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  "work": {
    "slug": "ennead-6",
    "name": "Ennead VI — Being, Number, the One"
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  "parents": [
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      "slug": "plotinus-enneads",
      "name": "Enneads",
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  "chapter": {
    "num": 6,
    "slug": "6-on-numbers",
    "title": "VI.6 — On Numbers",
    "of": 9,
    "words": 9033,
    "text": "## SIXTH TRACTATE\n\n\n#### SIXTH TRACTATE.\n\nON NUMBERS.\n\n\n## Section 1\n\n\n##### Section 1\n\n1. It is suggested that multiplicity is a falling away from The\nUnity, infinity being the complete departure, an innumerable\nmultiplicity, and that this is why unlimit is an evil and we evil at\nthe stage of multiplicity.\n\nA thing, in fact, becomes a manifold when, unable to remain\nself-centred, it flows outward and by that dissipation takes\nextension: utterly losing unity it becomes a manifold since there is\nnothing to bind part to part; when, with all this outflowing, it\nbecomes something definite, there is a magnitude.\n\nBut what is there so grievous in magnitude?\n\nGiven consciousness, there will be, since the thing must feel\nits exile, its sundrance from its essence. Everything seeks not the\nalien but itself; in that outward moving there is frustration or\ncompulsion; a thing most exists not when it takes multiplicity or\nextension but when it holds to its own being, that is when its\nmovement is inward. Desire towards extension is ignorance of the\nauthentically great, a movement not on the appropriate path but\ntowards the strange; to the possession of the self the way is inward.\n\nConsider the thing that has taken extension; broken into so many\nindependent items, it is now those several parts and not the thing\nit was; if that original is to persist, the members must stand\ncollected to their total; in other words, a thing is itself not by\nbeing extended but by remaining, in its degree, a unity: through\nexpansion and in the measure of the expansion, it is less itself;\nretaining unity, it retains its essential being.\n\nYet the universe has at once extension and beauty?\n\nYes; because it has not been allowed to slip away into the\nlimitless but is held fast by unity; and it has beauty in virtue of\nBeauty not of Magnitude; it needed Beauty to parry that magnitude;\nin the degree of its extension it was void of beauty and to that\ndegree ugly. Thus extension serves as Matter to Beauty since what\ncalls for its ordering is a multiplicity. The greater the expansion,\nthe greater the disorder and ugliness.\n\n\n## Section 2\n\n\n##### Section 2\n\n2. What, then, of the \"Number of the Infinite\"?\n\nTo begin with, how is Number consistent with infinity?\n\nObjects of sense are not unlimited and therefore the Number\napplying to them cannot be so. Nor is an enumerator able to number\nto infinity; though we double, multiply over and over again, we\nstill end with a finite number; though we range over past and\nfuture, and consider them, even, as a totality, we still end with\nthe finite.\n\nAre we then to dismiss absolute limitlessness and think merely\nthat there is always something beyond?\n\nNo; that more is not in the reckoner's power to produce;\nthe total\nstands already defined.\n\nIn the Intellectual the Beings are determined and with them\nNumber, the number corresponding to their total; in this\nsphere of our\nown- as we make a man a multiple by counting up his various\ncharacteristics, his beauty and the rest- we take each image of\nBeing and form a corresponding image of number; we multiply a\nnon-existent in and so produce multiple numbers; if we\nnumber years we\ndraw on the numbers in our own minds and apply them to the years;\nthese numbers are still our possession.\n\n\n## Section 3\n\n\n##### Section 3\n\n3. And there is the question How can the infinite have existence\nand remain unlimited: whatever is in actual existence is by that\nvery fact determined numerically.\n\nBut, first, if multiplicity holds a true place among Beings, how\ncan it be an evil?\n\nAs existent it possesses unity; it is a unit-multiple, saved\nfrom stark multiplicity; but it is of a lessened unity and, by that\ninwoven multiplicity, it is evil in comparison with unity pure. No\nlonger steadfast in that nature, but fallen, it is the less, while\nin virtue of the unity thence retained it keeps some value;\nmultiplicity has value in so far as it tends to return to, unity.