The Basic Works of Aristotle (Modern Library Classics) (140 page)

9
     That the actuality is also better and more valuable than the good potency is evident from the following argument.
(5)
Everything of which we say that it can do something, is alike capable of contraries, e. g. that of which we say that it can be well is the same as that which can be ill, and has both potencies at once; for the same potency is a potency of health and illness, of rest and motion, of building and throwing down, of being built and being thrown down. The capacity for contraries,
(10)
then, is present at the same time; but contraries cannot be present at the same time, and the actualities also cannot be present at the same time, e. g. health and illness. Therefore, while the good must be one of them, the capacity is both alike, or neither; the actuality,
(15)
then, is better. Also in the case of bad things the end or actuality must be worse than the potency; for that which ‘can’ is both contraries alike. Clearly, then, the bad does not exist apart from bad things; for the bad is in its nature posterior to the potency.
²⁵
And therefore we may also say that in the things which are from the beginning,
(20)
i. e. in eternal things, there is nothing bad, nothing defective, nothing perverted (for perversion is something bad).
²⁶

It is by an activity also that geometrical constructions are discovered; for we find them by dividing. If the figures had been already divided, the constructions would have been obvious; but as it is they
are present only potentially. Why are the angles of the triangle equal to two right angles? Because the angles about one point are equal to two right angles. If, then, the line parallel to the side had been already drawn upwards,
(25)
the reason would have been evident to any one as soon as he saw the figure. Why is the angle in a semicircle in all cases a right angle? If three lines are equal—the two which form the base, and the perpendicular from the centre—the conclusion is evident at a glance to one who knows the former proposition. Obviously, therefore, the potentially existing constructions are discovered by being brought to actuality; the reason is that the geometer’s thinking is an actuality; so that the potency proceeds from an actuality; and therefore it is by making constructions that people come to know them (though the single actuality is later in generation than the corresponding potency).
(30)

10
     The terms ‘being’ and ‘non-being’ are employed firstly with reference to the categories, and secondly with reference to the potency or actuality of these or their non-potency or non-actuality,
(35)
and thirdly in the sense of true and false.
[1051b]
This depends, on the side of the objects, on their being combined or separated, so that he who thinks the separated to be separated and the combined to be combined has the truth, while he whose thought is in a state contrary to that of the objects is in error. This being so,
(5)
when is what is called truth or falsity present, and when is it not? We must consider what we mean by these terms. It is not because we think truly that you are pale, that you
are
pale, but because you are pale we who say this have the truth. If, then, some things are always combined and cannot be separated, and others are always separated and cannot be combined,
(10)
while others are capable either of combination or of separation, ‘being’ is being combined and one, and ‘not being’ is being not combined but more than one. Regarding contingent facts, then, the same opinion or the same statement comes to be false and true, and it is possible for it to be at one time correct and at another erroneous; but regarding things that cannot be otherwise opinions are not at one time true and at another false,
(15)
but the same opinions are always true or always false.

But with regard to
incomposites
, what is being or not being, and truth or falsity? A thing of this sort is not composite, so as to ‘be’ when it is compounded, and not to ‘be’ if it is separated,
(20)
like ‘that the wood is white’ or ‘that the diagonal is incommensurable’; nor will truth and falsity be still present in the same way as in the previous cases. In fact, as truth is not the same in these cases, so also
being is not the same; but (
a
) truth or falsity is as follows—contact and assertion are truth (assertion not being the same as affirmation),
(25)
and ignorance is non-contact. For it is not possible to be in
error
regarding the question what a thing is, save in an accidental sense; and the same holds good regarding non-composite substances (for it is not possible to be in error about them). And they all exist actually, not potentially; for otherwise they would have come to be and ceased to be; but, as it is, being itself does not come to be (nor cease to be); for if it had done so it would have had to come out of something.
(30)
About the things, then, which are essences and actualities, it is not possible to be in error, but only to know them or not to know them. But we do inquire what they are, viz. whether they are of such and such a nature or not.

(
b
) As regards the ‘
being
’ that answers to truth and the ‘non-being’ that answers to falsity, in one case there is truth if the subject and the attribute are really combined, and falsity if they are not combined; in the other case,
(35)
if the object is existent it exists in a particular way, and if it does not exist in this way it does not exist at all.
²⁷
[1052a]
And truth means knowing these objects, and falsity does not exist, nor error, but only ignorance—and not an ignorance which is like blindness; for blindness is akin to a total absence of the faculty of thinking.

