No: all that ever appears upon it is brought in by the Idea: the Idea alone possesses: to it belongs the magnitude and all else that goes with the Reason-Principle or follows upon it. Quantity is given with the Ideal-Form in all the particular species – man, bird, and particular kind of bird. Enneads II,4,
The imaging of Quantity upon Matter by an outside power is not more surprising than the imaging of Quality; Quality is no doubt a Reason-Principle, but Quantity also – being measure, number – is equally so. Enneads II,4,
But this notion reduces all existence to qualified things or qualities: Quantity itself becomes a Quality and so does even Existence. Now this cannot be: if such things as Quantity and Existence are qualified, they are, by that very fact, not qualities: Quality is an addition to them; we must not commit the absurdity of giving the name Quality to something distinguishable from Quality, something therefore that is not Quality. Enneads II,4,
Succession or repetition gives us Number – dyad, triad, etc. – and the extent traversed is a matter of Magnitude; thus we have Quantity of Movement – in the form of number, dyad, triad, decade, or in the form of extent apprehended in what we may call the amount of the Movement: but, the idea of Time we have not. That definite Quantity is merely something occurring within Time, for, otherwise Time is not everywhere but is something belonging to Movement which thus would be its substratum or basic-stuff: once more, then, we would be making Time identical with Movement; for the extent of Movement is not something outside it but is simply its continuousness, and we need not halt upon the difference between the momentary and the continuous, which is simply one of manner and degree. The extended movement and its extent are not Time; they are in Time. Those that explain Time as extent of Movement must mean not the extent of the movement itself but something which determines its extension, something with which the movement keeps pace in its course. But what this something is, we are not told; yet it is, clearly, Time, that in which all Movement proceeds. This is what our discussion has aimed at from the first: “What, essentially, is Time?” It comes to this: we ask “What is Time?” and we are answered, “Time is the extension of Movement in Time!” Enneads III,7,
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 Intellectual Kosmos thus a manifold, Number and Quantity arise: Quality is the specific character of each of these ideas which stand as the principles from which all else derives. Enneads: V I
Bringing itself close to the divine Intellect, becoming, as it were, one with this, it seeks still further: What Being, now, has engendered this God, what is the Simplex preceding this multiple; what the cause at once of its existence and of its existing as a manifold; what the source of this Number, this Quantity? Number, Quantity, is not primal: obviously before even duality, there must stand the unity. 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,
And just as there is, primarily or secondarily, some form or idea from the monad in each of the successive numbers – the later still participating, though unequally, in the unit – so the series of Beings following upon The First bear, each, some form or idea derived from that source. In Number the participation establishes Quantity; in the realm of Being, the trace of The One establishes reality: existence is a trace of The One – our word for entity may probably be connected with that for unity. Enneads V,5,
The consideration of Quantity brings the same result: If production is undetermined in regard to Quantity, each thing has its distinct Reason-Principle: if there is a measured system the Quantity has been determined by the unrolling and unfolding of the Reason-Principles of all the existences. Enneads V,7,
Thus when the universe has reached its term, there will be a fresh beginning, since the entire Quantity which the Kosmos is to exhibit, every item that is to emerge in its course, all is laid up from the first in the Being that contains the Reason-Principles. Enneads V,7,
These considerations are sufficient for our purpose: let us now proceed to investigate the nature of Quantity. Enneads: VI I
We are told that number is Quantity in the primary sense, number together with all continuous magnitude, space and time: these are the standards to which all else that is considered as Quantity is referred, including motion which is Quantity because its time is quantitative – though perhaps, conversely, the time takes its continuity from the motion. 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
