MacKenna-Plotinus: quantity

But if we are to consider only the present and may not call in the past to make the total, why do we not reckon so in the case of time itself, where, in fact, we do not hesitate to add the past to the present and call the total greater? Why not suppose a quantity of happiness equivalent to a quantity of time? This would be no more than taking it lap by lap to correspond with time-laps instead of choosing to consider it as an indivisible, measurable only by the content of a given instant. Enneads   I,5,

When you know that you have become this perfect work, when you are self-gathered in the purity of your being, nothing now remaining that can shatter that inner unity, nothing from without clinging to the authentic man, when you find yourself wholly true to your essential nature, wholly that only veritable Light which is not measured by space, not narrowed to any circumscribed form nor again diffused as a thing void of term, but ever unmeasurable as something greater than all measure and more than all quantity – when you perceive that you have grown to this, you are now become very vision: now call up all your confidence, strike forward yet a step – you need a guide no longer – strain, and see. Enneads I,6,

But how can we conceive a thing having existence without having magnitude? We have only to think of things whose identity does not depend on their quantity – for certainly magnitude can be distinguished from existence as can many other forms and attributes. Enneads II,4,

In a word, every unembodied Kind must be classed as without quantity, and Matter is unembodied. Enneads II,4,

Besides quantitativeness itself [the Absolute-Principle] does not possess quantity, which belongs only to things participating in it, a consideration which shows that Quantitativeness is an Idea-Principle. A white object becomes white by the presence of whiteness; what makes an organism white or of any other variety of colour is not itself a specific colour but, so to speak, a specific Reason-Principle: in the same way what gives an organism a certain bulk is not itself a thing of magnitude but is Magnitude itself, the abstract Absolute, or the Reason-Principle. Enneads II,4,

Now, to begin with: extension is not an imperative condition of being a recipient; it is necessary only where it happens to be a property inherent to the recipient’s peculiar mode of being. The Soul, for example, contains all things but holds them all in an unextended unity; if magnitude were one of its attributes it would contain things in extension. Matter does actually contain in spatial extension what it takes in; but this is because itself is a potential recipient of spatial extension: animals and plants, in the same way, as they increase in size, take quality in parallel development with quantity, and they lose in the one as the other lessens. Enneads II,4,

Matter, in sum, is necessary to quality and to quantity, and, therefore, to body. Enneads II,4,

Their view is plausible because it rejects the notion of total admixture and because it recognizes that the masses of the mixing bodies must be whittled away if there is to be mixture without any gap, if, that is to say, each substance must be divided within itself through and through for complete interpenetration with the other. Their theory is confirmed by the cases in which two mixed substances occupy a greater space than either singly, especially a space equal to the conjoined extent of each: for, as they point out, in an absolute interpenetration the infusion of the one into the other would leave the occupied space exactly what it was before and, where the space occupied is not increased by the juxtaposition, they explain that some expulsion of air has made room for the incoming substance. They ask further, how a minor quantity of one substance can be spread out so as to interpenetrate a major quantity of another. In fact they have a multitude of arguments. Enneads: II VII.

But a lesser quantity permeates the entire extent of a larger; the smallest is sunk in the greatest; transfusion is exhibited unmistakably. In certain cases it is possible to pretend that there is no total penetration but there are manifest examples leaving no room for the pretence. In what they say of the spreading out of masses they cannot be thought very plausible; the extension would have to be considerable indeed in the case of a very small quantity [to be in true mixture with a very large mass]; for they do not suggest any such extension by change as that of water into air. Enneads: II VII.

Or again, it may be that magnitude is known incidentally [as a deduction] from the observation of colour. With an object at hand we know how much space is covered by the colour; at a distance, only that something is coloured, for the parts, quantitatively distinct among themselves, do not give us the precise knowledge of that quantity, the colours themselves reaching us only in a blurred impression. Enneads: II VIII.

Well, in hearing magnitude is known incidentally; but how? Touch conveys a direct impression of a visible object; what gives us the same direct impression of an object of hearing? The magnitude of a sound is known not by actual quantity but by degree of impact, by intensity – and this in no indirect knowledge; the ear appreciates a certain degree of force, exactly as the palate perceives by no indirect knowledge, a certain degree of sweetness. But the true magnitude of a sound is its extension; this the hearing may define to itself incidentally by deduction from the degree of intensity but not to the point of precision. The intensity is merely the definite effect at a particular spot; the magnitude is a matter of totality, the sum of space occupied. Enneads: II VIII.

