attribute of S', then 'S is
an animal'. The same is true also in the case of a property; for if
'to be capable of learning grammar is an attribute of S', then 'S
will be capable of learning grammar'. For none of these
attributes can possibly belong or not belong in part; they must
either belong or not belong absolutely. In the case of accidents,
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on the other hand, there is nothing to prevent an attribute (e.g.
whiteness or justice) belonging in part, so that it is not enough
to show that whiteness or justice is an attribute of a man in
order to show that he is white or just; for it is open to dispute it
and say that he is white or just in part only. Conversion, then, is
not a necessary process in the case of accidents.
We must also define the errors that occur in problems. They are
of two kinds, caused either by false statement or by
transgression of the established diction. For those who make
false statements, and say that an attribute belongs to thing
which does not belong to it, commit error; and those who call
objects by the names of other objects (e.g. calling a planetree a
'man') transgress the established terminology.
Now one commonplace rule is to look and see if a man has
ascribed as an accident what belongs in some other way. This
mistake is most commonly made in regard to the genera of
things, e.g. if one were to say that white happens (accidit) to be
a colour - for being a colour does not happen by accident to
white, but colour is its genus. The assertor may of course define
it so in so many words, saying (e.g.) that 'Justice happens
(accidit) to be a virtue'; but often even without such definition it
is obvious that he has rendered the genus as an accident; e.g.
suppose that one were to say that whiteness is coloured or that
walking is in motion. For a predicate drawn from the genus is
never ascribed to the species in an inflected form, but always
the genera are predicated of their species literally; for the
species take on both the name and the definition of their
genera. A man therefore who says that white is 'coloured' has
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not rendered 'coloured' as its genus, seeing that he has used an
inflected form, nor yet as its property or as its definition: for the
definition and property of a thing belong to it and to nothing
else, whereas many things besides white are coloured, e.g. a log,
a stone, a man, and a horse. Clearly then he renders it as an
accident.
Another rule is to examine all cases where a predicate has been
either asserted or denied universally to belong to something.
Look at them species by species, and not in their infinite
multitude: for then the inquiry will proceed more directly and
in fewer steps. You should look and begin with the most
primary groups, and then proceed in order down to those that
are not further divisible: e.g. if a man has said that the
knowledge of opposites is the same, you should look and see
whether it be so of relative opposites and of contraries and of
terms signifying the privation or presence of certain states, and
of contradictory terms. Then, if no clear result be reached so far
in these cases, you should again divide these until you come to
those that are not further divisible, and see (e.g.) whether it be
so of just deeds and unjust, or of the double and the half, or of
blindness and sight, or of being and not-being: for if in any case
it be shown that the knowledge of them is not the same we
shall have demolished the problem. Likewise, also, if the
predicate belongs in no case. This rule is convertible for both
destructive and constructive purposes: for if, when we have
suggested a division, the predicate appears to hold in all or in a
large number of cases, we may then claim that the other should
actually assert it universally, or else bring a negative instance to
show in what case it is not so: for if he does neither of these
things, a refusal to assert it will make him look absurd.
Another rule is to make definitions both of an accident and of
its subject, either of both separately or else of one of them, and
then look and see if anything untrue has been assumed as true
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in the definitions. Thus (e.g.) to see if it is possible to wrong a
god, ask what is 'to wrong? For if it be 'to injure deliberately',
clearly it is not possible for a god to be wronged: for it is
impossible that God should be injured. Again, to see if the good
man is jealous, ask who is the 'jealous' man and what is
'jealousy'. For if 'jealousy' is pain at the apparent success of
some well-behaved person, clearly the good man is not jealous:
for then he would be bad. Again, to see if the indignant man is
jealous, ask who each of them is: for then it will be obvious
whether the statement is true or false; e.g. if he is 'jealous' who
grieves at the successes of the good, and he is 'indignant' who
grieves at the successes of the evil, then clearly the indignant
man would not be jealous. A man should substitute definitions
also for the terms contained in his definitions, and not stop
until he comes to a familiar term: for often if the definition be
rendered whole, the point at issue is not cleared up, whereas if
for one of the terms used in the definition a definition be stated,
it becomes obvious.
Moreover, a man should make the problem into a proposition
for himself, and then bring a negative instance against it: for the
negative instance will be a ground of attack upon the assertion.
This rule is very nearly the same as the rule to look into cases
where a predicate has been attributed or denied universally: but
it differs in the turn of the argument.
Moreover, you should define what kind of things should be
called as most men call them, and what should not. For this is
useful both for establishing and for overthrowing a view: e.g.
you should say that we ought to use our terms to mean the
same things as most people mean by them, but when we ask
what kind of things are or are not of such and such a kind, we
should not here go with the multitude: e.g. it is right to call
'healthy' whatever tends to produce health, as do most men:
but in saying whether the object before us tends to produce
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health or not, we should adopt the language no longer of the
multitude but of the doctor.
Moreover, if a term be used in several senses, and it has been
laid down that it is or that it is not an attribute of S, you should
show your case of one of its several senses, if you cannot show
it of both. This rule is to be observed in cases where the
difference of meaning is undetected; for supposing this to be
obvious, then the other man will object that the point which he
himself questioned has not been discussed, but only the other
point. This commonplace rule is convertible for purposes both
of establishing and of overthrowing a view. For if we want to
establish a statement, we shall show that in one sense the
attribute belongs, if we cannot show it of both senses: whereas
if we are overthrowing a statement, we shall show that in one
sense the attribute does not belong, if we cannot show it of both
senses. Of course, in overthrowing a statement there is no need
to start the discussion by securing any admission, either when
the statement asserts or when it denies the attribute
universally: for if we show that in any case whatever the
attribute does not belong, we shall have demolished the
universal assertion of it, and likewise also if we show that it
belongs in a single case, we shall demolish the universal denial
of it. Whereas in establishing a statement we ought to secure a
preliminary admission that if it belongs in any case whatever, it
belongs universally, supposing this claim to be a plausible one.
For it is not enough to discuss a single instance in order to show
that an attribute belongs universally; e.g. to argue that if the
soul of man be immortal, then every soul is immortal, so that a
previous admission must be secured that if any soul whatever
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be immortal, then every soul is immortal. This is not to be done
in every case, but only whenever we are not easily able to quote
any single argument applying to all cases in common, as (e.g.)
the geometrician can argue that the triangle has its angles
equal to two right angles.
If, again, the variety of meanings of a term be obvious,
distinguish how many meanings it has before proceeding either
to demolish or to establish it: e.g. supposing 'the right' to mean
'the expedient' or 'the honourable', you should try either to
establish or to demolish both descriptions of the subject in
question; e.g. by showing that it is honourable and expedient, or
that it is neither honourable nor expedient. Supposing, however,
that it is impossible to show both, you should show the one,
adding an indication that it is true in the one sense and not in
the other. The same rule applies also when the number of
senses into which it is divided is more than two.
Again, consider those expressions whose meanings are many,
but differ not by way of ambiguity of a term, but in some other
way: e.g. 'The science of many things is one': here 'many things'
may mean the end and the means to that end, as (e.g.) medicine
is the science both of producing health and of dieting; or they
may be both of them ends, as the science of contraries is said to
be the same (for of contraries the one is no more an end than
the other); or again they may be an essential and an accidental
attribute, as (e.g.) the essential fact that the triangle has its
angles equal to two right angles, and the accidental fact that the
equilateral figure has them so: for it is because of the accident
of the equilateral triangle happening to be a triangle that we
know that it has its angles equal to two right angles. If, then, it
is not possible in any sense of the term that the science of
many things should be the same, it clearly is altogether
impossible that it should be so; or, if it is possible in some sense,
then clearly it is possible. Distinguish as many meanings as are
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required: e.g. if we want to establish a view, we should bring
forward all such meanings as admit that view and should divide
them only into those meanings which also are required for the
establishment of our case: whereas if we want to overthrow a
view, we should bring forward all that do not admit that view,
and leave the rest aside. We must deal also in these cases as
well with any uncertainty about the number of meanings
involved. Further, that one thing is, or is not, 'of another should
be established by means of the same commonplace rules; e.g.
that a particular science is of a particular thing, treated either
as an end or as a means to its end, or as accidentally connected
with it; or again that it is not 'of it in any of the aforesaid ways.
The same rule holds true also of desire and all other terms that
have more than one object. For the 'desire of X' may mean the
desire of it as an end (e.g. the desire of health) or as a means to
an end (e.g. the desire of being doctored), or as a thing desired
accidentally, as, in the case of wine, the sweet-toothed person
desires it not because it is wine but because it is sweet. For
essentially he desires the sweet, and only accidentally the wine:
for if it be dry, he no longer desires it. His desire for it is
therefore accidental. This rule is useful in dealing with relative
terms: for cases of this kind are generally cases of relative
terms.
Moreover, it is well to alter a term into one more familiar, e.g. to
substitute 'clear' for 'exact' in describing a conception, and
'being fussy' for 'being busy': for when the expression is made
more familiar, the thesis becomes easier to attack. This
commonplace rule also is available for both purposes alike, both
for establishing and for overthrowing a view.
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In order to show that contrary attributes belong to the same
thing, look at its genus; e.g. if we want to show that Tightness
and wrongness are possible in regard to perception, and to
perceive is to judge, while it is possible to judge rightly or
wrongly, then in regard to perception as well Tightness and
wrongness must be possible. In the present instance the proof
proceeds from the genus and relates to the species: for 'to
judge' is the genus of 'to perceive'; for the man who perceives
judges in a certain way. But per contra it may proceed from the
species to the genus: for all the attributes that belong to the
species belong to the genus as well; e.g. if there is a bad and a
good knowledge there is also a bad and a good disposition: for
'disposition' is the genus of knowledge. Now the former
commonplace argument is fallacious for purposes of
establishing a view, while the second is true. For there is no
necessity that all the attributes that belong to the genus should
belong also to the species; for 'animal' is flying and quadruped,
but not so 'man'. All the attributes, on the other hand, that
belong to the species must of necessity belong also to the
genus; for if 'man' is good, then animal also is good. On the
other hand, for purposes of overthrowing a view, the former
argument is true while the latter is fallacious; for all the
attributes which do not belong to the genus do not belong to the
species either; whereas all those that are wanting to the species
are not of necessity wanting to the genus.
Since those things of which the genus is predicated must also of
necessity have one of its species predicated of them, and since
those things that are possessed of the genus in question, or are
described by terms derived from that genus, must also of
necessity be possessed of one of its species or be described by
terms derived from one of its species (e.g. if to anything the
term 'scientific knowledge' be applied, then also there will be
applied to it the term 'grammatical' or 'musical' knowledge, or
knowledge of one of the other sciences; and if any one
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possesses scientific knowledge or is described by a term derived
from 'science', then he will also possess grammatical or musical
knowledge or knowledge of one of the other sciences, or will be
described by a term derived from one of them, e.g. as a
'grammarian' or a 'musician') - therefore if any expression be
asserted that is in any way derived from the genus (e.g. that the
soul is in motion), look and see whether it be possible for the
soul to be moved with any of the species of motion; whether
(e.g.) it can grow or be destroyed or come to be, and so forth
with all the other species of motion. For if it be not moved in
any of these ways, clearly it does not move at all. This
commonplace rule is common for both purposes, both for
overthrowing and for establishing a view: for if the soul moves
with one of the species of motion, clearly it does move; while if
it does not move with any of the species of motion, clearly it
does not move.
If you are not well equipped with an argument against the
assertion, look among the definitions, real or apparent, of the
thing before you, and if one is not enough, draw upon several.
For it will be easier to attack people when committed to a
definition: for an attack is always more easily made on
definitions.
Moreover, look and see in regard to the thing in question, what
it is whose reality conditions the reality of the thing in question,
or what it is whose reality necessarily follows if the thing in
question be real: if you wish to establish a view inquire what
there is on whose reality the reality of the thing in question will
follow (for if the former be shown to be real, then the thing in
question will also have been shown to be real); while if you
want to overthrow a view, ask what it is that is real if the thing
in question be real, for if we show that what follows from the
thing in question is unreal, we shall have demolished the thing
in question.
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Moreover, look at the time involved, to see if there be any
discrepancy anywhere: e.g. suppose a man to have stated that
what is being nourished of necessity grows: for animals are
always of necessity being nourished, but they do not always
grow. Likewise, also, if he has said that knowing is
remembering: for the one is concerned with past time, whereas
the other has to do also with the present and the future. For we
are said to know things present and future (e.g. that there will
be an eclipse), whereas it is impossible to remember anything
save what is in the past.
Moreover, there is the sophistic turn of argument, whereby we
draw our opponent into the kind of statement against which we
shall be well supplied with lines of argument. This process is
sometimes a real necessity, sometimes an apparent necessity,
sometimes neither an apparent nor a real necessity. It is really
necessary whenever the answerer has denied any view that
would be useful in attacking the thesis, and the questioner
thereupon addresses his arguments to the support of this view,
and when moreover the view in question happens to be one of a
kind on which he has a good stock of lines of argument.
Likewise, also, it is really necessary whenever he (the
questioner) first, by an induction made by means of the view
laid down, arrives at a certain statement and then tries to
demolish that statement: for when once this has been
demolished, the view originally laid down is demolished as well.
It is an apparent necessity, when the point to which the
discussion comes to be directed appears to be useful, and
relevant to the thesis, without being really so; whether it be that
the man who is standing up to the argument has refused to
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concede something, or whether he (the questioner) has first
reached it by a plausible induction based upon the thesis and
then tries to demolish it. The remaining case is when the point
to which the discussion comes to be directed is neither really
nor apparently necessary, and it is the answerer's luck to be
confuted on a mere side issue You should beware of the last of
the aforesaid methods; for it appears to be wholly disconnected
from, and foreign to, the art of dialectic. For this reason,
moreover, the answerer should not lose his temper, but assent
to those statements that are of no use in attacking the thesis,
adding an indication whenever he assents although he does not
agree with the view. For, as a rule, it increases the confusion of
questioners if, after all propositions of this kind have been
granted them, they can then draw no conclusion.
Moreover, any one who has made any statement whatever has
in a certain sense made several statements, inasmuch as each
statement has a number of necessary consequences: e.g. the
man who said 'X is a man' has also said that it is an animal and
that it is animate and a biped and capable of acquiring reason
and knowledge, so that by the demolition of any single one of
these consequences, of whatever kind, the original statement is
demolished as well. But you should beware here too of making a
change to a more difficult subject: for sometimes the
consequence, and sometimes the original thesis, is the easier to
demolish.
In regard to subjects which must have one and one only of two
predicates, as (e.g.) a man must have either a disease or health,
supposing we are well supplied as regards the one for arguing
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its presence or absence, we shall be well equipped as regards
the remaining one as well. This rule is convertible for both
purposes: for when we have shown that the one attribute
belongs, we shall have shown that the remaining one does not
belong; while if we show that the one does not belong, we shall
have shown that the remaining one does belong. Clearly then
the rule is useful for both purposes.
Moreover, you may devise a line of attack by reinterpreting a
term in its literal meaning, with the implication that it is most
fitting so to take it rather than in its established meaning: e.g.
the expression 'strong at heart' will suggest not the courageous
man, according to the use now established, but the man the
state of whose heart is strong; just as also the expression 'of a
good hope' may be taken to mean the man who hopes for good
things. Likewise also 'well-starred' may be taken to mean the
man whose star is good, as Xenocrates says 'well-starred is he
who has a noble soul'.' For a man's star is his soul.
Some things occur of necessity, others usually, others however it
may chance; if therefore a necessary event has been asserted to
occur usually, or if a usual event (or, failing such an event itself,
its contrary) has been stated to occur of necessity, it always
gives an opportunity for attack. For if a necessary event has
been asserted to occur usually, clearly the speaker has denied
an attribute to be universal which is universal, and so has made
a mistake: and so he has if he has declared the usual attribute
to be necessary: for then he declares it to belong universally
when it does not so belong. Likewise also if he has declared the
contrary of what is usual to be necessary. For the contrary of a
usual attribute is always a comparatively rare attribute: e.g. if
men are usually bad, they are comparatively seldom good, so
that his mistake is even worse if he has declared them to be
good of necessity. The same is true also if he has declared a
mere matter of chance to happen of necessity or usually; for a
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chance event happens neither of necessity nor usually. If the
thing happens usually, then even supposing his statement does
not distinguish whether he meant that it happens usually or
that it happens necessarily, it is open to you to discuss it on the
assumption that he meant that it happens necessarily: e.g. if he
has stated without any distinction that disinherited persons are
bad, you may assume in discussing it that he means that they
are so necessarily.
Moreover, look and see also if he has stated a thing to be an
accident of itself, taking it to be a different thing because it has
a different name, as Prodicus used to divide pleasures into joy
and delight and good cheer: for all these are names of the same
thing, to wit, Pleasure. If then any one says that joyfulness is an
accidental attribute of cheerfulness, he would be declaring it to
be an accidental attribute of itself.
Inasmuch as contraries can be conjoined with each other in six
ways, and four of these conjunctions constitute a contrariety,
we must grasp the subject of contraries, in order that it may
help us both in demolishing and in establishing a view. Well
then, that the modes of conjunction are six is clear: for either (1)
each of the contrary verbs will be conjoined to each of the
contrary objects; and this gives two modes: e.g. to do good to
friends and to do evil to enemies, or per contra to do evil to
friends and to do good to enemies. Or else (2) both verbs may be
attached to one object; and this too gives two modes, e.g. to do
good to friends and to do evil to friends, or to do good to
enemies and to do evil to enemies. Or (3) a single verb may be
attached to both objects: and this also gives two modes; e.g. to
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do good to friends and to do good to enemies, or to do evil to
friends and evil to enemies.
The first two then of the aforesaid conjunctions do not
constitute any contrariety; for the doing of good to friends is not
contrary to the doing of evil to enemies: for both courses are
desirable and belong to the same disposition. Nor is the doing of
evil to friends contrary to the doing of good to enemies: for both
of these are objectionable and belong to the same disposition:
and one objectionable thing is not generally thought to be the
contrary of another, unless the one be an expression denoting
an excess, and the other an expression denoting a defect: for an
excess is generally thought to belong to the class of
objectionable things, and likewise also a defect. But the other
four all constitute a contrariety. For to do good to friends is
contrary to the doing of evil to friends: for it proceeds from the
contrary disposition, and the one is desirable, and the other
objectionable. The case is the same also in regard to the other
conjunctions: for in each combination the one course is
desirable, and the other objectionable, and the one belongs to a
reasonable disposition and the other to a bad. Clearly, then,
from what has been said, the same course has more than one
contrary. For the doing of good to friends has as its contrary
both the doing of good to enemies and the doing of evil to
friends. Likewise, if we examine them in the same way, we shall
find that the contraries of each of the others also are two in
number. Select therefore whichever of the two contraries is
useful in attacking the thesis.
Moreover, if the accident of a thing have a contrary, see whether
it belongs to the subject to which the accident in question has
been declared to belong: for if the latter belongs the former
could not belong; for it is impossible that contrary predicates
should belong at the same time to the same thing.
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Or again, look and see if anything has been said about
something, of such a kind that if it be true, contrary predicates
must necessarily belong to the thing: e.g. if he has said that the
'Ideas' exist in us. For then the result will be that they are both
in motion and at rest, and moreover that they are objects both
of sensation and of thought. For according to the views of those
who posit the existence of Ideas, those Ideas are at rest and are
objects of thought; while if they exist in us, it is impossible that
they should be unmoved: for when we move, it follows
necessarily that all that is in us moves with us as well. Clearly
also they are objects of sensation, if they exist in us: for it is
through the sensation of sight that we recognize the Form
present in each individual.
Again, if there be posited an accident which has a contrary, look
and see if that which admits of the accident will admit of its
contrary as well: for the same thing admits of contraries. Thus
(e.g.) if he has asserted that hatred follows anger, hatred would
in that case be in the 'spirited faculty': for that is where anger is.
You should therefore look and see if its contrary, to wit,
friendship, be also in the 'spirited faculty': for if not - if
friendship is in the faculty of desire - then hatred could not
follow anger. Likewise also if he has asserted that the faculty of
desire is ignorant. For if it were capable of ignorance, it would be
capable of knowledge as well: and this is not generally held - I
mean that the faculty of desire is capable of knowledge. For
purposes, then, of overthrowing a view, as has been said, this
rule should be observed: but for purposes of establishing one,
though the rule will not help you to assert that the accident
actually belongs, it will help you to assert that it may possibly
belong. For having shown that the thing in question will not
admit of the contrary of the accident asserted, we shall have
shown that the accident neither belongs nor can possibly
belong; while on the other hand, if we show that the contrary
belongs, or that the thing is capable of the contrary, we shall not
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indeed as yet have shown that the accident asserted does
belong as well; our proof will merely have gone to this point,
that it is possible for it to belong.
8
Seeing that the modes of opposition are four in number, you
should look for arguments among the contradictories of your
terms, converting the order of their sequence, both when
demolishing and when establishing a view, and you should
secure them by means of induction - such arguments (e.g.) as
that man be an animal, what is not an animal is not a man':
and likewise also in other instances of contradictories. For in
those cases the sequence is converse: for 'animal' follows upon
'man but 'not-animal' does not follow upon 'not-man', but
conversely 'not-man' upon 'not-animal'. In all cases, therefore, a
postulate of this sort should be made, (e.g.) that 'If the
honourable is pleasant, what is not pleasant is not honourable,
while if the latter be untrue, so is the former'. Likewise, also, 'If
what is not pleasant be not honourable, then what is
honourable is pleasant'. Clearly, then, the conversion of the
sequence formed by contradiction of the terms of the thesis is a
method convertible for both purposes.
Then look also at the case of the contraries of S and P in the
thesis, and see if the contrary of the one follows upon the
contrary of the other, either directly or conversely, both when
you are demolishing and when you are establishing a view:
secure arguments of this kind as well by means of induction, so
far as may be required. Now the sequence is direct in a case
such as that of courage and cowardice: for upon the one of
them virtue follows, and vice upon the other; and upon the one
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it follows that it is desirable, while upon the other it follows that
it is objectionable. The sequence, therefore, in the latter case
also is direct; for the desirable is the contrary of the
objectionable. Likewise also in other cases. The sequence is, on
the other hand, converse in such a case as this: Health follows
upon vigour, but disease does not follow upon debility; rather
debility follows upon disease. In this case, then, clearly the
sequence is converse. Converse sequence is, however, rare in
the case of contraries; usually the sequence is direct. If,
therefore, the contrary of the one term does not follow upon the
contrary of the other either directly or conversely, clearly
neither does the one term follow upon the other in the
statement made: whereas if the one followed the other in the
case of the contraries, it must of necessity do so as well in the
original statement.
You should look also into cases of the privation or presence of a
state in like manner to the case of contraries. Only, in the case
of such privations the converse sequence does not occur: the
sequence is always bound to be direct: e.g. as sensation follows
sight, while absence of sensation follows blindness. For the
opposition of sensation to absence of sensation is an opposition
of the presence to the privation of a state: for the one of them is
a state, and the other the privation of it.
The case of relative terms should also be studied in like manner
to that of a state and its privation: for the sequence of these as
well is direct; e.g. if 3/1 is a multiple, then 1/3 is a fraction: for
3/1 is relative to 1/3, and so is a multiple to a fraction. Again, if
knowledge be a conceiving, then also the object of knowledge is
an object of conception; and if sight be a sensation, then also
the object of sight is an object of sensation. An objection may be
made that there is no necessity for the sequence to take place,
in the case of relative terms, in the way described: for the object
of sensation is an object of knowledge, whereas sensation is not
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knowledge. The objection is, however, not generally received as
really true; for many people deny that there is knowledge of
objects of sensation. Moreover, the principle stated is just as
useful for the contrary purpose, e.g. to show that the object of
sensation is not an object of knowledge, on the ground that
neither is sensation knowledge.
Again look at the case of the co-ordinates and inflected forms of
the terms in the thesis, both in demolishing and in establishing
it. By co-ordinates' are meant terms such as the following: 'Just
deeds' and the 'just man' are coordinates of 'justice', and
'courageous deeds' and the 'courageous man' are co-ordinates
of courage. Likewise also things that tend to produce and to
preserve anything are called co-ordinates of that which they
tend to produce and to preserve, as e.g. 'healthy habits' are co-
ordinates of 'health' and a 'vigorous constitutional' of a
'vigorous constitution' and so forth also in other cases. 'Co-
ordinate', then, usually describes cases such as these, whereas
'inflected forms' are such as the following: 'justly',
'courageously', 'healthily', and such as are formed in this way. It
is usually held that words when used in their inflected forms as
well are co-ordinates, as (e.g.) 'justly' in relation to justice, and
'courageously' to courage; and then 'co-ordinate' describes all
the members of the same kindred series, e.g. 'justice', 'just', of a
man or an act, 'justly'. Clearly, then, when any one member,
whatever its kind, of the same kindred series is shown to be
good or praiseworthy, then all the rest as well come to be shown
to be so: e.g. if 'justice' be something praiseworthy, then so will
'just', of a man or thing, and 'justly' connote something
praiseworthy. Then 'justly' will be rendered also 'praiseworthily',
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derived will by the same inflexion from 'the praiseworthy'
whereby 'justly' is derived from 'justice'.
Look not only in the case of the subject mentioned, but also in
the case of its contrary, for the contrary predicate: e.g. argue
that good is not necessarily pleasant; for neither is evil painful:
or that, if the latter be the case, so is the former. Also, if justice
be knowledge, then injustice is ignorance: and if 'justly' means
'knowingly' and 'skilfully', then 'unjustly' means 'ignorantly'
and 'unskilfully': whereas if the latter be not true, neither is the
former, as in the instance given just now: for 'unjustly' is more
likely to seem equivalent to 'skilfully' than to 'unskilfully'. This
commonplace rule has been stated before in dealing with the
sequence of contraries; for all we are claiming now is that the
contrary of P shall follow the contrary of S.
Moreover, look at the modes of generation and destruction of a
thing, and at the things which tend to produce or to destroy it,
both in demolishing and in establishing a view. For those things
whose modes of generation rank among good things, are
themselves also good; and if they themselves be good, so also
are their modes of generation. If, on the other hand, their
modes of generation be evil, then they themselves also are evil.
In regard to modes of destruction the converse is true: for if the
modes of destruction rank as good things, then they themselves
rank as evil things; whereas if the modes of destruction count
as evil, they themselves count as good. The same argument
applies also to things tending to produce and destroy: for things
whose productive causes are good, themselves also rank as
good; whereas if causes destructive of them are good, they
themselves rank as evil.
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10
Again, look at things which are like the subject in question, and
see if they are in like case; e.g. if one branch of knowledge has
more than one object, so also will one opinion; and if to possess
sight be to see, then also to possess hearing will be to hear.
Likewise also in the case of other things, both those which are
and those which are generally held to be like. The rule in
question is useful for both purposes; for if it be as stated in the
case of some one like thing, it is so with the other like things as
well, whereas if it be not so in the case of some one of them,
neither is it so in the case of the others. Look and see also
whether the cases are alike as regards a single thing and a
number of things: for sometimes there is a discrepancy. Thus, if
to 'know' a thing be to 'think of it, then also to 'know many
things' is to 'be thinking of many things'; whereas this is not
true; for it is possible to know many things but not to be
thinking of them. If, then, the latter proposition be not true,
neither was the former that dealt with a single thing, viz. that to
'know' a thing is to 'think of it.
Moreover, argue from greater and less degrees. In regard to
greater degrees there are four commonplace rules. One is: See
whether a greater degree of the predicate follows a greater
degree of the subject: e.g. if pleasure be good, see whether also a
greater pleasure be a greater good: and if to do a wrong be evil,
see whether also to do a greater wrong is a greater evil. Now
this rule is of use for both purposes: for if an increase of the
accident follows an increase of the subject, as we have said,
clearly the accident belongs; while if it does not follow, the
accident does not belong. You should establish this by
induction. Another rule is: If one predicate be attributed to two
subjects; then supposing it does not belong to the subject to
which it is the more likely to belong, neither does it belong
where it is less likely to belong; while if it does belong where it
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is less likely to belong, then it belongs as well where it is more
likely. Again: If two predicates be attributed to one subject, then
if the one which is more generally thought to belong does not
belong, neither does the one that is less generally thought to
belong; or, if the one that is less generally thought to belong
does belong, so also does the other. Moreover: If two predicates
be attributed to two subjects, then if the one which is more
usually thought to belong to the one subject does not belong,
neither does the remaining predicate belong to the remaining
subject; or, if the one which is less usually thought to belong to
the one subject does belong, so too does the remaining
predicate to the remaining subject.
Moreover, you can argue from the fact that an attribute belongs,
or is generally supposed to belong, in a like degree, in three
ways, viz. those described in the last three rules given in regard
to a greater degree.' For supposing that one predicate belongs, or
is supposed to belong, to two subjects in a like degree, then if it
does not belong to the one, neither does it belong to the other;
while if it belongs to the one, it belongs to the remaining one as
well. Or, supposing two predicates to belong in a like degree to
the same subject, then, if the one does not belong, neither does
the remaining one; while if the one does belong, the remaining
one belongs as well. The case is the same also if two predicates
belong in a like degree to two subjects; for if the one predicate
does not belong to the one subject, neither does the remaining
predicate belong to the remaining subject, while if the one
predicate does belong to the one subject, the remaining
predicate belongs to the remaining subject as well.
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11
You can argue, then, from greater or less or like degrees of truth
in the aforesaid number of ways. Moreover, you should argue
from the addition of one thing to another. If the addition of one
thing to another makes that other good or white, whereas
formerly it was not white or good, then the thing added will be
white or good - it will possess the character it imparts to the
whole as well. Moreover, if an addition of something to a given
object intensifies the character which it had as given, then the
thing added will itself as well be of that character. Likewise,
also, in the case of other attributes. The rule is not applicable in
all cases, but only in those in which the excess described as an
'increased intensity' is found to take place. The above rule is,
however, not convertible for overthrowing a view. For if the
thing added does not make the other good, it is not thereby
made clear whether in itself it may not be good: for the addition
of good to evil does not necessarily make the whole good, any
more than the addition of white to black makes the whole
white.
Again, any predicate of which we can speak of greater or less
degrees belongs also absolutely: for greater or less degrees of
good or of white will not be attributed to what is not good or
white: for a bad thing will never be said to have a greater or less
degree of goodness than another, but always of badness. This
rule is not convertible, either, for the purpose of overthrowing a
predication: for several predicates of which we cannot speak of
a greater degree belong absolutely: for the term 'man' is not
attributed in greater and less degrees, but a man is a man for all
that.
You should examine in the same way predicates attributed in a
given respect, and at a given time and place: for if the predicate
be possible in some respect, it is possible also absolutely.
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Likewise, also, is what is predicated at a given time or place: for
what is absolutely impossible is not possible either in any
respect or at any place or time. An objection may be raised that
in a given respect people may be good by nature, e.g. they may
be generous or temperately inclined, while absolutely they are
not good by nature, because no one is prudent by nature.
Likewise, also, it is possible for a destructible thing to escape
destruction at a given time, whereas it is not possible for it to
escape absolutely. In the same way also it is a good thing at
certain places to follow see and such a diet, e.g. in infected
areas, though it is not a good thing absolutely. Moreover, in
certain places it is possible to live singly and alone, but
absolutely it is not possible to exist singly and alone. In the
same way also it is in certain places honourable to sacrifice
one's father, e.g. among the Triballi, whereas, absolutely, it is not
honourable. Or possibly this may indicate a relativity not to
places but to persons: for it is all the same wherever they may
be: for everywhere it will be held honourable among the Triballi
themselves, just because they are Triballi. Again, at certain
times it is a good thing to take medicines, e.g. when one is ill,
but it is not so absolutely. Or possibly this again may indicate a
relativity not to a certain time, but to a certain state of health:
for it is all the same whenever it occurs, if only one be in that
state. A thing is 'absolutely' so which without any addition you
are prepared to say is honourable or the contrary. Thus (e.g.) you
will deny that to sacrifice one's father is honourable: it is
honourable only to certain persons: it is not therefore
honourable absolutely. On the other hand, to honour the gods
you will declare to be honourable without adding anything,
because that is honourable absolutely. So that whatever without
any addition is generally accounted to be honourable or
dishonourable or anything else of that kind, will be said to be so
'absolutely'.
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Book III
The question which is the more desirable, or the better, of two
or more things, should be examined upon the following lines:
only first of all it must be clearly laid down that the inquiry we
are making concerns not things that are widely divergent and
that exhibit great differences from one another (for nobody
raises any doubt whether happiness or wealth is more
desirable), but things that are nearly related and about which
we commonly discuss for which of the two we ought rather to
vote, because we do not see any advantage on either side as
compared with the other. Clearly, in such cases if we can show a
single advantage, or more than one, our judgement will record
our assent that whichever side happens to have the advantage
is the more desirable.
First, then, that which is more lasting or secure is more
desirable than that which is less so: and so is that which is
more likely to be chosen by the prudent or by the good man or
by the right law, or by men who are good in any particular line,
when they make their choice as such, or by the experts in
regard to any particular class of things; i.e. either whatever most
of them or what all of them would choose; e.g. in medicine or in
carpentry those things are more desirable which most, or all,
doctors would choose; or, in general, whatever most men or all
men or all things would choose, e.g. the good: for everything
aims at the good. You should direct the argument you intend to
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employ to whatever purpose you require. Of what is 'better' or
'more desirable' the absolute standard is the verdict of the
better science, though relatively to a given individual the
standard may be his own particular science.
In the second place, that which is known as 'an x' is more
desirable than that which does not come within the genus 'x' -
e.g. justice than a just man; for the former falls within the
genus 'good', whereas the other does not, and the former is
called 'a good', whereas the latter is not: for nothing which does
not happen to belong to the genus in question is called by the
generic name; e.g. a 'white man' is not 'a colour'. Likewise also
in other cases.
Also, that which is desired for itself is more desirable than that
which is desired for something else; e.g. health is more
desirable than gymnastics: for the former is desired for itself,
the latter for something else. Also, that which is desirable in
itself is more desirable than what is desirable per accidens; e.g.
justice in our friends than justice in our enemies: for the former
is desirable in itself, the latter per accidens: for we desire that
our enemies should be just per accidens, in order that they may
do us no harm. This last principle is the same as the one that
precedes it, with, however, a different turn of expression. For we
desire justice in our friends for itself, even though it will make
no difference to us, and even though they be in India; whereas
in our enemies we desire it for something else, in order that
they may do us no harm.
Also, that which is in itself the cause of good is more desirable
than what is so per accidens, e.g. virtue than luck (for the
former in itself, and the latter per accidens, the cause of good
things), and so in other cases of the same kind. Likewise also in
the case of the contrary; for what is in itself the cause of evil is
more objectionable than what is so per accidens, e.g. vice and
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chance: for the one is bad in itself, whereas chance is so per
accidens.