Are we then to consider numbers, and numbers only, as constituting the category of Quantity? If we mean numbers in themselves, they are substances, for the very good reason that they exist independently. If we mean numbers displayed in the objects participant in number, the numbers which give the count of the objects – ten horses or ten oxen, and not ten units – then we have a paradoxical result: first, the numbers in themselves, it would appear, are substances but the numbers in objects are not; and secondly, the numbers inhere in the objects as measures [of extension or weight], yet as standing outside the objects they have no measuring power, as do rulers and scales. If however their existence is independent, and they do not inhere in the objects, but are simply called in for the purpose of measurement, the objects will be quantities only to the extent of participating in Quantity. Enneads: VI I
So with the numbers themselves: how can they constitute the category of Quantity? They are measures; but how do measures come to be quantities or Quantity? Doubtless in that, existing as they do among the Existents and not being adapted to any of the other categories, they find their place under the influence of verbal suggestion and so are referred to the so-called category of Quantity. We see the unit mark off one measurement and then proceed to another; and number thus reveals the amount of a thing, and the mind measures by availing itself of the total figure. Enneads: VI I
Number then, whether regarded in itself or in the participant objects, belongs to the category of Quantity, but the participant objects do not. “Three yards long” does not fall under the category of Quantity, but only the three. 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
In sum, we hold that there is no single genus of Quantity. Only number is Quantity, the rest [magnitudes, space, time, motion] quantities only in a secondary degree. We have therefore not strictly one genus, but one category grouping the approximate with the primary and the secondary. 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
Suppose however that we do possess ourselves of objective truth when in comparing two points of time we pronounce one prior, or posterior, to the other, that priority does entail something distinct from the objects to which it refers; admit an objective truth behind the relation of left and right: does this apply also to magnitudes, and is the relation exhibiting excess and deficiency also something distinct from the quantities involved? Now one thing is double of another quite apart from our speech or thought; one thing possesses and another is possessed before we notice the fact; equals do not await our comparison but – and this applies to Quality as well as Quantity – rest upon an identity existing between the objects compared: in all the conditions in which we assert Relation the mutual relation exists over and above the objects; we perceive it as already existent; our knowledge is directed upon a thing, there to be known – a clear testimony to the reality of Relation. Enneads: VI I
With regard to Date: If “yesterday,” “to-morrow,” “last year” and similar terms denote parts of time, why should they not be included in the same genus as time? It would seem only reasonable to range under time the past, present and future, which are its species. But time is referred to Quantity; what then is the need for a separate category of Date? If we are told that past and future – including under past such definite dates as yesterday and last year which must clearly be subordinate to past time – and even the present “now” are not merely time but time – when, we reply, in the first place, that the notion of time – when involves time; that, further, if “yesterday” is time-gone-by, it will be a composite, since time and gone-by are distinct notions: we have two categories instead of the single one required. Enneads: VI I
The “category of Action”: The quantum has been regarded as a single genus on the ground that Quantity and Number are attributes of Substance and posterior to it; the quale has been regarded as another genus because Quality is an attribute of Substance: on the same principle it is maintained that since activity is an attribute of Substance, Action constitutes yet another genus. Enneads: VI I
Motion is thought of as imperfect, not because it is not an Act, but because, entirely an Act, it yet entails repetition [lacks finality]. It repeats, not in order that it may achieve actuality – it is already actual – but that it may attain a goal distinct from itself and posterior: it is not the motion itself that is then consummated but the result at which it aims. Walking is walking from the outset; when one should traverse a racecourse but has not yet done so, the deficiency lies not in the walking – not in the motion – but in the amount of walking accomplished; no matter what the amount, it is walking and motion already: a moving man has motion and a cutter cuts before there is any question of Quantity. And just as we can speak of Act without implying time, so we can of Motion, except in the sense of motion over a defined area; Act is timeless, and so is Motion pure and simple. 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