But, the phenomenon is more easily explained by the example of things of wide variety. Take mountains dotted with houses, woods and other land-marks; the observation of each detail gives us the means of calculating, by the single objects noted, the total extent covered: but, where no such detail of form reaches us, our vision, which deals with detail, has not the means towards the knowledge of the whole by measurement of any one clearly discerned magnitude. This applies even to objects of vision close at hand: where there is variety and the eye sweeps over all at one glance so that the forms are not all caught, the total appears the less in proportion to the detail which has escaped the eye; observe each single point and then you can estimate the volume precisely. Again, magnitudes of one colour and unbroken form trick the sense of quantity: the vision can no longer estimate by the particular; it slips away, not finding the stand-by of the difference between part and part. Enneads: II VIII.

But how can this follow on the conjunction when no unity has been produced by the two? Even if such a unity had been produced, it would be a unity of things not mutually sharing experiences but acting upon each other. And the question would then arise whether each was effective upon the other or whether the sole action was not that of one (the form) preventing the other [the Matter] from slipping away? But when any material thing is severed, must not the Matter be divided with it? Surely the bodily modification and other experience that have accompanied the sundering, must have occurred, identically, within the Matter? This reasoning would force the destructibility of Matter upon us: "the body is dissolved; then the Matter is dissolved." We would have to allow Matter to be a thing of quantity, a magnitude. But since it is not a magnitude it could not have the experiences that belong to magnitude and, on the larger scale, since it is not body it cannot know the experiences of body. Enneads III,6,

But the conception of Eternity demands something which is in its nature complete without sequence; it is not satisfied by something measured out to any remoter time or even by something limitless, but, in its limitless reach, still having the progression of futurity: it requires something immediately possessed of the due fullness of Being, something whose Being does not depend upon any quantity [such as instalments of time] but subsists before all quantity. Enneads III,7,

Itself having no quantity, it can have no contact with anything quantitative since its Life cannot be made a thing of fragments, in contradiction to the partlessness which is its character; it must be without parts in the Life as in the essence. Enneads III,7,

The extent of the Movement of the All, then? The Celestial Circuit may, no doubt, be thought of in terms of quantity. It answers to measure – in two ways. First there is space; the movement is commensurate with the area it passes through, and this area is its extent. But this gives us, still, space only, not Time. Secondly, the circuit, considered apart from distance traversed, has the extent of its continuity, of its tendency not to stop but to proceed indefinitely: but this is merely amplitude of Movement; search it, tell its vastness, and, still, Time has no more appeared, no more enters into the matter, than when one certifies a high pitch of heat; all we have discovered is Motion in ceaseless succession, like water flowing ceaselessly, motion and extent of motion. Enneads III,7,

If, on the other hand, Time is [not such an abstraction but] a Measure possessing a continuous extent of its own, it must have quantity, like a foot-rule; it must have magnitude: it will, clearly, be in the nature of a line traversing the path of Movement. But, itself thus sharing in the movement, how can it be a Measure of Movement? Why should the one of the two be the measure rather than the other? Besides an accompanying measure is more plausibly considered as a measure of the particular movement it accompanies than of Movement in general. Further, this entire discussion assumes continuous movement, since the accompanying principle; Time, is itself unbroken [but a full explanation implies justification of Time in repose]. Enneads III,7,

Let us, then, suppose Time to be this "measured Movement," measured by quantity. Now the Movement if it is to be measured requires a measure outside itself; this was the only reason for raising the question of the accompanying measure. In exactly the same way the measuring magnitude, in turn, will require a measure, because only when the standard shows such and such an extension can the degree of movement be appraised. Time then will be, not the magnitude accompanying the Movement, but that numerical value by which the magnitude accompanying the Movement is estimated. But that number can be only the abstract figure which represents the magnitude, and it is difficult to see how an abstract figure can perform the act of measuring. Enneads III,7,

