The Categories, Aristotle [best self help books to read .txt] 📗
- Author: Aristotle
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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.
Section 2
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,
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