Also, what is good absolutely is more desirable than what is
good for a particular person, e.g. recovery of health than a
surgical operation; for the former is good absolutely, the latter
only for a particular person, viz. the man who needs an
operation. So too what is good by nature is more desirable than
the good that is not so by nature, e.g. justice than the just man;
for the one is good by nature, whereas in the other case the
goodness is acquired. Also the attribute is more desirable which
belongs to the better and more honourable subject, e.g. to a god
rather than to a man, and to the soul rather than to the body. So
too the property of the better thing is better than the property
of the worse; e.g. the property of God than the property of man:
for whereas in respect of what is common in both of them they
do not differ at all from each other, in respect of their properties
the one surpasses the other. Also that is better which is
inherent in things better or prior or more honourable: thus (e.g.)
health is better than strength and beauty: for the former is
inherent in the moist and the dry, and the hot and the cold, in
fact in all the primary constituents of an animal, whereas the
others are inherent in what is secondary, strength being a
feature of the sinews and bones, while beauty is generally
supposed to consist in a certain symmetry of the limbs. Also the
end is generally supposed to be more desirable than the means,
and of two means, that which lies nearer the end. In general,
too, a means directed towards the end of life is more desirable
than a means to anything else, e.g. that which contributes to
happiness than that which contributes to prudence. Also the
competent is more desirable than the incompetent. Moreover, of
two productive agents that one is more desirable whose end is
better; while between a productive agent and an end we can
decide by a proportional sum whenever the excess of the one
end over the other is greater than that of the latter over its own
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productive means: e.g. supposing the excess of happiness over
health to be greater than that of health over what produces
health, then what produces happiness is better than health. For
what produces happiness exceeds what produces health just as
much as happiness exceeds health. But health exceeds what
produces health by a smaller amount; ergo, the excess of what
produces happiness over what produces health is greater than
that of health over what produces health. Clearly, therefore,
what produces happiness is more desirable than health: for it
exceeds the same standard by a greater amount. Moreover,
what is in itself nobler and more precious and praiseworthy is
more desirable than what is less so, e.g. friendship than wealth,
and justice than strength. For the former belong in themselves
to the class of things precious and praiseworthy, while the latter
do so not in themselves but for something else: for no one
prizes wealth for itself but always for something else, whereas
we prize friendship for itself, even though nothing else is likely
to come to us from it.
Moreover, whenever two things are very much like one another,
and we cannot see any superiority in the one over the other of
them, we should look at them from the standpoint of their
consequences. For the one which is followed by the greater good
is the more desirable: or, if the consequences be evil, that is
more desirable which is followed by the less evil. For though
both may be desirable, yet there may possibly be some
unpleasant consequence involved to turn the scale. Our survey
from the point of view of consequences lies in two directions,
for there are prior consequences and later consequences: e.g. if
a man learns, it follows that he was ignorant before and knows
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afterwards. As a rule, the later consequence is the better to
consider. You should take, therefore, whichever of the
consequences suits your purpose.
Moreover, a greater number of good things is more desirable
than a smaller, either absolutely or when the one is included in
the other, viz. the smaller number in the greater. An objection
may be raised suppose in some particular case the one is valued
for the sake of the other; for then the two together are not more
desirable than the one; e.g. recovery of health and health, than
health alone, inasmuch as we desire recovery of health for the
sake of health. Also it is quite possible for what is not good,
together with what is, to be more desirable than a greater
number of good things, e.g. the combination of happiness and
something else which is not good may be more desirable than
the combination of justice and courage. Also, the same things
are more valuable if accompanied than if unaccompanied by
pleasure, and likewise when free from pain than when attended
with pain.
Also, everything is more desirable at the season when it is of
greater consequence; e.g. freedom from pain in old age more
than in youth: for it is of greater consequence in old age. On the
same principle also, prudence is more desirable in old age; for
no man chooses the young to guide him, because he does not
expect them to be prudent. With courage, the converse is the
case, for it is in youth that the active exercise of courage is more
imperatively required. Likewise also with temperance; for the
young are more troubled by their passions than are their elders.
Also, that is more desirable which is more useful at every
season or at most seasons, e.g. justice and temperance rather
than courage: for they are always useful, while courage is only
useful at times. Also, that one of two things which if all possess,
we do not need the other thing, is more desirable than that
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which all may possess and still we want the other one as well.
Take the case of justice and courage; if everybody were just,
there would be no use for courage, whereas all might be
courageous, and still justice would be of use.
Moreover, judge by the destructions and losses and generations
and acquisitions and contraries of things: for things whose
destruction is more objectionable are themselves more
desirable. Likewise also with the losses and contraries of things;
for a thing whose loss or whose contrary is more objectionable
is itself more desirable. With the generations or acquisitions of
things the opposite is the case: for things whose acquisition or
generation is more desirable are themselves also desirable.
Another commonplace rule is that what is nearer to the good is
better and more desirable, i.e. what more nearly resembles the
good: thus justice is better than a just man. Also, that which is
more like than another thing to something better than itself, as
e.g. some say that Ajax was a better man than Odysseus
because he was more like Achilles. An objection may be raised
to this that it is not true: for it is quite possible that Ajax did not
resemble Achilles more nearly than Odysseus in the points
which made Achilles the best of them, and that Odysseus was a
good man, though unlike Achilles. Look also to see whether the
resemblance be that of a caricature, like the resemblance of a
monkey to a man, whereas a horse bears none: for the monkey
is not the more handsome creature, despite its nearer
resemblance to a man. Again, in the case of two things, if one is
more like the better thing while another is more like the worse,
then that is likely to be better which is more like the better. This
too, however, admits of an objection: for quite possibly the one
only slightly resembles the better, while the other strongly
resembles the worse, e.g. supposing the resemblance of Ajax to
Achilles to be slight, while that of Odysseus to Nestor is strong.
Also it may be that the one which is like the better type shows a
degrading likeness, whereas the one which is like the worse
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type improves upon it: witness the likeness of a horse to a
donkey, and that of a monkey to a man.
Another rule is that the more conspicuous good is more
desirable than the less conspicuous, and the more difficult than
the easier: for we appreciate better the possession of things that
cannot be easily acquired. Also the more personal possession is
more desirable than the more widely shared. Also, that which is
more free from connexion with evil: for what is not attended by
any unpleasantness is more desirable than what is so attended.
Moreover, if A be without qualification better than B, then also
the best of the members of A is better than the best of the
members of B; e.g. if Man be better than Horse, then also the
best man is better than the best horse. Also, if the best in A be
better than the best in B, then also A is better than B without
qualification; e.g. if the best man be better than the best horse,
then also Man is better than Horse without qualification.
Moreover, things which our friends can share are more desirable
than those they cannot. Also, things which we like rather to do
to our friend are more desirable than those we like to do to the
man in the street, e.g. just dealing and the doing of good rather
than the semblance of them: for we would rather really do good
to our friends than seem to do so, whereas towards the man in
the street the converse is the case.
Also, superfluities are better than necessities, and are
sometimes more desirable as well: for the good life is better
than mere life, and good life is a superfluity, whereas mere life
itself is a necessity. Sometimes, though, what is better is not
also more desirable: for there is no necessity that because it is
better it should also be more desirable: at least to be a
philosopher is better than to make money, but it is not more
desirable for a man who lacks the necessities of life. The
expression 'superfluity' applies whenever a man possesses the
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necessities of life and sets to work to secure as well other noble
acquisitions. Roughly speaking, perhaps, necessities are more
desirable, while superfluities are better.
Also, what cannot be got from another is more desirable than
what can be got from another as well, as (e.g.) is the case of
justice compared with courage. Also, A is more desirable if A is
desirable without B, but not B without A: power (e.g.) is not
desirable without prudence, but prudence is desirable without
power. Also, if of two things we repudiate the one in order to be
thought to possess the other, then that one is more desirable
which we wish to be thought to possess; thus (e.g.) we repudiate
the love of hard work in order that people may think us
geniuses.
Moreover, that is more desirable in whose absence it is less
blameworthy for people to be vexed; and that is more desirable
in whose absence it is more blameworthy for a man not to be
vexed.
Moreover, of things that belong to the same species one which
possesses the peculiar virtue of the species is more desirable
than one which does not. If both possess it, then the one which
possesses it in a greater degree is more desirable.
Moreover, if one thing makes good whatever it touches, while
another does not, the former is more desirable, just as also what
makes things warm is warmer than what does not. If both do
so, then that one is more desirable which does so in a greater
degree, or if it render good the better and more important object
- if (e.g.), the one makes good the soul, and the other the body.
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Moreover, judge things by their inflexions and uses and actions
and works, and judge these by them: for they go with each
other: e.g. if 'justly' means something more desirable than
'courageously', then also justice means something more
desirable than courage; and if justice be more desirable than
courage, then also 'justly' means something more desirable
than 'courageously'. Similarly also in the other cases.
Moreover, if one thing exceeds while the other falls short of the
same standard of good, the one which exceeds is the more
desirable; or if the one exceeds an even higher standard. Nay
more, if there be two things both preferable to something, the
one which is more highly preferable to it is more desirable than
the less highly preferable. Moreover, when the excess of a thing
is more desirable than the excess of something else, that thing
is itself also more desirable than the other, as (e.g.) friendship
than money: for an excess of friendship is more desirable than
an excess of money. So also that of which a man would rather
that it were his by his own doing is more desirable than what he
would rather get by another's doing, e.g. friends than money.
Moreover, judge by means of an addition, and see if the addition
of A to the same thing as B makes the whole more desirable
than does the addition of B. You must, however, beware of
adducing a case in which the common term uses, or in some
other way helps the case of, one of the things added to it, but
not the other, as (e.g.) if you took a saw and a sickle in
combination with the art of carpentry: for in the combination
the saw is a more desirable thing, but it is not a more desirable
thing without qualification. Again, a thing is more desirable if,
when added to a lesser good, it makes the whole greater good.
Likewise, also, you should judge by means of subtraction: for
the thing upon whose subtraction the remainder is a lesser
good may be taken to be a greater good, whichever it be whose
subtraction makes the remainder a lesser good.
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Also, if one thing be desirable for itself, and the other for the
look of it, the former is more desirable, as (e.g.) health than
beauty. A thing is defined as being desired for the look of it if,
supposing no one knew of it, you would not care to have it. Also,
it is more desirable both for itself and for the look of it, while
the other thing is desirable on the one ground alone. Also,
whichever is the more precious for itself, is also better and more
desirable. A thing may be taken to be more precious in itself
which we choose rather for itself, without anything else being
likely to come of it.
Moreover, you should distinguish in how many senses
'desirable' is used, and with a view to what ends, e.g.
expediency or honour or pleasure. For what is useful for all or
most of them may be taken to be more desirable than what is
not useful in like manner. If the same characters belong to both
things you should look and see which possesses them more
markedly, i.e. which of the two is the more pleasant or more
honourable or more expedient. Again, that is more desirable
which serves the better purpose, e.g. that which serves to
promote virtue more than that which serves to promote
pleasure. Likewise also in the case of objectionable things; for
that is more objectionable which stands more in the way of
what is desirable, e.g. disease more than ugliness: for disease is
a greater hindrance both to pleasure and to being good.
Moreover, argue by showing that the thing in question is in like
measure objectionable and desirable: for a thing of such a
character that a man might well desire and object to it alike is
less desirable than the other which is desirable only.
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Comparisons of things together should therefore be conducted
in the manner prescribed. The same commonplace rules are
useful also for showing that anything is simply desirable or
objectionable: for we have only to subtract the excess of one
thing over another. For if what is more precious be more
desirable, then also what is precious is desirable; and if what is
more useful be more desirable, then also what is useful is
desirable. Likewise, also, in the case of other things which admit
of comparisons of that kind. For in some cases in the very
course of comparing the things together we at once assert also
that each of them, or the one of them, is desirable, e.g.
whenever we call the one good 'by nature' and the other 'not by
nature': for dearly what is good by nature is desirable.
The commonplace rules relating to comparative degrees and
amounts ought to be taken in the most general possible form:
for when so taken they are likely to be useful in a larger number
of instances. It is possible to render some of the actual rules
given above more universal by a slight alteration of the
expression, e.g. that what by nature exhibits such and such a
quality exhibits that quality in a greater degree than what
exhibits it not by nature. Also, if one thing does, and another
does not, impart such and such a quality to that which
possesses it, or to which it belongs, then whichever does impart
it is of that quality in greater degree than the one which does
not impart it; and if both impart it, then that one exhibits it in a
greater degree which imparts it in a greater degree.
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Moreover, if in any character one thing exceeds and another
falls short of the same standard; also, if the one exceeds
something which exceeds a given standard, while the other
does not reach that standard, then clearly the first-named thing
exhibits that character in a greater degree. Moreover, you should
judge by means of addition, and see if A when added to the
same thing as B imparts to the whole such and such a character
in a more marked degree than B, or if, when added to a thing
which exhibits that character in a less degree, it imparts that
character to the whole in a greater degree. Likewise, also, you
may judge by means of subtraction: for a thing upon whose
subtraction the remainder exhibits such and such a character in
a less degree, itself exhibits that character in a greater degree.
Also, things exhibit such and such a character in a greater
degree if more free from admixture with their contraries; e.g.
that is whiter which is more free from admixture with black.
Moreover, apart from the rules given above, that has such and
such a character in greater degree which admits in a greater
degree of the definition proper to the given character; e.g. if the
definition of 'white' be 'a colour which pierces the vision', then
that is whiter which is in a greater degree a colour that pierces
the vision.
If the question be put in a particular and not in a universal
form, in the first place the universal constructive or destructive
commonplace rules that have been given may all be brought
into use. For in demolishing or establishing a thing universally
we also show it in particular: for if it be true of all, it is true also
of some, and if untrue of all, it is untrue of some. Especially
handy and of general application are the commonplace rules
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that are drawn from the opposites and co-ordinates and
inflexions of a thing: for public opinion grants alike the claim
that if all pleasure be good, then also all pain is evil, and the
claim that if some pleasure be good, then also some pain is evil.
Moreover, if some form of sensation be not a capacity, then also
some form of failure of sensation is not a failure of capacity.
Also, if the object of conception is in some cases an object of
knowledge, then also some form of conceiving is knowledge.
Again, if what is unjust be in some cases good, then also what is
just is in some cases evil; and if what happens justly is in some
cases evil, then also what happens unjustly is in some cases
good. Also, if what is pleasant is in some cases objectionable,
then pleasure is in some cases an objectionable thing. On the
same principle, also, if what is pleasant is in some cases
beneficial, then pleasure is in some cases a beneficial thing. The
case is the same also as regards the things that destroy, and the
processes of generation and destruction. For if anything that
destroys pleasure or knowledge be in some cases good, then we
may take it that pleasure or knowledge is in some cases an evil
thing. Likewise, also, if the destruction of knowledge be in some
cases a good thing or its production an evil thing, then
knowledge will be in some cases an evil thing; e.g. if for a man
to forget his disgraceful conduct be a good thing, and to
remember it be an evil thing, then the knowledge of his
disgraceful conduct may be taken to be an evil thing. The same
holds also in other cases: in all such cases the premiss and the
conclusion are equally likely to be accepted.
Moreover you should judge by means of greater or smaller or
like degrees: for if some member of another genus exhibit such
and such a character in a more marked degree than your object,
while no member of that genus exhibits that character at all,
then you may take it that neither does the object in question
exhibit it; e.g. if some form of knowledge be good in a greater
degree than pleasure, while no form of knowledge is good, then
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you may take it that pleasure is not good either. Also, you
should judge by a smaller or like degree in the same way: for so
you will find it possible both to demolish and to establish a
view, except that whereas both are possible by means of like
degrees, by means of a smaller degree it is possible only to
establish, not to overthrow. For if a certain form of capacity be
good in a like degree to knowledge, and a certain form of
capacity be good, then so also is knowledge; while if no form of
capacity be good, then neither is knowledge. If, too, a certain
form of capacity be good in a less degree than knowledge, and a
certain form of capacity be good, then so also is knowledge; but
if no form of capacity be good, there is no necessity that no
form of knowledge either should be good. Clearly, then, it is only
possible to establish a view by means of a less degree.
Not only by means of another genus can you overthrow a view,
but also by means of the same, if you take the most marked
instance of the character in question; e.g. if it be maintained
that some form of knowledge is good, then, suppose it to be
shown that prudence is not good, neither will any other kind be
good, seeing that not even the kind upon which there is most
general agreement is so. Moreover, you should go to work by
means of an hypothesis; you should claim that the attribute, if it
belongs or does not belong in one case, does so in a like degree
in all, e.g. that if the soul of man be immortal, so are other souls
as well, while if this one be not so, neither are the others. If,
then, it be maintained that in some instance the attribute
belongs, you must show that in some instance it does not
belong: for then it will follow, by reason of the hypothesis, that
it does not belong to any instance at all. If, on the other hand, it
be maintained that it does not belong in some instance, you
must show that it does belong in some instance, for in this way
it will follow that it belongs to all instances. It is clear that the
maker of the hypothesis universalizes the question, whereas it
was stated in a particular form: for he claims that the maker of
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a particular admission should make a universal admission,
inasmuch as he claims that if the attribute belongs in one
instance, it belongs also in all instances alike.
If the problem be indefinite, it is possible to overthrow a
statement in only one way; e.g. if a man has asserted that
pleasure is good or is not good, without any further definition.
For if he meant that a particular pleasure is good, you must
show universally that no pleasure is good, if the proposition in
question is to be demolished. And likewise, also, if he meant
that some particular pleasure is not good you must show
universally that all pleasure is good: it is impossible to demolish
it in any other way. For if we show that some particular pleasure
is not good or is good, the proposition in question is not yet
demolished. It is clear, then, that it is possible to demolish an
indefinite statement in one way only, whereas it can be
established in two ways: for whether we show universally that
all pleasure is good, or whether we show that a particular
pleasure is good, the proposition in question will have been
proved. Likewise, also, supposing we are required to argue that
some particular pleasure is not good, if we show that no
pleasure is good or that a particular pleasure is not good, we
shall have produced an argument in both ways, both universally
and in particular, to show that some particular pleasure is not
good. If, on the other hand, the statement made be definite, it
will be possible to demolish it in two ways; e.g. if it be
maintained that it is an attribute of some particular pleasure to
be good, while of some it is not: for whether it be shown that all
pleasure, or that no pleasure, is good, the proposition in
question will have been demolished. If, however, he has stated
that only one single pleasure is good, it is possible to demolish
it in three ways: for by showing that all pleasure, or that no
pleasure, or that more than one pleasure, is good, we shall have
demolished the statement in question. If the statement be
made still more definite, e.g. that prudence alone of the virtues
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is knowledge, there are four ways of demolishing it: for if it be
shown that all virtue is knowledge, or that no virtue is so, or
that some other virtue (e.g. justice) is so, or that prudence itself
is not knowledge, the proposition in question will have been
demolished.
It is useful also to take a look at individual instances, in cases
where some attribute has been said to belong or not to belong,
as in the case of universal questions. Moreover, you should take
a glance among genera, dividing them by their species until you
come to those that are not further divisible, as has been said
before:' for whether the attribute is found to belong in all cases
or in none, you should, after adducing several instances, claim
that he should either admit your point universally, or else bring
an objection showing in what case it does not hold. Moreover, in
cases where it is possible to make the accident definite either
specifically or numerically, you should look and see whether
perhaps none of them belongs, showing e.g. that time is not
moved, nor yet a movement, by enumerating how many species
there are of movement: for if none of these belong to time,
clearly it does not move, nor yet is a movement. Likewise, also,
you can show that the soul is not a number, by dividing all
numbers into either odd or even: for then, if the soul be neither
odd nor even, clearly it is not a number.
In regard then to Accident, you should set to work by means like
these, and in this manner.
Book IV
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Next we must go on to examine questions relating to Genus and
Property. These are elements in the questions that relate to
definitions, but dialecticians seldom address their inquiries to
these by themselves. If, then, a genus be suggested for
something that is, first take a look at all objects which belong to
the same genus as the thing mentioned, and see whether the
genus suggested is not predicated of one of them, as happens in
the case of an accident: e.g. if 'good' be laid down to be the
genus of 'pleasure', see whether some particular pleasure be not
good: for, if so, clearly good' is not the genus of pleasure: for the
genus is predicated of all the members of the same species.
Secondly, see whether it be predicated not in the category of
essence, but as an accident, as 'white' is predicated of 'snow', or
'self-moved' of the soul. For 'snow' is not a kind of 'white', and
therefore 'white' is not the genus of snow, nor is the soul a kind
of 'moving object': its motion is an accident of it, as it often is of
an animal to walk or to be walking. Moreover, 'moving' does not
seem to indicate the essence, but rather a state of doing or of
having something done to it. Likewise, also, 'white': for it
indicates not the essence of snow, but a certain quality of it. So
that neither of them is predicated in the category of 'essence'.
Especially you should take a look at the definition of Accident,
and see whether it fits the genus mentioned, as (e.g.) is also the
case in the instances just given. For it is possible for a thing to
be and not to be self-moved, and likewise, also, for it to be and
not to be white. So that neither of these attributes is the genus
but an accident, since we were saying that an accident is an
attribute which can belong to a thing and also not belong.
Moreover, see whether the genus and the species be not found
in the same division, but the one be a substance while the other
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is a quality, or the one be a relative while the other is a quality,
as (e.g.) 'slow' and 'swan' are each a substance, while 'white' is
not a substance but a quality, so that 'white' is not the genus
either of 'snow' or of 'swan'. Again, knowledge' is a relative,
while 'good' and 'noble' are each a quality, so that good, or
noble, is not the genus of knowledge. For the genera of relatives
ought themselves also to be relatives, as is the case with
'double': for multiple', which is the genus of 'double', is itself
also a relative. To speak generally, the genus ought to fall under
the same division as the species: for if the species be a
substance, so too should be the genus, and if the species be a
quality, so too the genus should be a quality; e.g. if white be a
quality, so too should colour be. Likewise, also, in other cases.
Again, see whether it be necessary or possible for the genus to
partake of the object which has been placed in the genus. 'To
partake' is defined as 'to admit the definition of that which is
partaken. Clearly, therefore, the species partake of the genera,
but not the genera of the species: for the species admits the
definition of the genus, whereas the genus does not admit that
of the species. You must look, therefore, and see whether the
genus rendered partakes or can possibly partake of the species,
e.g. if any one were to render anything as genus of 'being' or of
'unity': for then the result will be that the genus partakes of the
species: for of everything that is, 'being' and 'unity' are
predicated, and therefore their definition as well.
Moreover, see if there be anything of which the species rendered
is true, while the genus is not so, e.g. supposing 'being' or 'object
of knowledge' were stated to be the genus of 'object of opinion'.
For 'object of opinion' will be a predicate of what does not exist;
for many things which do not exist are objects of opinion;
whereas that 'being' or 'object of knowledge' is not predicated
of what does not exist is clear. So that neither 'being' nor 'object
of knowledge' is the genus of 'object of opinion': for of the
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objects of which the species is predicated, the genus ought to be
predicated as well.
Again, see whether the object placed in the genus be quite
unable to partake of any of its species: for it is impossible that it
should partake of the genus if it do not partake of any of its
species, except it be one of the species reached by the first
division: these do partake of the genus alone. If, therefore,
'Motion' be stated as the genus of pleasure, you should look and
see if pleasure be neither locomotion nor alteration, nor any of
the rest of the given modes of motion: for clearly you may then
take it that it does not partake of any of the species, and
therefore not of the genus either, since what partakes of the
genus must necessarily partake of one of the species as well: so
that pleasure could not be a species of Motion, nor yet be one of
the individual phenomena comprised under the term 'motion'.
For individuals as well partake in the genus and the species, as
(e.g.) an individual man partakes of both 'man' and 'animal'.
Moreover, see if the term placed in the genus has a wider
denotation than the genus, as (e.g.) 'object of opinion' has, as
compared with 'being': for both what is and what is not are
objects of opinion, so that 'object of opinion' could not be a
species of being: for the genus is always of wider denotation
than the species. Again, see if the species and its genus have an
equal denotation; suppose, for instance, that of the attributes
which go with everything, one were to be stated as a species
and the other as its genus, as for example Being and Unity: for
everything has being and unity, so that neither is the genus of
the other, since their denotation is equal. Likewise, also, if the
'first' of a series and the 'beginning' were to be placed one
under the other: for the beginning is first and the first is the
beginning, so that either both expressions are identical or at
any rate neither is the genus of the other. The elementary
principle in regard to all such cases is that the genus has a
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wider denotation than the species and its differentia: for the
differentia as well has a narrower denotation than the genus.
See also whether the genus mentioned fails, or might be
generally thought to fail, to apply to some object which is not
specifically different from the thing in question; or, if your
argument be constructive, whether it does so apply. For all
things that are not specifically different have the same genus. If,
therefore, it be shown to apply to one, then clearly it applies to
all, and if it fails to apply to one, clearly it fails to apply to any;
e.g. if any one who assumes 'indivisible lines' were to say that
the 'indivisible' is their genus. For the aforesaid term is not the
genus of divisible lines, and these do not differ as regards their
species from indivisible: for straight lines are never different
from each other as regards their species.
Look and see, also, if there be any other genus of the given
species which neither embraces the genus rendered nor yet
falls under it, e.g. suppose any one were to lay down that
'knowledge' is the genus of justice. For virtue is its genus as
well, and neither of these genera embraces the remaining one,
so that knowledge could not be the genus of justice: for it is
generally accepted that whenever one species falls under two
genera, the one is embraced by the other. Yet a principle of this
kind gives rise to a difficulty in some cases. For some people
hold that prudence is both virtue and knowledge, and that
neither of its genera is embraced by the other: although
certainly not everybody admits that prudence is knowledge. If,
however, any one were to admit the truth of this assertion, yet it
would still be generally agreed to be necessary that the genera
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of the same object must at any rate be subordinate either the
one to the other or both to the same, as actually is the case with
virtue and knowledge. For both fall under the same genus; for
each of them is a state and a disposition. You should look,
therefore, and see whether neither of these things is true of the
genus rendered; for if the genera be subordinate neither the one
to the other nor both to the same, then what is rendered could
not be the true genus.
Look, also, at the genus of the genus rendered, and so
continually at the next higher genus, and see whether all are
predicated of the species, and predicated in the category of
essence: for all the higher genera should be predicated of the
species in the category of essence. If, then, there be anywhere a
discrepancy, clearly what is rendered is not the true genus.
[Again, see whether either the genus itself, or one of its higher
genera, partakes of the species: for the higher genus does not
partake of any of the lower.] If, then, you are overthrowing a
view, follow the rule as given: if establishing one, then - suppose
that what has been named as genus be admitted to belong to
the species, only it be disputed whether it belongs as genus - it
is enough to show that one of its higher genera is predicated of
the species in the category of essence. For if one of them be
predicated in the category of essence, all of them, both higher
and lower than this one, if predicated at all of the species, will
be predicated of it in the category of essence: so that what has
been rendered as genus is also predicated in the category of
essence. The premiss that when one genus is predicated in the
category of essence, all the rest, if predicated at all, will be
predicated in the category of essence, should be secured by
induction. Supposing, however, that it be disputed whether
what has been rendered as genus belongs at all, it is not enough
to show that one of the higher genera is predicated of the
species in the category of essence: e.g. if any one has rendered
'locomotion' as the genus of walking, it is not enough to show
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that walking is 'motion' in order to show that it is 'locomotion',
seeing that there are other forms of motion as well; but one
must show in addition that walking does not partake of any of
the species of motion produced by the same division except
locomotion. For of necessity what partakes of the genus
partakes also of one of the species produced by the first division
of the genus. If, therefore, walking does not partake either of
increase or decrease or of the other kinds of motion, clearly it
would partake of locomotion, so that locomotion would be the
genus of walking.
Again, look among the things of which the given species is
predicated as genus, and see if what is rendered as its genus be
also predicated in the category of essence of the very things of
which the species is so predicated, and likewise if all the genera
higher than this genus are so predicated as well. For if there be
anywhere a discrepancy, clearly what has been rendered is not
the true genus: for had it been the genus, then both the genera
higher than it, and it itself, would all have been predicated in
the category of essence of those objects of which the species too
is predicated in the category of essence. If, then, you are
overthrowing a view, it is useful to see whether the genus fails
to be predicated in the category of essence of those things of
which the species too is predicated. If establishing a view, it is
useful to see whether it is predicated in the category of essence:
for if so, the result will be that the genus and the species will be
predicated of the same object in the category of essence, so that
the same object falls under two genera: the genera must
therefore of necessity be subordinate one to the other, and
therefore if it be shown that the one we wish to establish as
genus is not subordinate to the species, clearly the species
would be subordinate to it, so that you may take it as shown
that it is the genus.
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Look, also, at the definitions of the genera, and see whether
they apply both to the given species and to the objects which
partake of the species. For of necessity the definitions of its
genera must be predicated of the species and of the objects
which partake of the species: if, then, there be anywhere a
discrepancy, clearly what has been rendered is not the genus.
Again, see if he has rendered the differentia as the genus, e.g.
'immortal' as the genus of 'God'. For 'immortal' is a differentia
of 'living being', seeing that of living beings some are mortal
and others immortal. Clearly, then, a bad mistake has been
made; for the differentia of a thing is never its genus. And that
this is true is clear: for a thing's differentia never signifies its
essence, but rather some quality, as do 'walking' and 'biped'.
Also, see whether he has placed the differentia inside the
genus, e.g. by taking 'odd' as a number'. For 'odd' is a differentia
of number, not a species. Nor is the differentia generally
thought to partake of the genus: for what partakes of the genus
is always either a species or an individual, whereas the
differentia is neither a species nor an individual. Clearly,
therefore, the differentia does not partake of the genus, so that
'odd' too is no species but a differentia, seeing that it does not
partake of the genus.
Moreover, see whether he has placed the genus inside the
species, e.g. by taking 'contact' to be a 'juncture', or 'mixture' a
'fusion', or, as in Plato's definition,' 'locomotion' to be the same
as 'carriage'. For there is no necessity that contact should be
juncture: rather, conversely, juncture must be contact: for what
is in contact is not always joined, though what is joined is
always in contact. Likewise, also, in the remaining instances: for
mixture is not always a 'fusion' (for to mix dry things does not
fuse them), nor is locomotion always 'carriage'. For walking is
not generally thought to be carriage: for 'carriage' is mostly used
398
of things that change one place for another involuntarily, as
happens in the case of inanimate things. Clearly, also, the
species, in the instances given, has a wider denotation than the
genus, whereas it ought to be vice versa. Again, see whether he
has placed the differentia inside the species, by taking (e.g.)
'immortal' to be 'a god'. For the result will be that the species
has an equal or wider denotation: and this cannot be, for always
the differentia has an equal or a wider denotation than the
species. Moreover, see whether he has placed the genus inside
the differentia, by making 'colour' (e.g.) to be a thing that
'pierces', or 'number' a thing that is 'odd'. Also, see if he has
mentioned the genus as differentia: for it is possible for a man
to bring forward a statement of this kind as well, e.g. that
'mixture' is the differentia of 'fusion', or that change of place' is
the differentia of 'carriage'. All such cases should be examined
by means of the same principles: for they depend upon
common rules: for the genus should have a wider denotation
that its differentia, and also should not partake of its
differentia; whereas, if it be rendered in this manner, neither of
the aforesaid requirements can be satisfied: for the genus will
both have a narrower denotation than its differentia, and will
partake of it.
Again, if no differentia belonging to the genus be predicated of
the given species, neither will the genus be predicated of it; e.g.
of 'soul' neither 'odd' nor 'even' is predicated: neither therefore
is 'number'. Moreover, see whether the species is naturally prior
and abolishes the genus along with itself: for the contrary is the
general view. Moreover, if it be possible for the genus stated, or
for its differentia, to be absent from the alleged species, e.g. for
'movement' to be absent from the 'soul', or 'truth and falsehood'
from 'opinion', then neither of the terms stated could be its
genus or its differentia: for the general view is that the genus
and the differentia accompany the species, as long as it exists.
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Look and see, also, if what is placed in the genus partakes or
could possibly partake of any contrary of the genus: for in that
case the same thing will at the same time partake of contrary
things, seeing that the genus is never absent from it, while it
partakes, or can possibly partake, of the contrary genus as well.
Moreover, see whether the species shares in any character
which it is utterly impossible for any member of the genus to
have. Thus (e.g.) if the soul has a share in life, while it is
impossible for any number to live, then the soul could not be a
species of number.
You should look and see, also, if the species be a homonym of
the genus, and employ as your elementary principles those
already stated for dealing with homonymity: for the genus and
the species are synonymous.
Seeing that of every genus there is more than one species, look
and see if it be impossible that there should be another species
than the given one belonging to the genus stated: for if there
should be none, then clearly what has been stated could not be
a genus at all.
Look and see, also, if he has rendered as genus a metaphorical
expression, describing (e.g. 'temperance' as a 'harmony': a
'harmony': for a genus is always predicated of its species in its
literal sense, whereas 'harmony' is predicated of temperance
not in a literal sense but metaphorically: for a harmony always
consists in notes.
Moreover, if there be any contrary of the species, examine it.
The examination may take different forms; first of all see if the
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contrary as well be found in the same genus as the species,
supposing the genus to have no contrary; for contraries ought to
be found in the same genus, if there be no contrary to the
genus. Supposing, on the other hand, that there is a contrary to
the genus, see if the contrary of the species be found in the
contrary genus: for of necessity the contrary species must be in
the contrary genus, if there be any contrary to the genus. Each
of these points is made plain by means of induction. Again, see
whether the contrary of the species be not found in any genus
at all, but be itself a genus, e.g. 'good': for if this be not found in
any genus, neither will its contrary be found in any genus, but
will itself be a genus, as happens in the case of 'good' and 'evil':
for neither of these is found in a genus, but each of them is a
genus. Moreover, see if both genus and species be contrary to
something, and one pair of contraries have an intermediary, but
not the other. For if the genera have an intermediary, so should
their species as well, and if the species have, so should their
genera as well, as is the case with (1) virtue and vice and (2)
justice and injustice: for each pair has an intermediary. An
objection to this is that there is no intermediary between health
and disease, although there is one between evil and good. Or
see whether, though there be indeed an intermediary between
both pairs, i.e. both between the species and between the
genera, yet it be not similarly related, but in one case be a mere
negation of the extremes, whereas in the other case it is a
subject. For the general view is that the relation should be
similar in both cases, as it is in the cases of virtue and vice and
of justice and injustice: for the intermediaries between both are
mere negations. Moreover, whenever the genus has no contrary,
look and see not merely whether the contrary of the species be
found in the same genus, but the intermediate as well: for the
genus containing the extremes contains the intermediates as
well, as (e.g.) in the case of white and black: for 'colour' is the
genus both of these and of all the intermediate colours as well.
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An objection may be raised that 'defect' and 'excess' are found
in the same genus (for both are in the genus 'evil'), whereas
moderate amount', the intermediate between them, is found
not in 'evil' but in 'good'. Look and see also whether, while the
genus has a contrary, the species has none; for if the genus be
contrary to anything, so too is the species, as virtue to vice and
justice to injustice.
Likewise, also, if one were to look at other instances, one would
come to see clearly a fact like this. An objection may be raised
in the case of health and disease: for health in general is the
contrary of disease, whereas a particular disease, being a
species of disease, e.g. fever and ophthalmia and any other
particular disease, has no contrary.
If, therefore, you are demolishing a view, there are all these
ways in which you should make your examination: for if the
aforesaid characters do not belong to it, clearly what has been
rendered is not the genus. If, on the other hand, you are
establishing a view, there are three ways: in the first place, see
whether the contrary of the species be found in the genus
stated, suppose the genus have no contrary: for if the contrary
be found in it, clearly the species in question is found in it as
well. Moreover, see if the intermediate species is found in the
genus stated: for whatever genus contains the intermediate
contains the extremes as well. Again, if the genus have a
contrary, look and see whether also the contrary species is
found in the contrary genus: for if so, clearly also the species in
question is found in the genus in question.
Again, consider in the case of the inflexions and the co-
ordinates of species and genus, and see whether they follow
likewise, both in demolishing and in establishing a view. For
whatever attribute belongs or does not belong to one belongs or
does not belong at the same time to all; e.g. if justice be a
402
particular form of knowledge, then also 'justly' is 'knowingly'
and the just man is a man of knowledge: whereas if any of
these things be not so, then neither is any of the rest of them.