And, supposing that we discover a way in which it can, we still have not Time, the measure, but a particular quantity of Time, not at all the same thing: Time means something very different from any definite period: before all question as to quantity is the question as to the thing of which a certain quantity is present. Enneads III,7,

Further: Why should the mere presence of a number give us Time – a number measuring or measured; for the same number may be either – if Time is not given us by the fact of Movement itself, the Movement which inevitably contains in itself a succession of stages? To make the number essential to Time is like saying that magnitude has not its full quantity unless we can estimate that quantity. Enneads III,7,

And the reiterated observation of Movement – the same extent found to be traversed in such and such a period – will lead to the conception of a definite quantity of Time past. Enneads III,7,

This brings us to the fact that, in a certain sense, the Movement, the orbit of the universe, may legitimately be said to measure Time – in so far as that is possible at all – since any definite stretch of that circuit occupies a certain quantity of Time, and this is the only grasp we have of Time, our only understanding of it: what that circuit measures – by indication, that is – will be Time, manifested by the Movement but not brought into being by it. Enneads III,7,

Take a man walking and observe the advance he has made; that advance gives you the quantity of movement he is employing: and when you know that quantity – represented by the ground traversed by his feet, for, of course, we are supposing the bodily movement to correspond with the pace he has set within himself – you know also the movement that exists in the man himself before the feet move. Enneads III,7,

You must relate the body, carried forward during a given period of Time, to a certain quantity of Movement causing the progress and to the Time it takes, and that again to the Movement, equal in extension, within the man’s soul. Enneads III,7,

But, on the other hand, that first utterly indivisible Kind must be accompanied by a subsequent Essence, engendered by it and holding indivisibility from it but, in virtue of the necessary outgo from source, tending firmly towards the contrary, the wholly partible; this secondary Essence will take an intermediate Place between the first substance, the undivided, and that which is divisible in material things and resides in them. Its presence, however, will differ in one respect from that of colour and quantity; these, no doubt, are present identically and entire throughout diverse material masses, but each several manifestation of them is as distinct from every other as the mass is from the mass. Enneads IV,2,

What can justify this assigning of parts to the soul, the distinguishing one part from another? What quantity, or what difference of quality, can apply to a thing defined as a self-consistent whole of unbroken unity? Again, would perception be vested in that leading principle alone, or in the other phases as well? If a given experience bears only on that "leading principle," it would not be felt as lodged in any particular members of the organism; if, on the other hand, it fastens on some other phase of the soul – one not constituted for sensation – that phase cannot transmit any experience to the leading principle, and there can be no sensation. Enneads IV,2,

Part, as understood of body – uniform or varied – need not detain us; it is enough to indicate that, when part is mentioned in respect of things whose members are alike, it refers to mass and not to ideal-form [specific idea]: take for example, whiteness: the whiteness in a portion of milk is not a part of the whiteness of milk in general: we have the whiteness of a portion not a portion of whiteness; for whiteness is utterly without magnitude; has nothing whatever to do with quantity. Enneads IV,3,

In the case of the units of reckoning and of geometrical figure, exactly as in that of corporeal masses, partition must diminish the total; the part must be less than the whole; for these are things of quantity, and have their being as things of quantity; and – since they are not the ideal-form Quantity – they are subject to increase and decrease. Enneads IV,3,

The soul is not a thing of quantity; we are not to conceive of the All-Soul as some standard ten with particular souls as its constituent units. Enneads IV,3,

Supposing the soul to be at once a body and the cause of growth, then, if it is to keep pace with the substance it augments, it too must grow; that means it must add to itself a similar bodily material. For the added material must be either soul or soulless body: if soul, whence and how does it enter, and by what process is it adjoined [to the soul which by hypothesis is body]; if soulless, how does such an addition become soul, falling into accord with its precedent, making one thing with it, sharing the stored impressions and notions of that initial soul instead, rather, of remaining an alien ignoring all the knowledge laid up before? Would not such a soulless addition be subject to just such loss and gain of substance, in fact to the non-identity, which marks the rest of our material mass? And, if this were so, how explain our memories or our recognition of familiar things when we have no stably identical soul? Assume soul to be a body: now in the nature of body, characteristically divisible, no one of the parts can be identical with the entire being; soul, then, is a thing of defined size, and if curtailed must cease to be what it is; in the nature of a quantitative entity this must be so, for, if a thing of magnitude on diminution retains its identity in virtue of its quality, this is only saying that bodily and quantitatively it is different even if its identity consists in a quality quite independent of quantity. Enneads IV,7,

