soever things, therefore, that amount to the existence of any certain particular thing, and its subsistence in energy or activity, as regards these, I say, there is no possibility of labouring under deception, but either one understands them or he does not. But the inquiry as to the nature of anything is being instituted by us in respect of these natures, as to whether there are things of this sort at all, or not; and the fact is, the existence of a thing is as that which is true, and its non-existence as that which is false; in one way, if it is that which is compounded, it is true, whereas, in the other, if it is not a composite nature, it is false: and in another way, if we suppose it to exist in this way, it is true, but if not in this way, it is not true. Now, that which is true amounts to the intellectual apprehension of these,1 but that which is false does not exist, nor does it amount to deception, but ignorance; not, however, such as may be assimilated unto blindness, for blindness is just as if one, in short, did not possess the capacity of intellectually apprehending any subject. And it is also evident that, respecting things that are immovable, there is no deception as to the time when of their existence, supposing that one consider them as things that are immovable; for instance, the triangle-unless viewed as that which is subject to mutation-a mathematician will not consider as being at one time in possession of angles equal to two right angles, but at another not so, for it would undergo a certain mutation; yet he might consider one thing in this point of view, but not another: for example, that there be no even number, first, or that some are so, but that other numbers are not so. In regard, however, of one thing in number we cannot expect that he should entertain this opinion, for no longer would he do so as regards certain things, yet not as regards others; but he will speak truth or falsehood so far as he makes assertions of it as a thing that is invariably disposed in this way.

1 Aristotle's words are, тd dè åλnlès tò voeîv aůrá: how brief, yet how expressive!

BOOK IX.1

1. Unity, or the rò év denominated in respect

to motion, perception, and.

CHAPTER I.

THAT unity is denominated in many ways har been previously declared in our divisions on its multifarious predications; 2 and whereas it is denominated in many ways, there are summarily definition. arranged four modes of things that are styled one, primarily and essentially, but not according to accident For both that which is continuous, either simply considered, or especially what is so by nature, at least, and not by contact, or by a bond of connexion, such is one thing; and that in a more eminent degree is one thing, and prior to these of which the motion is more indivisible, and simple, rather. Moreover, is unity a thing of this sort; and in a more eminent degree is that which is a whole one thing, and that which possesses a certain form and species: but particularly we look for unity if a thing of this sort subsists by the constitution of Nature, and not by violent or abnormal means; in like manner as whatever things are joined together by glue, or by a nail, or by a chain, are one thing, but contains in itself the cause of its own continuity. And it is a thing of this kind in respect of its motion being one and indivisible in place and time; so that it is evident if anything by the constitution of Nature involves a principle of the earliest motion—I mean, such a principle as is primary—that it is the first magnitude; as, for example, I speak of the circular motion of a body, for this is the earliest motion. Therefore,

1 In book IX.-according to others, book X.-Aristotle having already examined fully into the subject of the тò ov, comes now to treat of the To ev, which, with the ontologist, are interchangeable terms. The points investigated in this book wear a decidedly logical aspect; and it has been thought that there has been some error or confusion in this portion of the Metaphysics.

2 The term ev has already been defined by Aristotle, in book IV. chap. vi.

3 popás: I have translated this word "body." It primarily refers to the actual motion of a body, and then to the body itself which is

in this way are some things one either as what is continuous or entire; others, however, are one of which the definition may be one. And things of this sort are such as those of which the intellectual apprehension is one, and such as those of which it is indivisible, and of which there is an indivisible apprehension of what is indivisible in form or number. In number, therefore, is the singular indivisible; but in form that is indivisible which resides in what is an object of knowledge, and in scientific knowledge itself: wherefore, that would be one thing primarily which is the cause of the subsistence of unity in substances. Therefore, no doubt, is unity denominated in such many ways, as both that which is continuous by the constitution of Nature, and is an entirety and a singular, and that which is universal. Now, all these are one in respect of the indivisibility—of the motion of some of them, but of the intellectual perception or the definition of others.

2. Certain dis

quiries relating

to unity.