Again, consider the case of things that bear a like relation to
one another. Thus (e.g.) the relation of the pleasant to pleasure
is like that of the useful to the good: for in each case the one
produces the other. If therefore pleasure be a kind of 'good',
then also the pleasant will be a kind of 'useful': for clearly it
may be taken to be productive of good, seeing that pleasure is
good. In the same way also consider the case of processes of
generation and destruction; if (e.g.) to build be to be active, then
to have built is to have been active, and if to learn be to
recollect, then also to have learnt is to have recollected, and if to
be decomposed be to be destroyed, then to have been
decomposed is to have been destroyed, and decomposition is a
kind of destruction. Consider also in the same way the case of
things that generate or destroy, and of the capacities and uses
of things; and in general, both in demolishing and in
establishing an argument, you should examine things in the
light of any resemblance of whatever description, as we were
saying in the case of generation and destruction. For if what
tends to destroy tends to decompose, then also to be destroyed
is to be decomposed: and if what tends to generate tends to
produce, then to be generated is to be produced, and generation
is production. Likewise, also, in the case of the capacities and
uses of things: for if a capacity be a disposition, then also to be
capable of something is to be disposed to it, and if the use of
anything be an activity, then to use it is to be active, and to have
used it is to have been active.
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If the opposite of the species be a privation, there are two ways
of demolishing an argument, first of all by looking to see if the
opposite be found in the genus rendered: for either the
privation is to be found absolutely nowhere in the same genus,
or at least not in the same ultimate genus: e.g. if the ultimate
genus containing sight be sensation, then blindness will not be
a sensation. Secondly, if there be a sensation. Secondly, if there
be a privation opposed to both genus and species, but the
opposite of the species be not found in the opposite of the
genus, then neither could the species rendered be in the genus
rendered. If, then, you are demolishing a view, you should follow
the rule as stated; but if establishing one there is but one way:
for if the opposite species be found in the opposite genus, then
also the species in question would be found in the genus in
question: e.g. if 'blindness' be a form of 'insensibility', then
'sight' is a form of 'sensation'.
Again, look at the negations of the genus and species and
convert the order of terms, according to the method described
in the case of Accident: e.g. if the pleasant be a kind of good,
what is not good is not pleasant. For were this no something not
good as well would then be pleasant. That, however, cannot be,
for it is impossible, if 'good' be the genus of pleasant, that
anything not good should be pleasant: for of things of which the
genus is not predicated, none of the species is predicated either.
Also, in establishing a view, you should adopt the same method
of examination: for if what is not good be not pleasant, then
what is pleasant is good, so that 'good' is the genus of
'pleasant'.
If the species be a relative term, see whether the genus be a
relative term as well: for if the species be a relative term, so too
is the genus, as is the case with 'double' and 'multiple': for each
is a relative term. If, on the other hand, the genus be a relative
term, there is no necessity that the species should be so as well:
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for 'knowledge 'is a relative term, but not so 'grammar'. Or
possibly not even the first statement would be generally
considered true: for virtue is a kind of 'noble' and a kind of
'good' thing, and yet, while 'virtue' is a relative term, 'good' and
'noble' are not relatives but qualities. Again, see whether the
species fails to be used in the same relation when called by its
own name, and when called by the name of its genus: e.g. if the
term 'double' be used to mean the double of a 'half, then also
the term 'multiple' ought to be used to mean multiple of a 'half.
Otherwise 'multiple' could not be the genus of 'double'.
Moreover, see whether the term fail to be used in the same
relation both when called by the name of its genus, and also
when called by those of all the genera of its genus. For if the
double be a multiple of a half, then 'in excess of 'will also be
used in relation to a 'half: and, in general, the double will be
called by the names of all the higher genera in relation to a
'half. An objection may be raised that there is no necessity for a
term to be used in the same relation when called by its own
name and when called by that of its genus: for 'knowledge' is
called knowledge 'of an object', whereas it is called a 'state' and
'disposition' not of an 'object' but of the 'soul'.
Again, see whether the genus and the species be used in the
same way in respect of the inflexions they take, e.g. datives and
genitives and all the rest. For as the species is used, so should
the genus be as well, as in the case of 'double' and its higher
genera: for we say both 'double of and 'multiple of a thing.
Likewise, also, in the case of 'knowledge': for both knowledge'
itself and its genera, e.g. 'disposition' and 'state', are said to be
'of something. An objection may be raised that in some cases it
is not so: for we say 'superior to' and 'contrary to' so and so,
whereas 'other', which is the genus of these terms, demands
not 'to' but 'than': for the expression is 'other than' so and so.
405
Again, see whether terms used in like case relationships fail to
yield a like construction when converted, as do 'double' and
'multiple'. For each of these terms takes a genitive both in itself
and in its converted form: for we say both a half of and 'a
fraction of something. The case is the same also as regards
both 'knowledge' and 'conception': for these take a genitive, and
by conversion an 'object of knowledge' and an 'object of
conception' are both alike used with a dative. If, then, in any
cases the constructions after conversion be not alike, clearly the
one term is not the genus of the other.
Again, see whether the species and the genus fail to be used in
relation to an equal number of things: for the general view is
that the uses of both are alike and equal in number, as is the
case with 'present' and 'grant'. For a present' is of something or
to some one, and also a 'grant' is of something and to some one:
and 'grant' is the genus of 'present', for a 'present' is a 'grant
that need not be returned'. In some cases, however, the number
of relations in which the terms are used happens not to be
equal, for while 'double' is double of something, we speak of 'in
excess' or 'greater' in something, as well as of or than
something: for what is in excess or greater is always in excess
in something, as well as in excess of something. Hence the
terms in question are not the genera of 'double', inasmuch as
they are not used in relation to an equal number of things with
the species. Or possibly it is not universally true that species
and genus are used in relation to an equal number of things.
See, also, if the opposite of the species have the opposite of the
genus as its genus, e.g. whether, if 'multiple' be the genus of
'double', 'fraction' be also the genus of 'half. For the opposite of
the genus should always be the genus of the opposite species. If,
then, any one were to assert that knowledge is a kind of
sensation, then also the object of knowledge will have to be a
kind of object of sensation, whereas it is not: for an object of
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knowledge is not always an object of sensation: for objects of
knowledge include some of the objects of intuition as well.
Hence 'object of sensation' is not the genus of 'object of
knowledge': and if this be so, neither is 'sensation' the genus of
'knowledge'.
Seeing that of relative terms some are of necessity found in, or
used of, the things in relation to which they happen at any time
to be used (e.g. 'disposition' and 'state' and 'balance'; for in
nothing else can the aforesaid terms possibly be found except
in the things in relation to which they are used), while others
need not be found in the things in relation to which they are
used at any time, though they still may be (e.g. if the term
'object of knowledge' be applied to the soul: for it is quite
possible that the knowledge of itself should be possessed by the
soul itself, but it is not necessary, for it is possible for this same
knowledge to be found in some one else), while for others,
again, it is absolutely impossible that they should be found in
the things in relation to which they happen at any time to be
used (as e.g. that the contrary should be found in the contrary
or knowledge in the object of knowledge, unless the object of
knowledge happen to be a soul or a man) - you should look,
therefore, and see whether he places a term of one kind inside a
genus that is not of that kind, e.g. suppose he has said that
'memory' is the 'abiding of knowledge'. For 'abiding' is always
found in that which abides, and is used of that, so that the
abiding of knowledge also will be found in knowledge. Memory,
then, is found in knowledge, seeing that it is the abiding of
knowledge. But this is impossible, for memory is always found
in the soul. The aforesaid commonplace rule is common to the
subject of Accident as well: for it is all the same to say that
'abiding' is the genus of memory, or to allege that it is an
accident of it. For if in any way whatever memory be the abiding
of knowledge, the same argument in regard to it will apply.
407
Again, see if he has placed what is a 'state' inside the genus
'activity', or an activity inside the genus 'state', e.g. by defining
'sensation' as 'movement communicated through the body': for
sensation is a 'state', whereas movement is an 'activity'.
Likewise, also, if he has said that memory is a 'state that is
retentive of a conception', for memory is never a state, but
rather an activity.
They also make a bad mistake who rank a 'state' within the
'capacity' that attends it, e.g. by defining 'good temper' as the
'control of anger', and 'courage' and 'justice' as 'control of fears'
and of 'gains': for the terms 'courageous' and 'good-tempered'
are applied to a man who is immune from passion, whereas
'self-controlled' describes the man who is exposed to passion
and not led by it. Quite possibly, indeed, each of the former is
attended by a capacity such that, if he were exposed to passion,
he would control it and not be led by it: but, for all that, this is
not what is meant by being 'courageous' in the one case, and
'good tempered' in the other; what is meant is an absolute
immunity from any passions of that kind at all.
Sometimes, also, people state any kind of attendant feature as
the genus, e.g. 'pain' as the genus of 'anger' and 'conception' as
that of conviction'. For both of the things in question follow in a
certain sense upon the given species, but neither of them is
genus to it. For when the angry man feels pain, the pain bas
appeared in him earlier than the anger: for his anger is not the
cause of his pain, but his pain of his anger, so that anger
emphatically is not pain. By the same reasoning, neither is
conviction conception: for it is possible to have the same
408
conception even without being convinced of it, whereas this is
impossible if conviction be a species of conception: for it is
impossible for a thing still to remain the same if it be entirely
transferred out of its species, just as neither could the same
animal at one time be, and at another not be, a man. If, on the
other hand, any one says that a man who has a conception
must of necessity be also convinced of it, then 'conception' and
'conviction' will be used with an equal denotation, so that not
even so could the former be the genus of the latter: for the
denotation of the genus should be wider.
See, also, whether both naturally come to be anywhere in the
same thing: for what contains the species contains the genus as
well: e.g. what contains 'white' contains 'colour' as well, and
what contains 'knowledge of grammar' contains 'knowledge' as
well. If, therefore, any one says that 'shame' is 'fear', or that
'anger' is 'pain', the result will be that genus and species are not
found in the same thing: for shame is found in the 'reasoning'
faculty, whereas fear is in the 'spirited' faculty, and 'pain' is
found in the faculty of 'desires', (for in this pleasure also is
found), whereas 'anger' is found in the 'spirited' faculty. Hence
the terms rendered are not the genera, seeing that they do not
naturally come to be in the same faculty as the species.
Likewise, also, if 'friendship' be found in the faculty of desires,
you may take it that it is not a form of 'wishing': for wishing is
always found in the 'reasoning' faculty. This commonplace rule
is useful also in dealing with Accident: for the accident and that
of which it is an accident are both found in the same thing, so
that if they do not appear in the same thing, clearly it is not an
accident.
Again, see if the species partakes of the genus attributed only in
some particular respect: for it is the general view that the genus
is not thus imparted only in some particular respect: for a man
is not an animal in a particular respect, nor is grammar
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knowledge in a particular respect only. Likewise also in other
instances. Look, therefore, and see if in the case of any of its
species the genus be imparted only in a certain respect; e.g. if
'animal' has been described as an 'object of perception' or of
'sight'. For an animal is an object of perception or of sight in a
particular respect only; for it is in respect of its body that it is
perceived and seen, not in respect of its soul, so that - 'object of
sight' and 'object of perception' could not be the genus of
'animal'.
Sometimes also people place the whole inside the part without
detection, defining (e.g.) 'animal' as an 'animate body'; whereas
the part is not predicated in any sense of the whole, so that
'body' could not be the genus of animal, seeing that it is a part.
See also if he has put anything that is blameworthy or
objectionable into the class 'capacity' or 'capable', e.g. by
defining a 'sophist' or a 'slanderer', or a 'thief as 'one who is
capable of secretly thieving other people's property'. For none of
the aforesaid characters is so called because he is 'capable' in
one of these respects: for even God and the good man are
capable of doing bad things, but that is not their character: for it
is always in respect of their choice that bad men are so called.
Moreover, a capacity is always a desirable thing: for even the
capacities for doing bad things are desirable, and therefore it is
we say that even God and the good man possess them; for they
are capable (we say) of doing evil. So then 'capacity' can never
be the genus of anything blameworthy. Else, the result will be
that what is blameworthy is sometimes desirable: for there will
be a certain form of capacity that is blameworthy.
Also, see if he has put anything that is precious or desirable for
its own sake into the class 'capacity' or 'capable' or 'productive'
of anything. For capacity, and what is capable or productive of
anything, is always desirable for the sake of something else.
410
Or see if he has put anything that exists in two genera or more
into one of them only. For some things it is impossible to place
in a single genus, e.g. the 'cheat' and the 'slanderer': for neither
he who has the will without the capacity, nor he who has the
capacity without the will, is a slanderer or cheat, but he who
has both of them. Hence he must be put not into one genus, but
into both the aforesaid genera.
Moreover, people sometimes in converse order render genus as
differentia, and differentia as genus, defining (e.g.)
astonishment as 'excess of wonderment' and conviction as
'vehemence of conception'. For neither 'excess' nor 'vehemence'
is the genus, but the differentia: for astonishment is usually
taken to be an 'excessive wonderment', and conviction to be a
'vehement conception', so that 'wonderment' and 'conception'
are the genus, while 'excess' and 'vehemence' are the
differentia. Moreover, if any one renders 'excess' and
'vehemence' as genera, then inanimate things will be convinced
and astonished. For 'vehemence' and 'excess' of a thing are
found in a thing which is thus vehement and in excess. If,
therefore, astonishment be excess of wonderment the
astonishment will be found in the wonderment, so that
'wonderment' will be astonished! Likewise, also, conviction will
be found in the conception, if it be 'vehemence of conception',
so that the conception will be convinced. Moreover, a man who
renders an answer in this style will in consequence find himself
calling vehemence vehement and excess excessive: for there is
such a thing as a vehement conviction: if then conviction be
'vehemence', there would be a 'vehement vehemence'. Likewise,
also, there is such a thing as excessive astonishment: if then
astonishment be an excess, there would be an 'excessive
excess'. Whereas neither of these things is generally believed,
any more than that knowledge is a knower or motion a moving
thing.
411
Sometimes, too, people make the bad mistake of putting an
affection into that which is affected, as its genus, e.g. those who
say that immortality is everlasting life: for immortality seems to
be a certain affection or accidental feature of life. That this
saying is true would appear clear if any one were to admit that a
man can pass from being mortal and become immortal: for no
one will assert that he takes another life, but that a certain
accidental feature or affection enters into this one as it is. So
then 'life' is not the genus of immortality.
Again, see if to an affection he has ascribed as genus the object
of which it is an affection, by defining (e.g.) wind as 'air in
motion'. Rather, wind is 'a movement of air': for the same air
persists both when it is in motion and when it is still. Hence
wind is not 'air' at all: for then there would also have been wind
when the air was not in motion, seeing that the same air which
formed the wind persists. Likewise, also, in other cases of the
kind. Even, then, if we ought in this instance to admit the point
that wind is 'air in motion', yet we should accept a definition of
the kind, not about all those things of which the genus is not
true, but only in cases where the genus rendered is a true
predicate. For in some cases, e.g. 'mud' or 'snow', it is not
generally held to be true. For people tell you that snow is 'frozen
water' and mud is earth mixed with moisture', whereas snow is
not water, nor mud earth, so that neither of the terms rendered
could be the genus: for the genus should be true of all its
species. Likewise neither is wine 'fermented water', as
Empedocles speaks of 'water fermented in wood';' for it simply
is not water at all.
412
Moreover, see whether the term rendered fail to be the genus of
anything at all; for then clearly it also fails to be the genus of
the species mentioned. Examine the point by seeing whether
the objects that partake of the genus fail to be specifically
different from one another, e.g. white objects: for these do not
differ specifically from one another, whereas of a genus the
species are always different, so that 'white' could not be the
genus of anything.
Again, see whether he has named as genus or differentia some
feature that goes with everything: for the number of attributes
that follow everything is comparatively large: thus (e.g.) 'Being'
and 'Unity' are among the number of attributes that follow
everything. If, therefore, he has rendered 'Being' as a genus,
clearly it would be the genus of everything, seeing that it is
predicated of everything; for the genus is never predicated of
anything except of its species. Hence Unity, inter alia, will be a
species of Being. The result, therefore, is that of all things of
which the genus is predicated, the species is predicated as well,
seeing that Being and Unity are predicates of absolutely
everything, whereas the predication of the species ought to be
of narrower range. If, on the other hand, he has named as
differentia some attribute that follows everything, clearly the
denotation of the differentia will be equal to, or wider than, that
of the genus. For if the genus, too, be some attribute that follows
everything, the denotation of the differentia will be equal to its
denotation, while if the genus do not follow everything, it will
be still wider.
Moreover, see if the description 'inherent in S' be used of the
genus rendered in relation to its species, as it is used of 'white'
in the case of snow, thus showing clearly that it could not be the
genus: for 'true of S' is the only description used of the genus in
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relation to its species. Look and see also if the genus fails to be
synonymous with its species. For the genus is always predicated
of its species synonymously.
Moreover, beware, whenever both species and genus have a
contrary, and he places the better of the contraries inside the
worse genus: for the result will be that the remaining species
will be found in the remaining genus, seeing that contraries are
found in contrary genera, so that the better species will be
found in the worse genus and the worse in the better: whereas
the usual view is that of the better species the genus too is
better. Also see if he has placed the species inside the worse
and not inside the better genus, when it is at the same time
related in like manner to both, as (e.g.) if he has defined the
'soul' as a 'form of motion' or 'a form of moving thing'. For the
same soul is usually thought to be a principle alike of rest and
of motion, so that, if rest is the better of the two, this is the
genus into which the soul should have been put.
Moreover, judge by means of greater and less degrees: if
overthrowing a view, see whether the genus admits of a greater
degree, whereas neither the species itself does so, nor any term
that is called after it: e.g. if virtue admits of a greater degree, so
too does justice and the just man: for one man is called 'more
just than another'. If, therefore, the genus rendered admits of a
greater degree, whereas neither the species does so itself nor
yet any term called after it, then what has been rendered could
not be the genus.
Again, if what is more generally, or as generally, thought to be
the genus be not so, clearly neither is the genus rendered. The
commonplace rule in question is useful especially in cases
where the species appears to have several predicates in the
category of essence, and where no distinction has been drawn
between them, and we cannot say which of them is genus; e.g.
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both 'pain' and the 'conception of a slight' are usually thought
to be predicates of 'anger in the category of essence: for the
angry man is both in pain and also conceives that he is slighted.
The same mode of inquiry may be applied also to the case of
the species, by comparing it with some other species: for if the
one which is more generally, or as generally, thought to be
found in the genus rendered be not found therein, then clearly
neither could the species rendered be found therein.
In demolishing a view, therefore, you should follow the rule as
stated. In establishing one, on the other hand, the
commonplace rule that you should see if both the genus
rendered and the species admit of a greater degree will not
serve: for even though both admit it, it is still possible for one
not to be the genus of the other. For both 'beautiful' and 'white'
admit of a greater degree, and neither is the genus of the other.
On the other hand, the comparison of the genera and of the
species one with another is of use: e.g. supposing A and B to
have a like claim to be genus, then if one be a genus, so also is
the other. Likewise, also, if what has less claim be a genus, so
also is what has more claim: e.g. if 'capacity' have more claim
than 'virtue' to be the genus of self-control, and virtue be the
genus, so also is capacity. The same observations will apply also
in the case of the species. For instance, supposing A and B to
have a like claim to be a species of the genus in question, then if
the one be a species, so also is the other: and if that which is
less generally thought to be so be a species, so also is that
which is more generally thought to be so.
Moreover, to establish a view, you should look and see if the
genus is predicated in the category of essence of those things of
which it has been rendered as the genus, supposing the species
rendered to be not one single species but several different ones:
for then clearly it will be the genus. If, on the other, the species
rendered be single, look and see whether the genus be
415
predicated in the category of essence of other species as well:
for then, again, the result will be that it is predicated of several
different species.
Since some people think that the differentia, too, is a predicate
of the various species in the category of essence, you should
distinguish the genus from the differentia by employing the
aforesaid elementary principles - (a) that the genus has a wider
denotation than the differentia; (b) that in rendering the
essence of a thing it is more fitting to state the genus than the
differentia: for any one who says that 'man' is an 'animal'
shows what man is better than he who describes him as
'walking'; also (c) that the differentia always signifies a quality
of the genus, whereas the genus does not do this of the
differentia: for he who says 'walking' describes an animal of a
certain quality, whereas he who says 'animal' describes an
animal of a certain quality, whereas he who says 'animal' does
not describe a walking thing of a certain quality
The differentia, then, should be distinguished from the genus in
this manner. Now seeing it is generally held that if what is
musical, in being musical, possesses knowledge in some
respect, then also 'music' is a particular kind of 'knowledge';
and also that if what walks is moved in walking, then 'walking'
is a particular kind of 'movement'; you should therefore
examine in the aforesaid manner any genus in which you want
to establish the existence of something; e.g. if you wish to prove
that 'knowledge' is a form of 'conviction', see whether the
knower in knowing is convinced: for then clearly knowledge
would be a particular kind of conviction. You should proceed in
the same way also in regard to the other cases of this kind.
Moreover, seeing that it is difficult to distinguish whatever
always follows along with a thing, and is not convertible with it,
from its genus, if A follows B universally, whereas B does not
416
follow A universally - as e.g. 'rest' always follows a 'calm' and
'divisibility' follows 'number', but not conversely (for the
divisible is not always a number, nor rest a calm) - you may
yourself assume in your treatment of them that the one which
always follows is the genus, whenever the other is not
convertible with it: if, on the other hand, some one else puts
forward the proposition, do not accept it universally. An
objection to it is that 'not-being' always follows what is 'coming
to be' (for what is coming to be is not) and is not convertible
with it (for what is not is not always coming to be), and that still
'not-being' is not the genus of 'coming to be': for 'not-being' has
not any species at all. Questions, then, in regard to Genus
should be investigated in the ways described.
BookV
The question whether the attribute stated is or is not a property,
should be examined by the following methods:
Any 'property' rendered is always either essential and
permanent or relative and temporary: e.g. it is an 'essential
property' of man to be 'by nature a civilized animal': a 'relative
property' is one like that of the soul in relation to the body, viz.
that the one is fitted to command, and the other to obey: a
'permanent property' is one like the property which belongs to
God, of being an 'immortal living being': a 'temporary property'
417
is one like the property which belongs to any particular man of
walking in the gymnasium.
[The rendering of a property 'relatively' gives rise either to two
problems or to four. For if he at the same time render this
property of one thing and deny it of another, only two problems
arise, as in the case of a statement that it is a property of a man,
in relation to a horse, to be a biped. For one might try both to
show that a man is not a biped, and also that a horse is a biped:
in both ways the property would be upset. If on the other hand
he render one apiece of two attributes to each of two things,
and deny it in each case of the other, there will then be four
problems; as in the case of a statement that it is a property of a
man in relation to a horse for the former to be a biped and the
latter a quadruped. For then it is possible to try to show both
that a man is not naturally a biped, and that he is a quadruped,
and also that the horse both is a biped, and is not a quadruped.
If you show any of these at all, the intended attribute is
demolished.]
An 'essential' property is one which is rendered of a thing in
comparison with everything else and distinguishes the said
thing from everything else, as does 'a mortal living being
capable of receiving knowledge' in the case of man. A 'relative'
property is one which separates its subject off not from
everything else but only from a particular definite thing, as does
the property which virtue possesses, in comparison with
knowledge, viz. that the former is naturally produced in more
than one faculty, whereas the latter is produced in that of
reason alone, and in those who have a reasoning faculty. A
'permanent' property is one which is true at every time, and
never fails, like being' compounded of soul and body', in the
case of a living creature. A 'temporary' property is one which is
true at some particular time, and does not of necessity always
418
follow; as, of some particular man, that he walks in the market-
place.
To render a property 'relatively' to something else means to
state the difference between them as it is found either
universally and always, or generally and in most cases: thus a
difference that is found universally and always, is one such as
man possesses in comparison with a horse, viz. being a biped:
for a man is always and in every case a biped, whereas a horse
is never a biped at any time. On the other hand, a difference
that is found generally and in most cases, is one such as the
faculty of reason possesses in comparison with that of desire
and spirit, in that the former commands, while the latter obeys:
for the reasoning faculty does not always command, but
sometimes also is under command, nor is that of desire and
spirit always under command, but also on occasion assumes
the command, whenever the soul of a man is vicious.
Of 'properties' the most 'arguable' are the essential and
permanent and the relative. For a relative property gives rise, as
we said before, to several questions: for of necessity the
questions arising are either two or four, or that arguments in
regard to these are several. An essential and a permanent
property you can discuss in relation to many things, or can
observe in relation to many periods of time: if essential', discuss
it in comparison with many things: for the property ought to
belong to its subject in comparison with every single thing that
is, so that if the subject be not distinguished by it in comparison
with everything else, the property could not have been rendered
correctly. So a permanent property you should observe in
relation to many periods of time; for if it does not or did not, or
is not going to, belong, it will not be a property. On the other
hand, about a temporary property we do not inquire further
than in regard to the time called 'the present'; and so
arguments in regard to it are not many; whereas an arguable'
419
question is one in regard to which it is possible for arguments
both numerous and good to arise.
The so-called 'relative' property, then, should be examined by
means of the commonplace arguments relating to Accident, to
see whether it belongs to the one thing and not to the other: on
the other hand, permanent and essential properties should be
considered by the following methods.
First, see whether the property has or has not been rendered
correctly. Of a rendering being incorrect or correct, one test is to
see whether the terms in which the property is stated are not or
are more intelligible - for destructive purposes, whether they
are not so, and for constructive purposes, whether they are so.
Of the terms not being more intelligible, one test is to see
whether the property which he renders is altogether more
unintelligible than the subject whose property he has stated:
for, if so, the property will not have been stated correctly. For the
object of getting a property constituted is to be intelligible: the
terms therefore in which it is rendered should be more
intelligible: for in that case it will be possible to conceive it more
adequately, e.g. any one who has stated that it is a property of
'fire' to 'bear a very close resemblance to the soul', uses the
term 'soul', which is less intelligible than 'fire' - for we know
better what fire is than what soul is -, and therefore a 'very
close resemblance to the soul' could not be correctly stated to
be a property of fire. Another test is to see whether the
attribution of A (property) to B (subject) fails to be more
intelligible. For not only should the property be more intelligible
than its subject, but also it should be something whose
420
attribution to the particular subject is a more intelligible
attribution. For he who does not know whether it is an attribute
of the particular subject at all, will not know either whether it
belongs to it alone, so that whichever of these results happens,
its character as a property becomes obscure. Thus (e.g.) a man
who has stated that it is a property of fire to be 'the primary
element wherein the soul is naturally found', has introduced a
subject which is less intelligible than 'fire', viz. whether the soul
is found in it, and whether it is found there primarily; and
therefore to be 'the primary element in which the soul is
naturally found' could not be correctly stated to be a property of
'fire'. On the other hand, for constructive purposes, see whether
the terms in which the property is stated are more intelligible,
and if they are more intelligible in each of the aforesaid ways.
For then the property will have been correctly stated in this
respect: for of constructive arguments, showing the correctness
of a rendering, some will show the correctness merely in this
respect, while others will show it without qualification. Thus
(e.g.) a man who has said that the 'possession of sensation' is a
property of 'animal' has both used more intelligible terms and
has rendered the property more intelligible in each of the
aforesaid senses; so that to 'possess sensation' would in this
respect have been correctly rendered as a property of 'animal'.
Next, for destructive purposes, see whether any of the terms
rendered in the property is used in more than one sense, or
whether the whole expression too signifies more than one
thing. For then the property will not have been correctly stated.
Thus (e.g.) seeing that to 'being natural sentient' signifies more
than one thing, viz. (1) to possess sensation, (2) to use one's
sensation, being naturally sentient' could not be a correct
statement of a property of 'animal'. The reason why the term
you use, or the whole expression signifying the property, should
not bear more than one meaning is this, that an expression
bearing more than one meaning makes the object described
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obscure, because the man who is about to attempt an argument
is in doubt which of the various senses the expression bears:
and this will not do, for the object of rendering the property is
that he may understand. Moreover, in addition to this, it is
inevitable that those who render a property after this fashion
should be somehow refuted whenever any one addresses his
syllogism to that one of the term's several meanings which does
not agree. For constructive purposes, on the other hand, see
whether both all the terms and also the expression as a whole
avoid bearing more than one sense: for then the property will
have been correctly stated in this respect. Thus (e.g.) seeing that
'body' does not bear several meanings, nor quickest to move
upwards in space', nor yet the whole expression made by
putting them together, it would be correct in this respect to say
that it is a property of fire to be the 'body quickest to move
upwards in space'.
Next, for destructive purposes, see if the term of which he
renders the property is used in more than one sense, and no
distinction has been drawn as to which of them it is whose
property he is stating: for then the property will not have been
correctly rendered. The reasons why this is so are quite clear
from what has been said above: for the same results are bound
to follow. Thus (e.g.) seeing that 'the knowledge of this' signifies
many things for it means (1) the possession of knowledge by it,
(2) the use of its knowledge by it, (3) the existence of knowledge
about it, (4) the use of knowledge about it - no property of the
'knowledge of this' could be rendered correctly unless he draw a
distinction as to which of these it is whose property he is
rendering. For constructive purposes, a man should see if the
term of which he is rendering the property avoids bearing many
senses and is one and simple: for then the property will have
been correctly stated in this respect. Thus (e.g.) seeing that
'man' is used in a single sense, 'naturally civilized animal'
would be correctly stated as a property of man.
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Next, for destructive purposes, see whether the same term has
been repeated in the property. For people often do this
undetected in rendering 'properties' also, just as they do in their
'definitions' as well: but a property to which this has happened
will not have been correctly stated: for the repetition of it
confuses the hearer; thus inevitably the meaning becomes
obscure, and further, such people are thought to babble.
Repetition of the same term is likely to happen in two ways; one
is, when a man repeatedly uses the same word, as would
happen if any one were to render, as a property of fire, 'the body
which is the most rarefied of bodies' (for he has repeated the
word 'body'); the second is, if a man replaces words by their
definitions, as would happen if any one were to render, as a
property of earth, 'the substance which is by its nature most
easily of all bodies borne downwards in space', and were then to
substitute 'substances of such and such a kind' for the word
'bodies': for 'body' and 'a substance of such and such a kind'
mean one and the same thing. For he will have repeated the
word 'substance', and accordingly neither of the properties
would be correctly stated. For constructive purposes, on the
other hand, see whether he avoids ever repeating the same
term; for then the property will in this respect have been
correctly rendered. Thus (e.g.) seeing that he who has stated
'animal capable of acquiring knowledge' as a property of man
has avoided repeating the same term several times, the
property would in this respect have been correctly rendered of
man.
Next, for destructive purposes, see whether he has rendered in
the property any such term as is a universal attribute. For one
which does not distinguish its subject from other things is
useless, and it is the business of the language Of 'properties', as
also of the language of definitions, to distinguish. In the case
contemplated, therefore, the property will not have been
correctly rendered. Thus (e.g.) a man who has stated that it is a
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property of knowledge to be a 'conception incontrovertible by
argument, because of its unity', has used in the property a term
of that kind, viz. 'unity', which is a universal attribute; and
therefore the property of knowledge could not have been
correctly stated. For constructive purposes, on the other hand,
see whether he has avoided all terms that are common to
everything and used a term that distinguishes the subject from
something: for then the property will in this respect have been
correctly stated. Thus (e.g.) inasmuch as he who has said that it
is a property of a 'living creature' to 'have a soul' has used no
term that is common to everything, it would in this respect
have been correctly stated to be a property of a 'living creature'
to 'have a soul'.
Next, for destructive purposes see whether he renders more
than one property of the same thing, without a definite proviso
that he is stating more than one: for then the property will not
have been correctly stated. For just as in the case of definitions
too there should be no further addition beside the expression
which shows the essence, so too in the case of properties
nothing further should be rendered beside the expression that
constitutes the property mentioned: for such an addition is
made to no purpose. Thus (e.g.) a man who has said that it is a
property of fire to be 'the most rarefied and lightest body' has
rendered more than one property (for each term is a true
predicate of fire alone); and so it could not be a correctly stated
property of fire to be 'the most rarefied and lightest body'. On
the other hand, for constructive purposes, see whether he has
avoided rendering more than one property of the same thing,
and has rendered one only: for then the property will in this
respect have been correctly stated. Thus (e.g.) a man who has
said that it is a property of a liquid to be a 'body adaptable to
every shape' has rendered as its property a single character and
not several, and so the property of 'liquid' would in this respect
have been correctly stated.
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Next, for destructive purposes, see whether he has employed
either the actual subject whose property he is rendering, or any
of its species: for then the property will not have been correctly
stated. For the object of rendering the property is that people
may understand: now the subject itself is just as unintelligible
as it was to start with, while any one of its species is posterior
to it, and so is no more intelligible. Accordingly it is impossible
to understand anything further by the use of these terms. Thus
(e.g.) any one who has said that it is property of 'animal' to be
'the substance to which «man» belongs as a species' has
employed one of its species, and therefore the property could
not have been correctly stated. For constructive purposes, on
the other hand, see whether he avoids introducing either the
subject itself or any of its species: for then the property will in
this respect have been correctly stated. Thus (e.g.) a man who
has stated that it is a property of a living creature to be
'compounded of soul and body' has avoided introducing among
the rest either the subject itself or any of its species, and
therefore in this respect the property of a 'living creature' would
have been correctly rendered.
You should inquire in the same way also in the case of other
terms that do or do not make the subject more intelligible: thus,
for destructive purposes, see whether he has employed
anything either opposite to the subject or, in general, anything
simultaneous by nature with it or posterior to it: for then the
property will not have been correctly stated. For an opposite is
simultaneous by nature with its opposite, and what is
simultaneous by nature or is posterior to it does not make its
subject more intelligible. Thus (e.g.) any one who has said that it
425
is a property of good to be 'the most direct opposite of evil', has
employed the opposite of good, and so the property of good
could not have been correctly rendered. For constructive
purposes, on the other hand, see whether he has avoided
employing anything either opposite to, or, in general,
simultaneous by nature with the subject, or posterior to it: for
then the property will in this respect have been correctly
rendered. Thus (e.g.) a man who has stated that it is a property
of knowledge to be 'the most convincing conception' has
avoided employing anything either opposite to, or simultaneous
by nature with, or posterior to, the subject; and so the property
of knowledge would in this respect have been correctly stated.
Next, for destructive purposes, see whether he has rendered as
property something that does not always follow the subject but
sometimes ceases to be its property: for then the property will
not have been correctly described. For there is no necessity
either that the name of the subject must also be true of
anything to which we find such an attribute belonging; nor yet
that the name of the subject will be untrue of anything to which
such an attribute is found not to belong. Moreover, in addition
to this, even after he has rendered the property it will not be
clear whether it belongs, seeing that it is the kind of attribute
that may fall: and so the property will not be clear. Thus (e.g.) a
man who has stated that it is a property of animal 'sometimes
to move and sometimes to stand still' rendered the kind of
property which sometimes is not a property, and so the
property could not have been correctly stated. For constructive
purposes, on the other hand, see whether he has rendered
something that of necessity must always be a property: for then
the property will have been in this respect correctly stated. Thus
(e.g.) a man who has stated that it is a property of virtue to be
'what makes its possessor good' has rendered as property
something that always follows, and so the property of virtue
would in this respect have been correctly rendered.