If however Possession is not to be predicated of Quality because Quality stands recognised as a category, nor of Quantity because the category of Quantity has been received, nor of parts because they have been assigned to the category of Substance, why should we predicate Possession of weapons, when they too are comprised in the accepted category of Substance? Shoes and weapons are clearly substances. Enneads: VI I
Further, how can States constitute a single genus, when there is such manifold diversity among them? How can we group together three yards long” and “white” – Quantity and Quality respectively? Or again Time and Place? How can “yesterday,” “last year,” “in the Lyceum,” “in the Academy,” be States at all? How can Time be in any sense a State? Neither is Time a State nor the events in Time, neither the objects in Space nor Space itself. Enneads: VI I
The above considerations – to which others, doubtless, might be added – suffice to show that these five are primary genera. But that they are the only primary genera, that there are no others, how can we be confident of this? Why do we not add unity to them? Quantity? Quality? Relation, and all else included by our various forerunners? As for unity: If the term is to mean a unity in which nothing else is present, neither Soul nor Intellect nor anything else, this can be predicated of nothing, and therefore cannot be a genus. If it denotes the unity present in Being, in which case we predicate Being of unity, this unity is not primal. Enneads VI,2,
We turn to ask why Quantity is not included among the primary genera, and Quality also. Enneads VI,2,
Quantity is not among the primaries, because these are permanently associated with Being. Motion is bound up with Actual Being [Being-in-Act], since it is its life; with Motion, Stability too gained its foothold in Reality; with these are associated Difference and Identity, so that they also are seen in conjunction with Being. But number [the basis of Quantity] is a posterior. It is posterior not only with regard to these genera but also within itself; in number the posterior is divided from the prior; this is a sequence in which the posteriors are latent in the priors [and do not appear simultaneously]. Number therefore cannot be included among the primary genera; whether it constitutes a genus at all remains to be examined. Enneads VI,2,
If, then, Quantity be constituted by a common element in both number and magnitude, we must ascertain the nature of this common element, and consider it, once discovered, as a posterior genus, not as one of the Primaries: thus failing of primary status, it must be related, directly or indirectly, to one of the Primaries. Enneads VI,2,
We may take it as clear that it is the nature of Quantity to indicate a certain quantum, and to measure the quantum of the particular; Quantity is moreover, in a sense, itself a quantum. But if the quantum is the common element in number and magnitude, either we have number as a primary with magnitude derived from it, or else number must consist of a blending of Motion and Stability, while magnitude will be a form of Motion or will originate in Motion, Motion going forth to infinity and Stability creating the unit by checking that advance. Enneads VI,2,
Why is Quality, again, not included among the Primaries? Because like Quantity it is a posterior, subsequent to Substance. Primary Substance must necessarily contain Quantity and Quality as its consequents; it cannot owe its subsistence to them, or require them for its completion: that would make it posterior to Quality and Quantity. Enneads VI,2,
As we survey this Magnitude with the beauty of Being within it and the glory and light around it, all contained in Intellect, we see, simultaneously, Quality already in bloom, and along with the continuity of its Act we catch a glimpse of Magnitude at Rest. Then, with one, two and three in Intellect, Magnitude appears as of three dimensions, with Quantity entire. Quantity thus given and Quality, both merging into one and, we may almost say, becoming one, there is at once shape. Difference slips in to divide both Quantity and Quality, and so we have variations in shape and differences of Quality. Identity, coming in with Difference, creates equality, Difference meanwhile introducing into Quantity inequality, whether in number or in magnitude: thus are produced circles and squares, and irregular figures, with number like and unlike, odd and even. Enneads VI,2,
The “mere predicates” fall under the category of Relation: such are cause and element. The accidents included in the composite substances ire found to be either Quality or Quantity; those which are inclusive are of the nature of Space and Time. Activities and experiences comprise Motions; consequents Space and Time, which are consequents respectively of the Composites and of Motion. Enneads VI,3,
The first three entities [Matter, Form, Composite] go, as we have discovered, to make a single common genus, the Sensible counterpart of Substance. Then follow in order Relation, Quantity, Quality, Time-during-which, Place-in-which, Motion; though, with Time and Space already included [under Relation], Time-during-which and Place-in-which become superfluous. Enneads VI,3,