Now, a single coition and a single sperm suffice to a twin birth or in the animal order to a litter; there is a splitting and diverging of the seed, every diverging part being obviously a whole: surely no honest mind can fail to gather that a thing in which part is identical with whole has a nature which transcends quantity, and must of necessity be without quantity: only so could it remain identical when quantity is filched from it, only by being indifferent to amount or extension, by being in essence something apart. Thus the Soul and the Reason-Principles are without quantity. Enneads IV,7,

Either this or, supposing the centre of consciousness to be a thing of quantity and extension, the sensible object will coincide with it point by point of their co-expansion so that any given point in the faculty will perceive solely what coincides with it in the object: and thus nothing in us could perceive any thing as a whole. Enneads IV,7,

In transferring to bodies the powers of the unembodied, this school leaves nothing to that higher order. And yet that it is precisely in virtue of bodiless powers that bodies possess their efficiency is clear from certain reflections: It will be admitted that quality and quantity are two different things, that body is always a thing of quantity but not always a thing of quality: matter is not qualified. This admitted, it will not be denied that quality, being a different thing from quantity, is a different thing from body. Obviously quality could not be body when it has not quantity as all body must; and, again, as we have said, body, any thing of mass, on being reduced to fragments, ceases to be what it was, but the quality it possessed remains intact in every particle – for instance the sweetness of honey is still sweetness in each speck – this shows that sweetness and all other qualities are not body. Enneads IV,7,

No: the soul, as we have shown, is not a mass, not a quantity. Enneads IV,7,

The Dyad is a secondary; deriving from unity, it finds in unity the determinant needed by its native indetermination: once there is any determination, there is Number, in the sense, of course, of the real [the archetypal] Number. And the soul is such a number or quantity. For the Primals are not masses or magnitudes; all of that gross order is later, real only to the sense-thought; even in seed the effective reality is not the moist substance but the unseen – that is to say Number [as the determinant of individual being] and the Reason-Principle [of the product to be]. Enneads: V I

Only by a leap can we reach to this One which is to be pure of all else, halting sharp in fear of slipping ever so little aside and impinging on the dual: for if we fail of the centre, we are in a duality which does not even include The authentic One but belongs on both sides, to the later order. The One does not bear to be numbered in with anything else, with a one or a two or any such quantity; it refuses to take number because it is measure and not the measured; it is no peer of other entities to be found among them; for thus, it and they alike would be included in some container and this would be its prior, the prior it cannot have. Not even essential [ideal or abstract] number can belong to The One and certainly not the still later number applying to quantities; for essential number first appears as providing duration to the divine Intellection, while quantitative number is that [still later and lower] which furnishes the Quantity found in conjunction with other things or which provides for Quantity independent of things, if this is to be thought of as number at all. The Principle which in objects having quantitative number looks to the unity from which they spring is a copy [or lower phase] of the Principle which in the earlier order of number [in essential or ideal number] looks to the veritable One; and it attains its existence without in the least degree dissipating or shattering that prior unity: the dyad has come into being, but the precedent monad still stands; and this monad is quite distinct within the dyad from either of the two constituent unities, since there is nothing to make it one rather than the other: being neither, but simply that thing apart, it is present without being inherent. Enneads V,5,

Supposing we grant that all things known as substances are homogeneous as possessing something denied to the other genera, what precisely is this something, this individuality, this subject which is never a predicate, this thing not present in any thing as in a subject, this thing which does not owe its essential character to any other thing, as a quality takes character from a body and a quantity from a substance, as time is related to motion and motion to the moved? The Second Substance is, it is true, a predicate. But predication in this case signifies a different relation from that just considered; it reveals the genus inherent in the subject and the subject’s essential character, whereas whiteness is predicated of a thing in the sense of being present in the thing. Enneads: VI I

