by Aristotle
And while in some cases the exercise is the ultimate thing (e.g. in sight the [25] ultimate thing is seeing, and no other product besides this results from sight), but from some things a product follows (e.g. from the art of building there results a house as well as the act of building), yet none the less the act is in the former case the end and in the latter more of an end than the mere potentiality is. For the act of building is the thing that is being built, and comes to be—and is—at the same time as the house.
Where, then, the result is something apart from the exercise, the actuality is in [30] the thing that is being made, e.g. the act of building is in the thing that is being built and that of weaving in the thing that is being woven, and similarly in all other cases, and in general the movement is in the thing that is being moved; but when there is no product apart from the actuality, the actuality is in the agents, e.g. the act of [35] seeing is in the seeing subject and that of theorizing in the theorizing subject and the life is in the soul (and therefore well-being also; for it is a certain kind of life). [1050b1] Obviously, therefore, the substance or form is actuality. From this argument it is obvious that actuality is prior in substance to potentiality; and as we have said, one actuality always precedes another in time right back to the actuality of the [5] eternal prime mover.
But actuality is prior in a higher sense also; for eternal things are prior in substance to perishable things, and no eternal thing exists potentially. The reason is this. Every potentiality is at one and the same time a potentiality for the opposite; for, while that which is not capable of being present in a subject cannot be present, everything that is capable of being may possibly not be actual. That, then, which is [10] capable of being may either be or not be; the same thing, then, is capable both of being and of not being. And that which is capable of not being may possibly not be; and that which may possibly not be is perishable, either without qualification, or in the precise sense in which it is said that it possibly may not be, i.e. either in respect [15] of place or quantity or quality; ‘without qualification’ means ‘in substance’. Nothing, then, which is without qualification imperishable is without qualification potentially (though there is nothing to prevent its being potentially in some respect, e.g. potentially of a certain quality or in a certain place); imperishable things, then, exist actually. Nor can anything which is of necessity be potential; yet these things are primary; for if these did not exist, nothing would exist. Nor does eternal movement, if there be such, exist potentially; and, if there is an eternal mover, it is [20] not potentially in motion (except in respect of ‘whence’ and ‘whither’; there is nothing to prevent its having matter for this). Therefore the sun and the stars and the whole heaven are ever active, and there is no fear that they may sometime stand still, as the natural philosophers fear they may. Nor do they tire in this activity; for movement does not imply for them, as it does for perishable things, the potentiality [25] for opposites, so that the continuity of the movement should be laborious; for it is that kind of substance which is matter and potentiality, not actuality, that causes this.
Imperishable things are imitated by those that are involved in change, e.g. earth and fire. For these also are ever active; for they have their movement of [30] themselves and in themselves. But the other potentialities, according to the distinction we have drawn above, are all potentialities for opposites; for that which can move another in this way can also move it not in this way, i.e. if it acts according to a rational formula. But the same non-rational potentialities can produce opposite results only by their presence or absence.
If, then, there are any entities or substances such as the dialecticians say the [35] Ideas are, there must be something much more scientific than the Idea of science [1051a1] and something more mobile than the Idea of movement; for these will be more of the nature of actualities, while the Ideas are potentialities for these. Obviously, then, actuality is prior both to potentiality and to every principle of change.
9 · That the good actuality is better and more valuable than the good [5] potentiality is evident from the following argument. 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 healthy is the same as that which can be ill, and has both potentialities at once; for one and the same potentiality is a potentiality for health and illness, for [10] rest and motion, for building and throwing down, for being built and being thrown down. The capacity for contraries 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 one of them must be the good, but the [15] capacity is both the contraries alike, or neither; the actuality, then, is better. And in the case of bad things, the end or actuality must be worse than the potentiality; 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 potentiality. And therefore we may also say that in the things [20] which are from the beginning, i.e. in eternal things, there is nothing bad, nothing defective, nothing perverted (for perversion is something bad).
It is by actualization also that geometrical relations are discovered; for it is by dividing the given figures that people discover them. If they had been already divided, the relations would have been obvious; but as it is the divisions are present only potentially. Why are the angles of the triangle equal to two right angles? [25] Because the angles about one point are equal to two right angles. If, then, the line parallel to the side had been already drawn, the theorem 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? Because 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 this premise.
Obviously, therefore, the potentially existing relations are discovered by being [30] brought to actuality (the reason being that thinking is the actuality of thought); so that potentiality is discovered from actuality (and therefore it is by an act of construction that people acquire the knowledge), though the single actuality is later in generation.