426
Next, for destructive purposes, see whether in rendering the
property of the present time he has omitted to make a definite
proviso that it is the property of the present time which he is
rendering: for else the property will not have been correctly
stated. For in the first place, any unusual procedure always
needs a definite proviso: and it is the usual procedure for
everybody to render as property some attribute that always
follows. In the second place, a man who omits to provide
definitely whether it was the property of the present time
which he intended to state, is obscure: and one should not give
any occasion for adverse criticism. Thus (e.g.) a man who has
stated it as the property of a particular man 'to be sitting with a
particular man', states the property of the present time, and so
he cannot have rendered the property correctly, seeing that he
has described it without any definite proviso. For constructive
purposes, on the other hand, see whether, in rendering the
property of the present time, he has, in stating it, made a
definite proviso that it is the property of the present time that
he is stating: for then the property will in this respect have been
correctly stated. Thus (e.g.) a man who has said that it is the
property of a particular man 'to be walking now', has made this
distinction in his statement, and so the property would have
been correctly stated.
Next, for destructive purposes, see whether he has rendered a
property of the kind whose appropriateness is not obvious
except by sensation: for then the property will not have been
correctly stated. For every sensible attribute, once it is taken
beyond the sphere of sensation, becomes uncertain. For it is not
clear whether it still belongs, because it is evidenced only by
sensation. This principle will be true in the case of any
attributes that do not always and necessarily follow. Thus (e.g.)
any one who has stated that it is a property of the sun to be 'the
brightest star that moves over the earth', has used in describing
the property an expression of that kind, viz. 'to move over the
427
earth', which is evidenced by sensation; and so the sun's
property could not have been correctly rendered: for it will be
uncertain, whenever the sun sets, whether it continues to move
over the earth, because sensation then fails us. For constructive
purposes, on the other hand, see whether he has rendered the
property of a kind that is not obvious to sensation, or, if it be
sensible, must clearly belong of necessity: for then the property
will in this respect have been correctly stated. Thus (e.g.) a man
who has stated that it is a property of a surface to be 'the
primary thing that is coloured', has introduced amongst the rest
a sensible quality, 'to be coloured', but still a quality such as
manifestly always belongs, and so the property of 'surface'
would in this respect have been correctly rendered.
Next, for destructive purposes, see whether he has rendered the
definition as a property: for then the property will not have
been correctly stated: for the property of a thing ought not to
show its essence. Thus (e.g.) a man who has said that it is the
property of man to be 'a walking, biped animal' has rendered a
property of man so as to signify his essence, and so the property
of man could not have been correctly rendered. For constructive
purposes, on the other hand, see whether the property which
he has rendered forms a predicate convertible with its subject,
without, however, signifying its essence: for then the property
will in this respect have been correctly rendered. Thus (e.g.) he
who has stated that it is a property of man to be a 'naturally
civilized animal' has rendered the property so as to be
convertible with its subject, without, however, showing its
essence, and so the property of man' would in this respect have
been correctly rendered.
Next, for destructive purposes, see whether he has rendered the
property without having placed the subject within its essence.
For of properties, as also of definitions, the first term to be
rendered should be the genus, and then the rest of it should be
428
appended immediately afterwards, and should distinguish its
subject from other things. Hence a property which is not stated
in this way could not have been correctly rendered. Thus (e.g.) a
man who has said that it is a property of a living creature to
'have a soul' has not placed 'living creature' within its essence,
and so the property of a living creature could not have been
correctly stated. For constructive purposes, on the other hand,
see whether a man first places within its essence the subject
whose property he is rendering, and then appends the rest: for
then the property will in this respect have been correctly
rendered. Thus (e.g.) he who has stated that is a property of
man to be an 'animal capable of receiving knowledge', has
rendered the property after placing the subject within its
essence, and so the property of 'man' would in this respect have
been correctly rendered.
The inquiry, then, whether the property has been correctly
rendered or no, should be made by these means. The question,
on the other hand, whether what is stated is or is not a property
at all, you should examine from the following points of view. For
the commonplace arguments which establish absolutely that
the property is accurately stated will be the same as those that
constitute it a property at all: accordingly they will be described
in the course of them.
Firstly, then, for destructive purposes, take a look at each
subject of which he has rendered the property, and see (e.g.) if it
fails to belong to any of them at all, or to be true of them in that
particular respect, or to be a property of each of them in respect
of that character of which he has rendered the property: for
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then what is stated to be a property will not be a property. Thus,
for example, inasmuch as it is not true of the geometrician that
he 'cannot be deceived by an argument' (for a geometrician is
deceived when his figure is misdrawn), it could not be a
property of the man of science that he is not deceived by an
argument. For constructive purposes, on the other hand, see
whether the property rendered be true of every instance, and
true in that particular respect: for then what is stated not to be
a property will be a property. Thus, for example, in as much as
the description 'an animal capable of receiving knowledge' is
true of every man, and true of him qua man, it would be a
property of man to be 'an animal capable of receiving
knowledge', commonplace rule means - for destructive
purposes, see if the description fails to be true of that of which
the name is true; and if the name fails to be true of that of
which the description is true: for constructive purposes, on the
other hand, see if the description too is predicated of that of
which the name is predicated, and if the name too is predicated
of that of which the description is predicated.]
Next, for destructive purposes, see if the description fails to
apply to that to which the name applies, and if the name fails to
apply to that to which the description applies: for then what is
stated to be a property will not be a property. Thus (e.g.)
inasmuch as the description 'a living being that partakes of
knowledge' is true of God, while 'man' is not predicated of God,
to be a living being that partakes of knowledge' could not be a
property of man. For constructive purposes, on the other hand,
see if the name as well be predicated of that of which the
description is predicated, and if the description as well be
predicated of that of which the name is predicated. For then
what is stated not to be a property will be a property. Thus (e.g.)
the predicate 'living creature' is true of that of which 'having a
soul' is true, and 'having a soul' is true of that of which the
430
predicate 'living creature' is true; and so 'having a soul would be
a property of 'living creature'.
Next, for destructive purposes, see if he has rendered a subject
as a property of that which is described as 'in the subject': for
then what has been stated to be a property will not be a
property. Thus (e.g.) inasmuch as he who has rendered 'fire' as
the property of 'the body with the most rarefied particles', has
rendered the subject as the property of its predicate, 'fire' could
not be a property of 'the body with the most rarefied particles'.
The reason why the subject will not be a property of that which
is found in the subject is this, that then the same thing will be
the property of a number of things that are specifically
different. For the same thing has quite a number of specifically
different predicates that belong to it alone, and the subject will
be a property of all of these, if any one states the property in
this way. For constructive purposes, on the other hand, see if he
has rendered what is found in the subject as a property of the
subject: for then what has been stated not to be a property will
be a property, if it be predicated only of the things of which it
has been stated to be the property. Thus (e.g.) he who has said
that it is a property of 'earth' to be 'specifically the heaviest
body' has rendered of the subject as its property something that
is said of the thing in question alone, and is said of it in the
manner in which a property is predicated, and so the property
of earth would have been rightly stated.
Next, for destructive purposes, see if he has rendered the
property as partaken of: for then what is stated to be a property
will not be a property. For an attribute of which the subject
partakes is a constituent part of its essence: and an attribute of
that kind would be a differentia applying to some one species.
E.g. inasmuch as he who has said that 'walking on two feet' is
property of man has rendered the property as partaken of,
'walking on two feet' could not be a property of 'man'. For
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constructive purposes, on the other hand, see if he has avoided
rendering the property as partaken of, or as showing the
essence, though the subject is predicated convertibly with it: for
then what is stated not to be a property will be a property. Thus
(e.g.) he who has stated that to be 'naturally sentient' is a
property of 'animal' has rendered the property neither as
partaken of nor as showing the essence, though the subject is
predicated convertibly with it; and so to be 'naturally sentient'
would be a property of 'animal'.
Next, for destructive purposes, see if the property cannot
possibly belong simultaneously, but must belong either as
posterior or as prior to the attribute described in the name: for
then what is stated to be a property will not be a property either
never, or not always. Thus (e.g.) inasmuch as it is possible for
the attribute 'walking through the market-place' to belong to an
object as prior and as posterior to the attribute 'man', 'walking
through the market-place' could not be a property of 'man'
either never, or not always. For constructive purposes, on the
other hand, see if it always and of necessity belongs
simultaneously, without being either a definition or a
differentia: for then what is stated not to be a property will be a
property. Thus (e.g.) the attribute 'an animal capable of receiving
knowledge' always and of necessity belongs simultaneously
with the attribute 'man', and is neither differentia nor definition
of its subject, and so 'an animal capable of receiving knowledge'
would be a property of 'man'.
Next, for destructive purposes, see if the same thing fails to be a
property of things that are the same as the subject, so far as
they are the same: for then what is stated to be a property will
not be a property. Thus, for example, inasmuch as it is no
property of a 'proper object of pursuit' to 'appear good to certain
persons', it could not be a property of the 'desirable' either to
'appear good to certain persons': for 'proper object of pursuit'
432
and 'desirable' mean the same. For constructive purposes, on
the other hand, see if the same thing be a property of
something that is the same as the subject, in so far as it is the
same. For then is stated not to be a property will be a property.
Thus (e.g.) inasmuch as it is called a property of a man, in so far
as he is a man, 'to have a tripartite soul', it would also be a
property of a mortal, in so far as he is a mortal, to have a
tripartite soul. This commonplace rule is useful also in dealing
with Accident: for the same attributes ought either to belong or
not belong to the same things, in so far as they are the same.
Next, for destructive purposes, see if the property of things that
are the same in kind as the subject fails to be always the same
in kind as the alleged property: for then neither will what is
stated to be the property of the subject in question. Thus (e.g.)
inasmuch as a man and a horse are the same in kind, and it is
not always a property of a horse to stand by its own initiative, it
could not be a property of a man to move by his own initiative;
for to stand and to move by his own initiative are the same in
kind, because they belong to each of them in so far as each is an
'animal'. For constructive purposes, on the other hand, see if of
things that are the same in kind as the subject the property that
is the same as the alleged property is always true: for then what
is stated not to be a property will be a property. Thus (e.g.) since
it is a property of man to be a 'walking biped,' it would also be a
property of a bird to be a 'flying biped': for each of these is the
same in kind, in so far as the one pair have the sameness of
species that fall under the same genus, being under the genus
'animal', while the other pair have that of differentiae of the
genus, viz. of 'animal'. This commonplace rule is deceptive
whenever one of the properties mentioned belongs to some one
species only while the other belongs to many, as does 'walking
quadruped'.
433
Inasmuch as 'same' and 'different' are terms used in several
senses, it is a job to render to a sophistical questioner a
property that belongs to one thing and that only. For an
attribute that belongs to something qualified by an accident will
also belong to the accident taken along with the subject which
it qualifies; e.g. an attribute that belongs to 'man' will belong
also to 'white man', if there be a white man, and one that
belongs to 'white man' will belong also to 'man'. One might,
then, bring captious criticism against the majority of properties,
by representing the subject as being one thing in itself, and
another thing when combined with its accident, saying, for
example, that 'man' is one thing, and white man' another, and
moreover by representing as different a certain state and what
is called after that state. For an attribute that belongs to the
state will belong also to what is called after that state, and one
that belongs to what is called after a state will belong also to
the state: e.g. inasmuch as the condition of the scientist is
called after his science, it could not be a property of 'science'
that it is 'incontrovertible by argument'; for then the scientist
also will be incontrovertible by argument. For constructive
purposes, however, you should say that the subject of an
accident is not absolutely different from the accident taken
along with its subject; though it is called 'another' thing
because the mode of being of the two is different: for it is not
the same thing for a man to be a man and for a white man to be
a white man. Moreover, you should take a look along at the
inflections, and say that the description of the man of science is
wrong: one should say not 'it' but 'he is incontrovertible by
argument'; while the description of Science is wrong too: one
should say not 'it' but 'she is incontrovertible by argument'. For
against an objector who sticks at nothing the defence should
stick at nothing.
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Next, for destructive purposes, see if, while intending to render
an attribute that naturally belongs, he states it in his language
in such a way as to indicate one that invariably belongs: for
then it would be generally agreed that what has been stated to
be a property is upset. Thus (e.g.) the man who has said that
'biped' is a property of man intends to render the attribute that
naturally belongs, but his expression actually indicates one that
invariably belongs: accordingly, 'biped' could not be a property
of man: for not every man is possessed of two feet. For
constructive purposes, on the other hand, see if he intends to
render the property that naturally belongs, and indicates it in
that way in his language: for then the property will not be upset
in this respect. Thus (e.g.) he who renders as a property of 'man'
the phrase 'an animal capable of receiving knowledge' both
intends, and by his language indicates, the property that
belongs by nature, and so 'an animal capable of receiving
knowledge' would not be upset or shown in that respect not to
be a property of man.
Moreover, as regards all the things that are called as they are
primarily after something else, or primarily in themselves, it is a
job to render the property of such things. For if you render a
property as belonging to the subject that is so called after
something else, then it will be true of its primary subject as
well; whereas if you state it of its primary subject, then it will be
predicated also of the thing that is so called after this other.
Thus (e.g.) if any one renders , coloured' as the property of
'surface', 'coloured' will be true of body as well; whereas if he
render it of 'body', it will be predicated also of 'surface'. Hence
the name as well will not be true of that of which the
description is true.
435
In the case of some properties it mostly happens that some
error is incurred because of a failure to define how as well as to
what things the property is stated to belong. For every one tries
to render as the property of a thing something that belongs to it
either naturally, as 'biped' belongs to 'man', or actually, as
'having four fingers' belongs to a particular man, or specifically,
as 'consisting of most rarefied particles' belongs to 'fire', or
absolutely, as 'life' to 'living being', or one that belongs to a
thing only as called after something else, as 'wisdom' to the
'soul', or on the other hand primarily, as 'wisdom' to the
'rational faculty', or because the thing is in a certain state, as
'incontrovertible by argument' belongs to a 'scientist' (for simply
and solely by reason of his being in a certain state will he be
'incontrovertible by argument'), or because it is the state
possessed by something, as 'incontrovertible by argument'
belongs to 'science', or because it is partaken of, as 'sensation'
belongs to 'animal' (for other things as well have sensation, e.g.
man, but they have it because they already partake of 'animal'),
or because it partakes of something else, as 'life' belongs to a
particular kind of 'living being'. Accordingly he makes a mistake
if he has failed to add the word 'naturally', because what
belongs naturally may fail to belong to the thing to which it
naturally belongs, as (e.g.) it belongs to a man to have two feet:
so too he errs if he does not make a definite proviso that he is
rendering what actually belongs, because one day that attribute
will not be what it now is, e.g. the man's possession of four
fingers. So he errs if he has not shown that he states a thing to
be such and such primarily, or that he calls it so after something
else, because then its name too will not be true of that of which
the description is true, as is the case with 'coloured', whether
rendered as a property of 'surface' or of 'body'. So he errs if he
has not said beforehand that he has rendered a property to a
thing either because that thing possesses a state, or because it
is a state possessed by something; because then it will not be a
436
property. For, supposing he renders the property to something
as being a state possessed, it will belong to what possesses that
state; while supposing he renders it to what possesses the state,
it will belong to the state possessed, as did 'incontrovertible by
argument' when stated as a property of 'science' or of the
'scientist'. So he errs if he has not indicated beforehand that the
property belongs because the thing partakes of, or is partaken
of by, something; because then the property will belong to
certain other things as well. For if he renders it because its
subject is partaken of, it will belong to the things which partake
of it; whereas if he renders it because its subject partakes of
something else, it will belong to the things partaken of, as (e.g.)
if he were to state 'life' to be a property of a 'particular kind of
living being', or just of 'living being. So he errs if he has not
expressly distinguished the property that belongs specifically,
because then it will belong only to one of the things that fall
under the term of which he states the property: for the
superlative belongs only to one of them, e.g. 'lightest' as applied
to 'fire'. Sometimes, too, a man may even add the word
'specifically', and still make a mistake. For the things in
question should all be of one species, whenever the word
'specifically' is added: and in some cases this does not occur, as
it does not, in fact, in the case of fire. For fire is not all of one
species; for live coals and flame and light are each of them 'fire',
but are of different species. The reason why, whenever
'specifically' is added, there should not be any species other
than the one mentioned, is this, that if there be, then the
property in question will belong to some of them in a greater
and to others in a less degree, as happens with 'consisting of
most rarefied particles' in the case of fire: for 'light' consists of
more rarefied particles than live coals and flame. And this
should not happen unless the name too be predicated in a
greater degree of that of which the description is truer;
otherwise the rule that where the description is truer the name
437
too should be truer is not fulfilled. Moreover, in addition to this,
the same attribute will be the property both of the term which
has it absolutely and of that element therein which has it in the
highest degree, as is the condition of the property 'consisting of
most rarefied particles' in the case of 'fire': for this same
attribute will be the property of 'light' as well: for it is 'light' that
'consists of the most rarefied particles'. If, then, any one else
renders a property in this way one should attack it; for oneself,
one should not give occasion for this objection, but should
define in what manner one states the property at the actual
time of making the statement.
Next, for destructive purposes, see if he has stated a thing as a
property of itself: for then what has been stated to be a property
will not be a property. For a thing itself always shows its own
essence, and what shows the essence is not a property but a
definition. Thus (e.g.) he who has said that 'becoming' is a
property of 'beautiful' has rendered the term as a property of
itself (for 'beautiful' and 'becoming' are the same); and so
'becoming' could not be a property of 'beautiful'. For
constructive purposes, on the other hand, see if he has avoided
rendering a thing as a property of itself, but has yet stated a
convertible predicate: for then what is stated not to be a
property will be a property. Thus he who has stated 'animate
substance' as a property of 'living-creature' has not stated
'living-creature' as a property of itself, but has rendered a
convertible predicate, so that 'animate substance' would be a
property of 'living-creature'.
Next, in the case of things consisting of like parts, you should
look and see, for destructive purposes, if the property of the
whole be not true of the part, or if that of the part be not
predicated of the whole: for then what has been stated to be the
property will not be a property. In some cases it happens that
this is so: for sometimes in rendering a property in the case of
438
things that consist of like parts a man may have his eye on the
whole, while sometimes he may address himself to what is
predicated of the part: and then in neither case will it have been
rightly rendered. Take an instance referring to the whole: the
man who has said that it is a property of the 'sea' to be 'the
largest volume of salt water', has stated the property of
something that consists of like parts, but has rendered an
attribute of such a kind as is not true of the part (for a particular
sea is not 'the largest volume of salt water'); and so the largest
volume of salt water' could not be a property of the 'sea'. Now
take one referring to the part: the man who has stated that it is
a property of 'air' to be 'breathable' has stated the property of
something that consists of like parts, but he has stated an
attribute such as, though true of some air, is still not predicable
of the whole (for the whole of the air is not breathable); and so
'breathable' could not be a property of 'air'. For constructive
purposes, on the other hand, see whether, while it is true of
each of the things with similar parts, it is on the other hand a
property of them taken as a collective whole: for then what has
been stated not to be a property will be a property. Thus (e.g.)
while it is true of earth everywhere that it naturally falls
downwards, it is a property of the various particular pieces of
earth taken as 'the Earth', so that it would be a property of
'earth' 'naturally to fall downwards'.
Next, look from the point of view of the respective opposites,
and first (a) from that of the contraries, and see, for destructive
purposes, if the contrary of the term rendered fails to be a
property of the contrary subject. For then neither will the
contrary of the first be a property of the contrary of the second.
439
Thus (e.g.) inasmuch as injustice is contrary to justice, and the
lowest evil to the highest good, but 'to be the highest good' is
not a property of 'justice', therefore 'to be the lowest evil' could
not be a property of 'injustice'. For constructive purposes, on the
other hand, see if the contrary is the property of the contrary:
for then also the contrary of the first will be the property of the
contrary of the second. Thus (e.g.) inasmuch as evil is contrary
to good, and objectionable to desirable, and 'desirable' is a
property of 'good', 'objectionable' would be a property of 'evil'.
Secondly (h) look from the point of view of relative opposites
and see, for destructive purposes, if the correlative of the term
rendered fails to be a property of the correlative of the subject:
for then neither will the correlative of the first be a property of
the correlative of the second. Thus (e.g.) inasmuch as 'double' is
relative to 'half, and 'in excess' to 'exceeded', while 'in excess'
is not a property of 'double', exceeded' could not be a property
of 'half. For constructive purposes, on the other hand, see if the
correlative of the alleged property is a property of the subject's
correlative: for then also the correlative of the first will be a
property of the correlative of the second: e.g. inasmuch as
'double' is relative to 'half, and the proportion 1:2 is relative to
the proportion 2:1, while it is a property of 'double' to be 'in the
proportion of 2 to 1', it would be a property of 'half to be 'in the
proportion of 1 to 2'.
Thirdly (c) for destructive purposes, see if an attribute described
in terms of a state (X) fails to be a property of the given state (Y):
for then neither will the attribute described in terms of the
privation (of X) be a property of the privation (of Y). Also if, on
the other hand, an attribute described in terms of the privation
(of X) be not a property of the given privation (of Y), neither will
the attribute described in terms of the state (X) be a property of
the state (Y).Thus, for example, inasmuch as it is not predicated
as a property of 'deafness' to be a 'lack of sensation', neither
440
could it be a property of 'hearing' to be a 'sensation'. For
constructive purposes, on the other hand, see if an attribute
described in terms of a state (X) is a property of the given state
(Y): for then also the attribute that is described in terms of the
privation (of X) will be a property of the privation (of Y). Also, if
an attribute described in terms of a privation (of X) be a
property of the privation (of Y), then also the attribute that is
described in terms of the state (X) will be a property of the state
(Y). Thus (e.g.) inasmuch as 'to see' is a property of 'sight',
inasmuch as we have sight, 'failure to see' would be a property
of 'blindness', inasmuch as we have not got the sight we should
naturally have.
Next, look from the point of view of positive and negative terms;
and first (a) from the point of view of the predicates taken by
themselves. This common-place rule is useful only for a
destructive purpose. Thus (e.g.) see if the positive term or the
attribute described in terms of it is a property of the subject: for
then the negative term or the attribute described in terms of it
will not be a property of the subject. Also if, on the other hand,
the negative term or the attribute described in terms of it is a
property of the subject, then the positive term or the attribute
described in terms of it will not be a property of the subject: e.g.
inasmuch as 'animate' is a property of 'living creature',
'inanimate' could not be a property of 'living creature'.
Secondly (b) look from the point of view of the predicates,
positive or negative, and their respective subjects; and see, for
destructive purposes, if the positive term falls to be a property
of the positive subject: for then neither will the negative term
be a property of the negative subject. Also, if the negative term
fails to be a property of the negative subject, neither will the
positive term be a property of the positive subject. Thus (e.g.)
inasmuch as 'animal' is not a property of 'man', neither could
'not-animal' be a property of 'not-man'. Also if 'not-animal'
441
seems not to be a property of 'not-man', neither will 'animal' be
a property of 'man'. For constructive purposes, on the other
hand, see if the positive term is a property of the positive
subject: for then the negative term will be a property of the
negative subject as well. Also if the negative term be a property
of the negative subject, the positive will be a property of the
positive as well. Thus (e.g.) inasmuch as it is a property of 'not-
living being' 'not to live', it would be a property of 'living being'
'to live': also if it seems to be a property of 'living being' 'to live',
it will also seem to be a property of 'not-living being' 'not to
live'.
Thirdly (c) look from the point of view of the subjects taken by
themselves, and see, for destructive purposes, if the property
rendered is a property of the positive subject: for then the same
term will not be a property of the negative subject as well. Also,
if the term rendered be a property of the negative subject, it will
not be a property of the positive. Thus (e.g.) inasmuch as
'animate' is a property of 'living creature', 'animate' could not
be a property of 'not-living creature'. For constructive purposes,
on the other hand, if the term rendered fails to be a property of
the affirmative subject it would be a property of the negative.
This commonplace rule is, however, deceptive: for a positive
term is not a property of a negative, or a negative of a positive.
For a positive term does not belong at all to a negative, while a
negative term, though it belongs to a positive, does not belong
as a property.
Next, look from the point of view of the coordinate members of
a division, and see, for destructive purposes, if none of the co-
ordinate members (parallel with the property rendered) be a
property of any of the remaining set of co-ordinate members
(parallel with the subject): for then neither will the term stated
be a property of that of which it is stated to be a property. Thus
(e.g.) inasmuch as 'sensible living being' is not a property of any
442
of the other living beings, 'intelligible living being' could not be
a property of God. For constructive purposes, on the other hand,
see if some one or other of the remaining co-ordinate members
(parallel with the property rendered) be a property of each of
these co-ordinate members (parallel with the subject): for then
the remaining one too will be a property of that of which it has
been stated not to be a property. Thus (e.g.) inasmuch as it is a
property of 'wisdom' to be essentially 'the natural virtue of the
rational faculty', then, taking each of the other virtues as well in
this way, it would be a property of 'temperance' to be essentially
'the natural virtue of the faculty of desire'.
Next, look from the point of view of the inflexions, and see, for
destructive purposes, if the inflexion of the property rendered
fails to be a property of the inflexion of the subject: for then
neither will the other inflexion be a property of the other
inflexion. Thus (e.g.) inasmuch as 'beautifully' is not a property
of 'justly', neither could 'beautiful' be a property of 'just'. For
constructive purposes, on the other hand, see if the inflexion of
the property rendered is a property of the inflexion of the
subject: for then also the other inflexion will be a property of
the other inflexion. Thus (e.g.) inasmuch as 'walking biped' is a
property of man, it would also be any one's property 'as a man'
to be described 'as a walking biped'. Not only in the case of the
actual term mentioned should one look at the inflexions, but
also in the case of its opposites, just as has been laid down in
the case of the former commonplace rules as well.' Thus, for
destructive purposes, see if the inflexion of the opposite of the
property rendered fails to be the property of the inflexion of the
opposite of the subject: for then neither will the inflexion of the
other opposite be a property of the inflexion of the other
opposite. Thus (e.g.) inasmuch as 'well' is not a property of
'justly', neither could 'badly' be a property of 'unjustly'. For
constructive purposes, on the other hand, see if the inflexion of
the opposite of the property originally suggested is a property of
443
the inflexion of the opposite of the original subject: for then
also the inflexion of the other opposite will be a property of the
inflexion of the other opposite. Thus (e.g.) inasmuch as 'best' is
a property of 'the good', 'worst' also will be a property of 'the
evil'.
Next, look from the point of view of things that are in a like
relation, and see, for destructive purposes, if what is in a
relation like that of the property rendered fails to be a property
of what is in a relation like that of the subject: for then neither
will what is in a relation like that of the first be a property of
what is in a relation like that of the second. Thus (e.g.)
inasmuch as the relation of the builder towards the production
of a house is like that of the doctor towards the production of
health, and it is not a property of a doctor to produce health, it
could not be a property of a builder to produce a house. For
constructive purposes, on the other hand, see if what is in a
relation like that of the property rendered is a property of what
is in a relation like that of the subject: for then also what is in a
relation like that of the first will be a property of what is in a
relation like that of the second. Thus (e.g.) inasmuch as the
relation of a doctor towards the possession of ability to produce
health is like that of a trainer towards the possession of ability
to produce vigour, and it is a property of a trainer to possess the
ability to produce vigour, it would be a property of a doctor to
possess the ability to produce health.
Next look from the point of view of things that are identically
related, and see, for destructive purposes, if the predicate that is
identically related towards two subjects fails to be a property of
444
the subject which is identically related to it as the subject in
question; for then neither will the predicate that is identically
related to both subjects be a property of the subject which is
identically related to it as the first. If, on the other hand, the
predicate which is identically related to two subjects is the
property of the subject which is identically related to it as the
subject in question, then it will not be a property of that of
which it has been stated to be a property, (e.g.) inasmuch as
prudence is identically related to both the noble and the base,
since it is knowledge of each of them, and it is not a property of
prudence to be knowledge of the noble, it could not be a
property of prudence to be knowledge of the base. If, on the
other hand, it is a property of prudence to be the knowledge of
the noble, it could not be a property of it to be the knowledge of
the base.] For it is impossible for the same thing to be a property
of more than one subject. For constructive purposes, on the
other hand, this commonplace rule is of no use: for what is
'identically related' is a single predicate in process of
comparison with more than one subject.
Next, for destructive purposes, see if the predicate qualified by
the verb 'to be' fails to be a property of the subject qualified by
the verb 'to be': for then neither will the destruction of the one
be a property of the other qualified by the verb 'to be destroyed',
nor will the 'becoming'the one be a property of the other
qualified by the verb 'to become'. Thus (e.g.) inasmuch as it is
not a property of 'man' to be an animal, neither could it be a
property of becoming a man to become an animal; nor could
the destruction of an animal be a property of the destruction of
a man. In the same way one should derive arguments also from
'becoming' to 'being' and 'being destroyed', and from 'being
destroyed' to 'being' and to 'becoming' exactly as they have just
been given from 'being' to 'becoming' and 'being destroyed'. For
constructive purposes, on the other hand, see if the subject set
down as qualified by the verb 'to be' has the predicate set down
445
as so qualified, as its property: for then also the subject
qualified by the very 'to become' will have the predicate
qualified by 'to become' as its property, and the subject
qualified by the verb to be destroyed' will have as its property
the predicate rendered with this qualification. Thus, for
example, inasmuch as it is a property of man to be a mortal, it
would be a property of becoming a man to become a mortal,
and the destruction of a mortal would be a property of the
destruction of a man. In the same way one should derive
arguments also from 'becoming' and 'being destroyed' both to
'being' and to the conclusions that follow from them, exactly as
was directed also for the purpose of destruction.
Next take a look at the 'idea' of the subject stated, and see, for
destructive purposes, if the suggested property fails to belong to
the 'idea' in question, or fails to belong to it in virtue of that
character which causes it to bear the description of which the
property was rendered: for then what has been stated to be a
property will not be a property. Thus (e.g.) inasmuch as 'being
motionless' does not belong to 'man-himself qua 'man', but
qua 'idea', it could not be a property of 'man' to be motionless.
For constructive purposes, on the other hand, see if the property
in question belongs to the idea, and belongs to it in that respect
in virtue of which there is predicated of it that character of
which the predicate in question has been stated not to be a
property: for then what has been stated not to be a property will
be a property. Thus (e.g.) inasmuch as it belongs to 'living-
creature-itself to be compounded of soul and body, and further
this belongs to it qua 'living-creature', it would be a property of
'living-creature' to be compounded of soul and body.
446
8
Next look from the point of view of greater and less degrees,
and first (a) for destructive purposes, see if what is more-P fails
to be a property of what is more-S: for then neither will what is
less-P be a property of what is less-S, nor least-P of least-S, nor
most-P of most-S, nor P simply of S simply. Thus (e.g.) inasmuch
as being more highly coloured is not a property of what is more
a body, neither could being less highly coloured be a property of
what is less a body, nor being coloured be a property of body at
all. For constructive purposes, on the other hand, see if what is
more-P is a property of what is more-S: for then also what is
less-P will be a property of what is less S, and least-P of least-S,
and most-P of most-S, and P simply of S simply. Thus (e.g.)
inasmuch as a higher degree of sensation is a property of a
higher degree of life, a lower degree of sensation also would be a
property of a lower degree of life, and the highest of the highest
and the lowest of the lowest degree, and sensation simply of life
simply.
Also you should look at the argument from a simple predication
to the same qualified types of predication, and see, for
destructive purposes, if P simply fails to be a property of S
simply; for then neither will more-P be a property of more-S,
nor less-P of less-S, nor most-P of most-S, nor least-P of least-S.
Thus (e.g.) inasmuch as 'virtuous' is not a property of 'man',
neither could 'more virtuous' be a property of what is 'more
human'. For constructive purposes, on the other hand, see if P
simply is a property of S simply: for then more P also will be a
property of more-S, and less-P of less-S, and least-P of least-S,
and most-P of most-S. Thus (e.g.) a tendency to move upwards
by nature is a property of fire, and so also a greater tendency to
move upwards by nature would be a property of what is more
fiery. In the same way too one should look at all these matters
from the point of view of the others as well.
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Secondly (b) for destructive purposes, see if the more likely
property fails to be a property of the more likely subject: for
then neither will the less likely property be a property of the
less likely subject. Thus (e.g.) inasmuch as 'perceiving' is more
likely to be a property of 'animal' than 'knowing' of 'man', and
'perceiving' is not a property of 'animal', 'knowing' could not be
a property of 'man'. For constructive purposes, on the other
hand, see if the less likely property is a property of the less
likely subject; for then too the more likely property will be a
property of the more likely subject. Thus (e.g.) inasmuch as 'to
be naturally civilized' is less likely to be a property of man than
'to live' of an animal, and it is a property of man to be naturally
civilized, it would be a property of animal to live.
Thirdly (c) for destructive purposes, see if the predicate fails to
be a property of that of which it is more likely to be a property:
for then neither will it be a property of that of which it is less
likely to be a property: while if it is a property of the former, it
will not be a property of the latter. Thus (e.g.) inasmuch as 'to be
coloured' is more likely to be a property of a 'surface' than of a
'body', and it is not a property of a surface, 'to be coloured'
could not be a property of 'body'; while if it is a property of a
'surface', it could not be a property of a 'body'. For constructive
purposes, on the other hand, this commonplace rule is not of
any use: for it is impossible for the same thing to be a property
of more than one thing.
Fourthly (d) for destructive purposes, see if what is more likely
to be a property of a given subject fails to be its property: for
then neither will what is less likely to be a property of it be its
property. Thus (e.g.) inasmuch as 'sensible' is more likely than
'divisible' to be a property of 'animal', and 'sensible' is not a
property of animal, 'divisible' could not be a property of animal.
For constructive purposes, on the other hand, see if what is less
likely to be a property of it is a property; for then what is more
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likely to be a property of it will be a property as well. Thus, for
example, inasmuch as 'sensation' is less likely to be a property
of 'animal' than life', and 'sensation' is a property of animal,
'life' would be a property of animal.
Next, look from the point of view of the attributes that belong in
a like manner, and first (a) for destructive purposes, see if what
is as much a property fails to be a property of that of which it is
as much a property: for then neither will that which is as much
a property as it be a property of that of which it is as much a
property. Thus (e.g.) inasmuch as 'desiring' is as much a
property of the faculty of desire as reasoning' is a property of
the faculty of reason, and desiring is not a property of the
faculty of desire, reasoning could not be a property of the
faculty of reason. For constructive purposes, on the other hand,
see if what is as much a property is a property of that of which
it is as much a property: for then also what is as much a
property as it will be a property of that of which it is as much a
property. Thus (e.g.) inasmuch as it is as much a property of 'the
faculty of reason' to be 'the primary seat of wisdom' as it is of
'the faculty of desire' to be 'the primary seat of temperance',
and it is a property of the faculty of reason to be the primary
seat of wisdom, it would be a property of the faculty of desire to
be the primary seat of temperance.
Secondly (b) for destructive purposes, see if what is as much a
property of anything fails to be a property of it: for then neither
will what is as much a property be a property of it. Thus (e.g.)
inasmuch as 'seeing' is as much a property of man as 'hearing',
and 'seeing' is not a property of man, 'hearing' could not be a
property of man. For constructive purposes, on the other hand,
see if what is as much a property of it is its property: for then
what is as much a property of it as the former will be its
property as well. Thus (e.g.) it is as much a property of the soul
to be the primary possessor of a part that desires as of a part
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that reasons, and it is a property of the soul to be the primary-
possessor of a part that desires, and so it be a property of the
soul to be the primary possessor of a part that reasons.