If it is maintained that the continuous is a Quantity by the fact of its continuity, then the discrete will not be a Quantity. If, on the contrary, the continuous possesses Quantity as an accident, what is there common to both continuous and discrete to make them quantities? Suppose we concede that numbers are quantities: we are merely allowing them the name of quantity; the principle which gives them this name remains obscure. Enneads: VI I

On the other hand, line and surface and body are not called quantities; they are called magnitudes: they become known as quantities only when they are rated by number-two yards, three yards. Even the natural body becomes a quantity when measured, as does the space which it occupies; but this is quantity accidental, not quantity essential; what we seek to grasp is not accidental quantity but Quantity independent and essential, Quantity-Absolute. Three oxen is not a quantity; it is their number, the three, that is Quantity; for in three oxen we are dealing with two categories. So too with a line of a stated length, a surface of a given area; the area will be a quantity but not the surface, which only comes under that category when it constitutes a definite geometric figure. Enneads: VI I

Why then are magnitudes classed as quantities? Not because they are so in the strict sense, but because they approximate to Quantity, and because objects in which magnitudes inhere are themselves designated as quantities. We call a thing great or small from its participation in a high number or a low. True, greatness and smallness are not claimed to be quantities, but relations: but it is by their apparent possession of quantity that they are thought of as relations. All this, however, needs more careful examination. Enneads: VI I

We have however to enquire in what sense the abstract numbers are substances. Can it be that they are also in a manner quantitative? Into whatever category they fall, the other numbers [those inherent in objects] can have nothing in common with them but the name. 5>Speech, time, motion – in what sense are these quantities? Let us begin with speech. It is subject to measurement, but only in so far as it is sound; it is not a quantity in its essential nature, which nature is that it be significant, as noun and verb are significant. The air is its Matter, as it is Matter to verb and noun, the components of speech. Enneads: VI I

To be more precise, we may define speech as an impact [made upon the outer air by the breath], though it is not so much the impact as the impression which the impact produces and which, as it were, imposes Form [upon the air]. Speech, thus, is rather an action than a quantity – an action with a significance. Though perhaps it would be truer to say that while this motion, this impact, is an action, the counter-motion is an experience [or Passion]; or each may be from different points of view either an action or an experience: or we may think of speech as action upon a substrate [air] and experience within that substrate. Enneads: VI I

With regard to time, if it is to be thought of as a measure, we must determine what it is that applies this measure. It must clearly be either Soul or the Present Moment. If on the contrary we take time to be something measured and regard it as being of such and such extension – a year, for example – then we may consider it as a quantity: essentially however time is of a different nature; the very fact that we can attribute this or that length to it shows us that it is not length: in other words, time is not Quantity. Quantity in the strict sense is the Quantity not inbound with things; if things became quantities by mere participation in Quantity, then Substance itself would be identical with Quantity. Enneads: VI I

Equality and inequality must be regarded as properties of Quantity-Absolute, not of the participants, or of them not essentially but only accidentally: such participants as "three yards’ length," which becomes a quantity, not as belonging to a single genus of Quantity, but by being subsumed under the one head, the one category. Enneads: VI I

It may be urged that "the past" is in its nature indefinite, while "yesterday" and "last year" are definite. We reply, first, that we demand some place in our classification for the past: secondly, that "yesterday," as definite past, is necessarily definite time. But definite time implies a certain quantity of time: therefore, if time is quantitative, each of the terms in question must signify a definite quantity. Enneads: VI I

Such then is the result of separating Act from Motion: Act, we aver, is timeless; yet we are forced to maintain not only that time is necessary to quantitative motion, but, unreservedly, that Motion is quantitative in its very nature; though indeed, if it were a case of motion occupying a day or some other quantity of time, the exponents of this view would be the first to admit that Quantity is present to Motion only by way of accident. Enneads: VI I

We have to ask ourselves whether there are not certain Acts which without the addition of a time-element will be thought of as imperfect and therefore classed with motions. Take for instance living and life. The life of a definite person implies a certain adequate period, just as his happiness is no merely instantaneous thing. Life and happiness are, in other words, of the nature ascribed to Motion: both therefore must be treated as motions, and Motion must be regarded as a unity, a single genus; besides the quantity and quality belonging to Substance we must take count of the motion manifested in it. Enneads: VI I

