No More Learning

350 BC

CATEGORIES

by Aristotle

translated by E. M. Edghill

1

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'.

2

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.

3

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.

4

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.

5

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 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 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.

6

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.

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.

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, "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.

It is in the case of space that quantity most plausibly appears to
admit of a contrary.
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 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 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.

6

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.

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.

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, "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.

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.

7

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.

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.

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. 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.