Thirdly (c) for destructive purposes, see if it fails to be a
property of that of which it is as much a property: for then
neither will it be a property of that of which it is as much a
property as of the former, while if it be a property of the former,
it will not be a property of the other. Thus (e.g.) inasmuch as 'to
burn' is as much a property of 'flame' as of 'live coals', and 'to
burn' is not a property of flame, 'to burn' could not be a
property of live coals: while if it is a property of flame, it could
not be a property of live coals. For constructive purposes, on the
other hand, this commonplace rule is of no use.
The rule based on things that are in a like relation' differs from
the rule based on attributes that belong in a like manner,'
because the former point is secured by analogy, not from
reflection on the belonging of any attribute, while the latter is
judged by a comparison based on the fact that an attribute
belongs.
Next, for destructive purposes, see if in rendering the property
potentially, he has also through that potentiality rendered the
property relatively to something that does not exist, when the
potentiality in question cannot belong to what does not exist:
for then what is stated to be a property will not be a property.
Thus (e.g.) he who has said that 'breathable' is a property of 'air'
has, on the one hand, rendered the property potentially (for that
is 'breathable' which is such as can be breathed), and on the
other hand has also rendered the property relatively to what
does not exist: - for while air may exist, even though there exist
no animal so constituted as to breathe the air, it is not possible
to breathe it if no animal exist: so that it will not, either, be a
property of air to be such as can be breathed at a time when
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there exists no animal such as to breathe it and so it follows
that 'breathable' could not be a property of air.
For constructive purposes, see if in rendering the property
potentially he renders the property either relatively to
something that exists, or to something that does not exist,
when the potentiality in question can belong to what does not
exist: for then what has been stated not to be a property will be
a property. Thus e.g.) he who renders it as a property of 'being'
to be 'capable of being acted upon or of acting', in rendering the
property potentially, has rendered the property relatively to
something that exists: for when 'being' exists, it will also be
capable of being acted upon or of acting in a certain way: so
that to be 'capable of being acted upon or of acting' would be a
property of 'being'.
Next, for destructive purposes, see if he has stated the property
in the superlative: for then what has been stated to be a
property will not be a property. For people who render the
property in that way find that of the object of which the
description is true, the name is not true as well: for though the
object perish the description will continue in being none the
less; for it belongs most nearly to something that is in being. An
example would be supposing any one were to render 'the
lightest body' as a property of 'fire': for, though fire perish, there
eh re will still be some form of body that is the lightest, so that
'the lightest body' could not be a property of fire. For
constructive purposes, on the other hand, see if he has avoided
rendering the property in the superlative: for then the property
will in this respect have been property of man has not rendered
the property correctly stated. Thus (e.g.) inasmuch as he in the
superlative, the property would in who states 'a naturally
civilized animal' as a this respect have been correctly stated.
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Book VI
The discussion of Definitions falls into five parts. For you have
to show either (1) that it is not true at all to apply the expression
as well to that to which the term is applied (for the definition of
Man ought to be true of every man); or (2) that though the object
has a genus, he has failed to put the object defined into the
genus, or to put it into the appropriate genus (for the framer of a
definition should first place the object in its genus, and then
append its differences: for of all the elements of the definition
the genus is usually supposed to be the principal mark of the
essence of what is defined): or (3) that the expression is not
peculiar to the object (for, as we said above as well, a definition
ought to be peculiar): or else (4) see if, though he has observed
all the aforesaid cautions, he has yet failed to define the object,
that is, to express its essence. (5) It remains, apart from the
foregoing, to see if he has defined it, but defined it incorrectly.
Whether, then, the expression be not also true of that of which
the term is true you should proceed to examine according to the
commonplace rules that relate to Accident. For there too the
question is always 'Is so and so true or untrue?': for whenever
we argue that an accident belongs, we declare it to be true,
while whenever we argue that it does not belong, we declare it
to be untrue. If, again, he has failed to place the object in the
appropriate genus, or if the expression be not peculiar to the
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object, we must go on to examine the case according to the
commonplace rules that relate to genus and property.
It remains, then, to prescribe how to investigate whether the
object has been either not defined at all, or else defined
incorrectly. First, then, we must proceed to examine if it has
been defined incorrectly: for with anything it is easier to do it
than to do it correctly. Clearly, then, more mistakes are made in
the latter task on account of its greater difficulty. Accordingly
the attack becomes easier in the latter case than in the former.
Incorrectness falls into two branches: (1) first, the use of obscure
language (for the language of a definition ought to be the very
clearest possible, seeing that the whole purpose of rendering it
is to make something known); (secondly, if the expression used
be longer than is necessary: for all additional matter in a
definition is superfluous. Again, each of the aforesaid branches
is divided into a number of others.
One commonplace rule, then, in regard to obscurity is, See if the
meaning intended by the definition involves an ambiguity with
any other, e.g. 'Becoming is a passage into being', or 'Health is
the balance of hot and cold elements'. Here 'passage' and
'balance' are ambiguous terms: it is accordingly not clear which
of the several possible senses of the term he intends to convey.
Likewise also, if the term defined be used in different senses
and he has spoken without distinguishing between them: for
then it is not clear to which of them the definition rendered
applies, and one can then bring a captious objection on the
ground that the definition does not apply to all the things
whose definition he has rendered: and this kind of thing is
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particularly easy in the case where the definer does not see the
ambiguity of his terms. Or, again, the questioner may himself
distinguish the various senses of the term rendered in the
definition, and then institute his argument against each: for if
the expression used be not adequate to the subject in any of its
senses, it is clear that he cannot have defined it in any sense
aright.
Another rule is, See if he has used a metaphorical expression,
as, for instance, if he has defined knowledge as
'unsupplantable', or the earth as a 'nurse', or temperance as a
'harmony'. For a metaphorical expression is always obscure. It is
possible, also, to argue sophistically against the user of a
metaphorical expression as though he had used it in its literal
sense: for the definition stated will not apply to the term
defined, e.g. in the case of temperance: for harmony is always
found between notes. Moreover, if harmony be the genus of
temperance, then the same object will occur in two genera of
which neither contains the other: for harmony does not contain
virtue, nor virtue harmony. Again, see if he uses terms that are
unfamiliar, as when Plato describes the eye as 'brow-shaded', or
a certain spider as poison-fanged', or the marrow as
'boneformed'. For an unusual phrase is always obscure.
Sometimes a phrase is used neither ambiguously, nor yet
metaphorically, nor yet literally, as when the law is said to be
the 'measure' or 'image' of the things that are by nature just.
Such phrases are worse than metaphor; for the latter does make
its meaning to some extent clear because of the likeness
involved; for those who use metaphors do so always in view of
some likeness: whereas this kind of phrase makes nothing
clear; for there is no likeness to justify the description 'measure'
or 'image', as applied to the law, nor is the law ordinarily so
called in a literal sense. So then, if a man says that the law is
literally a 'measure' or an 'image', he speaks falsely: for an
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image is something produced by imitation, and this is not found
in the case of the law. If, on the other hand, he does not mean
the term literally, it is clear that he has used an unclear
expression, and one that is worse than any sort of metaphorical
expression.
Moreover, see if from the expression used the definition of the
contrary be not clear; for definitions that have been correctly
rendered also indicate their contraries as well. Or, again, see if,
when it is merely stated by itself, it is not evident what it
defines: just as in the works of the old painters, unless there
were an inscription, the figures used to be unrecognizable.
If, then, the definition be not clear, you should proceed to
examine on lines such as these. If, on the other hand, he has
phrased the definition redundantly, first of all look and see
whether he has used any attribute that belongs universally,
either to real objects in general, or to all that fall under the
same genus as the object defined: for the mention of this is sure
to be redundant. For the genus ought to divide the object from
things in general, and the differentia from any of the things
contained in the same genus. Now any term that belongs to
everything separates off the given object from absolutely
nothing, while any that belongs to all the things that fall under
the same genus does not separate it off from the things
contained in the same genus. Any addition, then, of that kind
will be pointless.
Or see if, though the additional matter may be peculiar to the
given term, yet even when it is struck out the rest of the
expression too is peculiar and makes clear the essence of the
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term. Thus, in the definition of man, the addition 'capable of
receiving knowledge' is superfluous; for strike it out, and still
the expression is peculiar and makes clear his essence.
Speaking generally, everything is superfluous upon whose
removal the remainder still makes the term that is being
defined clear. Such, for instance, would also be the definition of
the soul, assuming it to be stated as a 'self-moving number'; for
the soul is just 'the self-moving', as Plato defined it. Or perhaps
the expression used, though appropriate, yet does not declare
the essence, if the word 'number' be eliminated. Which of the
two is the real state of the case it is difficult to determine
clearly: the right way to treat the matter in all cases is to be
guided by convenience. Thus (e.g.) it is said that the definition of
phlegm is the 'undigested moisture that comes first off food'.
Here the addition of the word 'undigested' is superfluous,
seeing that 'the first' is one and not many, so that even when
undigested' is left out the definition will still be peculiar to the
subject: for it is impossible that both phlegm and also
something else should both be the first to arise from the food.
Or perhaps the phlegm is not absolutely the first thing to come
off the food, but only the first of the undigested matters, so that
the addition 'undigested' is required; for stated the other way
the definition would not be true unless the phlegm comes first
of all.
Moreover, see if anything contained in the definition fails to
apply to everything that falls under the same species: for this
sort of definition is worse than those which include an attribute
belonging to all things universally. For in that case, if the
remainder of the expression be peculiar, the whole too will be
peculiar: for absolutely always, if to something peculiar
anything whatever that is true be added, the whole too becomes
peculiar. Whereas if any part of the expression do not apply to
everything that falls under the same species, it is impossible
that the expression as a whole should be peculiar: for it will not
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be predicated convertibly with the object; e.g. 'a walking biped
animal six feet high': for an expression of that kind is not
predicated convertibly with the term, because the attribute 'six
feet high' does not belong to everything that falls under the
same species.
Again, see if he has said the same thing more than once, saying
(e.g.) 'desire' is a 'conation for the pleasant'. For 'desire' is
always 'for the pleasant', so that what is the same as desire will
also be 'for the pleasant'. Accordingly our definition of desire
becomes 'conation-for-the-pleasant': for the word 'desire' is the
exact equivalent of the words 'conation-for-the-pleasant', so
that both alike will be 'for the pleasant'. Or perhaps there is no
absurdity in this; for consider this instance: 'Man is a biped':
therefore, what is the same as man is a biped: but 'a walking
biped animal' is the same as man, and therefore walking biped
animal is a biped'. But this involves no real absurdity. For 'biped'
is not a predicate of 'walking animal': if it were, then we should
certainly have 'biped' predicated twice of the same thing; but as
a matter of fact the subject said to be a biped is'a walking biped
animal', so that the word 'biped' is only used as a predicate
once. Likewise also in the case of 'desire' as well: for it is not
'conation' that is said to be 'for the pleasant', but rather the
whole idea, so that there too the predication is only made once.
Absurdity results, not when the same word is uttered twice, but
when the same thing is more than once predicated of a subject;
e.g. if he says, like Xenocrates, that wisdom defines and
contemplates reality:' for definition is a certain type of
contemplation, so that by adding the words 'and contemplates'
over again he says the same thing twice over. Likewise, too,
those fail who say that 'cooling' is 'the privation of natural heat'.
For all privation is a privation of some natural attribute, so that
the addition of the word 'natural' is superfluous: it would have
been enough to say 'privation of heat', for the word 'privation'
shows of itself that the heat meant is natural heat.
457
Again, see if a universal have been mentioned and then a
particular case of it be added as well, e.g. 'Equity is a remission
of what is expedient and just'; for what is just is a branch of
what is expedient and is therefore included in the latter term:
its mention is therefore redundant, an addition of the particular
after the universal has been already stated. So also, if he defines
'medicine' as 'knowledge of what makes for health in animals
and men', or 'the law' as 'the image of what is by nature noble
and just'; for what is just is a branch of what is noble, so that he
says the same thing more than once.
Whether, then, a man defines a thing correctly or incorrectly
you should proceed to examine on these and similar lines. But
whether he has mentioned and defined its essence or no,
should be examined as follows: First of all, see if he has failed to
make the definition through terms that are prior and more
intelligible. For the reason why the definition is rendered is to
make known the term stated, and we make things known by
taking not any random terms, but such as are prior and more
intelligible, as is done in demonstrations (for so it is with all
teaching and learning); accordingly, it is clear that a man who
does not define through terms of this kind has not defined at
all. Otherwise, there will be more than one definition of the
same thing: for clearly he who defines through terms that are
prior and more intelligible has also framed a definition, and a
better one, so that both would then be definitions of the same
object. This sort of view, however, does not generally find
acceptance: for of each real object the essence is single: if, then,
there are to be a number of definitions of the same thing, the
essence of the object will be the same as it is represented to be
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in each of the definitions, and these representations are not the
same, inasmuch as the definitions are different. Clearly, then,
any one who has not defined a thing through terms that are
prior and more intelligible has not defined it at all.
The statement that a definition has not been made through
more intelligible terms may be understood in two senses, either
supposing that its terms are absolutely less intelligible, or
supposing that they are less intelligible to us: for either sense is
possible. Thus absolutely the prior is more intelligible than the
posterior, a point, for instance, than a line, a line than a plane,
and a plane than a solid; just as also a unit is more intelligible
than a number; for it is the prius and starting-point of all
number. Likewise, also, a letter is more intelligible than a
syllable. Whereas to us it sometimes happens that the converse
is the case: for the solid falls under perception most of all -
more than a plane - and a plane more than a line, and a line
more than a point; for most people learn things like the former
earlier than the latter; for any ordinary intelligence can grasp
them, whereas the others require an exact and exceptional
understanding.
Absolutely, then, it is better to try to make what is posterior
known through what is prior, inasmuch as such a way of
procedure is more scientific. Of course, in dealing with persons
who cannot recognize things through terms of that kind, it may
perhaps be necessary to frame the expression through terms
that are intelligible to them. Among definitions of this kind are
those of a point, a line, and a plane, all of which explain the
prior by the posterior; for they say that a point is the limit of a
line, a line of a plane, a plane of a solid. One must, however, not
fail to observe that those who define in this way cannot show
the essential nature of the term they define, unless it so
happens that the same thing is more intelligible both to us and
also absolutely, since a correct definition must define a thing
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through its genus and its differentiae, and these belong to the
order of things which are absolutely more intelligible than, and
prior to, the species. For annul the genus and differentia, and
the species too is annulled, so that these are prior to the
species. They are also more intelligible; for if the species be
known, the genus and differentia must of necessity be known
as well (for any one who knows what a man is knows also what
'animal' and 'walking' are), whereas if the genus or the
differentia be known it does not follow of necessity that the
species is known as well: thus the species is less intelligible.
Moreover, those who say that such definitions, viz. those which
proceed from what is intelligible to this, that, or the other man,
are really and truly definitions, will have to say that there are
several definitions of one and the same thing. For, as it happens,
different things are more intelligible to different people, not the
same things to all; and so a different definition would have to
be rendered to each several person, if the definition is to be
constructed from what is more intelligible to particular
individuals. Moreover, to the same people different things are
more intelligible at different times; first of all the objects of
sense; then, as they become more sharpwitted, the converse; so
that those who hold that a definition ought to be rendered
through what is more intelligible to particular individuals would
not have to render the same definition at all times even to the
same person. It is clear, then, that the right way to define is not
through terms of that kind, but through what is absolutely more
intelligible: for only in this way could the definition come
always to be one and the same. Perhaps, also, what is absolutely
intelligible is what is intelligible, not to all, but to those who are
in a sound state of understanding, just as what is absolutely
healthy is what is healthy to those in a sound state of body. All
such points as this ought to be made very precise, and made
use of in the course of discussion as occasion requires. The
demolition of a definition will most surely win a general
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approval if the definer happens to have framed his expression
neither from what is absolutely more intelligible nor yet from
what is so to us.
One form, then, of the failure to work through more intelligible
terms is the exhibition of the prior through the posterior, as we
remarked before.' Another form occurs if we find that the
definition has been rendered of what is at rest and definite
through what is indefinite and in motion: for what is still and
definite is prior to what is indefinite and in motion.
Of the failure to use terms that are prior there are three forms:
(1) The first is when an opposite has been defined through its
opposite, e.g.i. good through evil: for opposites are always
simultaneous by nature. Some people think, also, that both are
objects of the same science, so that the one is not even more
intelligible than the other. One must, however, observe that it is
perhaps not possible to define some things in any other way,
e.g. the double without the half, and all the terms that are
essentially relative: for in all such cases the essential being is
the same as a certain relation to something, so that it is
impossible to understand the one term without the other, and
accordingly in the definition of the one the other too must be
embraced. One ought to learn up all such points as these, and
use them as occasion may seem to require.
(2) Another is - if he has used the term defined itself. This
passes unobserved when the actual name of the object is not
used, e.g. supposing any one had defined the sun as a star that
appears by day'. For in bringing in 'day' he brings in the sun. To
detect errors of this sort, exchange the word for its definition,
e.g. the definition of 'day' as the 'passage of the sun over the
earth'. Clearly, whoever has said 'the passage of the sun over
the earth' has said 'the sun', so that in bringing in the 'day' he
has brought in the sun.
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(3) Again, see if he has defined one coordinate member of a
division by another, e.g. 'an odd number' as 'that which is
greater by one than an even number'. For the co-ordinate
members of a division that are derived from the same genus are
simultaneous by nature and 'odd' and 'even' are such terms: for
both are differentiae of number.
Likewise also, see if he has defined a superior through a
subordinate term, e.g. 'An «even number» is «a number divisible
into halves»', or '«the good» is a «state of virtue» '. For 'half is
derived from 'two', and 'two' is an even number: virtue also is a
kind of good, so that the latter terms are subordinate to the
former. Moreover, in using the subordinate term one is bound to
use the other as well: for whoever employs the term 'virtue'
employs the term 'good', seeing that virtue is a certain kind of
good: likewise, also, whoever employs the term 'half employs
the term 'even', for to be 'divided in half means to be divided
into two, and two is even.
Generally speaking, then, one commonplace rule relates to the
failure to frame the expression by means of terms that are prior
and more intelligible: and of this the subdivisions are those
specified above. A second is, see whether, though the object is in
a genus, it has not been placed in a genus. This sort of error is
always found where the essence of the object does not stand
first in the expression, e.g. the definition of 'body' as 'that which
has three dimensions', or the definition of 'man', supposing any
one to give it, as 'that which knows how to count': for it is not
stated what it is that has three dimensions, or what it is that
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knows how to count: whereas the genus is meant to indicate
just this, and is submitted first of the terms in the definition.
Moreover, see if, while the term to be defined is used in relation
to many things, he has failed to render it in relation to all of
them; as (e.g.) if he define 'grammar' as the 'knowledge how to
write from dictation': for he ought also to say that it is a
knowledge how to read as well. For in rendering it as
'knowledge of writing' has no more defined it than by rendering
it as 'knowledge of reading': neither in fact has succeeded, but
only he who mentions both these things, since it is impossible
that there should be more than one definition of the same
thing. It is only, however, in some cases that what has been said
corresponds to the actual state of things: in some it does not,
e.g. all those terms which are not used essentially in relation to
both things: as medicine is said to deal with the production of
disease and health; for it is said essentially to do the latter, but
the former only by accident: for it is absolutely alien to
medicine to produce disease. Here, then, the man who renders
medicine as relative to both of these things has not defined it
any better than he who mentions the one only. In fact he has
done it perhaps worse, for any one else besides the doctor is
capable of producing disease.
Moreover, in a case where the term to be defined is used in
relation to several things, see if he has rendered it as relative to
the worse rather than to the better; for every form of knowledge
and potentiality is generally thought to be relative to the best.
Again, if the thing in question be not placed in its own proper
genus, one must examine it according to the elementary rules
in regard to genera, as has been said before.'
Moreover, see if he uses language which transgresses the genera
of the things he defines, defining, e.g. justice as a 'state that
produces equality' or 'distributes what is equal': for by defining
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it so he passes outside the sphere of virtue, and so by leaving
out the genus of justice he fails to express its essence: for the
essence of a thing must in each case bring in its genus. It is the
same thing if the object be not put into its nearest genus; for
the man who puts it into the nearest one has stated all the
higher genera, seeing that all the higher genera are predicated
of the lower. Either, then, it ought to be put into its nearest
genus, or else to the higher genus all the differentiae ought to
be appended whereby the nearest genus is defined. For then he
would not have left out anything: but would merely have
mentioned the subordinate genus by an expression instead of
by name. On the other hand, he who mentions merely the
higher genus by itself, does not state the subordinate genus as
well: in saying 'plant' a man does not specify 'a tree'.
Again, in regard to the differentiae, we must examine in like
manner whether the differentiae, too, that he has stated be
those of the genus. For if a man has not defined the object by
the differentiae peculiar to it, or has mentioned something such
as is utterly incapable of being a differentia of anything, e.g.
'animal' or 'substance', clearly he has not defined it at all: for
the aforesaid terms do not differentiate anything at all. Further,
we must see whether the differentia stated possesses anything
that is co-ordinate with it in a division; for, if not, clearly the
one stated could not be a differentia of the genus. For a genus is
always divided by differentiae that are co-ordinate members of
a division, as, for instance, by the terms 'walking', 'flying',
'aquatic', and 'biped'. Or see if, though the contrasted differentia
exists, it yet is not true of the genus, for then, clearly, neither of
them could be a differentia of the genus; for differentiae that
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are co-ordinates in a division with the differentia of a thing are
all true of the genus to which the thing belongs. Likewise, also,
see if, though it be true, yet the addition of it to the genus fails
to make a species. For then, clearly, this could not be a specific
differentia of the genus: for a specific differentia, if added to the
genus, always makes a species. If, however, this be no true
differentia, no more is the one adduced, seeing that it is a co-
ordinate member of a division with this.
Moreover, see if he divides the genus by a negation, as those do
who define line as 'length without breadth': for this means
simply that it has not any breadth. The genus will then be found
to partake of its own species: for, since of everything either an
affirmation or its negation is true, length must always either
lack breadth or possess it, so that 'length' as well, i.e. the genus
of 'line', will be either with or without breadth. But 'length
without breadth' is the definition of a species, as also is 'length
with breadth': for 'without breadth' and 'with breadth' are
differentiae, and the genus and differentia constitute the
definition of the species. Hence the genus would admit of the
definition of its species. Likewise, also, it will admit of the
definition of the differentia, seeing that one or the other of the
aforesaid differentiae is of necessity predicated of the genus.
The usefulness of this principle is found in meeting those who
assert the existence of 'Ideas': for if absolute length exist, how
will it be predicable of the genus that it has breadth or that it
lacks it? For one assertion or the other will have to be true of
'length' universally, if it is to be true of the genus at all: and this
is contrary to the fact: for there exist both lengths which have,
and lengths which have not, breadth. Hence the only people
against whom the rule can be employed are those who assert
that a genus is always numerically one; and this is what is done
by those who assert the real existence of the 'Ideas'; for they
allege that absolute length and absolute animal are the genus.
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It may be that in some cases the definer is obliged to employ a
negation as well, e.g. in defining privations. For 'blind' means a
thing which cannot see when its nature is to see. There is no
difference between dividing the genus by a negation, and
dividing it by such an affirmation as is bound to have a negation
as its co-ordinate in a division, e.g. supposing he had defined
something as 'length possessed of breadth'; for co-ordinate in
the division with that which is possessed of breadth is that
which possesses no breadth and that only, so that again the
genus is divided by a negation.
Again, see if he rendered the species as a differentia, as do
those who define 'contumely' as 'insolence accompanied by
jeering'; for jeering is a kind of insolence, i.e. it is a species and
not a differentia.
Moreover, see if he has stated the genus as the differentia, e.g.
'Virtue is a good or noble state: for 'good' is the genus of 'virtue'.
Or possibly 'good' here is not the genus but the differentia, on
the principle that the same thing cannot be in two genera of
which neither contains the other: for 'good' does not include
'state', nor vice versa: for not every state is good nor every good
a 'state'. Both, then, could not be genera, and consequently, if
'state' is the genus of virtue, clearly 'good' cannot be its genus:
it must rather be the differentia'. Moreover, 'a state' indicates
the essence of virtue, whereas 'good' indicates not the essence
but a quality: and to indicate a quality is generally held to be
the function of the differentia. See, further, whether the
differentia rendered indicates an individual rather than a
quality: for the general view is that the differentia always
expresses a quality.
Look and see, further, whether the differentia belongs only by
accident to the object defined. For the differentia is never an
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accidental attribute, any more than the genus is: for the
differentia of a thing cannot both belong and not belong to it.
Moreover, if either the differentia or the species, or any of the
things which are under the species, is predicable of the genus,
then he could not have defined the term. For none of the
aforesaid can possibly be predicated of the genus, seeing that
the genus is the term with the widest range of all. Again, see if
the genus be predicated of the differentia; for the general view
is that the genus is predicated, not of the differentia, but of the
objects of which the differentia is predicated. Animal (e.g.) is
predicated of 'man' or 'ox' or other walking animals, not of the
actual differentia itself which we predicate of the species. For if
'animal' is to be predicated of each of its differentiae, then
'animal' would be predicated of the species several times over;
for the differentiae are predicates of the species. Moreover, the
differentiae will be all either species or individuals, if they are
animals; for every animal is either a species or an individual.
Likewise you must inquire also if the species or any of the
objects that come under it is predicated of the differentia: for
this is impossible, seeing that the differentia is a term with a
wider range than the various species. Moreover, if any of the
species be predicated of it, the result will be that the differentia
is a species: if, for instance, 'man' be predicated, the differentia
is clearly the human race. Again, see if the differentia fails to be
prior to the species: for the differentia ought to be posterior to
the genus, but prior to the species.
Look and see also if the differentia mentioned belongs to a
different genus, neither contained in nor containing the genus
in question. For the general view is that the same differentia
cannot be used of two non-subaltern genera. Else the result will
be that the same species as well will be in two non-subaltern
genera: for each of the differentiae imports its own genus, e.g.
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'walking' and 'biped' import with them the genus 'animal'. If,
then, each of the genera as well is true of that of which the
differentia is true, it clearly follows that the species must be in
two non-subaltern genera. Or perhaps it is not impossible for
the same differentia to be used of two non-subaltern genera,
and we ought to add the words 'except they both be subordinate
members of the same genus'. Thus 'walking animal' and 'flying
animal' are non-subaltern genera, and 'biped' is the differentia
of both. The words 'except they both be subordinate members of
the same genus' ought therefore to be added; for both these are
subordinate to 'animal'. From this possibility, that the same
differentia may be used of two non-subaltern genera, it is clear
also that there is no necessity for the differentia to carry with it
the whole of the genus to which it belongs, but only the one or
the other of its limbs together with the genera that are higher
than this, as 'biped' carries with it either 'flying' or 'walking
animal'.
See, too, if he has rendered 'existence in' something as the
differentia of a thing's essence: for the general view is that
locality cannot differentiate between one essence and another.
Hence, too, people condemn those who divide animals by
means of the terms 'walking' and 'aquatic', on the ground that
'walking' and 'aquatic' indicate mere locality. Or possibly in this
case the censure is undeserved; for 'aquatic' does not mean 'in'
anything; nor does it denote a locality, but a certain quality: for
even if the thing be on the dry land, still it is aquatic: and
likewise a land-animal, even though it be in the water, will still
be a and not an aquatic-animal. But all the same, if ever the
differentia does denote existence in something, clearly he will
have made a bad mistake.
Again, see if he has rendered an affection as the differentia: for
every affection, if intensified, subverts the essence of the thing,
while the differentia is not of that kind: for the differentia is
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generally considered rather to preserve that which it
differentiates; and it is absolutely impossible for a thing to exist
without its own special differentia: for if there be no 'walking',
there will be no 'man'. In fact, we may lay down absolutely that
a thing cannot have as its differentia anything in respect of
which it is subject to alteration: for all things of that kind, if
intensified, destroy its essence. If, then, a man has rendered any
differentia of this kind, he has made a mistake: for we undergo
absolutely no alteration in respect of our differentiae.
Again, see if he has failed to render the differentia of a relative
term relatively to something else; for the differentiae of relative
terms are themselves relative, as in the case also of knowledge.
This is classed as speculative, practical and productive; and
each of these denotes a relation: for it speculates upon
something, and produces something and does something.
Look and see also if the definer renders each relative term
relatively to its natural purpose: for while in some cases the
particular relative term can be used in relation to its natural
purpose only and to nothing else, some can be used in relation
to something else as well. Thus sight can only be used for
seeing, but a strigil can also be used to dip up water. Still, if any
one were to define a strigil as an instrument for dipping water,
he has made a mistake: for that is not its natural function. The
definition of a thing's natural function is 'that for which it
would be used by the prudent man, acting as such, and by the
science that deals specially with that thing'.
Or see if, whenever a term happens to be used in a number of
relations, he has failed to introduce it in its primary relation: e.g.
by defining 'wisdom' as the virtue of 'man' or of the 'soul,'
rather than of the 'reasoning faculty': for 'wisdom' is the virtue
primarily of the reasoning faculty: for it is in virtue of this that
both the man and his soul are said to be wise.
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Moreover, if the thing of which the term defined has been
stated to be an affection or disposition, or whatever it may be,
be unable to admit it, the definer has made a mistake. For every
disposition and every affection is formed naturally in that of
which it is an affection or disposition, as knowledge, too, is
formed in the soul, being a disposition of soul. Sometimes,
however, people make bad mistakes in matters of this sort, e.g.
all those who say that 'sleep' is a 'failure of sensation', or that
'perplexity' is a state of 'equality between contrary reasonings',
or that 'pain' is a 'violent disruption of parts that are naturally
conjoined'. For sleep is not an attribute of sensation, whereas it
ought to be, if it is a failure of sensation. Likewise, perplexity is
not an attribute of opposite reasonings, nor pain of parts
naturally conjoined: for then inanimate things will be in pain,
since pain will be present in them. Similar in character, too, is
the definition of 'health', say, as a 'balance of hot and cold
elements': for then health will be necessarily exhibited by the
hot and cold elements: for balance of anything is an attribute
inherent in those things of which it is the balance, so that
health would be an attribute of them. Moreover, people who
define in this way put effect for cause, or cause for effect. For
the disruption of parts naturally conjoined is not pain, but only
a cause of pain: nor again is a failure of sensation sleep, but the
one is the cause of the other: for either we go to sleep because
sensation fails, or sensation fails because we go to sleep.
Likewise also an equality between contrary reasonings would be
generally considered to be a cause of perplexity: for it is when
we reflect on both sides of a question and find everything alike
to be in keeping with either course that we are perplexed which
of the two we are to do.
Moreover, with regard to all periods of time look and see
whether there be any discrepancy between the differentia and
the thing defined: e.g. supposing the 'immortal' to be defined as
a 'living thing immune at present from destruction'. For a living
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thing that is immune 'at present' from destruction will be
immortal 'at present'. Possibly, indeed, in this case this result
does not follow, owing to the ambiguity of the words 'immune
at present from destruction': for it may mean either that the
thing has not been destroyed at present, or that it cannot be
destroyed at present, or that at present it is such that it never
can be destroyed. Whenever, then, we say that a living thing is
at present immune from destruction, we mean that it is at
present a living thing of such a kind as never to be destroyed:
and this is equivalent to saying that it is immortal, so that it is
not meant that it is immortal only at present. Still, if ever it does
happen that what has been rendered according to the definition
belongs in the present only or past, whereas what is meant by
the word does not so belong, then the two could not be the
same. So, then, this commonplace rule ought to be followed, as
we have said.
You should look and see also whether the term being defined is
applied in consideration of something other than the definition
rendered. Suppose (e.g.) a definition of 'justice' as the 'ability to
distribute what is equal'. This would not be right, for 'just'
describes rather the man who chooses, than the man who is
able to distribute what is equal: so that justice could not be an
ability to distribute what is equal: for then also the most just
man would be the man with the most ability to distribute what
is equal.
Moreover, see if the thing admits of degrees, whereas what is
rendered according to the definition does not, or, vice versa,
what is rendered according to the definition admits of degrees
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while the thing does not. For either both must admit them or
else neither, if indeed what is rendered according to the
definition is the same as the thing. Moreover, see if, while both
of them admit of degrees, they yet do not both become greater
together: e.g. suppose sexual love to be the desire for
intercourse: for he who is more intensely in love has not a more
intense desire for intercourse, so that both do not become
intensified at once: they certainly should, however, had they
been the same thing.
Moreover, suppose two things to be before you, see if the term
to be defined applies more particularly to the one to which the
content of the definition is less applicable. Take, for instance,
the definition of 'fire' as the 'body that consists of the most
rarefied particles'. For 'fire' denotes flame rather than light, but
flame is less the body that consists of the most rarefied
particles than is light: whereas both ought to be more applicable
to the same thing, if they had been the same. Again, see if the
one expression applies alike to both the objects before you,
while the other does not apply to both alike, but more
particularly to one of them.
Moreover, see if he renders the definition relative to two things
taken separately: thus, the beautiful' is 'what is pleasant to the
eyes or to the ears»: or 'the real' is 'what is capable of being
acted upon or of acting'. For then the same thing will be both
beautiful and not beautiful, and likewise will be both real and
not real. For 'pleasant to the ears' will be the same as 'beautiful',
so that 'not pleasant to the ears' will be the same as 'not
beautiful': for of identical things the opposites, too, are
identical, and the opposite of 'beautiful' is 'not beautiful', while
of 'pleasant to the ears' the opposite is not pleasant to the cars':
clearly, then, 'not pleasant to the ears' is the same thing as 'not
beautiful'. If, therefore, something be pleasant to the eyes but
not to the ears, it will be both beautiful and not beautiful. In like
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manner we shall show also that the same thing is both real and
unreal.
Moreover, of both genera and differentiae and all the other
terms rendered in definitions you should frame definitions in
lieu of the terms, and then see if there be any discrepancy
between them.
8
If the term defined be relative, either in itself or in respect of its
genus, see whether the definition fails to mention that to which
the term, either in itself or in respect of its genus, is relative, e.g.
if he has defined 'knowledge' as an 'incontrovertible conception'
or 'wishing' as 'painless conation'. For of everything relative the
essence is relative to something else, seeing that the being of
every relative term is identical with being in a certain relation to
something. He ought, therefore, to have said that knowledge is
'conception of a knowable' and that wishing is 'conation for a
good'. Likewise, also, if he has defined 'grammar' as 'knowledge
of letters': whereas in the definition there ought to be rendered
either the thing to which the term itself is relative, or that,
whatever it is, to which its genus is relative. Or see if a relative
term has been described not in relation to its end, the end in
anything being whatever is best in it or gives its purpose to the
rest. Certainly it is what is best or final that should be stated,
e.g. that desire is not for the pleasant but for pleasure: for this is
our purpose in choosing what is pleasant as well.
Look and see also if that in relation to which he has rendered
the term be a process or an activity: for nothing of that kind is
an end, for the completion of the activity or process is the end
rather than the process or activity itself. Or perhaps this rule is
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not true in all cases, for almost everybody prefers the present
experience of pleasure to its cessation, so that they would count
the activity as the end rather than its completion.
Again see in some cases if he has failed to distinguish the
quantity or quality or place or other differentiae of an object;
e.g. the quality and quantity of the honour the striving for
which makes a man ambitious: for all men strive for honour, so
that it is not enough to define the ambitious man as him who
strives for honour, but the aforesaid differentiae must be added.
Likewise, also, in defining the covetous man the quantity of
money he aims at, or in the case of the incontinent man the
quality of the pleasures, should be stated. For it is not the man
who gives way to any sort of pleasure whatever who is called
incontinent, but only he who gives way to a certain kind of
pleasure. Or again, people sometimes define night as a 'shadow
on the earth', or an earthquake as a movement of the earth', or
a cloud as 'condensation of the air', or a wind as a 'movement of
the air'; whereas they ought to specify as well quantity, quality,
place, and cause. Likewise, also, in other cases of the kind: for by
omitting any differentiae whatever he fails to state the essence
of the term. One should always attack deficiency. For a
movement of the earth does not constitute an earthquake, nor a
movement of the air a wind, irrespective of its manner and the
amount involved.
