MacKenna-Plotinus: Number

Now all that is Number and Reason-Principle is outside of boundlessness: these bestow bound and settlement and order in general upon all else: neither anything that has been brought under order nor any Order-Absolute is needed to bring them under order. The thing that has to be brought under order [e.g., Matter] is other than the Ordering Principle which is Limit and Definiteness and Reason-Principle. Therefore, necessarily, the thing to be brought under order and to definiteness must be in itself a thing lacking delimitation. Enneads   II,4,

If the Soul were material and had magnitude, it would be difficult, indeed quite impossible, to make it appear to be immune, unchangeable, when any of such emotions lodge in it. And even considering it as an Authentic Being, devoid of magnitude and necessarily indestructible, we must be very careful how we attribute any such experiences to it or we will find ourselves unconsciously making it subject to dissolution. If its essence is a Number or as we hold a Reason-Principle, under neither head could it be susceptible of feeling. We can think, only, that it entertains unreasoned reasons and experiences unexperienced, all transmuted from the material frames, foreign and recognized only by parallel, so that it possesses in a kind of non-possession and knows affection without being affected. How this can be demands enquiry. Enneads III,6,

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,

"A Number, a Measure, belonging to Movement?" Enneads III,7,

Time, we are told, is the number outside Movement and measuring it, like the tens applied to the reckoning of the horses and cows but not inherent in them: we are not told what this Number is; yet, applied or not, it must, like that decade, have some nature of its own. Enneads III,7,

If, then, the Soul withdrew, sinking itself again into its primal unity, Time would disappear: the origin of Time, clearly, is to be traced to the first stir of the Soul’s tendency towards the production of the sensible universe with the consecutive act ensuing. This is how "Time" – as we read – "came into Being simultaneously" with this All: the Soul begot at once the Universe and Time; in that activity of the Soul this Universe sprang into being; the activity is Time, the Universe is a content of Time. No doubt it will be urged that we read also of the orbit of the Stars being Times": but do not forget what follows; "the stars exist," we are told, "for the display and delimitation of Time," and "that there may be a manifest Measure." No indication of Time could be derived from [observation of] the Soul; no portion of it can be seen or handled, so it could not be measured in itself, especially when there was as yet no knowledge of counting; therefore the Soul brings into being night and day; in their difference is given Duality – from which, we read, arises the concept of Number. Enneads III,7,

But, if in the total the organization in which they have their being is compact of variety – as it must be since every Reason-Principle is a unity of multiplicity and variety, and may be thought of as a psychic animated organism having many shapes at its command – if this is so and all constitutes a system in which being is not cut adrift from being, if there is nothing chance – borne among beings as there is none even in bodily organisms, then it follows that Number must enter into the scheme; for, once again, Being must be stable; the members of the Intellectual must possess identity, each numerically one; this is the condition of individuality. Where, as in bodily masses, the Idea is not essentially native, and the individuality is therefore in flux, existence under ideal form can rise only out of imitation of the Authentic Existences; these last, on the contrary, not rising out of any such conjunction [as the duality of Idea and dead Matter] have their being in that which is numerically one, that which was from the beginning, and neither becomes what it has not been nor can cease to be what it is. Enneads IV,3,

Let us keep in mind what we have laid down: The being we are considering is a living unity and, therefore, necessarily self-sympathetic: it is under a law of reason, and therefore the unfolding process of its life must be self-accordant: that life has no haphazard, but knows only harmony and ordinance: all the groupings follow reason: all single beings within it, all the members of this living whole in their choral dance are under a rule of Number. Enneads IV,4,

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

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

Thus by what we call the Number and the Dyad of that higher realm, we mean Reason Principles and the Intellectual-Principle: but while the Dyad is, as regards that sphere, undetermined – representing, as it were, the underly [or Matter] of The One – the later Number [or Quantity] – that which rises from the Dyad [Intellectual-Principle] and The One – is not Matter to the later existents but is their forming-Idea, for all of them take shape, so to speak, from the ideas rising within this. The determination of the Dyad is brought about partly from its object – The One – and partly from itself, as is the case with all vision in the act of sight: intellection [the Act of the Dyad] is vision occupied upon The One. Enneads: V I