If we had to ascertain the nature of body and the place it holds in the universe, surely we should take some sample of body, say stone, and examine into what constituents it may be divided. There would be what we think of as the substrate of stone, its quantity – in this case, a magnitude; its quality – for example, the colour of stone. As with stone, so with every other body: we should see that in this thing, body, there are three distinguishable characteristics – the pseudo-substance, the quantity, the quality – though they all make one and are only logically trisected, the three being found to constitute the unit thing, body. If motion were equally inherent in its constitution, we should include this as well, and the four would form a unity, the single body depending upon them all for its unity and characteristic nature. Enneads VI,2,

Again, you must add to it to divide it into species; for there can be no differentiae in unity as there are in Substance. The mind accepts differences of Being, but differences within unity there cannot be. Every differentia introduces a duality destroying the unity; for the addition of any one thing always does away with the previous quantity. Enneads VI,2,

Magnitude [extended quantity] is in a still higher degree posterior and composite, for it contains within itself number, line and surface. Now if continuous magnitude derives its quantity from number, and number is not a genus, how can magnitude hold that status? Besides, magnitudes, like numbers, admit of priority and posteriority. Enneads VI,2,

What then can this "part" be? Matter may be suggested. But are we actually to maintain that the particular sensible substance consists of a conglomeration of qualities and Matter, while Sensible Substance as a whole is merely the sum of these coagulations in the uniform Matter, each one separately forming a quale or a quantum or else a thing of many qualities? Is it true to say that everything whose absence leaves subsistence incomplete is a part of the particular substance, while all that is accidental to the substance already existent takes independent rank and is not submerged in the mixture which constitutes this so-called substance? I decline to allow that whatever combines in this way with anything else is Substance if it helps to produce a single mass having quantity and quality, whereas taken by itself and divorced from this complementary function it is a quality: not everything which composes the amalgam is Substance, but only the amalgam as a whole. Enneads VI,3,

The straight line is, thus, a quantity plus a differentia; but it is not on that account a composite made up of straightness and line: if it be a composite, the composite possesses a differentiae of its own. Enneads VI,3,

But [if the line is a quantity] why is not the product of three lines included in Quantity? The answer is that a triangle consists not merely of three lines but of three lines in a particular disposition, a quadrilateral of four lines in a particular disposition: even the straight line involves disposition as well as quantity. Enneads VI,3,

Holding that the straight line is not mere quantity, we should naturally proceed to assert that the line as limited is not mere quantity, but for the fact that the limit of a line is a point, which is in the same category, Quantity. Similarly, the limited surface will be a quantity, since lines, which have a far better right than itself to this category, constitute its limits. With the introduction of the limited surface – rectangle, hexagon, polygon – into the category of Quantity, this category will be brought to include every figure whatsoever. Enneads VI,3,

When each of the entities bound up with the pseudo-substance is taken apart from the rest, the name of Quality is given to that one among them, by which without pointing to essence or quantity or motion we signify the distinctive mark, the type or aspect of a thing – for example, the beauty or ugliness of a body. This beauty – need we say? – is identical in name only with Intellectual Beauty: it follows that the term "Quality" as applied to the Sensible and the Intellectual is necessarily equivocal; even blackness and whiteness are different in the two spheres. Enneads VI,3,

How can we so dispart Being? We cannot break Life into parts; if the total was Life, the fragment is not. But we do not thus sunder Intelligence, one intelligence in this man, another in that? No; such a fragment would not be Intelligence. But the Being of the individual? Once more, if the total thing is Being, then a fragment could not be. Are we told that in a body, a total of parts, every member is also a body? But here we are dividing not body but a particular quantity of body, each of those divisions being described as body in virtue of possessing the Form or Idea that constitutes body; and this Idea has no magnitude, is incapable of magnitude. Enneads VI,4,

We may not make this principle the lesser, or if in the sense of mass we do, we must not begin to mistrust the power of that less to stretch to the greater. Of course, we have in fact no right to affirm it less or to measure the thing of magnitude against that which has none; as well talk of a doctor’s skill being smaller than his body. This greatness is not to be thought of in terms of quantity; the greater and less of body have nothing to do with soul. Enneads VI,4,