Moreover, in the case of conations, and in any other cases
where it applies, see if the word 'apparent' is left out, e.g.
'wishing is a conation after the good', or 'desire is a conation
after the pleasant' - instead of saying 'the apparently good', or
'pleasant'. For often those who exhibit the conation do not
perceive what is good or pleasant, so that their aim need not be
really good or pleasant, but only apparently so. They ought,
therefore, to have rendered the definition also accordingly. On
the other hand, any one who maintains the existence of Ideas
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ought to be brought face to face with his Ideas, even though he
does render the word in question: for there can be no Idea of
anything merely apparent: the general view is that an Idea is
always spoken of in relation to an Idea: thus absolute desire is
for the absolutely pleasant, and absolute wishing is for the
absolutely good; they therefore cannot be for an apparent good
or an apparently pleasant: for the existence of an absolutely -
apparently - good or pleasant would be an absurdity.
Moreover, if the definition be of the state of anything, look at
what is in the state, while if it be of what is in the state, look at
the state: and likewise also in other cases of the kind. Thus if
the pleasant be identical with the beneficial, then, too, the man
who is pleased is benefited. Speaking generally, in definitions of
this sort it happens that what the definer defines is in a sense
more than one thing: for in defining knowledge, a man in a
sense defines ignorance as well, and likewise also what has
knowledge and what lacks it, and what it is to know and to be
ignorant. For if the first be made clear, the others become in a
certain sense clear as well. We have, then, to be on our guard in
all such cases against discrepancy, using the elementary
principles drawn from consideration of contraries and of
coordinates.
Moreover, in the case of relative terms, see if the species is
rendered as relative to a species of that to which the genus is
rendered as relative, e.g. supposing belief to be relative to some
object of belief, see whether a particular belief is made relative
to some particular object of belief: and, if a multiple be relative
to a fraction, see whether a particular multiple be made relative
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to a particular fraction. For if it be not so rendered, clearly a
mistake has been made.
See, also, if the opposite of the term has the opposite definition,
whether (e.g.) the definition of 'half is the opposite of that of
'double': for if 'double' is 'that which exceeds another by an
equal amount to that other', 'half is 'that which is exceeded by
an amount equal to itself. In the same way, too, with contraries.
For to the contrary term will apply the definition that is
contrary in some one of the ways in which contraries are
conjoined. Thus (e.g.) if 'useful'='productive of good',
'injurious'=productive of evil' or 'destructive of good', for one or
the other of thee is bound to be contrary to the term originally
used. Suppose, then, neither of these things to be the contrary
of the term originally used, then clearly neither of the
definitions rendered later could be the definition of the contrary
of the term originally defined: and therefore the definition
originally rendered of the original term has not been rightly
rendered either. Seeing, moreover, that of contraries, the one is
sometimes a word forced to denote the privation of the other, as
(e.g.) inequality is generally held to be the privation of equality
(for 'unequal' merely describes things that are not equal'), it is
therefore clear that that contrary whose form denotes the
privation must of necessity be defined through the other;
whereas the other cannot then be defined through the one
whose form denotes the privation; for else we should find that
each is being interpreted by the other. We must in the case of
contrary terms keep an eye on this mistake, e.g. supposing any
one were to define equality as the contrary of inequality: for
then he is defining it through the term which denotes privation
of it. Moreover, a man who so defines is bound to use in his
definition the very term he is defining; and this becomes clear,
if for the word we substitute its definition. For to say 'inequality'
is the same as to say 'privation of equality'. Therefore equality
so defined will be 'the contrary of the privation of equality', so
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that he would have used the very word to be defined. Suppose,
however, that neither of the contraries be so formed as to
denote privation, but yet the definition of it be rendered in a
manner like the above, e.g. suppose 'good' to be defined as 'the
contrary of evil', then, since it is clear that 'evil' too will be 'the
contrary of good' (for the definition of things that are contrary
in this must be rendered in a like manner), the result again is
that he uses the very term being defined: for 'good' is inherent
in the definition of 'evil'. If, then, 'good' be the contrary of evil,
and evil be nothing other than the 'contrary of good', then
'good' will be the 'contrary of the contrary of good'. Clearly,
then, he has used the very word to be defined.
Moreover, see if in rendering a term formed to denote privation,
he has failed to render the term of which it is the privation, e.g.
the state, or contrary, or whatever it may be whose privation it
is: also if he has omitted to add either any term at all in which
the privation is naturally formed, or else that in which it is
naturally formed primarily, e.g. whether in defining 'ignorance'
a privation he has failed to say that it is the privation of
'knowledge'; or has failed to add in what it is naturally formed,
or, though he has added this, has failed to render the thing in
which it is primarily formed, placing it (e.g.) in 'man' or in 'the
soul', and not in the 'reasoning faculty': for if in any of these
respects he fails, he has made a mistake. Likewise, also, if he
has failed to say that 'blindness' is the 'privation of sight in an
eye': for a proper rendering of its essence must state both of
what it is the privation and what it is that is deprived.
Examine further whether he has defined by the expression 'a
privation' a term that is not used to denote a privation: thus a
mistake of this sort also would be generally thought to be
incurred in the case of 'error' by any one who is not using it as a
merely negative term. For what is generally thought to be in
error is not that which has no knowledge, but rather that which
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has been deceived, and for this reason we do not talk of
inanimate things or of children as 'erring'. 'Error', then, is not
used to denote a mere privation of knowledge.
10
Moreover, see whether the like inflexions in the definition apply
to the like inflexions of the term; e.g. if 'beneficial' means
'productive of health', does 'beneficially' mean productively of
health' and a 'benefactor' a 'producer of health?
Look too and see whether the definition given will apply to the
Idea as well. For in some cases it will not do so; e.g. in the
Platonic definition where he adds the word 'mortal' in his
definitions of living creatures: for the Idea (e.g. the absolute
Man) is not mortal, so that the definition will not fit the Idea. So
always wherever the words 'capable of acting on' or 'capable of
being acted upon' are added, the definition and the Idea are
absolutely bound to be discrepant: for those who assert the
existence of Ideas hold that they are incapable of being acted
upon, or of motion. In dealing with these people even
arguments of this kind are useful.
Further, see if he has rendered a single common definition of
terms that are used ambiguously. For terms whose definition
corresponding their common name is one and the same, are
synonymous; if, then, the definition applies in a like manner to
the whole range of the ambiguous term, it is not true of any one
of the objects described by the term. This is, moreover, what
happens to Dionysius' definition of 'life' when stated as 'a
movement of a creature sustained by nutriment, congenitally
present with it': for this is found in plants as much as in
animals, whereas 'life' is generally understood to mean not one
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kind of thing only, but to be one thing in animals and another in
plants. It is possible to hold the view that life is a synonymous
term and is always used to describe one thing only, and
therefore to render the definition in this way on purpose: or it
may quite well happen that a man may see the ambiguous
character of the word, and wish to render the definition of the
one sense only, and yet fail to see that he has rendered a
definition common to both senses instead of one peculiar to the
sense he intends. In either case, whichever course he pursues,
he is equally at fault. Since ambiguous terms sometimes pass
unobserved, it is best in questioning to treat such terms as
though they were synonymous (for the definition of the one
sense will not apply to the other, so that the answerer will be
generally thought not to have defined it correctly, for to a
synonymous term the definition should apply in its full range),
whereas in answering you should yourself distinguish between
the senses. Further, as some answerers call 'ambiguous' what is
really synonymous, whenever the definition rendered fails to
apply universally, and, vice versa, call synonymous what is
really ambiguous supposing their definition applies to both
senses of the term, one should secure a preliminary admission
on such points, or else prove beforehand that so-and-so is
ambiguous or synonymous, as the case may be: for people are
more ready to agree when they do not foresee what the
consequence will be. If, however, no admission has been made,
and the man asserts that what is really synonymous is
ambiguous because the definition he has rendered will not
apply to the second sense as well, see if the definition of this
second meaning applies also to the other meanings: for if so,
this meaning must clearly be synonymous with those others.
Otherwise, there will be more than one definition of those other
meanings, for there are applicable to them two distinct
definitions in explanation of the term, viz. the one previously
rendered and also the later one. Again, if any one were to define
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a term used in several senses, and, finding that his definition
does not apply to them all, were to contend not that the term is
ambiguous, but that even the term does not properly apply to
all those senses, just because his definition will not do so either,
then one may retort to such a man that though in some things
one must not use the language of the people, yet in a question
of terminology one is bound to employ the received and
traditional usage and not to upset matters of that sort.
11
Suppose now that a definition has been rendered of some
complex term, take away the definition of one of the elements
in the complex, and see if also the rest of the definition defines
the rest of it: if not, it is clear that neither does the whole
definition define the whole complex. Suppose, e.g. that some
one has defined a 'finite straight line' as 'the limit of a finite
plane, such that its centre is in a line with its extremes'; if now
the definition of a finite line' be the 'limit of a finite plane', the
rest (viz. 'such that its centre is in a line with its extremes')
ought to be a definition of straight'. But an infinite straight line
has neither centre nor extremes and yet is straight so that this
remainder does not define the remainder of the term.
Moreover, if the term defined be a compound notion, see if the
definition rendered be equimembral with the term defined. A
definition is said to be equimembral with the term defined
when the number of the elements compounded in the latter is
the same as the number of nouns and verbs in the definition.
For the exchange in such cases is bound to be merely one of
term for term, in the case of some if not of all, seeing that there
are no more terms used now than formerly; whereas in a
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definition terms ought to be rendered by phrases, if possible in
every case, or if not, in the majority. For at that rate, simple
objects too could be defined by merely calling them by a
different name, e.g. 'cloak' instead of 'doublet'.
The mistake is even worse, if actually a less well known term be
substituted, e.g. 'pellucid mortal' for 'white man': for it is no
definition, and moreover is less intelligible when put in that
form.
Look and see also whether, in the exchange of words, the sense
fails still to be the same. Take, for instance, the explanation of
'speculative knowledge' as 'speculative conception': for
conception is not the same as knowledge - as it certainly ought
to be if the whole is to be the same too: for though the word
'speculative' is common to both expressions, yet the remainder
is different.
Moreover, see if in replacing one of the terms by something else
he has exchanged the genus and not the differentia, as in the
example just given: for 'speculative' is a less familiar term than
knowledge; for the one is the genus and the other the
differentia, and the genus is always the most familiar term of
all; so that it is not this, but the differentia, that ought to have
been changed, seeing that it is the less familiar. It might be held
that this criticism is ridiculous: because there is no reason why
the most familiar term should not describe the differentia, and
not the genus; in which case, clearly, the term to be altered
would also be that denoting the genus and not the differentia.
If, however, a man is substituting for a term not merely another
term but a phrase, clearly it is of the differentia rather than of
the genus that a definition should be rendered, seeing that the
object of rendering the definition is to make the subject
familiar; for the differentia is less familiar than the genus.
481
If he has rendered the definition of the differentia, see whether
the definition rendered is common to it and something else as
well: e.g. whenever he says that an odd number is a 'number
with a middle', further definition is required of how it has a
middle: for the word 'number' is common to both expressions,
and it is the word 'odd' for which the phrase has been
substituted. Now both a line and a body have a middle, yet they
are not 'odd'; so that this could not be a definition of 'odd'. If, on
the other hand, the phrase 'with a middle' be used in several
senses, the sense here intended requires to be defined. So that
this will either discredit the definition or prove that it is no
definition at all.
12
Again, see if the term of which he renders the definition is a
reality, whereas what is contained in the definition is not, e.g.
Suppose 'white' to be defined as 'colour mingled with fire': for
what is bodiless cannot be mingled with body, so that 'colour'
'mingled with fire' could not exist, whereas 'white' does exist.
Moreover, those who in the case of relative terms do not
distinguish to what the object is related, but have described it
only so as to include it among too large a number of things, are
wrong either wholly or in part; e.g. suppose some one to have
defined 'medicine' as a science of Reality'. For if medicine be
not a science of anything that is real, the definition is clearly
altogether false; while if it be a science of some real thing, but
not of another, it is partly false; for it ought to hold of all reality,
if it is said to be of Reality essentially and not accidentally: as is
the case with other relative terms: for every object of knowledge
is a term relative to knowledge: likewise, also, with other
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relative terms, inasmuch as all such are convertible. Moreover, if
the right way to render account of a thing be to render it as it is
not in itself but accidentally, then each and every relative term
would be used in relation not to one thing but to a number of
things. For there is no reason why the same thing should not be
both real and white and good, so that it would be a correct
rendering to render the object in relation to any one whatsoever
of these, if to render what it is accidentally be a correct way to
render it. It is, moreover, impossible that a definition of this sort
should be peculiar to the term rendered: for not only but the
majority of the other sciences too, have for their object some
real thing, so that each will be a science of reality. Clearly, then,
such a definition does not define any science at all; for a
definition ought to be peculiar to its own term, not general.
Sometimes, again, people define not the thing but only the
thing in a good or perfect condition. Such is the definition of a
rhetorician as 'one who can always see what will persuade in
the given circumstances, and omit nothing'; or of a thief, as 'one
who pilfers in secret': for clearly, if they each do this, then the
one will be a good rhetorician, and the other a good thief:
whereas it is not the actual pilfering in secret, but the wish to
do it, that constitutes the thief.
Again, see if he has rendered what is desirable for its own sake
as desirable for what it produces or does, or as in any way
desirable because of something else, e.g. by saying that justice is
'what preserves the laws' or that wisdom is 'what produces
happiness'; for what produces or preserves something else is
one of the things desirable for something else. It might be said
that it is possible for what is desirable in itself to be desirable
for something else as well: but still to define what is desirable in
itself in such a way is none the less wrong: for the essence
contains par excellence what is best in anything, and it is better
for a thing to be desirable in itself than to be desirable for
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something else, so that this is rather what the definition too
ought to have indicated.
13
See also whether in defining anything a man has defined it as
an 'A and B', or as a 'product of A and B' or as an A+B\ If he
defines it as and B', the definition will be true of both and yet of
neither of them; suppose, e.g. justice to be defined as
'temperance and courage.' For if of two persons each has one of
the two only, both and yet neither will be just: for both together
have justice, and yet each singly fails to have it. Even if the
situation here described does not so far appear very absurd
because of the occurrence of this kind of thing in other cases
also (for it is quite possible for two men to have a mina between
them, though neither of them has it by himself), yet least that
they should have contrary attributes surely seems quite absurd;
and yet this will follow if the one be temperate and yet a
coward, and the other, though brave, be a profligate; for then
both will exhibit both justice and injustice: for if justice be
temperance and bravery, then injustice will be cowardice and
profligacy. In general, too, all the ways of showing that the
whole is not the same as the sum of its parts are useful in
meeting the type just described; for a man who defines in this
way seems to assert that the parts are the same as the whole.
The arguments are particularly appropriate in cases where the
process of putting the parts together is obvious, as in a house
and other things of that sort: for there, clearly, you may have the
parts and yet not have the whole, so that parts and whole
cannot be the same.
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If, however, he has said that the term being defined is not 'A and
B' but the 'product of A and B', look and see in the first place if A
and B cannot in the nature of things have a single product: for
some things are so related to one another that nothing can
come of them, e.g. a line and a number. Moreover, see if the
term that has been defined is in the nature of things found
primarily in some single subject, whereas the things which he
has said produce it are not found primarily in any single subject,
but each in a separate one. If so, clearly that term could not be
the product of these things: for the whole is bound to be in the
same things wherein its parts are, so that the whole will then be
found primarily not in one subject only, but in a number of
them. If, on the other hand, both parts and whole are found
primarily in some single subject, see if that medium is not the
same, but one thing in the case of the whole and another in
that of the parts. Again, see whether the parts perish together
with the whole: for it ought to happen, vice versa, that the
whole perishes when the parts perish; when the whole
perishes, there is no necessity that the parts should perish too.
Or again, see if the whole be good or evil, and the parts neither,
or, vice versa, if the parts be good or evil and the whole neither.
For it is impossible either for a neutral thing to produce
something good or bad, or for things good or bad to produce a
neutral thing. Or again, see if the one thing is more distinctly
good than the other is evil, and yet the product be no more good
than evil, e.g. suppose shamelessness be defined as 'the product
of courage and false opinion': here the goodness of courage
exceeds the evil of false opinion; accordingly the product of
these ought to have corresponded to this excess, and to be
either good without qualification, or at least more good than
evil. Or it may be that this does not necessarily follow, unless
each be in itself good or bad; for many things that are
productive are not good in themselves, but only in combination;
or, per contra, they are good taken singly, and bad or neutral in
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combination. What has just been said is most clearly illustrated
in the case of things that make for health or sickness; for some
drugs are such that each taken alone is good, but if they are
both administered in a mixture, bad.
Again, see whether the whole, as produced from a better and
worse, fails to be worse than the better and better than the
worse element. This again, however, need not necessarily be the
case, unless the elements compounded be in themselves good;
if they are not, the whole may very well not be good, as in the
cases just instanced.
Moreover, see if the whole be synonymous with one of the
elements: for it ought not to be, any more than in the case of
syllables: for the syllable is not synonymous with any of the
letters of which it is made up.
Moreover, see if he has failed to state the manner of their
composition: for the mere mention of its elements is not
enough to make the thing intelligible. For the essence of any
compound thing is not merely that it is a product of so-and-so,
but that it is a product of them compounded in such and such a
way, just as in the case of a house: for here the materials do not
make a house irrespective of the way they are put together.
If a man has defined an object as 'A+B', the first thing to be said
is that A+B' means the same either as A and B', or as the
'product of A and B.' for 'honey+water' means either the honey
and the water, or the 'drink made of honey and water'. If, then,
he admits that A+B' is + B' is the same as either of these two
things, the same criticisms will apply as have already been
given for meeting each of them. Moreover, distinguish between
the different senses in which one thing may be said to be '+'
another, and see if there is none of them in which A could be
said to exist '+ B.' Thus e.g. supposing the expression to mean
that they exist either in some identical thing capable of
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containing them (as e.g. justice and courage are found in the
soul), or else in the same place or in the same time, and if this
be in no way true of the A and B in question, clearly the
definition rendered could not hold of anything, as there is no
possible way in which A can exist B'. If, however, among the
various senses above distinguished, it be true that A and B are
each found in the same time as the other, look and see if
possibly the two are not used in the same relation. Thus e.g.
suppose courage to have been defined as 'daring with right
reasoning': here it is possible that the person exhibits daring in
robbery, and right reasoning in regard to the means of health:
but he may have 'the former quality+the latter' at the same
time, and not as yet be courageous! Moreover, even though both
be used in the same relation as well, e.g. in relation to medical
treatment (for a man may exhibit both daring and right
reasoning in respect of medical treatment), still, none the less,
not even this combination of 'the one+the other 'makes him
'courageous'. For the two must not relate to any casual object
that is the same, any more than each to a different object;
rather, they must relate to the function of courage, e.g. meeting
the perils of war, or whatever is more properly speaking its
function than this.
Some definitions rendered in this form fail to come under the
aforesaid division at all, e.g. a definition of anger as 'pain with a
consciousness of being slighted'. For what this means to say is
that it is because of a consciousness of this sort that the pain
occurs; but to occur 'because of a thing is not the same as to
occur '+ a thing' in any of its aforesaid senses.
487
14
Again, if he have described the whole compounded as the
'composition' of these things (e.g. 'a living creature' as a
'composition of soul and body'), first of all see whether he has
omitted to state the kind of composition, as (e.g.) in a definition
of 'flesh' or 'bone' as the 'composition of fire, earth, and air'. For
it is not enough to say it is a composition, but you should also
go on to define the kind of composition: for these things do not
form flesh irrespective of the manner of their composition, but
when compounded in one way they form flesh, when in
another, bone. It appears, moreover, that neither of the
aforesaid substances is the same as a 'composition' at all: for a
composition always has a decomposition as its contrary,
whereas neither of the aforesaid has any contrary. Moreover, if
it is equally probable that every compound is a composition or
else that none is, and every kind of living creature, though a
compound, is never a composition, then no other compound
could be a composition either.
Again, if in the nature of a thing two contraries are equally
liable to occur, and the thing has been defined through the one,
clearly it has not been defined; else there will be more than one
definition of the same thing; for how is it any more a definition
to define it through this one than through the other, seeing that
both alike are naturally liable to occur in it? Such is the
definition of the soul, if defined as a substance capable of
receiving knowledge: for it has a like capacity for receiving
ignorance.
Also, even when one cannot attack the definition as a whole for
lack of acquaintance with the whole, one should attack some
part of it, if one knows that part and sees it to be incorrectly
rendered: for if the part be demolished, so too is the whole
definition. Where, again, a definition is obscure, one should first
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of all correct and reshape it in order to make some part of it
clear and get a handle for attack, and then proceed to examine
it. For the answerer is bound either to accept the sense as taken
by the questioner, or else himself to explain clearly whatever it
is that his definition means. Moreover, just as in the assemblies
the ordinary practice is to move an emendation of the existing
law and, if the emendation is better, they repeal the existing
law, so one ought to do in the case of definitions as well: one
ought oneself to propose a second definition: for if it is seen to
be better, and more indicative of the object defined, clearly the
definition already laid down will have been demolished, on the
principle that there cannot be more than one definition of the
same thing.
In combating definitions it is always one of the chief
elementary principles to take by oneself a happy shot at a
definition of the object before one, or to adopt some correctly
expressed definition. For one is bound, with the model (as it
were) before one's eyes, to discern both any shortcoming in any
features that the definition ought to have, and also any
superfluous addition, so that one is better supplied with lines of
attack.
As to definitions, then, let so much suffice.
Book VII
489
Whether two things are 'the same' or 'different', in the most
literal of the meanings ascribed to 'sameness' (and we said' that
'the same' applies in the most literal sense to what is
numerically one), may be examined in the light of their
inflexions and coordinates and opposites. For if justice be the
same as courage, then too the just man is the same as the brave
man, and 'justly' is the same as 'bravely'. Likewise, too, in the
case of their opposites: for if two things be the same, their
opposites also will be the same, in any of the recognized forms
of opposition. For it is the same thing to take the opposite of the
one or that of the other, seeing that they are the same. Again it
may be examined in the light of those things which tend to
produce or to destroy the things in question of their formation
and destruction, and in general of any thing that is related in
like manner to each. For where things are absolutely the same,
their formations and destructions also are the same, and so are
the things that tend to produce or to destroy them. Look and
see also, in a case where one of two things is said to be
something or other in a superlative degree, if the other of these
alleged identical things can also be described by a superlative in
the same respect. Thus Xenocrates argues that the happy life
and the good life are the same, seeing that of all forms of life
the good life is the most desirable and so also is the happy life:
for 'the most desirable' and the greatest' apply but to one thing.'
Likewise also in other cases of the kind. Each, however, of the
two things termed 'greatest' or most desirable' must be
numerically one: otherwise no proof will have been given that
they are the same; for it does not follow because
Peloponnesians and Spartans are the bravest of the Greeks, that
Peloponnesians are the same as Spartans, seeing that
'Peloponnesian' is not any one person nor yet 'Spartan'; it only
follows that the one must be included under the other as
'Spartans' are under 'Peloponnesians': for otherwise, if the one
490
class be not included under the other, each will be better than
the other. For then the Peloponnesians are bound to be better
than the Spartans, seeing that the one class is not included
under the other; for they are better than anybody else. Likewise
also the Spartans must perforce be better than the
Peloponnesians; for they too are better than anybody else; each
then is better than the other! Clearly therefore what is styled
'best' and 'greatest' must be a single thing, if it is to be proved to
be 'the same' as another. This also is why Xenocrates fails to
prove his case: for the happy life is not numerically single, nor
yet the good life, so that it does not follow that, because they are
both the most desirable, they are therefore the same, but only
that the one falls under the other.
Again, look and see if, supposing the one to be the same as
something, the other also is the same as it: for if they be not
both the same as the same thing, clearly neither are they the
same as one another.
Moreover, examine them in the light of their accidents or of the
things of which they are accidents: for any accident belonging
to the one must belong also to the other, and if the one belong
to anything as an accident, so must the other also. If in any of
these respects there is a discrepancy, clearly they are not the
same.
See further whether, instead of both being found in one class of
predicates, the one signifies a quality and the other a quantity
or relation. Again, see if the genus of each be not the same, the
one being 'good' and the other evil', or the one being 'virtue' and
the other 'knowledge': or see if, though the genus is the same,
the differentiae predicted of either be not the same, the one
(e.g.) being distinguished as a 'speculative' science, the other as
a 'practical' science. Likewise also in other cases.
491
Moreover, from the point of view of 'degrees', see if the one
admits an increase of degree but not the other, or if though both
admit it, they do not admit it at the same time; just as it is not
the case that a man desires intercourse more intensely, the
more intensely he is in love, so that love and the desire for
intercourse are not the same.
Moreover, examine them by means of an addition, and see
whether the addition of each to the same thing fails to make
the same whole; or if the subtraction of the same thing from
each leaves a different remainder. Suppose (e.g.) that he has
declared 'double a half to be the same as 'a multiple of a half:
then, subtracting the words 'a half from each, the remainders
ought to have signified the same thing: but they do not; for
'double' and 'a multiple of do not signify the same thing.
Inquire also not only if some impossible consequence results
directly from the statement made, that A and B are the same,
but also whether it is possible for a supposition to bring it
about; as happens to those who assert that 'empty' is the same
as 'full of air': for clearly if the air be exhausted, the vessel will
not be less but more empty, though it will no longer be full of
air. So that by a supposition, which may be true or may be false
(it makes no difference which), the one character is annulled
and not the other, showing that they are not the same.
Speaking generally, one ought to be on the look-out for any
discrepancy anywhere in any sort of predicate of each term, and
in the things of which they are predicated. For all that is
predicated of the one should be predicated also of the other,
and of whatever the one is a predicate, the other should be a
predicate of it as well.
Moreover, as 'sameness' is a term used in many senses, see
whether things that are the same in one way are the same also
in a different way. For there is either no necessity or even no
492
possibility that things that are the same specifically or
generically should be numerically the same, and it is with the
question whether they are or are not the same in that sense
that we are concerned.
Moreover, see whether the one can exist without the other; for,
if so, they could not be the same.
Such is the number of the commonplace rules that relate to
'sameness'. It is clear from what has been said that all the
destructive commonplaces relating to sameness are useful also
in questions of definition, as was said before:' for if what is
signified by the term and by the expression be not the same,
clearly the expression rendered could not be a definition. None
of the constructive commonplaces, on the other hand, helps in
the matter of definition; for it is not enough to show the
sameness of content between the expression and the term, in
order to establish that the former is a definition, but a definition
must have also all the other characters already announced.
This then is the way, and these the arguments, whereby the
attempt to demolish a definition should always be made. If, on
the other hand, we desire to establish one, the first thing to
observe is that few if any who engage in discussion arrive at a
definition by reasoning: they always assume something of the
kind as their starting points - both in geometry and in
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arithmetic and the other studies of that kind. In the second
place, to say accurately what a definition is, and how it should
be given, belongs to another inquiry. At present it concerns us
only so far as is required for our present purpose, and
accordingly we need only make the bare statement that to
reason to a thing's definition and essence is quite possible. For if
a definition is an expression signifying the essence of the thing
and the predicates contained therein ought also to be the only
ones which are predicated of the thing in the category of
essence; and genera and differentiae are so predicated in that
category: it is obvious that if one were to get an admission that
so and so are the only attributes predicated in that category, the
expression containing so and so would of necessity be a
definition; for it is impossible that anything else should be a
definition, seeing that there is not anything else predicated of
the thing in the category of essence.
That a definition may thus be reached by a process of reasoning
is obvious. The means whereby it should be established have
been more precisely defined elsewhere, but for the purposes of
the inquiry now before us the same commonplace rules serve.
For we have to examine into the contraries and other opposites
of the thing, surveying the expressions used both as wholes and
in detail: for if the opposite definition defines that opposite
term, the definition given must of necessity be that of the term
before us. Seeing, however, that contraries may be conjoined in
more than one way, we have to select from those contraries the
one whose contrary definition seems most obvious. The
expressions, then, have to be examined each as a whole in the
way we have said, and also in detail as follows. First of all, see
that the genus rendered is correctly rendered; for if the contrary
thing be found in the contrary genus to that stated in the
definition, and the thing before you is not in that same genus,
then it would clearly be in the contrary genus: for contraries
must of necessity be either in the same genus or in contrary
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genera. The differentiae, too, that are predicated of contraries
we expect to be contrary, e.g. those of white and black, for the
one tends to pierce the vision, while the other tends to
compress it. So that if contrary differentiae to those in the
definition are predicated of the contrary term, then those
rendered in the definition would be predicated of the term
before us. Seeing, then, that both the genus and the differentiae
have been rightly rendered, clearly the expression given must
be the right definition. It might be replied that there is no
necessity why contrary differentiae should be predicated of
contraries, unless the contraries be found within the same
genus: of things whose genera are themselves contraries it may
very well be that the same differentia is used of both, e.g. of
justice and injustice; for the one is a virtue and the other a vice
of the soul: 'of the soul', therefore, is the differentia in both
cases, seeing that the body as well has its virtue and vice. But
this much at least is true, that the differentiae of contraries are
either contrary or else the same. If, then, the contrary
differentia to that given be predicated of the contrary term and
not of the one in hand, clearly the differentia stated must be
predicated of the latter. Speaking generally, seeing that the
definition consists of genus and differentiae, if the definition of
the contrary term be apparent, the definition of the term before
you will be apparent also: for since its contrary is found either
in the same genus or in the contrary genus, and likewise also
the differentiae predicated of opposites are either contrary to, or
the same as, each other, clearly of the term before you there will
be predicated either the same genus as of its contrary, while, of
its differentiae, either all are contrary to those of its contrary, or
at least some of them are so while the rest remain the same; or,
vice versa, the differentiae will be the same and the genera
contrary; or both genera and differentiae will be contrary. And
that is all; for that both should be the same is not possible; else
contraries will have the same definition.
495
Moreover, look at it from the point of view of its inflexions and
coordinates. For genera and definitions are bound to correspond
in either case. Thus if forgetfulness be the loss of knowledge, to
forget is to lose knowledge, and to have forgotten is to have lost
knowledge. If, then, any one whatever of these is agreed to, the
others must of necessity be agreed to as well. Likewise, also, if
destruction is the decomposition of the thing's essence, then to
be destroyed is to have its essence decomposed, and
'destructively' means 'in such a way as to decompose its
essence'; if again 'destructive' means 'apt to decompose
something's essence', then also 'destruction' means 'the
decomposition of its essence'. Likewise also with the rest: an
admission of any one of them whatever, and all the rest are
admitted too.
Moreover, look at it from the point of view of things that stand
in relations that are like each other. For if 'healthy' means
'productive of health', 'vigorous' too will mean 'productive of
vigour', and 'useful' will mean 'productive of good.' For each of
these things is related in like manner to its own peculiar end, so
that if one of them is defined as 'productive of that end, this
will also be the definition of each of the rest as well.
Moreover, look at it from the point of and like degrees, in all the
ways in which it is possible to establish a result by comparing
two and two together. Thus if A defines a better than B defines
and B is a definition of so too is A of a. Further, if As claim to
define a is like B's to define B, and B defines B, then A too
defines a. This examination from the point of view of greater
degrees is of no use when a single definition is compared with
two things, or two definitions with one thing; for there cannot
possibly be one definition of two things or two of the same
thing.
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The most handy of all the commonplace arguments are those
just mentioned and those from co-ordinates and inflexions, and
these therefore are those which it is most important to master
and to have ready to hand: for they are the most useful on the
greatest number of occasions. Of the rest, too, the most
important are those of most general application: for these are
the most effective, e.g. that you should examine the individual
cases, and then look to see in the case of their various species
whether the definition applies. For the species is synonymous
with its individuals. This sort of inquiry is of service against
those who assume the existence of Ideas, as has been said
before.' Moreover see if a man has used a term metaphorically,
or predicated it of itself as though it were something different.
So too if any other of the commonplace rules is of general
application and effective, it should be employed.
That it is more difficult to establish than to overthrow a
definition, is obvious from considerations presently to be urged.
For to see for oneself, and to secure from those whom one is
questioning, an admission of premisses of this sort is no simple
matter, e.g. that of the elements of the definition rendered the
one is genus and the other differentia, and that only the genus
and differentiae are predicated in the category of essence. Yet
without these premisses it is impossible to reason to a
definition; for if any other things as well are predicated of the
thing in the category of essence, there is no telling whether the
formula stated or some other one is its definition, for a
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definition is an expression indicating the essence of a thing. The
point is clear also from the following: It is easier to draw one
conclusion than many. Now in demolishing a definition it is
sufficient to argue against one point only (for if we have
overthrown any single point whatsoever, we shall have
demolished the definition); whereas in establishing a definition,
one is bound to bring people to the view that everything
contained in the definition is attributable. Moreover, in
establishing a case, the reasoning brought forward must be
universal: for the definition put forward must be predicated of
everything of which the term is predicated, and must moreover
be convertible, if the definition rendered is to be peculiar to the
subject. In overthrowing a view, on the other hand, there is no
longer any necessity to show one's point universally: for it is
enough to show that the formula is untrue of any one of the
things embraced under the term.
Further, even supposing it should be necessary to overthrow
something by a universal proposition, not even so is there any
need to prove the converse of the proposition in the process of
overthrowing the definition. For merely to show that the
definition fails to be predicated of every one of the things of
which the term is predicated, is enough to overthrow it
universally: and there is no need to prove the converse of this in
order to show that the term is predicated of things of which the
expression is not predicated. Moreover, even if it applies to
everything embraced under the term, but not to it alone, the
definition is thereby demolished.
The case stands likewise in regard to the property and genus of
a term also. For in both cases it is easier to overthrow than to
establish. As regards the property this is clear from what has
been said: for as a rule the property is rendered in a complex
phrase, so that to overthrow it, it is only necessary to demolish
one of the terms used, whereas to establish it is necessary to
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reason to them all. Then, too, nearly all the other rules that
apply to the definition will apply also to the property of a thing.
For in establishing a property one has to show that it is true of
everything included under the term in question, whereas to
overthrow one it is enough to show in a single case only that it
fails to belong: further, even if it belongs to everything falling
under the term, but not to that only, it is overthrown in this case
as well, as was explained in the case of the definition. In regard
to the genus, it is clear that you are bound to establish it in one
way only, viz. by showing that it belongs in every case, while of
overthrowing it there are two ways: for if it has been shown that
it belongs either never or not in a certain case, the original
statement has been demolished. Moreover, in establishing a
genus it is not enough to show that it belongs, but also that it
belongs as genus has to be shown; whereas in overthrowing it,
it is enough to show its failure to belong either in some
particular case or in every case. It appears, in fact, as though,
just as in other things to destroy is easier than to create, so in
these matters too to overthrow is easier than to establish.
In the case of an accidental attribute the universal proposition
is easier to overthrow than to establish; for to establish it, one
has to show that it belongs in every case, whereas to overthrow
it, it is enough to show that it does not belong in one single
case. The particular proposition is, on the contrary, easier to
establish than to overthrow: for to establish it, it is enough to
show that it belongs in a particular instance, whereas to
overthrow it, it has to be shown that it never belongs at all.
