No More Learning

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. 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
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 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 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.

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 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.

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 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.

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, 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 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 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.

9

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 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'.

(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 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
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 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 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. (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.

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.

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 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.

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 '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.