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,

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

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

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,

How then does the universal Intellect produce the particulars while, in virtue of its Reason-Principle, remaining a unity? In other words, how do the various grades of Being, as we call them, arise from the four primaries? Here is this great, this infinite Intellect, not given to idle utterance but to sheer intellection, all-embracing, integral, no part, no individual: how, we ask, can it possibly be the source of all this plurality? Number at all events it possesses in the objects of its contemplation: it is thus one and many, and the many are powers, wonderful powers, not weak but, being pure, supremely great and, so to speak, full to overflowing powers in very truth, knowing no limit, so that they are infinite, infinity, Magnitude-Absolute. Enneads VI,2,

What, then, of the "Number of the Infinite"? To begin with, how is Number consistent with infinity? Objects of sense are not unlimited and therefore the Number applying to them cannot be so. Nor is an enumerator able to number to infinity; though we double, multiply over and over again, we still end with a finite number; though we range over past and future, and consider them, even, as a totality, we still end with the finite. Enneads VI,6,

In the Intellectual the Beings are determined and with them Number, the number corresponding to their total; in this sphere of our own – as we make a man a multiple by counting up his various characteristics, his beauty and the rest – we take each image of Being and form a corresponding image of number; we multiply a non-existent in and so produce multiple numbers; if we number years we draw on the numbers in our own minds and apply them to the years; these numbers are still our possession. Enneads VI,6,

If, on the contrary, Number is a direct production of the Intellectual-Principle [an Idea in itself], there is the question whether it preceded or followed the other Ideas. Enneads VI,6,

Plato, where he says that men arrived at the conception of Number by way of the changes of day and night – thus making the concept depend upon variation among things – seems to hold that the things numerable precede and by their differences produce number: Number then would consist in a process within the human mind passing onwards from thing to thing; it results by the fact that the mind takes count, that is when the mind traverses things and reports their differences; observing pure identity unbroken by difference, it says One. But there is the passage where he tells us that the veritable Number has Being, is a Being; this is the opposed view that Number is no product of the reckoning mind but a reality in itself, the concept of which is reawakened in the mind by changes in things of sense. Enneads VI,6,

What then is the veritable nature of Number? Is it an accompaniment upon each substance, something seen in the things as in a man we see one man, in a being one being and in the total of presentations the total of number? But how explain the dyad and triad? How comes the total to be unitary and any particular number to be brought under unity? The theory offers a multiplicity of units, and no number is reducible to unity but the simple "one." It might be suggested that a dyad is that thing – or rather what is observed upon that thing – which has two powers combined, a compound thing related to a unity: or numbers might be what the Pythagoreans seem to hold them in their symbolic system in which Justice, for example, is a Tetrad: but this is rather to add the number, a number of manifold unity like the decad, to the multiplicity of the thing which yet is one thing. Now it is not so that we treat the ten things; we bring them together and apply the figure ten to the several items. Or rather in that case we say ten, but when the several items form a unity we say decad. This would apply in the Intellectual as in the sensible. Enneads VI,6,

As then there is a Life-Form primal – which therefore is the Life-Form Absolute – and there is Intellectual-Principle or Being, Authentic Being, these, we affirm, contain all living things and all Number, and Absolute Justice and Beauty and all of that order; for we ascribe an existence of their own to Absolute Man, Absolute Number, Absolute Justice. It remains to discover, in so far as such knowledge is possible, how these distinct entities come to be and what is the manner of their being. Enneads VI,6,

Thus it is clear that Number cannot be dependent upon the Living-Form since unity and duality existed before that; nor does it rise in the Intellectual-Principle since before that there existed Real Being which is both one and numerous. Enneads VI,6,

It remains then to consider whether Being by its distinction produced Number or Number produced that distinction. It is certain that either Number was the cause of Being, movement, rest, identity and difference, or these the cause of Number. Enneads VI,6,

The first question is whether Number can exist in and of itself or is dependent upon things – Two being something observed in two things, Three in three; and so of the arithmetical One, for if this could exist apart from numbered objects it could exist also before the divisions of Being. Enneads VI,6,

But could it precede Being itself? For the present we must take it that Being precedes Number, is its source. But if One means one being and the duality two beings, then unity precedes Being, and Number precedes the Beings. Enneads VI,6,

Let us consider: When we think of the existence and the fine appearance of a man as forming one thing, that unity is certainly thought of as subsequent to a precedent duality; when we group a horse with a dog, the duality is obviously the subsequent. But think of that which brings man or horse or dog into being or produces them, with full intention, from where they lie latent within itself: the producer must say "I begin with a first, I pass on to a second; that makes two; counting myself there are three." Of course there was no such numbering even of Beings for their production, since the due number was known from the very beginning; but this consideration serves to show that all Number precedes the very Beings themselves. Enneads VI,6,