It is clear also that the easiest thing of all is to overthrow a
definition. For on account of the number of statements involved
we are presented in the definition with the greatest number of
points for attack, and the more plentiful the material, the
quicker an argument comes: for there is more likelihood of a
mistake occurring in a large than in a small number of things.
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Moreover, the other rules too may be used as means for
attacking a definition: for if either the formula be not peculiar,
or the genus rendered be the wrong one, or something included
in the formula fail to belong, the definition is thereby
demolished. On the other hand, against the others we cannot
bring all of the arguments drawn from definitions, nor yet of the
rest: for only those relating to accidental attributes apply
generally to all the aforesaid kinds of attribute. For while each
of the aforesaid kinds of attribute must belong to the thing in
question, yet the genus may very well not belong as a property
without as yet being thereby demolished. Likewise also the
property need not belong as a genus, nor the accident as a
genus or property, so long as they do belong. So that it is
impossible to use one set as a basis of attack upon the other
except in the case of definition. Clearly, then, it is the easiest of
all things to demolish a definition, while to establish one is the
hardest. For there one both has to establish all those other
points by reasoning (i.e. that the attributes stated belong, and
that the genus rendered is the true genus, and that the formula
is peculiar to the term), and moreover, besides this, that the
formula indicates the essence of the thing; and this has to be
done correctly.
Of the rest, the property is most nearly of this kind: for it is
easier to demolish, because as a rule it contains several terms;
while it is the hardest to establish, both because of the number
of things that people must be brought to accept, and, besides
this, because it belongs to its subject alone and is predicated
convertibly with its subject.
The easiest thing of all to establish is an accidental predicate:
for in other cases one has to show not only that the predicate
belongs, but also that it belongs in such and such a particular
way: whereas in the case of the accident it is enough to show
merely that it belongs. On the other hand, an accidental
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predicate is the hardest thing to overthrow, because it affords
the least material: for in stating accident a man does not add
how the predicate belongs; and accordingly, while in other cases
it is possible to demolish what is said in two ways, by showing
either that the predicate does not belong, or that it does not
belong in the particular way stated, in the case of an accidental
predicate the only way to demolish it is to show that it does not
belong at all.
The commonplace arguments through which we shall be well
supplied with lines of argument with regard to our several
problems have now been enumerated at about sufficient length.
Book VIII
Next there fall to be discussed the problems of arrangement
and method in pitting questions. Any one who intends to frame
questions must, first of all, select the ground from which he
should make his attack; secondly, he must frame them and
arrange them one by one to himself; thirdly and lastly, he must
proceed actually to put them to the other party. Now so far as
the selection of his ground is concerned the problem is one
alike for the philosopher and the dialectician; but how to go on
to arrange his points and frame his questions concerns the
dialectician only: for in every problem of that kind a reference
to another party is involved. Not so with the philosopher, and
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the man who is investigating by himself: the premisses of his
reasoning, although true and familiar, may be refused by the
answerer because they lie too near the original statement and
so he foresees what will follow if he grants them: but for this
the philosopher does not care. Nay, he may possibly be even
anxious to secure axioms as familiar and as near to the
question in hand as possible: for these are the bases on which
scientific reasonings are built up.
The sources from which one's commonplace arguments should
be drawn have already been described:' we have now to discuss
the arrangement and formation of questions and first to
distinguish the premisses, other than the necessary premisses,
which have to be adopted. By necessary premisses are meant
those through which the actual reasoning is constructed. Those
which are secured other than these are of four kinds; they serve
either inductively to secure the universal premiss being granted,
or to lend weight to the argument, or to conceal the conclusion,
or to render the argument more clear. Beside these there is no
other premiss which need be secured: these are the ones
whereby you should try to multiply and formulate your
questions. Those which are used to conceal the conclusion
serve a controversial purpose only; but inasmuch as an
undertaking of this sort is always conducted against another
person, we are obliged to employ them as well.
The necessary premisses through which the reasoning is
effected, ought not to be propounded directly in so many words.
Rather one should soar as far aloof from them as possible. Thus
if one desires to secure an admission that the knowledge of
contraries is one, one should ask him to admit it not of
contraries, but of opposites: for, if he grants this, one will then
argue that the knowledge of contraries is also the same, seeing
that contraries are opposites; if he does not, one should secure
the admission by induction, by formulating a proposition to that
502
effect in the case of some particular pair of contraries. For one
must secure the necessary premisses either by reasoning or by
induction, or else partly by one and partly by the other,
although any propositions which are too obvious to be denied
may be formulated in so many words. This is because the
coming conclusion is less easily discerned at the greater
distance and in the process of induction, while at the same
time, even if one cannot reach the required premisses in this
way, it is still open to one to formulate them in so many words.
The premisses, other than these, that were mentioned above,
must be secured with a view to the latter. The way to employ
them respectively is as follows: Induction should proceed from
individual cases to the universal and from the known to the
unknown; and the objects of perception are better known, to
most people if not invariably. Concealment of one's plan is
obtained by securing through prosyllogisms the premisses
through which the proof of the original proposition is going to
be constructed - and as many of them as possible. This is likely
to be effected by making syllogisms to prove not only the
necessary premisses but also some of those which are required
to establish them. Moreover, do not state the conclusions of
these premisses but draw them later one after another; for this
is likely to keep the answerer at the greatest possible distance
from the original proposition. Speaking generally, a man who
desires to get information by a concealed method should so put
his questions that when he has put his whole argument and
has stated the conclusion, people still ask 'Well, but why is
that?' This result will be secured best of all by the method above
described: for if one states only the final conclusion, it is
unclear how it comes about; for the answerer does not foresee
on what grounds it is based, because the previous syllogisms
have not been made articulate to him: while the final syllogism,
showing the conclusion, is likely to be kept least articulate if we
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lay down not the secured propositions on which it is based, but
only the grounds on which we reason to them.
It is a useful rule, too, not to secure the admissions claimed as
the bases of the syllogisms in their proper order, but alternately
those that conduce to one conclusion and those that conduce to
another; for, if those which go together are set side by side, the
conclusion that will result from them is more obvious in
advance.
One should also, wherever possible, secure the universal
premiss by a definition relating not to the precise terms
themselves but to their co-ordinates; for people deceive
themselves, whenever the definition is taken in regard to a co-
ordinate, into thinking that they are not making the admission
universally. An instance would be, supposing one had to secure
the admission that the angry man desires vengeance on
account of an apparent slight, and were to secure this, that
'anger' is a desire for vengeance on account of an apparent
slight: for, clearly, if this were secured, we should have
universally what we intend. If, on the other hand, people
formulate propositions relating to the actual terms themselves,
they often find that the answerer refuses to grant them because
on the actual term itself he is readier with his objection, e.g.
that the 'angry man' does not desire vengeance, because we
become angry with our parents, but we do not desire vengeance
on them. Very likely the objection is not valid; for upon some
people it is vengeance enough to cause them pain and make
them sorry; but still it gives a certain plausibility and air of
reasonableness to the denial of the proposition. In the case,
however, of the definition of 'anger' it is not so easy to find an
objection.
Moreover, formulate your proposition as though you did so not
for its own sake, but in order to get at something else: for people
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are shy of granting what an opponent's case really requires.
Speaking generally, a questioner should leave it as far as
possible doubtful whether he wishes to secure an admission of
his proposition or of its opposite: for if it be uncertain what
their opponent's argument requires, people are more ready to
say what they themselves think.
Moreover, try to secure admissions by means of likeness: for
such admissions are plausible, and the universal involved is less
patent; e.g. make the other person admit that as knowledge and
ignorance of contraries is the same, so too perception of
contraries is the same; or vice versa, that since the perception is
the same, so is the knowledge also. This argument resembles
induction, but is not the same thing; for in induction it is the
universal whose admission is secured from the particulars,
whereas in arguments from likeness, what is secured is not the
universal under which all the like cases fall.
It is a good rule also, occasionally to bring an objection against
oneself: for answerers are put off their guard against those who
appear to be arguing impartially. It is useful too, to add that 'So
and so is generally held or commonly said'; for people are shy of
upsetting the received opinion unless they have some positive
objection to urge: and at the same time they are cautious about
upsetting such things because they themselves too find them
useful. Moreover, do not be insistent, even though you really
require the point: for insistence always arouses the more
opposition. Further, formulate your premiss as though it were a
mere illustration: for people admit the more readily a
proposition made to serve some other purpose, and not
required on its own account. Moreover, do not formulate the
very proposition you need to secure, but rather something from
which that necessarily follows: for people are more willing to
admit the latter, because it is not so clear from this what the
result will be, and if the one has been secured, the other has
505
been secured also. Again, one should put last the point which
one most wishes to have conceded; for people are specially
inclined to deny the first questions put to them, because most
people in asking questions put first the points which they are
most eager to secure. On the other hand, in dealing with some
people propositions of this sort should be put forward first: for
ill-tempered men admit most readily what comes first, unless
the conclusion that will result actually stares them in the face,
while at the close of an argument they show their ill-temper.
Likewise also with those who consider themselves smart at
answering: for when they have admitted most of what you want
they finally talk clap-trap to the effect that the conclusion does
not follow from their admissions: yet they say 'Yes' readily,
confident in their own character, and imagining that they
cannot suffer any reverse. Moreover, it is well to expand the
argument and insert things that it does not require at all, as do
those who draw false geometrical figures: for in the multitude
of details the whereabouts of the fallacy is obscured. For this
reason also a questioner sometimes evades observation as he
adds in a corner what, if he formulated it by itself, would not be
granted.
For concealment, then, the rules which should be followed are
the above. Ornament is attained by induction and distinction of
things closely akin. What sort of process induction is obvious: as
for distinction, an instance of the kind of thing meant is the
distinction of one form of knowledge as better than another by
being either more accurate, or concerned with better objects; or
the distinction of sciences into speculative, practical, and
productive. For everything of this kind lends additional
ornament to the argument, though there is no necessity to say
them, so far as the conclusion goes.
For clearness, examples and comparisons should be adduced,
and let the illustrations be relevant and drawn from things that
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we know, as in Homer and not as in Choerilus; for then the
proposition is likely to become clearer.
In dialectics, syllogism should be employed in reasoning against
dialecticians rather than against the crowd: induction, on the
other hand, is most useful against the crowd. This point has
been treated previously as well.' In induction, it is possible in
some cases to ask the question in its universal form, but in
others this is not easy, because there is no established general
term that covers all the resemblances: in this case, when people
need to secure the universal, they use the phrase 'in all cases of
this sort'. But it is one of the very hardest things to distinguish
which of the things adduced are 'of this sort', and which are
not: and in this connexion people often throw dust in each
others' eyes in their discussion, the one party asserting the
likeness of things that are not alike, and the other disputing the
likeness of things that are. One ought, therefore, to try oneself
to coin a word to cover all things of the given sort, so as to leave
no opportunity either to the answerer to dispute, and say that
the thing advanced does not answer to a like description, or to
the questioner to suggest falsely that it does answer to a like
description, for many things appear to answer to like
descriptions that do not really do so.
If one has made an induction on the strength of several cases
and yet the answerer refuses to grant the universal proposition,
then it is fair to demand his objection. But until one has oneself
stated in what cases it is so, it is not fair to demand that he
shall say in what cases it is not so: for one should make the
induction first, and then demand the objection. One ought,
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moreover, to claim that the objections should not be brought in
reference to the actual subject of the proposition, unless that
subject happen to be the one and only thing of the kind, as for
instance two is the one prime number among the even
numbers: for, unless he can say that this subject is unique of its
kind, the objector ought to make his objection in regard to some
other. People sometimes object to a universal proposition, and
bring their objection not in regard to the thing itself, but in
regard to some homonym of it: thus they argue that a man can
very well have a colour or a foot or a hand other than his own,
for a painter may have a colour that is not his own, and a cook
may have a foot that is not his own. To meet them, therefore,
you should draw the distinction before putting your question in
such cases: for so long as the ambiguity remains undetected, so
long will the objection to the proposition be deemed valid. If,
however, he checks the series of questions by an objection in
regard not to some homonym, but to the actual thing asserted,
the questioner should withdraw the point objected to, and form
the remainder into a universal proposition, until he secures
what he requires; e.g. in the case of forgetfulness and having
forgotten: for people refuse to admit that the man who has lost
his knowledge of a thing has forgotten it, because if the thing
alters, he has lost knowledge of it, but he has not forgotten it.
Accordingly the thing to do is to withdraw the part objected to,
and assert the remainder, e.g. that if a person have lost
knowledge of a thing while it still remains, he then has
forgotten it. One should similarly treat those who object to the
statement that 'the greater the good, the greater the evil that is
its opposite': for they allege that health, which is a less good
thing than vigour, has a greater evil as its opposite: for disease
is a greater evil than debility. In this case too, therefore, we have
to withdraw the point objected to; for when it has been
withdrawn, the man is more likely to admit the proposition, e.g.
that 'the greater good has the greater evil as its opposite, unless
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the one good involves the other as well', as vigour involves
health. This should be done not only when he formulates an
objection, but also if, without so doing, he refuses to admit the
point because he foresees something of the kind: for if the point
objected to be withdrawn, he will be forced to admit the
proposition because he cannot foresee in the rest of it any case
where it does not hold true: if he refuse to admit it, then when
asked for an objection he certainly will be unable to render one.
Propositions that are partly false and partly true are of this type:
for in the case of these it is possible by withdrawing a part to
leave the rest true. If, however, you formulate the proposition on
the strength of many cases and he has no objection to bring,
you may claim that he shall admit it: for a premiss is valid in
dialectics which thus holds in several instances and to which
no objection is forthcoming.
Whenever it is possible to reason to the same conclusion either
through or without a reduction per impossibile, if one is
demonstrating and not arguing dialectically it makes no
difference which method of reasoning be adopted, but in
argument with another reasoning per impossibile should be
avoided. For where one has reasoned without the reduction per
impossibile, no dispute can arise; if, on the other hand, one does
reason to an impossible conclusion, unless its falsehood is too
plainly manifest, people deny that it is impossible, so that the
questioners do not get what they want.
One should put forward all propositions that hold true of
several cases, and to which either no objection whatever
appears or at least not any on the surface: for when people
cannot see any case in which it is not so, they admit it for true.
The conclusion should not be put in the form of a question; if it
be, and the man shakes his head, it looks as if the reasoning
had failed. For often, even if it be not put as a question but
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advanced as a consequence, people deny it, and then those who
do not see that it follows upon the previous admissions do not
realize that those who deny it have been refuted: when, then,
the one man merely asks it as a question without even saying
that it so follows, and the other denies it, it looks altogether as if
the reasoning had failed.
Not every universal question can form a dialectical proposition
as ordinarily understood, e.g. 'What is man?' or 'How many
meanings has «the good»?' For a dialectical premiss must be of
a form to which it is possible to reply 'Yes' or 'No', whereas to
the aforesaid it is not possible. For this reason questions of this
kind are not dialectical unless the questioner himself draws
distinctions or divisions before expressing them, e.g. 'Good
means this, or this, does it not?' For questions of this sort are
easily answered by a Yes or a No. Hence one should endeavour
to formulate propositions of this kind in this form. It is at the
same time also perhaps fair to ask the other man how many
meanings of 'the good' there are, whenever you have yourself
distinguished and formulated them, and he will not admit them
at all.
Any one who keeps on asking one thing for a long time is a bad
inquirer. For if he does so though the person questioned keeps
on answering the questions, clearly he asks a large number of
questions, or else asks the same question a large number of
times: in the one case he merely babbles, in the other he fails to
reason: for reasoning always consists of a small number of
premisses. If, on the other hand, he does it because the person
questioned does not answer the questions, he is at fault in not
taking him to task or breaking off the discussion.
510
There are certain hypotheses upon which it is at once difficult
to bring, and easy to stand up to, an argument. Such (e.g.) are
those things which stand first and those which stand last in the
order of nature. For the former require definition, while the
latter have to be arrived at through many steps if one wishes to
secure a continuous proof from first principles, or else all
discussion about them wears the air of mere sophistry: for to
prove anything is impossible unless one begins with the
appropriate principles, and connects inference with inference
till the last are reached. Now to define first principles is just
what answerers do not care to do, nor do they pay any attention
if the questioner makes a definition: and yet until it is clear
what it is that is proposed, it is not easy to discuss it. This sort
of thing happens particularly in the case of the first principles:
for while the other propositions are shown through these, these
cannot be shown through anything else: we are obliged to
understand every item of that sort by a definition. The
inferences, too, that lie too close to the first principle are hard to
treat in argument: for it is not possible to bring many arguments
in regard to them, because of the small number of those steps,
between the conclusion and the principle, whereby the
succeeding propositions have to be shown. The hardest,
however, of all definitions to treat in argument are those that
employ terms about which, in the first place, it is uncertain
whether they are used in one sense or several, and, further,
whether they are used literally or metaphorically by the definer.
For because of their obscurity, it is impossible to argue upon
such terms; and because of the impossibility of saying whether
this obscurity is due to their being used metaphorically, it is
impossible to refute them.
In general, it is safe to suppose that, whenever any problem
proves intractable, it either needs definition or else bears either
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several senses, or a metaphorical sense, or it is not far removed
from the first principles; or else the reason is that we have yet
to discover in the first place just this - in which of the aforesaid
directions the source of our difficulty lies: when we have made
this clear, then obviously our business must be either to define
or to distinguish, or to supply the intermediate premisses: for it
is through these that the final conclusions are shown.
It often happens that a difficulty is found in discussing or
arguing a given position because the definition has not been
correctly rendered: e.g. 'Has one thing one contrary or many?':
here when the term 'contraries' has been properly defined, it is
easy to bring people to see whether it is possible for the same
thing to have several contraries or not: in the same way also
with other terms requiring definition. It appears also in
mathematics that the difficulty in using a figure is sometimes
due to a defect in definition; e.g. in proving that the line which
cuts the plane parallel to one side divides similarly both the line
which it cuts and the area; whereas if the definition be given,
the fact asserted becomes immediately clear: for the areas have
the same fraction subtracted from them as have the sides: and
this is the definition of 'the same ratio'. The most primary of the
elementary principles are without exception very easy to show,
if the definitions involved, e.g. the nature of a line or of a circle,
be laid down; only the arguments that can be brought in regard
to each of them are not many, because there are not many
intermediate steps. If, on the other hand, the definition of the
starting-points be not laid down, to show them is difficult and
may even prove quite impossible. The case of the significance of
verbal expressions is like that of these mathematical
conceptions.
One may be sure then, whenever a position is hard to discuss,
that one or other of the aforesaid things has happened to it.
Whenever, on the other hand, it is a harder task to argue to the
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point claimed, i.e. the premiss, than to the resulting position, a
doubt may arise whether such claims should be admitted or
not: for if a man is going to refuse to admit it and claim that you
shall argue to it as well, he will be giving the signal for a harder
undertaking than was originally proposed: if, on the other hand,
he grants it, he will be giving the original thesis credence on the
strength of what is less credible than itself. If, then, it is
essential not to enhance the difficulty of the problem, he had
better grant it; if, on the other hand, it be essential to reason
through premisses that are better assured, he had better refuse.
In other words, in serious inquiry he ought not to grant it,
unless he be more sure about it than about the conclusion;
whereas in a dialectical exercise he may do so if he is merely
satisfied of its truth. Clearly, then, the circumstances under
which such admissions should be claimed are different for a
mere questioner and for a serious teacher.
As to the formulation, then, and arrangement of one's
questions, about enough has been said.
With regard to the giving of answers, we must first define what
is the business of a good answerer, as of a good questioner. The
business of the questioner is so to develop the argument as to
make the answerer utter the most extrvagant paradoxes that
necessarily follow because of his position: while that of the
answerer is to make it appear that it is not he who is
responsible for the absurdity or paradox, but only his position:
for one may, perhaps, distinguish between the mistake of taking
up a wrong position to start with, and that of not maintaining it
properly, when once taken up.
513
Inasmuch as no rules are laid down for those who argue for the
sake of training and of examination: - and the aim of those
engaged in teaching or learning is quite different from that of
those engaged in a competition; as is the latter from that of
those who discuss things together in the spirit of inquiry: for a
learner should always state what he thinks: for no one is even
trying to teach him what is false; whereas in a competition the
business of the questioner is to appear by all means to produce
an effect upon the other, while that of the answerer is to appear
unaffected by him; on the other hand, in an assembly of
disputants discussing in the spirit not of a competition but of
an examination and inquiry, there are as yet no articulate rules
about what the answerer should aim at, and what kind of things
he should and should not grant for the correct or incorrect
defence of his position: - inasmuch, then, as we have no
tradition bequeathed to us by others, let us try to say something
upon the matter for ourselves.
The thesis laid down by the answerer before facing the
questioner's argument is bound of necessity to be one that is
either generally accepted or generally rejected or else is neither:
and moreover is so accepted or rejected either absolutely or else
with a restriction, e.g. by some given person, by the speaker or
by some one else. The manner, however, of its acceptance or
rejection, whatever it be, makes no difference: for the right way
to answer, i.e. to admit or to refuse to admit what has been
asked, will be the same in either case. If, then, the statement
laid down by the answerer be generally rejected, the conclusion
aimed at by the questioner is bound to be one generally
accepted, whereas if the former be generally accepted, the latter
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is generally rejected: for the conclusion which the questioner
tries to draw is always the opposite of the statement laid down.
If, on the other hand, what is laid down is generally neither
rejected nor accepted, the conclusion will be of the same type
as well. Now since a man who reasons correctly demonstrates
his proposed conclusion from premisses that are more
generally accepted, and more familiar, it is clear that (1) where
the view laid down by him is one that generally is absolutely
rejected, the answerer ought not to grant either what is thus
absolutely not accepted at all, or what is accepted indeed, but
accepted less generally than the questioner's conclusion. For if
the statement laid down by the answerer be generally rejected,
the conclusion aimed at by the questioner will be one that is
generally accepted, so that the premisses secured by the
questioner should all be views generally accepted, and more
generally accepted than his proposed conclusion, if the less
familiar is to be inferred through the more familiar.
Consequently, if any of the questions put to him be not of this
character, the answerer should not grant them. (2) If, on the
other hand, the statement laid down by the answerer be
generally accepted without qualification, clearly the conclusion
sought by the questioner will be one generally rejected without
qualification. Accordingly, the answerer should admit all views
that are generally accepted and, of those that are not generally
accepted, all that are less generally rejected than the conclusion
sought by the questioner. For then he will probably be thought
to have argued sufficiently well. (3) Likewise, too, if the
statement laid down by the answerer be neither rejected
generally nor generally accepted; for then, too, anything that
appears to be true should be granted, and, of the views not
generally accepted, any that are more generally accepted than
the questioner's conclusion; for in that case the result will be
that the arguments will be more generally accepted. If, then, the
view laid down by the answerer be one that is generally
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accepted or rejected without qualification, then the views that
are accepted absolutely must be taken as the standard of
comparison: whereas if the view laid down be one that is not
generally accepted or rejected, but only by the answerer, then
the standard whereby the latter must judge what is generally
accepted or not, and must grant or refuse to grant the point
asked, is himself. If, again, the answerer be defending some one
else's opinion, then clearly it will be the latter's judgement to
which he must have regard in granting or denying the various
points. This is why those, too, who introduce other's opinions,
e.g. that 'good and evil are the same thing, as Heraclitus says,'
refuse to admit the impossibility of contraries belonging at the
same time to the same thing; not because they do not
themselves believe this, but because on Heraclitus' principles
one has to say so. The same thing is done also by those who
take on the defence of one another's positions; their aim being
to speak as would the man who stated the position.
It is clear, then, what the aims of the answerer should be,
whether the position he lays down be a view generally accepted
without qualification or accepted by some definite person. Now
every question asked is bound to involve some view that is
either generally held or generally rejected or neither, and is also
bound to be either relevant to the argument or irrelevant: if
then it be a view generally accepted and irrelevant, the
answerer should grant it and remark that it is the accepted
view: if it be a view not generally accepted and irrelevant, he
should grant it but add a comment that it is not generally
accepted, in order to avoid the appearance of being a simpleton.
If it be relevant and also be generally accepted, he should admit
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that it is the view generally accepted but say that it lies too
close to the original proposition, and that if it be granted the
problem proposed collapses. If what is claimed by the
questioner be relevant but too generally rejected, the answerer,
while admitting that if it be granted the conclusion sought
follows, should yet protest that the proposition is too absurd to
be admitted. Suppose, again, it be a view that is neither rejected
generally nor generally accepted, then, if it be irrelevant to the
argument, it may be granted without restriction; if, however, it
be relevant, the answerer should add the comment that, if it be
granted, the original problem collapses. For then the answerer
will not be held to be personally accountable for what happens
to him, if he grants the several points with his eyes open, and
also the questioner will be able to draw his inference, seeing
that all the premisses that are more generally accepted than the
conclusion are granted him. Those who try to draw an inference
from premisses more generally rejected than the conclusion
clearly do not reason correctly: hence, when men ask these
things, they ought not to be granted.
The questioner should be met in a like manner also in the case
of terms used obscurely, i.e. in several senses. For the answerer,
if he does not understand, is always permitted to say 'I do not
understand': he is not compelled to reply 'Yes' or 'No' to a
question which may mean different things. Clearly, then, in the
first place, if what is said be not clear, he ought not to hesitate
to say that he does not understand it; for often people
encounter some difficulty from assenting to questions that are
not clearly put. If he understands the question and yet it covers
many senses, then supposing what it says to be universally true
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or false, he should give it an unqualified assent or denial: if, on
the other hand, it be partly true and partly false, he should add
a comment that it bears different senses, and also that in one it
is true, in the other false: for if he leave this distinction till later,
it becomes uncertain whether originally as well he perceived
the ambiguity or not. If he does not foresee the ambiguity, but
assents to the question having in view the one sense of the
words, then, if the questioner takes it in the other sense, he
should say, 'That was not what I had in view when I admitted it;
I meant the other sense': for if a term or expression covers more
than one thing, it is easy to disagree. If, however, the question is
both clear and simple, he should answer either 'Yes' or 'No'.
8
A premiss in reasoning always either is one of the constituent
elements in the reasoning, or else goes to establish one of these:
(and you can always tell when it is secured in order to establish
something else by the fact of a number of similar questions
being put: for as a rule people secure their universal by means
either of induction or of likeness): - accordingly the particular
propositions should all be admitted, if they are true and
generally held. On the other hand, against the universal one
should try to bring some negative instance; for to bring the
argument to a standstill without a negative instance, either real
or apparent, shows ill-temper. If, then, a man refuses to grant
the universal when supported by many instances, although he
has no negative instance to show, he obviously shows ill-
temper. If, moreover, he cannot even attempt a counter-proof
that it is not true, far more likely is he to be thought ill-
tempered - although even counter-proof is not enough: for we
often hear arguments that are contrary to common opinions,
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whose solution is yet difficult, e.g. the argument of Zeno that it
is impossible to move or to traverse the stadium; - but still, this
is no reason for omitting to assert the opposites of these views.
If, then, a man refuses to admit the proposition without having
either a negative instance or some counter-argument to bring
against it, clearly he is ill-tempered: for ill-temper in argument
consists in answering in ways other than the above, so as to
wreck the reasoning.
Before maintaining either a thesis or a definition the answerer
should try his hand at attacking it by himself; for clearly his
business is to oppose those positions from which questioners
demolish what he has laid down.
He should beware of maintaining a hypothesis that is generally
rejected: and this it may be in two ways: for it may be one
which results in absurd statements, e.g. suppose any one were
to say that everything is in motion or that nothing is; and also
there are all those which only a bad character would choose,
and which are implicitly opposed to men's wishes, e.g. that
pleasure is the good, and that to do injustice is better than to
suffer it. For people then hate him, supposing him to maintain
them not for the sake of argument but because he really thinks
them.
10
Of all arguments that reason to a false conclusion the right
solution is to demolish the point on which the fallacy that
occurs depends: for the demolition of any random point is no
solution, even though the point demolished be false. For the
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argument may contain many falsehoods, e.g. suppose some one
to secure the premisses, 'He who sits, writes' and 'Socrates is
sitting': for from these it follows that 'Socrates is writing'. Now
we may demolish the proposition 'Socrates is sitting', and still
be no nearer a solution of the argument; it may be true that the
point claimed is false; but it is not on that that fallacy of the
argument depends: for supposing that any one should happen
to be sitting and not writing, it would be impossible in such a
case to apply the same solution. Accordingly, it is not this that
needs to be demolished, but rather that 'He who sits, writes': for
he who sits does not always write. He, then, who has
demolished the point on which the fallacy depends, has given
the solution of the argument completely. Any one who knows
that it is on such and such a point that the argument depends,
knows the solution of it, just as in the case of a figure falsely
drawn. For it is not enough to object, even if the point
demolished be a falsehood, but the reason of the fallacy should
also be proved: for then it would be clear whether the man
makes his objection with his eyes open or not.
There are four possible ways of preventing a man from working
his argument to a conclusion. It can be done either by
demolishing the point on which the falsehood that comes about
depends, or by stating an objection directed against the
questioner: for often when a solution has not as a matter of fact
been brought, yet the questioner is rendered thereby unable to
pursue the argument any farther. Thirdly, one may object to the
questions asked: for it may happen that what the questioner
wants does not follow from the questions he has asked because
he has asked them badly, whereas if something additional be
granted the conclusion comes about. If, then, the questioner be
unable to pursue his argument farther, the objection would
properly be directed against the questioner; if he can do so, then
it would be against his questions. The fourth and worst kind of
objection is that which is directed to the time allowed for
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discussion: for some people bring objections of a kind which
would take longer to answer than the length of the discussion
in hand.
There are then, as we said, four ways of making objections: but
of them the first alone is a solution: the others are just
hindrances and stumbling-blocks to prevent the conclusions.
11
Adverse criticism of an argument on its own merits, and of it
when presented in the form of questions, are two different
things. For often the failure to carry through the argument
correctly in discussion is due to the person questioned, because
he will not grant the steps of which a correct argument might
have been made against his position: for it is not in the power of
the one side only to effect properly a result that depends on
both alike. Accordingly it sometimes becomes necessary to
attack the speaker and not his position, when the answerer lies
in wait for the points that are contrary to the questioner and
becomes abusive as well: when people lose their tempers in this
way, their argument becomes a contest, not a discussion.
Moreover, since arguments of this kind are held not for the sake
of instruction but for purposes of practice and examination,
clearly one has to reason not only to true conclusions, but also
to false ones, and not always through true premisses, but
sometimes through false as well. For often, when a true
proposition is put forward, the dialectician is compelled to
demolish it: and then false propositions have to be formulated.
Sometimes also when a false proposition is put forward, it has
to be demolished by means of false propositions: for it is
possible for a given man to believe what is not the fact more
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firmly than the truth. Accordingly, if the argument be made to
depend on something that he holds, it will be easier to persuade
or help him. He, however, who would rightly convert any one to
a different opinion should do so in a dialectical and not in a
contentious manner, just as a geometrician should reason
geometrically, whether his conclusion be false or true: what
kind of syllogisms are dialectical has already been said. The
principle that a man who hinders the common business is a
bad partner, clearly applies to an argument as well; for in
arguments as well there is a common aim in view, except with
mere contestants, for these cannot both reach the same goal;
for more than one cannot possibly win. It makes no difference
whether he effects this as answerer or as questioner: for both
he who asks contentious questions is a bad dialectician, and
also he who in answering fails to grant the obvious answer or to
understand the point of the questioner's inquiry. What has been
said, then, makes it clear that adverse criticism is not to be
passed in a like strain upon the argument on its own merits,
and upon the questioner: for it may very well be that the
argument is bad, but that the questioner has argued with the
answerer in the best possible way: for when men lose their
tempers, it may perhaps be impossible to make one's inferences
straight-forwardly as one would wish: we have to do as we can.
Inasmuch as it is indeterminate when people are claiming the
admission of contrary things, and when they are claiming what
originally they set out to prove - for often when they are talking
by themselves they say contrary things, and admit afterwards
what they have previously denied; for which reason they often
assent, when questioned, to contrary things and to what
originally had to be proved - the argument is sure to become
vitiated. The responsibility, however, for this rests with the
answerer, because while refusing to grant other points, he does
grant points of that kind. It is, then, clear that adverse criticism
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is not to be passed in a like manner upon questioners and upon
their arguments.
In itself an argument is liable to five kinds of adverse criticism:
(1) The first is when neither the proposed conclusion nor indeed
any conclusion at all is drawn from the questions asked, and
when most, if not all, of the premisses on which the conclusion
rests are false or generally rejected, when, moreover, neither
any withdrawals nor additions nor both together can bring the
conclusions about.
(2) The second is, supposing the reasoning, though constructed
from the premisses, and in the manner, described above, were
to be irrelevant to the original position.
(3) The third is, supposing certain additions would bring an
inference about but yet these additions were to be weaker than
those that were put as questions and less generally held than
the conclusion.
(4) Again, supposing certain withdrawals could effect the same:
for sometimes people secure more premisses than are
necessary, so that it is not through them that the inference
comes about.
(5) Moreover, suppose the premisses be less generally held and
less credible than the conclusion, or if, though true, they require
more trouble to prove than the proposed view.
One must not claim that the reasoning to a proposed view shall
in every case equally be a view generally accepted and
convincing: for it is a direct result of the nature of things that
some subjects of inquiry shall be easier and some harder, so
that if a man brings people to accept his point from opinions
that are as generally received as the case admits, he has argued
his case correctly. Clearly, then, not even the argument itself is
523
open to the same adverse criticism when taken in relation to
the proposed conclusion and when taken by itself. For there is
nothing to prevent the argument being open to reproach in
itself, and yet commendable in relation to the proposed
conclusion, or again, vice versa, being commendable in itself,
and yet open to reproach in relation to the proposed conclusion,
whenever there are many propositions both generally held and
also true whereby it could easily be proved. It is possible also
that an argument, even though brought to a conclusion, may
sometimes be worse than one which is not so concluded,
whenever the premisses of the former are silly, while its
conclusion is not so; whereas the latter, though requiring
certain additions, requires only such as are generally held and
true, and moreover does not rest as an argument on these
additions. With those which bring about a true conclusion by
means of false premisses, it is not fair to find fault: for a false
conclusion must of necessity always be reached from a false
premiss, but a true conclusion may sometimes be drawn even
from false premisses; as is clear from the Analytics.
Whenever by the argument stated something is demonstrated,
but that something is other than what is wanted and has no
bearing whatever on the conclusion, then no inference as to the
latter can be drawn from it: and if there appears to be, it will be
a sophism, not a proof. A philosopheme is a demonstrative
inference: an epichireme is a dialectical inference: a sophism is
a contentious inference: an aporeme is an inference that
reasons dialectically to a contradiction.
If something were to be shown from premisses, both of which
are views generally accepted, but not accepted with like
conviction, it may very well be that the conclusion shown is
something held more strongly than either. If, on the other hand,
general opinion be for the one and neither for nor against the
other, or if it be for the one and against the other, then, if the
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pro and con be alike in the case of the premisses, they will be
alike for the conclusion also: if, on the other hand, the one
preponderates, the conclusion too will follow suit.
It is also a fault in reasoning when a man shows something
through a long chain of steps, when he might employ fewer
steps and those already included in his argument: suppose him
to be showing (e.g.) that one opinion is more properly so called
than another, and suppose him to make his postulates as
follows: 'x-in-itself is more fully x than anything else': 'there
genuinely exists an object of opinion in itself: therefore 'the
object-of-opinion-in-itself is more fully an object of opinion
than the particular objects of opinion'. Now 'a relative term is
more fully itself when its correlate is more fully itself: and
'there exists a genuine opinion-in-itself, which will be «opinion»
in a more accurate sense than the particular opinions': and it
has been postulated both that 'a genuine opinion-in-itself
exists', and that 'x-in-itself is more fully x than anything else':
therefore 'this will be opinion in a more accurate sense'.