Thus we have five genera, counting the first three entities as one. If the first three are not massed into a unity, the series will be Matter, Form, Composite, Relation, Quantity, Quality, Motion. The last three may, again, be included in Relation, which is capable of bearing this wider extension. Enneads VI,3,
What, then, we have to ask, is the constant element in the first three entities? What is it that identifies them with their inherent Substance? Is it the capacity to serve as a base? But Matter, we maintain, serves as the base and seat of Form: Form, thus, will be excluded from the category of Substance. Again, the Composite is the base and seat of attributes: hence, Form combined with Matter will be the basic ground of Composites, or at any rate of all posteriors of the Composite – Quantity, Quality, Motion, and the rest. Enneads VI,3,
Do we infer that fire and water are not Substance? They certainly are not Substance because they are visible. Why, then? Because they possess Matter? No. Or Form? No. Nor because they involve a Couplement of Matter and Form. Then why are they Substance? By existing. But does not Quantity exist, and Quality? This anomaly is to be explained by an equivocation in the term “existence.” Enneads VI,3,
Passing to Quantity and the quantum, we have to consider the view which identifies them with number and magnitude on the ground that everything quantitative is numbered among Sensible things or rated by the extension of its substrate: we are here, of course, discussing not Quantity in isolation, but that which causes a piece of wood to be three yards long and gives the five in “five horses,” Enneads VI,3,
Now we have often maintained that number and magnitude are to be regarded as the only true quantities, and that Space and Time have no right to be conceived as quantitative: Time as the measure of Motion should be assigned to Relation, while Space, being that which circumscribes Body, is also a relative and falls under the same category; though continuous, it is, like Motion, not included in Quantity. Enneads VI,3,
On the other hand, why do we not find in the category of Quantity “great” and “small”? It is some kind of Quantity which gives greatness to the great; greatness is not a relative, though greater and smaller are relatives, since these, like doubleness, imply an external correlative. Enneads VI,3,
It follows that we must allow contrariety to Quantity: whenever we speak of great and small, our notions acknowledge this contrariety by evolving opposite images, as also when we refer to many and few; indeed, “few” and “many” call for similar treatment to “small” and “great.” Enneads VI,3,
Quantity, then, appears whenever there is a progression from the unit or the point: if either progression comes to a rapid halt, we have respectively “few” and “small”; if it goes forward and does not quickly cease, “many” and “great.” Enneads VI,3,
To judge from these instances, there is contrariety in Quantity. Place we may neglect as not strictly coming under the category of Quantity; if it were admitted, “above” could only be a contrary if there were something in the universe which was “below”: as referring to the partial, the terms “above” and “below” are used in a purely relative sense, and must go with “right” and “left” into the category of Relation. Enneads VI,3,
Syllable and discourse are only indirectly quantities or substrates of Quantity; it is voice that is quantitative: but voice is a kind of Motion; it must accordingly in any case [quantity or no quantity] be referred to Motion, as must activity also. Enneads VI,3,
But how are we to differentiate the continuous, comprising as it does line, surface and solid? The line may be rated as of one dimension, the surface as of two dimensions, the solid as of three, if we are only making a calculation and do not suppose that we are dividing the continuous into its species; for it is an invariable rule that numbers, thus grouped as prior and posterior, cannot be brought into a common genus; there is no common basis in first, second and third dimensions. Yet there is a sense in which they would appear to be equal – namely, as pure measures of Quantity: of higher and lower dimensions, they are not however more or less quantitative. 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,
If however by classing the triangle and the rectangle as qualia we propose to bring figures under Quality, we are not thereby precluded from assigning the same object to more categories than one: in so far as it is a magnitude – a magnitude of such and such a size – it will belong to Quantity; in so far as it presents a particular shape, to Quality. Enneads VI,3,
Again, when I find Quality bound up with Substance, I regard it as substantial quality: I am not less, but far more, disposed to see in figures or shapes [qualitative] varieties of Quantity. Besides, if we are not to regard them as varieties of magnitude, to what genus are we to assign them? Suppose, then, that we allow differences of magnitude; we commit ourselves to a specific classification of the magnitudes so differentiated. Enneads VI,3,