Clearly no participant can participate in itself; self-participation would be merely identity. Body, then, as participant does not participate in body; body it has; its participation must be in what is not body. So too magnitude does not participate in magnitude; it has it: not even in addition of quantity does the initial magnitude participate in magnitude: the two cubits do not themselves become three cubits; what occurs is that an object totalling to a certain quantity now totals to another: for magnitude to participate in magnitude the actual two cubits must themselves become the new three [which cannot occur]. Enneads VI,4,

If, then, the divided and quantitatively extended is to participate in another Kind, is to have any sort of participation, it can participate only in something undivided, unextended, wholly outside of quantity. Therefore, that which is to be introduced by the participation must enter as itself an omnipresent indivisible. Enneads VI,4,

We have, of course, no slight aid to conviction, indeed the very strongest, in the exposition of the character of that principle. It is not like a stone, some vast block lying where it lies, covering the space of its own extension, held within its own limits, having a fixed quantity of mass and of assigned stone-power. It is a First Principle, measureless, not bounded within determined size – such measurement belongs to another order – and therefore it is all-power, nowhere under limit. Being so, it is outside of Time. Enneads VI,5,

Consider the life in any living thing; it does not reach only to some fixed point, unable to permeate the entire being; it is omnipresent. If on this again we are asked How, we appeal to the character of this power, not subject to quantity but such that though you divide it mentally for ever you still have the same power, infinite to the core; in it there is no Matter to make it grow less and less according to the measured mass. Enneads VI,5,

Here with us a man will say "I wish I had such and such a quantity of gold" – or "such and such a number of houses." Gold is one thing: the wish is not to bring the numerical quantity into gold but to bring the gold to quantity; the quantity, already present in the mind, is to be passed on to the gold so that it acquire that numerical value. Enneads VI,6,

Number then pre-exists and is the cause by which produced things participate in quantity. Enneads VI,6,

If by division the one identical mass can become a duality without loss of quantity, clearly the unity it possessed and by this destructive division lost was something distinct. What may be alternatively present and absent to the same subject must be classed among Real-Beings, regardless of position; an accidental elsewhere, it must have reality in itself whether it be manifested in things of sense or in the Intellectual – an accidental in the Laters but self-existent in the higher, especially in the First in its aspect of Unity developing into Being. We may be told that Unity may lose that character without change in itself, becoming duality by association with something else; but this is not true; unity does not become two things; neither the added nor what takes the addition becomes two; each remains the one thing it was; the duality is predicable of the group only, the unity remaining unchanged in each of those unchanged constituents. Enneads VI,6,

You see something which you pronounce to be a unity; that thing possesses also size, form, and a host of other characteristics you might name; size, bulk, sweetness, bitterness and other Ideas are actually present in the thing; it surely cannot be thought that, while every conceivable quality has Real-Being, quantity [Number] has not and that while continuous quantity exists, discrete quantity does not and this though continuous quantity is measured by the discrete. No: as size by the presence of Magnitude, and Oneness by the presence of Unity, so with Duality and all the other numerical modes. Enneads VI,6,

But here we may be questioned about these numbers which we describe as the primal and authentic: "Where do you place these numbers, in what genus among Beings? To everyone they seem to come under Quantity and you have certainly brought Quantity in, where you say that discrete Quantity equally with the continuous holds place among Beings; but you go on to say that there are the numbers belonging to the Firsts and then talk of other numbers quite distinct, those of reckoning; tell us how you arrange all this, for there is difficulty here. And then, the unity in sense-things – is that a quantity or is quantity here just so many units brought together, the unity being the starting-point of quantity but not quantity itself? And, if the starting-point, is it a kindred thing or of another genus? All this you owe it to us to make clear." Enneads VI,6,

By this analysis and totalling, you get quantity; but there are two objects under consideration and each of these is one; each of the unities contributes to the complete being and the oneness is inherent in each; this is another kind of number; number essential; even the duality so formed is no posterior; it does not signify a quantity apart from the thing but the quantity in the essence which holds the thing together. The number here is no mere result of your detailing; the things exist of themselves and are not brought together by your reckoning, but what has it to do with essential reality that you count one man in with another? There is here no resultant unity such as that of a choir – the decad is real only to you who count the ten; in the ten of your reckoning there cannot be a decad without a unitary basis; it is you that make the ten by your counting, by fixing that tenness down to quantity; in choir and army there is something more than that, something not of your placing. Enneads VI,6,