Wherein lies the viciousness of the reasoning? Simply in that it
conceals the ground on which the argument depends.
12
An argument is clear in one, and that the most ordinary, sense,
if it be so brought to a conclusion as to make no further
questions necessary: in another sense, and this is the type most
usually advanced, when the propositions secured are such as
compel the conclusion, and the argument is concluded through
premisses that are themselves conclusions: moreover, it is so
also if some step is omitted that generally is firmly accepted.
525
An argument is called fallacious in four senses: (1) when it
appears to be brought to a conclusion, and is not really so -
what is called 'contentious' reasoning: (2) when it comes to a
conclusion but not to the conclusion proposed - which happens
principally in the case of reductiones ad impossibile: (3) when it
comes to the proposed conclusion but not according to the
mode of inquiry appropriate to the case, as happens when a
non-medical argument is taken to be a medical one, or one
which is not geometrical for a geometrical argument, or one
which is not dialectical for dialectical, whether the result
reached be true or false: (4) if the conclusion be reached through
false premisses: of this type the conclusion is sometimes false,
sometimes true: for while a false conclusion is always the result
of false premisses, a true conclusion may be drawn even from
premisses that are not true, as was said above as well.
Fallacy in argument is due to a mistake of the arguer rather
than of the argument: yet it is not always the fault of the arguer
either, but only when he is not aware of it: for we often accept
on its merits in preference to many true ones an argument
which demolishes some true proposition if it does so from
premisses as far as possible generally accepted. For an
argument of that kind does demonstrate other things that are
true: for one of the premisses laid down ought never to be there
at all, and this will then be demonstrated. If, however, a true
conclusion were to be reached through premisses that are false
and utterly childish, the argument is worse than many
arguments that lead to a false conclusion, though an argument
which leads to a false conclusion may also be of this type.
Clearly then the first thing to ask in regard to the argument in
itself is, 'Has it a conclusion?'; the second, 'Is the conclusion
true or false?'; the third, 'Of what kind of premisses does it
consist?': for if the latter, though false, be generally accepted,
the argument is dialectical, whereas if, though true, they be
generally rejected, it is bad: if they be both false and also
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entirely contrary to general opinion, clearly it is bad, either
altogether or else in relation to the particular matter in hand.
13
Of the ways in which a questioner may beg the original
question and also beg contraries the true account has been
given in the Analytics:' but an account on the level of general
opinion must be given now.
People appear to beg their original question in five ways: the
first and most obvious being if any one begs the actual point
requiring to be shown: this is easily detected when put in so
many words; but it is more apt to escape detection in the case
of different terms, or a term and an expression, that mean the
same thing. A second way occurs whenever any one begs
universally something which he has to demonstrate in a
particular case: suppose (e.g.) he were trying to prove that the
knowledge of contraries is one and were to claim that the
knowledge of opposites in general is one: for then he is
generally thought to be begging, along with a number of other
things, that which he ought to have shown by itself. A third way
is if any one were to beg in particular cases what he undertakes
to show universally: e.g. if he undertook to show that the
knowledge of contraries is always one, and begged it of certain
pairs of contraries: for he also is generally considered to be
begging independently and by itself what, together with a
number of other things, he ought to have shown. Again, a man
begs the question if he begs his conclusion piecemeal:
supposing e.g. that he had to show that medicine is a science of
what leads to health and to disease, and were to claim first the
one, then the other; or, fifthly, if he were to beg the one or the
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other of a pair of statements that necessarily involve one other;
e.g. if he had to show that the diagonal is incommensurable
with the side, and were to beg that the side is incommensurable
with the diagonal.
The ways in which people assume contraries are equal in
number to those in which they beg their original question. For it
would happen, firstly, if any one were to beg an opposite
affirmation and negation; secondly, if he were to beg the
contrary terms of an antithesis, e.g. that the same thing is good
and evil; thirdly, suppose any one were to claim something
universally and then proceed to beg its contradictory in some
particular case, e.g. if having secured that the knowledge of
contraries is one, he were to claim that the knowledge of what
makes for health or for disease is different; or, fourthly, suppose
him, after postulating the latter view, to try to secure universally
the contradictory statement. Again, fifthly, suppose a man begs
the contrary of the conclusion which necessarily comes about
through the premisses laid down; and this would happen
suppose, even without begging the opposites in so many words,
he were to beg two premisses such that this contradictory
statement that is opposite to the first conclusion will follow
from them. The securing of contraries differs from begging the
original question in this way: in the latter case the mistake lies
in regard to the conclusion; for it is by a glance at the
conclusion that we tell that the original question has been
begged: whereas contrary views lie in the premisses, viz. in a
certain relation which they bear to one another.
528
14
The best way to secure training and practice in arguments of
this kind is in the first place to get into the habit of converting
the arguments. For in this way we shall be better equipped for
dealing with the proposition stated, and after a few attempts we
shall know several arguments by heart. For by 'conversion' of an
argument is meant the taking the reverse of the conclusion
together with the remaining propositions asked and so
demolishing one of those that were conceded: for it follows
necessarily that if the conclusion be untrue, some one of the
premisses is demolished, seeing that, given all the premisses,
the conclusion was bound to follow. Always, in dealing with any
proposition, be on the look-out for a line of argument both pro
and con: and on discovering it at once set about looking for the
solution of it: for in this way you will soon find that you have
trained yourself at the same time in both asking questions and
answering them. If we cannot find any one else to argue with,
we should argue with ourselves. Select, moreover, arguments
relating to the same thesis and range them side by side: for this
produces a plentiful supply of arguments for carrying a point by
sheer force, and in refutation also it is of great service,
whenever one is well stocked with arguments pro and con: for
then you find yourself on your guard against contrary
statements to the one you wish to secure. Moreover, as
contributing to knowledge and to philosophic wisdom the
power of discerning and holding in one view the results of
either of two hypotheses is no mean instrument; for it then
only remains to make a right choice of one of them. For a task of
this kind a certain natural ability is required: in fact real natural
ability just is the power right to choose the true and shun the
false. Men of natural ability can do this; for by a right liking or
disliking for whatever is proposed to them they rightly select
what is best.
529
It is best to know by heart arguments upon those questions
which are of most frequent occurrence, and particularly in
regard to those propositions which are ultimate: for in
discussing these answerers frequently give up in despair.
Moreover, get a good stock of definitions: and have those of
familiar and primary ideas at your fingers' ends: for it is
through these that reasonings are effected. You should try,
moreover, to master the heads under which other arguments
mostly tend to fall. For just as in geometry it is useful to be
practised in the elements, and in arithmetic to have the
multiplication table up to ten at one's fingers' ends - and indeed
it makes a great difference in one's knowledge of the multiples
of other numbers too - likewise also in arguments it is a great
advantage to be well up in regard to first principles, and to have
a thorough knowledge of premisses at the tip of one's tongue.
For just as in a person with a trained memory, a memory of
things themselves is immediately caused by the mere mention
of their loci, so these habits too will make a man readier in
reasoning, because he has his premisses classified before his
mind's eye, each under its number. It is better to commit to
memory a premiss of general application than an argument: for
it is difficult to be even moderately ready with a first principle,
or hypothesis.
Moreover, you should get into the habit of turning one
argument into several, and conceal your procedure as darkly as
you can: this kind of effect is best produced by keeping as far as
possible away from topics akin to the subject of the argument.
This can be done with arguments that are entirely universal, e.g.
the statement that 'there cannot be one knowledge of more
than one thing': for that is the case with both relative terms and
contraries and co-ordinates.
Records of discussions should be made in a universal form,
even though one has argued only some particular case: for this
530
will enable one to turn a single rule into several. A like rule
applies in Rhetoric as well to enthymemes. For yourself,
however, you should as far as possible avoid universalizing your
reasonings. You should, moreover, always examine arguments
to see whether they rest on principles of general application: for
all particular arguments really reason universally, as well, i.e. a
particular demonstration always contains a universal
demonstration, because it is impossible to reason at all without
using universals.
You should display your training in inductive reasoning against
a young man, in deductive against an expert. You should try,
moreover, to secure from those skilled in deduction their
premisses, from inductive reasoners their parallel cases; for this
is the thing in which they are respectively trained. In general,
too, from your exercises in argumentation you should try to
carry away either a syllogism on some subject or a refutation or
a proposition or an objection, or whether some one put his
question properly or improperly (whether it was yourself or
some one else) and the point which made it the one or the
other. For this is what gives one ability, and the whole object of
training is to acquire ability, especially in regard to propositions
and objections. For it is the skilled propounder and objector
who is, speaking generally, a dialectician. To formulate a
proposition is to form a number of things into one - for the
conclusion to which the argument leads must be taken
generally, as a single thing - whereas to formulate an objection
is to make one thing into many; for the objector either
distinguishes or demolishes, partly granting, partly denying the
statements proposed.
Do not argue with every one, nor practise upon the man in the
street: for there are some people with whom any argument is
bound to degenerate. For against any one who is ready to try all
means in order to seem not to be beaten, it is indeed fair to try
531
all means of bringing about one's conclusion: but it is not good
form. Wherefore the best rule is, not lightly to engage with
casual acquaintances, or bad argument is sure to result. For you
see how in practising together people cannot refrain from
contentious argument.
It is best also to have ready-made arguments relating to those
questions in which a very small stock will furnish us with
arguments serviceable on a very large number of occasions.
These are those that are universal, and those in regard to which
it is rather difficult to produce points for ourselves from matters
of everyday experience.
532
Aristotle - On Sophistical Refutations
[Translated by W. A. Pickard-Cambridge]
Let us now discuss sophistic refutations, i.e. what appear to be
refutations but are really fallacies instead. We will begin in the
natural order with the first.
That some reasonings are genuine, while others seem to be so
but are not, is evident. This happens with arguments, as also
elsewhere, through a certain likeness between the genuine and
the sham. For physically some people are in a vigorous
condition, while others merely seem to be so by blowing and
rigging themselves out as the tribesmen do their victims for
sacrifice; and some people are beautiful thanks to their beauty,
while others seem to be so, by dint of embellishing themselves.
So it is, too, with inanimate things; for of these, too, some are
really silver and others gold, while others are not and merely
seem to be such to our sense; e.g. things made of litharge and
tin seem to be of silver, while those made of yellow metal look
golden. In the same way both reasoning and refutation are
sometimes genuine, sometimes not, though inexperience may
make them appear so: for inexperienced people obtain only, as
it were, a distant view of these things. For reasoning rests on
certain statements such that they involve necessarily the
assertion of something other than what has been stated,
through what has been stated: refutation is reasoning involving
the contradictory of the given conclusion. Now some of them do
not really achieve this, though they seem to do so for a number
of reasons; and of these the most prolific and usual domain is
533
the argument that turns upon names only. It is impossible in a
discussion to bring in the actual things discussed: we use their
names as symbols instead of them; and therefore we suppose
that what follows in the names, follows in the things as well,
just as people who calculate suppose in regard to their counters.
But the two cases (names and things) are not alike. For names
are finite and so is the sum-total of formulae, while things are
infinite in number. Inevitably, then, the same formulae, and a
single name, have a number of meanings. Accordingly just as, in
counting, those who are not clever in manipulating their
counters are taken in by the experts, in the same way in
arguments too those who are not well acquainted with the force
of names misreason both in their own discussions and when
they listen to others. For this reason, then, and for others to be
mentioned later, there exists both reasoning and refutation that
is apparent but not real. Now for some people it is better worth
while to seem to be wise, than to be wise without seeming to be
(for the art of the sophist is the semblance of wisdom without
the reality, and the sophist is one who makes money from an
apparent but unreal wisdom); for them, then, it is clearly
essential also to seem to accomplish the task of a wise man
rather than to accomplish it without seeming to do so. To
reduce it to a single point of contrast it is the business of one
who knows a thing, himself to avoid fallacies in the subjects
which he knows and to be able to show up the man who makes
them; and of these accomplishments the one depends on the
faculty to render an answer, and the other upon the securing of
one. Those, then, who would be sophists are bound to study the
class of arguments aforesaid: for it is worth their while: for a
faculty of this kind will make a man seem to be wise, and this is
the purpose they happen to have in view.
Clearly, then, there exists a class of arguments of this kind, and
it is at this kind of ability that those aim whom we call sophists.
Let us now go on to discuss how many kinds there are of
534
sophistical arguments, and how many in number are the
elements of which this faculty is composed, and how many
branches there happen to be of this inquiry, and the other
factors that contribute to this art.
Of arguments in dialogue form there are four classes:
Didactic, Dialectical, Examination-arguments, and Contentious
arguments. Didactic arguments are those that reason from the
principles appropriate to each subject and not from the
opinions held by the answerer (for the learner should take
things on trust): dialectical arguments are those that reason
from premisses generally accepted, to the contradictory of a
given thesis: examination-arguments are those that reason
from premisses which are accepted by the answerer and which
any one who pretends to possess knowledge of the subject is
bound to know-in what manner, has been defined in another
treatise: contentious arguments are those that reason or appear
to reason to a conclusion from premisses that appear to be
generally accepted but are not so. The subject, then, of
demonstrative arguments has been discussed in the Analytics,
while that of dialectic arguments and examination-arguments
has been discussed elsewhere: let us now proceed to speak of
the arguments used in competitions and contests.
535
First we must grasp the number of aims entertained by those
who argue as competitors and rivals to the death. These are five
in number, refutation, fallacy, paradox, solecism, and fifthly to
reduce the opponent in the discussion to babbling - i.e. to
constrain him to repeat himself a number of times: or it is to
produce the appearance of each of these things without the
reality. For they choose if possible plainly to refute the other
party, or as the second best to show that he is committing some
fallacy, or as a third best to lead him into paradox, or fourthly to
reduce him to solecism, i.e. to make the answerer, in
consequence of the argument, to use an ungrammatical
expression; or, as a last resort, to make him repeat himself.
There are two styles of refutation: for some depend on the
language used, while some are independent of language. Those
ways of producing the false appearance of an argument which
depend on language are six in number: they are ambiguity,
amphiboly, combination, division of words, accent, form of
expression. Of this we may assure ourselves both by induction,
and by syllogistic proof based on this - and it may be on other
assumptions as well - that this is the number of ways in which
we might fall to mean the same thing by the same names or
expressions. Arguments such as the following depend upon
ambiguity. 'Those learn who know: for it is those who know
their letters who learn the letters dictated to them'. For to
'learn' is ambiguous; it signifies both 'to understand' by the use
of knowledge, and also 'to acquire knowledge'. Again, 'Evils are
good: for what needs to be is good, and evils must needs be'. For
536
'what needs to be' has a double meaning: it means what is
inevitable, as often is the case with evils, too (for evil of some
kind is inevitable), while on the other hand we say of good
things as well that they 'need to be'. Moreover, 'The same man
is both seated and standing and he is both sick and in health:
for it is he who stood up who is standing, and he who is
recovering who is in health: but it is the seated man who stood
up, and the sick man who was recovering'. For 'The sick man
does so and so', or 'has so and so done to him' is not single in
meaning: sometimes it means 'the man who is sick or is seated
now', sometimes 'the man who was sick formerly'. Of course,
the man who was recovering was the sick man, who really was
sick at the time: but the man who is in health is not sick at the
same time: he is 'the sick man' in the sense not that he is sick
now, but that he was sick formerly. Examples such as the
following depend upon amphiboly: 'I wish that you the enemy
may capture'. Also the thesis, 'There must be knowledge of
what one knows': for it is possible by this phrase to mean that
knowledge belongs to both the knower and the known. Also,
'There must be sight of what one sees: one sees the pillar: ergo
the pillar has sight'. Also, 'What you profess to-be, that you
profess to-be: you profess a stone to-be: ergo you profess-to-be
a stone'. Also, 'Speaking of the silent is possible': for 'speaking of
the silent' also has a double meaning: it may mean that the
speaker is silent or that the things of which he speaks are so.
There are three varieties of these ambiguities and amphibolies:
(1) When either the expression or the name has strictly more
than one meaning, e.g. aetos and the 'dog'; (2) when by custom
we use them so; (3) when words that have a simple sense taken
alone have more than one meaning in combination; e.g.
'knowing letters'. For each word, both 'knowing' and 'letters',
possibly has a single meaning: but both together have more
than one - either that the letters themselves have knowledge or
that someone else has it of them.
537
Amphiboly and ambiguity, then, depend on these modes of
speech. Upon the combination of words there depend instances
such as the following: 'A man can walk while sitting, and can
write while not writing'. For the meaning is not the same if one
divides the words and if one combines them in saying that 'it is
possible to walk-while-sitting' and write while not writing. The
same applies to the latter phrase, too, if one combines the
words 'to write-while-not-writing': for then it means that he has
the power to write and not to write at once; whereas if one does
not combine them, it means that when he is not writing he has
the power to write. Also, 'He now if he has learnt his letters'.
Moreover, there is the saying that 'One single thing if you can
carry a crowd you can carry too'.
Upon division depend the propositions that 5 is 2 and 3, and
odd, and that the greater is equal: for it is that amount and
more besides. For the same phrase would not be thought always
to have the same meaning when divided and when combined,
e.g. 'I made thee a slave once a free man', and 'God-like Achilles
left fifty a hundred men'.
An argument depending upon accent it is not easy to construct
in unwritten discussion; in written discussions and in poetry it
is easier. Thus (e.g.) some people emend Homer against those
who criticize as unnatural his expression to men ou
kataputhetai ombro. For they solve the difficulty by a change of
accent, pronouncing the ou with an acuter accent. Also, in the
passage about Agamemnon's dream, they say that Zeus did not
himself say 'We grant him the fulfilment of his prayer', but that
he bade the dream grant it. Instances such as these, then, turn
upon the accentuation.
Others come about owing to the form of expression used, when
what is really different is expressed in the same form, e.g. a
masculine thing by a feminine termination, or a feminine thing
538
by a masculine, or a neuter by either a masculine or a feminine;
or, again, when a quality is expressed by a termination proper to
quantity or vice versa, or what is active by a passive word, or a
state by an active word, and so forth with the other divisions
previously' laid down. For it is possible to use an expression to
denote what does not belong to the class of actions at all as
though it did so belong. Thus (e.g.) 'flourishing' is a word which
in the form of its expression is like 'cutting' or 'building': yet the
one denotes a certain quality - i.e. a certain condition - while
the other denotes a certain action. In the same manner also in
the other instances.
Refutations, then, that depend upon language are drawn from
these common-place rules. Of fallacies, on the other hand, that
are independent of language there are seven kinds:
(1) that which depends upon Accident:
(2) the use of an expression absolutely or not absolutely but
with some qualification of respect or place, or time, or relation:
(3) that which depends upon ignorance of what 'refutation' is:
(4) that which depends upon the consequent:
(5) that which depends upon assuming the original conclusion:
(6) stating as cause what is not the cause:
(7) the making of more than one question into one.
Fallacies, then, that depend on Accident occur whenever any
attribute is claimed to belong in like manner to a thing and to
539
its accident. For since the same thing has many accidents there
is no necessity that all the same attributes should belong to all
of a thing's predicates and to their subject as well. Thus (e.g.), 'If
Coriscus be different from «man», he is different from himself:
for he is a man': or 'If he be different from Socrates, and
Socrates be a man, then', they say, 'he has admitted that
Coriscus is different from a man, because it so happens (accidit)
that the person from whom he said that he (Coriscus) is
different is a man'.
Those that depend on whether an expression is used absolutely
or in a certain respect and not strictly, occur whenever an
expression used in a particular sense is taken as though it were
used absolutely, e.g. in the argument 'If what is not is the object
of an opinion, then what is not is': for it is not the same thing
'to be x' and 'to be' absolutely. Or again, 'What is, is not, if it is
not a particular kind of being, e.g. if it is not a man.' For it is not
the same thing 'not to be x' and 'not to be' at all: it looks as if it
were, because of the closeness of the expression, i.e. because 'to
be x' is but little different from 'to be', and 'not to be x' from 'not
to be'. Likewise also with any argument that turns upon the
point whether an expression is used in a certain respect or used
absolutely. Thus e.g. 'Suppose an Indian to be black all over, but
white in respect of his teeth; then he is both white and not
white.' Or if both characters belong in a particular respect, then,
they say, 'contrary attributes belong at the same time'. This kind
of thing is in some cases easily seen by any one, e.g. suppose a
man were to secure the statement that the Ethiopian is black,
and were then to ask whether he is white in respect of his
teeth; and then, if he be white in that respect, were to suppose
at the conclusion of his questions that therefore he had proved
dialectically that he was both white and not white. But in some
cases it often passes undetected, viz. in all cases where,
whenever a statement is made of something in a certain
respect, it would be generally thought that the absolute
540
statement follows as well; and also in all cases where it is not
easy to see which of the attributes ought to be rendered strictly.
A situation of this kind arises, where both the opposite
attributes belong alike: for then there is general support for the
view that one must agree absolutely to the assertion of both, or
of neither: e.g. if a thing is half white and half black, is it white
or black?
Other fallacies occur because the terms 'proof or 'refutation'
have not been defined, and because something is left out in
their definition. For to refute is to contradict one and the same
attribute - not merely the name, but the reality - and a name
that is not merely synonymous but the same name - and to
confute it from the propositions granted, necessarily, without
including in the reckoning the original point to be proved, in the
same respect and relation and manner and time in which it was
asserted. A 'false assertion' about anything has to be defined in
the same way. Some people, however, omit some one of the said
conditions and give a merely apparent refutation, showing (e.g.)
that the same thing is both double and not double: for two is
double of one, but not double of three. Or, it may be, they show
that it is both double and not double of the same thing, but not
that it is so in the same respect: for it is double in length but not
double in breadth. Or, it may be, they show it to be both double
and not double of the same thing and in the same respect and
manner, but not that it is so at the same time: and therefore
their refutation is merely apparent. One might, with some
violence, bring this fallacy into the group of fallacies dependent
on language as well.
Those that depend on the assumption of the original point to be
proved, occur in the same way, and in as many ways, as it is
possible to beg the original point; they appear to refute because
men lack the power to keep their eyes at once upon what is the
same and what is different.
541
The refutation which depends upon the consequent arises
because people suppose that the relation of consequence is
convertible. For whenever, suppose A is, B necessarily is, they
then suppose also that if B is, A necessarily is. This is also the
source of the deceptions that attend opinions based on sense-
perception. For people often suppose bile to be honey because
honey is attended by a yellow colour: also, since after rain the
ground is wet in consequence, we suppose that if the ground is
wet, it has been raining; whereas that does not necessarily
follow. In rhetoric proofs from signs are based on consequences.
For when rhetoricians wish to show that a man is an adulterer,
they take hold of some consequence of an adulterous life, viz.
that the man is smartly dressed, or that he is observed to
wander about at night. There are, however, many people of
whom these things are true, while the charge in question is
untrue. It happens like this also in real reasoning; e.g. Melissus'
argument, that the universe is eternal, assumes that the
universe has not come to be (for from what is not nothing could
possibly come to be) and that what has come to be has done so
from a first beginning. If, therefore, the universe has not come
to be, it has no first beginning, and is therefore eternal. But this
does not necessarily follow: for even if what has come to be
always has a first beginning, it does not also follow that what
has a first beginning has come to be; any more than it follows
that if a man in a fever be hot, a man who is hot must be in a
fever.
The refutation which depends upon treating as cause what is
not a cause, occurs whenever what is not a cause is inserted in
the argument, as though the refutation depended upon it. This
kind of thing happens in arguments that reason ad impossible:
for in these we are bound to demolish one of the premisses. If,
then, the false cause be reckoned in among the questions that
are necessary to establish the resulting impossibility, it will
often be thought that the refutation depends upon it, e.g. in the
542
proof that the 'soul' and 'life' are not the same: for if coming-to-
be be contrary to perishing, then a particular form of perishing
will have a particular form of coming-to-be as its contrary: now
death is a particular form of perishing and is contrary to life:
life, therefore, is a coming to-be, and to live is to come-to-be. But
this is impossible: accordingly, the 'soul' and 'life' are not the
same. Now this is not proved: for the impossibility results all
the same, even if one does not say that life is the same as the
soul, but merely says that life is contrary to death, which is a
form of perishing, and that perishing has 'coming-to-be' as its
contrary. Arguments of that kind, then, though not inconclusive
absolutely, are inconclusive in relation to the proposed
conclusion. Also even the questioners themselves often fail
quite as much to see a point of that kind.
Such, then, are the arguments that depend upon the
consequent and upon false cause. Those that depend upon the
making of two questions into one occur whenever the plurality
is undetected and a single answer is returned as if to a single
question. Now, in some cases, it is easy to see that there is more
than one, and that an answer is not to be given, e.g. 'Does the
earth consist of sea, or the sky?' But in some cases it is less
easy, and then people treat the question as one, and either
confess their defeat by failing to answer the question, or are
exposed to an apparent refutation. Thus 'Is A and is B a man?'
'Yes.' 'Then if any one hits A and B, he will strike a man'
(singular), 'not men' (plural). Or again, where part is good and
part bad, 'is the whole good or bad?' For whichever he says, it is
possible that he might be thought to expose himself to an
apparent refutation or to make an apparently false statement:
for to say that something is good which is not good, or not good
which is good, is to make a false statement. Sometimes,
however, additional premisses may actually give rise to a
genuine refutation; e.g. suppose a man were to grant that the
descriptions 'white' and 'naked' and 'blind' apply to one thing
543
and to a number of things in a like sense. For if 'blind' describes
a thing that cannot see though nature designed it to see, it will
also describe things that cannot see though nature designed
them to do so. Whenever, then, one thing can see while another
cannot, they will either both be able to see or else both be blind;
which is impossible.
The right way, then, is either to divide apparent proofs and
refutations as above, or else to refer them all to ignorance of
what 'refutation' is, and make that our starting-point: for it is
possible to analyse all the aforesaid modes of fallacy into
breaches of the definition of a refutation. In the first place, we
may see if they are inconclusive: for the conclusion ought to
result from the premisses laid down, so as to compel us
necessarily to state it and not merely to seem to compel us.
Next we should also take the definition bit by bit, and try the
fallacy thereby. For of the fallacies that consist in language,
some depend upon a double meaning, e.g. ambiguity of words
and of phrases, and the fallacy of like verbal forms (for we
habitually speak of everything as though it were a particular
substance) - while fallacies of combination and division and
accent arise because the phrase in question or the term as
altered is not the same as was intended. Even this, however,
should be the same, just as the thing signified should be as well,
if a refutation or proof is to be effected; e.g. if the point concerns
a doublet, then you should draw the conclusion of a 'doublet',
not of a 'cloak'. For the former conclusion also would be true,
but it has not been proved; we need a further question to show
that 'doublet' means the same thing, in order to satisfy any one
who asks why you think your point proved.
544
Fallacies that depend on Accident are clear cases of ignoratio
elenchi when once 'proof has been defined. For the same
definition ought to hold good of 'refutation' too, except that a
mention of 'the contradictory' is here added: for a refutation is a
proof of the contradictory. If, then, there is no proof as regards
an accident of anything, there is no refutation. For supposing,
when A and B are, C must necessarily be, and C is white, there is
no necessity for it to be white on account of the syllogism. So, if
the triangle has its angles equal to two right-angles, and it
happens to be a figure, or the simplest element or starting
point, it is not because it is a figure or a starting point or
simplest element that it has this character. For the
demonstration proves the point about it not qua figure or qua
simplest element, but qua triangle. Likewise also in other cases.
If, then, refutation is a proof, an argument which argued per
accidens could not be a refutation. It is, however, just in this
that the experts and men of science generally suffer refutation
at the hand of the unscientific: for the latter meet the scientists
with reasonings constituted per accidens; and the scientists for
lack of the power to draw distinctions either say 'Yes' to their
questions, or else people suppose them to have said 'Yes',
although they have not.
Those that depend upon whether something is said in a certain
respect only or said absolutely, are clear cases of ignoratio
elenchi because the affirmation and the denial are not
concerned with the same point. For of 'white in a certain
respect' the negation is 'not white in a certain respect', while of
'white absolutely' it is 'not white, absolutely'. If, then, a man
treats the admission that a thing is 'white in a certain respect'
as though it were said to be white absolutely, he does not effect
a refutation, but merely appears to do so owing to ignorance of
what refutation is.
545
The clearest cases of all, however, are those that were
previously described' as depending upon the definition of a
'refutation': and this is also why they were called by that name.
For the appearance of a refutation is produced because of the
omission in the definition, and if we divide fallacies in the
above manner, we ought to set 'Defective definition' as a
common mark upon them all.
Those that depend upon the assumption of the original point
and upon stating as the cause what is not the cause, are clearly
shown to be cases of ignoratio elenchi through the definition
thereof. For the conclusion ought to come about 'because these
things are so', and this does not happen where the premisses
are not causes of it: and again it should come about without
taking into account the original point, and this is not the case
with those arguments which depend upon begging the original
point.
Those that depend upon the assumption of the original point
and upon stating as the cause what is not the cause, are clearly
shown to be cases of ignoratio elenchi through the definition
thereof. For the conclusion ought to come about 'because these
things are so', and this does not happen where the premisses
are not causes of it: and again it should come about without
taking into account the original point, and this is not the case
with those arguments which depend upon begging the original
point.
Those that depend upon the consequent are a branch of
Accident: for the consequent is an accident, only it differs from
the accident in this, that you may secure an admission of the
accident in the case of one thing only (e.g. the identity of a
yellow thing and honey and of a white thing and swan),
whereas the consequent always involves more than one thing:
for we claim that things that are the same as one and the same
546
thing are also the same as one another, and this is the ground of
a refutation dependent on the consequent. It is, however, not
always true, e.g. suppose that and B are the same as C per
accidens; for both 'snow' and the 'swan' are the same as
something white'. Or again, as in Melissus' argument, a man
assumes that to 'have been generated' and to 'have a beginning'
are the same thing, or to 'become equal' and to 'assume the
same magnitude'. For because what has been generated has a
beginning, he claims also that what has a beginning has been
generated, and argues as though both what has been generated
and what is finite were the same because each has a beginning.
Likewise also in the case of things that are made equal he
assumes that if things that assume one and the same
magnitude become equal, then also things that become equal
assume one magnitude: i.e. he assumes the consequent.
Inasmuch, then, as a refutation depending on accident consists
in ignorance of what a refutation is, clearly so also does a
refutation depending on the consequent. We shall have further
to examine this in another way as well.
Those fallacies that depend upon the making of several
questions into one consist in our failure to dissect the definition
of 'proposition'. For a proposition is a single statement about a
single thing. For the same definition applies to 'one single thing
only' and to the 'thing', simply, e.g. to 'man' and to 'one single
man only' and likewise also in other cases. If, then, a 'single
proposition' be one which claims a single thing of a single thing,
a 'proposition', simply, will also be the putting of a question of
that kind. Now since a proof starts from propositions and
refutation is a proof, refutation, too, will start from propositions.
If, then, a proposition is a single statement about a single thing,
it is obvious that this fallacy too consists in ignorance of what a
refutation is: for in it what is not a proposition appears to be
one. If, then, the answerer has returned an answer as though to
a single question, there will be a refutation; while if he has
547
returned one not really but apparently, there will be an
apparent refutation of his thesis. All the types of fallacy, then,
fall under ignorance of what a refutation is, some of them
because the contradiction, which is the distinctive mark of a
refutation, is merely apparent, and the rest failing to conform to
the definition of a proof.
The deception comes about in the case of arguments that
depend on ambiguity of words and of phrases because we are
unable to divide the ambiguous term (for some terms it is not
easy to divide, e.g. 'unity', 'being', and 'sameness'), while in
those that depend on combination and division, it is because we
suppose that it makes no difference whether the phrase be
combined or divided, as is indeed the case with most phrases.
Likewise also with those that depend on accent: for the
lowering or raising of the voice upon a phrase is thought not to
alter its meaning - with any phrase, or not with many. With
those that depend on the of expression it is because of the
likeness of expression. For it is hard to distinguish what kind of
things are signified by the same and what by different kinds of
expression: for a man who can do this is practically next door to
the understanding of the truth. A special reason why a man is
liable to be hurried into assent to the fallacy is that we suppose
every predicate of everything to be an individual thing, and we
understand it as being one with the thing: and we therefore
treat it as a substance: for it is to that which is one with a thing
or substance, as also to substance itself, that 'individually' and
'being' are deemed to belong in the fullest sense. For this
reason, too, this type of fallacy is to be ranked among those that
depend on language; in the first place, because the deception is
548
effected the more readily when we are inquiring into a problem
in company with others than when we do so by ourselves (for
an inquiry with another person is carried on by means of
speech, whereas an inquiry by oneself is carried on quite as
much by means of the object itself); secondly a man is liable to
be deceived, even when inquiring by himself, when he takes
speech as the basis of his inquiry: moreover the deception
arises out of the likeness (of two different things), and the
likeness arises out of the language. With those fallacies that
depend upon Accident, deception comes about because we
cannot distinguish the sameness and otherness of terms, i.e.
their unity and multiplicity, or what kinds of predicate have all
the same accidents as their subject. Likewise also with those
that depend on the Consequent: for the consequent is a branch
of Accident. Moreover, in many cases appearances point to this
- and the claim is made that if is inseparable from B, so also is B
from With those that depend upon an imperfection in the
definition of a refutation, and with those that depend upon the
difference between a qualified and an absolute statement, the
deception consists in the smallness of the difference involved;
for we treat the limitation to the particular thing or respect or
manner or time as adding nothing to the meaning, and so grant
the statement universally. Likewise also in the case of those
that assume the original point, and those of false cause, and all
that treat a number of questions as one: for in all of them the
deception lies in the smallness of the difference: for our failure
to be quite exact in our definition of 'premiss' and of 'proof is
due to the aforesaid reason.
549
8
Since we know on how many points apparent syllogisms
depend, we know also on how many sophistical syllogisms and
refutations may depend. By a sophistical refutation and
syllogism I mean not only a syllogism or refutation which
appears to be valid but is not, but also one which, though it is
valid, only appears to be appropriate to the thing in question.
These are those which fail to refute and prove people to be
ignorant according to the nature of the thing in question, which
was the function of the art of examination. Now the art of
examining is a branch of dialectic: and this may prove a false
conclusion because of the ignorance of the answerer. Sophistic
refutations on the other hand, even though they prove the
contradictory of his thesis, do not make clear whether he is
ignorant: for sophists entangle the scientist as well with these
arguments.
That we know them by the same line of inquiry is clear: for the
same considerations which make it appear to an audience that
the points required for the proof were asked in the questions
and that the conclusion was proved, would make the answerer
think so as well, so that false proof will occur through all or
some of these means: for what a man has not been asked but
thinks he has granted, he would also grant if he were asked. Of
course, in some cases the moment we add the missing
question, we also show up its falsity, e.g. in fallacies that depend
on language and on solecism. If then, fallacious proofs of the
contradictory of a thesis depend on their appearing to refute, it
is clear that the considerations on which both proofs of false
conclusions and an apparent refutation depend must be the
same in number. Now an apparent refutation depends upon the
elements involved in a genuine one: for the failure of one or
other of these must make the refutation merely apparent, e.g.
that which depends on the failure of the conclusion to follow
550
from the argument (the argument ad impossible) and that
which treats two questions as one and so depends upon a flaw
in the premiss, and that which depends on the substitution of
an accident for an essential attribute, and - a branch of the last
- that which depends upon the consequent: more over, the
conclusion may follow not in fact but only verbally: then,
instead of proving the contradictory universally and in the same
respect and relation and manner, the fallacy may b 