It is evident also that about unchangeable things there can be no error in respect of time,
(5)
if we assume them to be unchangeable. e. g. if we suppose that the triangle does not change, we shall not suppose that at one time its angles are equal to two right angles while at another time they are not (for that would imply change). It is possible, however, to suppose that one member of such a class has a certain attribute and another has not; e. g. while we
may
suppose that no even number is prime, we
may
suppose that some are and some are not. But regarding a numerically single number not even this form of error is possible; for we cannot in this case suppose that one instance has an attribute and another has not,
(10)
but whether our judgement be true or false, it is implied that the fact is eternal.

¹
Cf. vii, viii.

²
Cf. vii. 1.

³
Cf. ix. 1048
^a
27–
^b
6.

⁴
Cf. v. 12.

⁵
i. e. the event would not happen if the passive factor were different. What is oily cannot necessarily be crushed, nor what is yielding burnt.

⁶
i. e. with the rational formula.

⁷
The object of knowledge is always a form, which is eternal. The matter which makes things perishable is no object for knowledge.

⁸
Cf. iv. 5, 6.

⁹
Cf. 1047
^a
24–26.

¹⁰
sc
. so related that if the reality of
A
implies the reality of
B
the possibility of
A
implies the possibility of
B
.

¹¹
sc
. if
A
is possible.

¹²
sc
. so related that the reality of
A
implies the reality of
B
.

¹³
Cf. ix. 1–5.

¹⁴
Cf. v. 11.

¹⁵
Cf. vii. 7, 8.

¹⁶
Cf.
Phys
. vi. 6.

¹⁷
The reference is apparently to a tricky painting in which the figure was painted so as to stand out in high relief.

¹⁸
1049
^b
17–29.

¹⁹
e. g. Empedocles (Cf.
De Caelo
, 284
^a
24–6).

²⁰
sc
. the heavenly bodies.

²¹
i. e. they are both movers and moved.

²²
Cf.
^b
8–12.

²³
The Platonists are meant; Cf. i. 987
^b
31.

²⁴
The Idea, being the universal apart from its special manifestations, will be a potentiality, and will therefore be inferior to the corresponding particulars—e. g. the Idea of science will be inferior to particular acts of scientific thought.

²⁵
sc
. while the eternal and substantial must be better than the potency.

²⁶
The paragraph seems to be directed against Plato: Cf.
Rep
. 402
C
, 476
A
,
Theaet
. 176
E
,
Laws
896
E
, 898
C
.

²⁷
i. e. we have not here
A
and
B
, which may or may not be combined, but
A
, which if it exists at all exists as
A
.

1
      We have said previously,
(15)
in our distinction of the various meanings of words,
¹
that ‘one’ has several meanings; the things that are
directly and of their own nature and not accidentally called one may be summarized under four heads, though the word is used in more senses. (1) There is the continuous, either in general, or especially that which is continuous by nature and not by contact nor by being tied together; and of these, that has more unity and is prior,
(20)
whose movement
²
is more indivisible and simpler. (2) That which is a whole and has a certain shape and form is
one
in a still higher degree; and especially if a thing is of this sort by nature, and not by force like the things which are unified by glue or nails or by being tied together, i. e. if it has in itself the cause of its continuity.
(25)
A thing is of this sort because its movement is one and indivisible in place and time; so that evidently if a thing has by nature a principle of movement that is of the first kind (i. e. local movement) and the first in that kind (i. e. circular movement), this is in the primary sense one extended thing. Some things, then, are one in this way,
qua
continuous or whole, and the other things that are one are those whose definition is one. Of this sort are the things the thought of which is one,
(30)
i. e. those the thought of which is indivisible; and it is indivisible if the thing is indivisible in kind or in number. (3) In number, then, the individual is indivisible, and (4) in kind, that which in intelligibility and in knowledge is indivisible, so that that which causes substances to be one
³
must be one in the primary sense. ‘One’, then, has all these meanings—the naturally continuous and the whole, and the individual and the universal.
(35)
And all these are one because in some cases the movement, in others the thought or the definition is indivisible.