But how do you come to have a number to place? The Number inherent apart from any enumeration has its own manner of being, but the other, that resulting upon the appearance of an external to be appraised by the Number within yourself, is either an Act of these inherent numbers or an Act in accordance with them; in counting we produce number and so bring quantity into being just as in walking we bring a certain movement into being. Enneads VI,6,

When you enumerate two things – say, animal and beauty – each of these remains one thing; the number is your production; it lay within yourself; it is you that elaborate quantity, here the dyad. But when you declare virtue to be a Tetrad, you are affirming a Tetrad which does actually exist; the parts, so to speak, make one thing; you are taking as the object of your act a Unity – Tetrad to which you accommodate the Tetrad within yourself. Enneads VI,6,

How, then, do we come to use the term? Is it that we think of Number as we think of an infinite line, not with the idea that any such lire exists but that even the very greatest – that of the [path of the] universe, for example – may be thought of as still greater? So it might be with number; let it be fixed, yet we still are free to think of its double, though not of course to produce the doubled quantity since it is impossible to join to the actual what is no more than a conception, a phantasm, private to ourselves. Enneads VI,6,

It is our view that there does exist an infinite line, among the Intellectual Beings: for There a line would not be quantitative and being without quantity could be numerically infinite. This however would be in another mode than that of limitless extension. In what mode then? In that the conception of the Absolute Line does not include the conception of limit. Enneads VI,6,

But what sort of thing is the Line in the Intellectual and what place does it hold? It is later than Number since unity is observed in it; it rises at one point and traverses one course and simply lacks the quantity that would be the measure of the distance. Enneads VI,6,

In the realm of process anything coming to be must come to be something; to every thing its distinctive shape: but what shape can that have which no one has shaped? It can be none of existing things; yet it is all: none, in that beings are later; all, as the wellspring from which they flow. That which can make all can have, itself, no extension; it must be limitless and so without magnitude; magnitude itself is of the Later and cannot be an element in that which is to bring it into being. The greatness of the Authentic cannot be a greatness of quantity; all extension must belong to the subsequent: the Supreme is great in the sense only that there can be nothing mightier, nothing to equal it, nothing with anything in common with it: how then could anything be equal to any part of its content? Its eternity and universal reach entail neither measure nor measurelessness; given either, how could it be the measure of things? So with shape: granted beauty, the absence of shape or form to be grasped is but enhancement of desire and love; the love will be limitless as the object is, an infinite love. Enneads VI,7,

Generative of all, The Unity is none of all; neither thing nor quantity nor quality nor intellect nor soul; not in motion, not at rest, not in place, not in time: it is the self-defined, unique in form or, better, formless, existing before Form was, or Movement or Rest, all of which are attachments of Being and make Being the manifold it is. Enneads VI,8,

This we can but name The Unity, indicating it to each other by a designation that points to the concept of its partlessness while we are in reality striving to bring our own minds to unity. We are not to think of such unity and partlessness as belong to point or monad; the veritable unity is the source of all such quantity which could not exist unless first there existed Being and Being’s Prior: we are not, then, to think in the order of point and monad but to use these – in their rejection of magnitude and partition – as symbols for the higher concept. Enneads VI,8,

In what sense, then, do we assert this Unity, and how is it to be adjusted to our mental processes? Its oneness must not be entitled to that of monad and point: for these the mind abstracts extension and numerical quantity and rests upon the very minutest possible, ending no doubt in the partless but still in something that began as a partible and is always lodged in something other than itself. The Unity was never in any other and never belonged to the partible: nor is its impartibility that of extreme minuteness; on the contrary it is great beyond anything, great not in extension but in power, sizeless by its very greatness as even its immediate sequents are impartible not in mass but in might. We must therefore take the Unity as infinite not in measureless extension or numerable quantity but in fathomless depths of power. Enneads VI,8,