It is requisite, however, to understand that we should not assume that the same assertions should tinctions in inbe made alike in the inquiries both as to what sort of things are styled one, and what is the nature of the existence of unity, and what is the definition of it; for unity is predicated in thus many ways, and each of those things will be one in which any one of these modes will be inherent. The being or existence of unity, however, sometimes will be in accordance with one of these, and sometimes with another which also is nearer to the name, but those are one in regard of capacity; just as, also, if it may be expedient to discuss the subject relating to element and cause, it would be necessary, in the treatment of these matters, both to frame distinctions and to assign the definition of the name. For fire, in one sense, is an element,—and perhaps, also, with the Infinite 2 in itself this is the case, or it is something else of the sort,—and, in another sense, it is not so; for the essence of element is not the same thing with the essence of fire and of element; but so far forth as fire is a certain thing and Carried along. The subject here glanced at is treated of at large by Aristotle in the eighth book of the Physics, where the perpetuity of natural motion is investigated.

The Leipsic edition puts a stop after ovixeîov, omitted in the text I have followed.

2 The subject of the Infinite is examined into in book X. chap. x.

a certain nature, so far is it an element; but the name signi. fies that this particular quality is an accident in this, because there is something subsisting from this as from a thing that is primarily inherent. So, also, is it in the case of cause and unity, and all things of this sort. Wherefore, also, the essence or existence of one consists in being indivisible; namely, in being this certain particular thing, and incapable of a separate subsistence either in place or form, or in the faculty of thought, or in that which is entire, and has been made the subject of definition.

3. Unity, as a

But especially doth the nature or essence of measure, found unity consist in being the first measure of every in quantity. genus, and the principal portions of quantity;1 for from this quarter, likewise, hath it proceeded to other things, for measure is that whereby quantity is known. But quantity, so far forth as it is quantity, is known either by unity or by number; for every number is known by unity. Wherefore, every quantity, so far forth as it is quantity, is discoverable by unity; and that by which as primary it is known, this itself is one. Wherefore, unity is a first principle of number, so far forth as it is number. And hence, also, in the case of other things, that is denominated a measure whereby as primary each thing is known; and the measure of everything is one in length, in breadth, in depth, in gravity, in velocity. For gravity and velocity are what is common in the case of contraries, for in a twofold sense may each of them be taken; as, for instance, gravity is both that which involves any momentum whatsoever, and that which possesses a superabundance of momentum and velocity is both that which involves any motion whatever, and an excess of motion; for likewise is there a certain velocity even of that which is slow, and there is a certain gravity of that which is rather light.

4. Measure derivable from number in regard of other

:

Now, a measure and first principle in all of these is a sort of unity, and a thing that is indivisible; since to give an instance-in lines, also, quantities, e. g. they employ that which measures a foot as a thing that is indivisible: for everywhere, or in

lines, &c.;

If we do not allow the truth of this view of unity, it is implied, in what Aristotle lays down that even the notion of quantity would be inconceivable.

every instance, do investigators search for measure as a certain unity, and as a thing that is indivisible; and this constitutes what is simple, either in the quality or in the quantity. Wheresoever, indeed, therefore, there does not appear to be anything subtracted or added, this is the most accurate measure. Wherefore, the measure of number1 is the most precise of all measures, for the monad they have posited as in every way indivisible; but, in the case of other things, they imitate a measure of this sort: for from a stadium and a talent, and that which is invariably greater, would anything that has been both added and taken away rather escape our notice, than from that which is less. Wherefore, that from which, considered as primary, a thing does not admit of subsisting according to sense, this all men constitute as a measure, both of things moist and dry, and of gravity and magnitude; and they imagine that they then know the quantity of a thing when they happen to know it by means of this measure. And, therefore, also, motion do and in regard they measure by a simple motion, and one which of motion. is the most rapid; for this involves the very smallest possible duration.2 Wherefore, in astronomy a unity of this kind is a first principle and a measure-for their hypothesis is, that the motion of the heavens is equable, and that it is of the utmost velocity; and, in accordance with this, astronomers adjust the other motions--and in music diesis is adopted as a measure, because it constitutes the least perceptible sound;3 and in the case of vocal sounds it is an element of speech that is such. And all these things in this way are a certain one, not in such a manner as that the one is a thing common to them, but in such a way as has been declared. A measure is not, however, invariably one in number, but sometimes more than one; as, for instance, two dieses such as are not understood according to hearing, but are contained in the definitions ; and the vocal sounds by which we measure are more numerous, and the diameter of the square, likewise, is

5. Certain con

siderations set down relating

to measure.

And hence it is that the mathematical sciences are characterised fer so much of certainty and precision.

2 Vide Locke's Essay, book I. chap. xiv.

3 The word dieois has been already explained, in a note, p. 124, as a term in music, meaning something the same as our demi-semi-quaver. It occurs in the Posterior Analytics, book I. chap. xxiii.