But if Number thus preceded the Beings, then it is not included among them? The truth is that it existed within the Authentic Being but not as applying to it, for Being was still unparted; the potentiality of Number existed and so produced the division within Being, put in travail with multiplicity; Number must be either the substance of Being or its Activity; the Life-Form as such and the Intellectual-Principle must be Number. Clearly Being is to be, thought of as Number Collective, while the Beings are Number unfolded: the Intellectual-Principle is Number moving within itself, while the Living-Form is Number container of the universe. Even Being is the outcome of the Unity, and, since the prior is unity, the secondary must be Number. Enneads VI,6,

Hence it is that the Forms have been described as Henads and Numbers. This is the authentic Number; the other, the "monadic" is its image. The Authentic is that made manifest in the Forms and helping to bring them to be; primally it is the Number in the Authentic Being, inherent to it and preceding the Beings, serving to them as root, fount, first principle. Enneads VI,6,

When it takes lot with multiplicity, Being becomes Number by the fact of awakening to manifoldness; – before, it was a preparation, so to speak, of the Beings, their fore-promise, a total of henads offering a stay for what was to be based upon them. Enneads VI,6,

If the Beings preceded the number and this were discerned upon them at the stirring, to such and such a total, of the numbering principle, then the actual number of the Beings would be a chance not a choice; since that total is not a matter of chance, Number is a causing principle preceding that determined total. Enneads VI,6,

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

How does the mind pronounce? By being able to enumerate; that is by knowing Number: but in order to this, Number must be in existence, and that that Principle should not know its own total content is absurd, impossible. Enneads VI,6,

It is with Number as with Good. When we pronounce things to be good either we mean that they are in their own nature so or we affirm goodness as an accidental in them. Dealing with the primals, the goodness we have in mind is that First Hypostasis; where the goodness is an accidental we imply the existence of a Principle of Good as a necessary condition of the accidental presence; there must be some source of that good which is observed elsewhere, whether this source be an Absolute Good or something that of its own nature produces the good. Similarly with number; in attributing the decad to things we affirm either the truly existent decad or, where the decadhood is accidental, we necessarily posit the self-subsistent decad, decad not associated; if things are to be described as forming a decad, then either they must be of themselves the decad or be preceded by that which has no other being than that of decadhood. Enneads VI,6,

It must be urged as a general truth that anything affirmed of a subject not itself either found its way in from outside or is the characteristic Act of that subject; and supposing the predicated attribute to show no variation of presence and absence but to be always present, then, if the subject is a Real Being so also is the accidental in an equal degree; or, failing Real Being, it at least belongs to the existents, it exists. In the case when the subject can be thought of as remaining without its Act, yet that Act is inbound with it even though to our minds it appears as a later; when on the contrary the subject cannot be conceived without the attribute-man, for example, without unity – then the attribute is either not later but concomitant or, being essential to the existence, is precedent. In our view, Unity and Number are precedent. Enneads VI,6,

Supposing that first henad alone to exist, it must obviously be lodged either in the thing of completest Being or at all events in the thing most completely a unity. If in the thing of completest Being, then the other henads are but nominal and cannot be ranked with the first henad, or else Number becomes a collection of unlike monads and there are differences among monads [an impossibility]. If that first henad is to be taken as lodged in the thing of completest unity, there is the question why that most perfect unity should require the first henad to give it unity. Enneads VI,6,

Since all this is impossible, then, before any particular can be thought of as a unit, there must exist a unity bare, unrelated by very essence. If in that realm also there must be a unity apart from anything that can be called one thing, why should there not exist another unity as well? Each particular, considered in itself, would be a manifold of monads, totalling to a collective unity. If however Nature produces continuously – or rather has produced once for all – not halting at the first production but bringing a sort of continuous unity into being, then it produces the minor numbers by the sheer fact of setting an early limit to its advance: outgoing to a greater extent – not in the sense of moving from point to point but in its inner changes – it would produce the larger numbers; to each number so emerging it would attach the due quantities and the appropriate thing, knowing that without this adaptation to Number the thing could not exist or would be a stray, something outside, at once, of both Number and Reason. Enneads VI,6,

As to the How of participation, the enquiry is that of all participation in Ideal Forms; we must note, however, that the presence of the Decad in the looser totals is different from its presence in the continuous; there is difference again in its presence within many powers where multiplicity is concentred in unity; arrived at the Intellectuals, there too we discover Number, the Authentic Number, no longer entering the alien, Decad-Absolute not Decad of some particular Intellectual group. Enneads VI,6,