10 · The terms ‘being’ and ‘non-being’ are employed firstly with reference to the categories, and secondly with reference to the potentiality or actuality of these [1051b1] or their opposites, while being and non-being in the strictest sense are truth and falsity4. The condition of this in the objects is 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, when is what is called truth or falsity present, and when is it [5] not? We must consider what we mean by these terms. It is not because we think that you are white, that you are white, but because you are white 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, while others are capable [10] 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 at one time to have the truth and at another to be in error; but regarding things that [15] cannot be otherwise opinions are not at one time true and at another false, but the same opinions are always true or always false.
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, like the white wood or the incommensurability of the diagonal; nor [20] 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 truth or falsity is as follows—contact and assertion are truth (assertion not being the same as affirmation), and ignorance is non-contact. For it i
s not possible to be in error [25] 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 come to be and cease to be; but, as it is, being itself does not come to be (nor cease to be); for if it did it would have to come out of something. About the things, then, [30] which are essences and exist in actuality, it is not possible to be in error, but only to think them or not to think them. Inquiry about their ‘what’ takes the form of asking whether they are of such and such a nature or not.
As regards being in the sense of truth and not being in the sense of 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, 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; and truth [1052a1] means thinking 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, if we assume them to be unchangeable. E.g. if we suppose that the [5] 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 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; but whether our [10] judgement be true or false, it is implied that the fact is eternal.
BOOK X (I)
[15] 1 · We have said previously, in our distinction of the various meanings of words, that ‘one’ has several meanings; while it is used in many senses, the things that are primarily and of their own nature and not accidentally called one may be summarized under four heads. (1) There is the continuous, either in general, or [20] especially that which is continuous by nature and not by contact nor by bonds; and of these, those things have more unity and are prior, whose movement 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 [25] together, i.e. if it has in itself something which is the cause of its continuity. 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. The things, then, which are in this way one are either continuous1 or whole, and the other things that are one are those whose [30] formula is one. Of this sort are the things the thought of which is one, 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 must be one in the primary sense. ‘One,’ then, has all these [35] meanings—the naturally continuous, the whole, the individual, and the universal. And all these are one because in some cases the movement, in others the thought or [1052b1] the formula, is indivisible.
But it must be observed that the questions, what sort of things are said to be one, and on the other hand what it is to be one and what is the formula of it, should not be assumed to be the same. ‘One’ has all these meanings, and each of those [5] 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, and sometimes something else, which is even nearer to the word ‘one’, while these other things approximate to its force. This is also true of ‘element’ or ‘cause’, if one had both to specify the things of which it is predicable and to give the definition of the word. For in a sense fire is an element [10] (and doubtless ‘the indefinite’ or something else of the sort is by its own nature the element), 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 [15] made of it as a primary constituent. And so with ‘cause’ and ‘one’ and all such terms. For this reason to be one is to be indivisible (being essentially a ‘this’ and capable of existing apart either in place or in form or thought); or perhaps to be whole and indivisible; but it is especially to be the first measure of a kind, and above all of quantity; for it is from this that it has been extended to the other categories. For measure is that by which quantity is known; and quantity qua quantity is known [20] 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 [25] first known, and the measure of each is a ‘one’—in length, in breadth, in depth, in weight, in speed. (Weight and speed are common to both contraries; 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 [30] has a certain speed and the light a certain weight.)
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. Now where it is thought impossible [35] to take away or to add, there the measure is exact. Hence that of number is most exact; for we posit the unit as absolutely indivisible; and in all other cases we imitate [1053a1] this sort of measure. For in the case of a furlong or a talent or of anything 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, as far as our perception goes, [5] 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 they know movement too by the simple movement and the quickest; for this occupies least time. And therefore in astronomy a ‘one’ of this sort is the starting-point and measure (for they assume the [10] 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 one 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; [15] e.g. the quarter-tones (not to the ear, 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 so are all spatial magnitudes. 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. The one is indivisible just because the first of each [20] 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 absolutely indivisible, while the former must be placed among things which are undivided in perception, as has been said already,—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, and in particular that of length is a [25] length, that of breadth a breadth, that of articulate sounds 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 supposition does not really correspond—it is as if one supposed that the measure of units is units, and not a [30] unit, for number is a plurality of units.)
Knowledge also, and perception, we call the measure of things, for the same reason, because we 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 a certain number of times to us. But Protagoras says man is the [1053b1] measure of all things, meaning really 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. They are saying nothing, then, while appearing to be saying something remarkable. Evidently, then, being one in the strictest sense, if we [5] define it according to the meaning of the word, is a measure, and especially of quantity, and secondly of quality. And some things will be one if they are indivisible in quantity, and others if they are indivisible in quality; therefore that which is one is indivisible, either absolutely or qua one.