But it must be observed that the questions, what sort of things are said to be one, and what it is to be one and what is the definition of it, should not be assumed to be the same.
[1052b]
‘One’ has all these meanings, and each of the things to which one of these kinds of unity belongs will be one; but ‘to be one’ will sometimes mean being one of these things,
(5)
and sometimes being something else which is even nearer to the meaning of the
word
‘one’ while these other things approximate to its
application
. This is also true of ‘element’ or ‘cause’, if one had both to specify the things of which it is predicable and to render the definition of the word. For in a sense fire is an element (and doubtless also ‘the indefinite’ or something else of the sort is by its own nature the element),
(10)
but in a sense it is not; for it is not the same thing to be fire and to be an element, but while as a particular thing with a nature of its own fire is an element, the name
‘element’ means that it has this attribute, that there is something which is made of it as a primary constituent. And so with ‘cause’ and ‘one’ and all such terms.
(15)
For this reason, too, ‘to be one’ means ‘to be indivisible, being essentially a “this” and capable of being isolated either in place, or in form or thought’; or perhaps ‘to be whole and indivisible’; but it means especially ‘to be the first measure of a kind’, and most strictly of quantity; for it is from this that it has been extended to the other categories.
(20)
For measure is that by which quantity is known; and quantity
qua
quantity is known either by a ‘one’ or by a number, and all number is known by a ‘one’. Therefore all quantity
qua
quantity is known by the one, and that by which quantities are primarily known is the one itself; and so the one is the starting-point of number
qua
number. And hence in the other classes too ‘measure’ means that by which each is first known,
(25)
and the measure of each is a unit—in length, in breadth, in depth, in weight, in speed. (The words ‘weight’ and ‘speed’ are common to both contraries;
⁴
for each of them has two meanings—‘weight’ means both that which has any amount of gravity and that which has an excess of gravity, and ‘speed’ both that which has any amount of movement and that which has an excess of movement; for even the slow has a certain speed and the comparatively light a certain weight.
(30)
)

In all these, then, the measure and starting-point is something one and indivisible, since even in lines we treat as indivisible the line a foot long. For everywhere we seek as the measure something one and indivisible; and this is that which is simple either in quality or in quantity.
(35)
Now where it is thought impossible to take away or to add, there the measure is exact (hence that of number is most exact; for we posit the unit as indivisible in every respect); but in all other cases we imitate this sort of measure.
[1053a]
For in the case of a furlong or a talent or of anything comparatively large any addition or subtraction might more easily escape our notice than in the case of something smaller; so that the first thing from which,
(5)
as far as our perception goes, nothing can be subtracted, all men make the measure, whether of liquids or of solids, whether of weight or of size; and they think they know the quantity when they know it by means of this measure. And indeed they know movement too by the simple movement and the quickest; for this occupies least time.
(10)
And so in astronomy a ‘one’ of this sort is the starting-point and measure (for they assume the movement of the heavens to be uniform and the quickest, and judge the others by reference to it), and in music the quarter-tone (because it is the least interval), and in speech
the letter. And all these are ones in this sense—not that ‘one’ is something predicable in the same sense of all of these, but in the sense we have mentioned.

But the measure is not always one in number—sometimes there are several; e. g. the quarter-tones (not to the ear,
(15)
but as determined by the ratios) are two, and the articulate sounds by which we measure are more than one, and the diagonal of the square and its side are measured by two quantities, and all spatial magnitudes reveal similar varieties of unit. Thus, then, the one is the measure of all things, because we come to know the elements in the substance by dividing the things either in respect of quantity or in respect of kind.
(20)
And the one is indivisible just because the first of each class of things is indivisible. But it is not in the same way that every ‘one’ is indivisible, e. g. a foot and a unit; the latter is indivisible in every respect, while the former must be placed among things which are undivided to perception, as has been said already
⁵
—only to perception, for doubtless every continuous thing is divisible.

The measure is always homogeneous with the thing measured; the measure of spatial magnitudes is a spatial magnitude,
(25)
and in particular that of length is a length, that of breadth a breadth, that of articulate sound an articulate sound, that of weight a weight, that of units a unit. (For we must state the matter so, and not say that the measure of numbers is a number; we ought indeed to say this if we were to use the corresponding form of words, but the claim does not really correspond—it is as if one claimed that the measure of units is units,
(30)
and not a unit; number is a plurality of
units
.)

Knowledge, also, and perception, we call the measure of things for the same reason, because we come to know something by them—while as a matter of fact they are measured rather than measure other things. But it is with us as if some one else measured us and we came to know how big we are by seeing that he applied the cubit-measure to such and such a fraction of us. But Protagoras says ‘man is the measure of all things’,
(35)
as if he had said ‘the man who knows’ or ‘the man who perceives’; and these because they have respectively knowledge and perception, which we say are the measures of objects.
[1053b]
Such thinkers are saying nothing, then, while they appear to be saying something remarkable.

Evidently, then, unity in the strictest sense, if we define it according to the meaning of the word, is a measure, and most properly of quantity,
(5)
and secondly of quality. And some things will be one if they are indivisible in quantity, and others if they are indivisible in
quality; and so that which is one is indivisible, either absolutely or
qua
one.