We must repeat: The Collective Being, the Authentic, There, is at once Being and Intellectual-Principle and the Complete Living Form; thus it includes the total of living things; the Unity There is reproduced by the unity of this living universe in the degree possible to it – for the sense-nature as such cannot compass that transcendental unity – thus that Living-All is inevitably Number-Entire: if the Number were not complete, the All would be deficient to the extent of some number, and if every number applicable to living things were not contained in it, it would not be the all-comprehending Life-Form. Therefore, Number exists before every living thing, before the collective Life-Form. Enneads VI,6,

Again: Man exists in the Intellectual and with him all other living things, both by possession of Real-Being and because that is the Life-Form Complete. Even the man of this sphere is a member of the Intellectual since that is the Life-Form Complete; every living thing by virtue of having life, is There, There in the Life-form, and man is There also, in the Intellectual, in so far as he is intellect, for all intelligences are severally members of That. Now all this means Number There. Yet even in Intellect Number is not present primally; its presence There is the reckoning of the Acts of Intellectual-Principle; it tallies with the justice in Intellectual-Principle, its moral wisdom, its virtues, its knowledge, all whose possession makes That Principle what it is. Enneads VI,6,

Next we come to Being, fully realized, and this is the seat of Number; by Number, Being brings forth the Beings; its movement is planned to Number; it establishes the numbers of its offspring before bringing them to be, in the same way as it establishes its own unity by linking pure Being to the First: the numbers do not link the lower to the First; it suffices that Being is so linked; for Being, in taking form as Number, binds its members to itself. As a unity, it suffers no division, remaining self-constant; as a thing of division, containing its chosen total of members, it knows that total and so brings forth Number, a phase therefore of its content: its development of part is ruled by the powers of Number, and the Beings it produces sum to that Number. Thus Number, the primal and true, is Principle and source of actuality to the Beings. Enneads VI,6,

Hence it is that in our sphere, also, Number accompanies the coming to be of particular things and to suppose another number than the actual is to suppose the production of something else or of nothing. 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,

But what of that "Number within us having its own manner of being"? It is the Number of our essence. "Our essence" we read "partakes of Number and harmony and, also, is Number and harmony." "Neither body nor magnitude," someone says: soul, then, is Number since it is essence. The number belonging to body is an essence of the order of body; the number belonging to soul constitutes the essences of souls. Enneads VI,6,

But what of the Infinite Number we hear of; does not all this reasoning set it under limit? And rightly so if the thing is to be a number; limitlessness and number are in contradiction. 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,

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,

It appears then that Number in that realm is definite; it is we that can conceive the "More than is present"; the infinity lies in our counting: in the Real is no conceiving more than has been conceived; all stands entire; no number has been or could be omitted to make addition possible. It might be described as infinite in the sense that it has not been measured – who is there to measure it? – but it is solely its own, a concentrated unit, entire, not ringed round by any boundary; its manner of being is settled for it by itself alone. None of the Real-Beings is under limit; what is limited, measured, is what needs measure to prevent it running away into the unbounded. There every being is Measure; and therefore it is that all is beautiful. Because that is a living thing it is beautiful, holding the highest life, the complete, a life not tainted towards death, nothing mortal there, nothing dying. Nor is the life of that Absolute Living-Form some feeble flickering; it is primal, the brightest, holding all that life has of radiance; it is that first light which the souls There draw upon for their life and bring with them when they come here. It knows for what purpose it lives, towards What it lives, from Whence it lives; for the Whence of its life is the Whither... and close above it stands the wisdom of all, the collective Intellectual-Principle, knit into it, one with it, colouring it to a higher goodness, by kneading wisdom into it, making its beauty still more august. Even here the august and veritably beautiful life is the life in wisdom, here dimly seen, There purely. For There wisdom gives sight to the seer and power for the fuller living and in that tenser life both to see and to become what is seen. Enneads VI,6,

There is nothing with which the unity would be more plausibly identified than with Being; either it is Being as a given man is man or it will correspond to the Number which rules in the realm of the particular; it will be a number applying to a certain unique thing as the number two applies to others. Enneads VI,8,

Now if Number is a thing among things, then clearly so this unity must be; we would have to discover what thing of things it is. If Number is not a thing but an operation of the mind moving out to reckon, then the unity will not be a thing. Enneads VI,8,