How far is it true that equality and inequality are characteristic of Quantity? Triangles, it is significant, are said to be similar rather than equal. But we also refer to magnitudes as similar, and the accepted connotation of similarity does not exclude similarity or dissimilarity in Quantity. It may, of course, be the case that the term “similarity” has a different sense here from that understood in reference to Quality. Enneads VI,3,
Furthermore, if we are told that equality and inequality are characteristic of Quantity, that is not to deny that similarity also may be predicated of certain quantities. If, on the contrary, similarity and dissimilarity are to be confined to Quality, the terms as applied to Quantity must, as we have said, bear a different meaning. Enneads VI,3,
But suppose similarity to be identical in both genera; Quantity and Quality must then be expected to reveal other properties held in common. Enneads VI,3,
May the truth be this: that similarity is predicable of Quantity only in so far as Quantity possesses [qualitative] differences? But as a general rule differences are grouped with that of which they are differences, especially when the difference is a difference of that thing alone. If in one case the difference completes the substance and not in another, we inevitably class it with that which it completes, and only consider it as independent when it is not complementary: when we say “completes the substance,” we refer not to Subtance as such but to the differentiated substance; the particular object is to be thought of as receiving an accession which is non-substantial. Enneads VI,3,
We must not however fad to observe that we predicate equality of triangles, rectangles, and figures generally, whether plane or solid: this may be given as a ground for regarding equality and inequality as characteristic of Quantity. Enneads VI,3,
We have spoken of Quality as combining with other entities, Matter and Quantity, to form the complete Sensible Substance; this Substance, so called, may be supposed to constitute the manifold world of Sense, which is not so much an essence as a quale. Thus, for the essence of fire we must look to the Reason-Principle; what produces the visible aspect is, properly speaking, a quale. Enneads VI,3,
Here a difficulty may be raised: we divide the varieties of Substance and their functions and activities, fair or foul or indeed of any kind whatsoever, on the basis of Quality, Quantity rarely, if ever, entering into the differences which produce species; Quantity, again, we divide in accordance with qualities of its own: how then are we to divide Quality itself into species? what differences are we to employ, and from what genus shall we take them? To take them from Quality itself would be no less absurd than setting up substances as differences of substances. Enneads VI,3,
We must therefore reflect whether it may be taken as an invariable rule that Quality is never a differentia of Quality, any more than Substance is a differentia of Substance, or Quantity of Quantity. Enneads VI,3,
Furthermore, it cannot lay claim to the category of Relation on the mere ground that it has an attributive and not a self-centred existence: on this ground, Quality too would find itself in that same category; for Quality is an attribute and contained in an external: and the same is true of Quantity. Enneads VI,3,
If we are agreed that Quality and Quantity, though attributive, are real entities, and on the basis of this reality distinguishable as Quality and Quantity respectively: then, on the same principle, since Motion, though an attribute has a reality prior to its attribution, it is incumbent upon us to discover the intrinsic nature of this reality. We must never be content to regard as a relative something which exists prior to its attribution, but only that which is engendered by Relation and has no existence apart from the relation to which it owes its name: the double, strictly so called, takes birth and actuality in juxtaposition with a yard’s length, and by this very process of being juxtaposed with a correlative acquires the name and exhibits the fact of being double. Enneads VI,3,
What, then, is that entity, called Motion, which, though attributive, has an independent reality, which makes its attribution possible – the entity corresponding to Quality, Quantity and Substance? But first, perhaps, we should make sure that there is nothing prior to Motion and predicated of it as its genus. Enneads VI,3,
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,
Be it so; we begin by pointing out a distinction: You take one thing with another – for we must first deal with objects of sense – a dog and a man, or two men; or you take a group and affirm ten, a decad of men: in this case the number affirmed is not a Reality, even as Reality goes in the sphere of sense, but is purely Quantity: similarly when you resolve into units, breaking up the decad, those units are your principle of Quantity since the single individual is not a unity absolute. Enneads VI,6,