\n\nBut how explain the unlimited? It would seem that either it is\namong beings and so is limited or, if unlimited, is not among beings\nbut, at best, among things of process such as Time. To be brought to\nlimit it must be unlimited; not the limited but the unlimited is the\nsubject of limitation, since between the limited and the unlimited\nthere is no intermediate to accept the principle of limitation. The\nunlimited recoils by very nature from the Idea of limit,\nthough it may\nbe caught and held by it from without:- the recoil, of course, is\nnot from one place to another; the limitless can have nothing to do\nwith place which arises only with the limiting of the\nunlimited. Hence\nwhat is known as the flux of the unlimited is not to be understood\nas local change; nor does any other sort of recognisable\nmotion belong\nto it in itself; therefore the limitless cannot move: neither can it\nbe at rest: in what, since all place is later? Its movement means\nlittle more than that it is not fixed in rest.\n\nIs it, then, suspended at some one point, or rocking to and fro?\n\nNo; any such poising, with or without side motion, could be\nknown only by place [which Matter precedes].\n\nHow, then, are we to form any conception of its being?\n\nWe must fasten on the bare notion and take what that gives us-\nopposites that still are not opposed: we think of large and small\nand the unlimited becomes either, of stationary and moving, and it\nwill be either of these. But primarily it can be neither in any\ndefined degree, or at once it is under limit. Limitless in this\nunlimited and undefined way, it is able to appear as either of a\npair of opposites: draw near, taking care to throw no net of limit\nover it, and you have something that slips away; you come upon no\nunity for so it would be defined; approach the thing as a unit, and\nyou find it manifold; call it a manifold, and again you falsify, for\nwhen the single thing is not a unity neither is the total a\nmanifold. In one manifestation it takes the appearance of\nmovement, in\nanother of rest, as the mind envisages it.\n\nAnd there is movement in its lack of consciousness; it has\npassed out of Intellectual-Principle, slid away. That it cannot\nbreak free but is under compulsion from without to keep to its\ncircling with no possibility of advance, in this would be its rest.\nThus it is not true to speak of Matter as being solely in flux.\n\n\n## Section 4\n\n\n##### Section 4\n\n4. We have to enquire into the existence of the Numbers in the\nIntellectual. Are they Ideas added to the other Ideas? Or are they\nno more than necessary concomitants to the Ideas?\n\nIn the latter case, Being, as the first [in the Intellectual]\nwould give us the conception of the Monad; then since Being produces\nmotion and rest, Three exists; and so on for all the other members\nof the realm of Being. Or perhaps there is one monad for each\nmember, or a monad for the first, with a dyad for its next, since\nthere exists a series, and a corresponding number for every\nsuccessive\ntotal, decad for ten, and so on.\n\nIf, on the contrary, Number is a direct production of the\nIntellectual-Principle [an Idea in itself], there is the question\nwhether it preceded or followed the other Ideas.\n\nPlato, where he says that men arrived at the conception of\nNumber by way of the changes of day and night- thus making\nthe concept\ndepend upon variation among things- seems to hold that the things\nnumerable precede and by their differences produce number:\nNumber then\nwould consist in a process within the human mind passing onwards\nfrom thing to thing; it results by the fact that the mind\ntakes count,\nthat is when the mind traverses things and reports their\ndifferences; observing pure identity unbroken by difference, it says\nOne. But there is the passage where he tells us that the veritable\nNumber has Being, is a Being; this is the opposed view that Number\nis no product of the reckoning mind but a reality in itself, the\nconcept of which is reawakened in the mind by changes in things of\nsense.\n\n\n## Section 5\n\n\n##### Section 5\n\n5. What then is the veritable nature of Number?\n\nIs it an accompaniment upon each substance, something seen in\nthe things as in a man we see one man, in a being one being\nand in the\ntotal of presentations the total of number?\n\nBut how explain the dyad and triad? How comes the total to be\nunitary and any particular number to be brought under unity? The\ntheory offers a multiplicity of units, and no number is reducible to\nunity but the simple \"one.\" It might be suggested that a dyad is\nthat thing- or rather what is observed upon that thing- which has\ntwo powers combined, a compound thing related to a unity: or numbers\nmight be what the Pythagoreans seem to hold them in their symbolic\nsystem in which Justice, for example, is a Tetrad: but this is\nrather to add the number, a number of manifold unity like the\ndecad, to the multiplicity of the thing which yet is one thing. Now\nit is not so that we treat the ten things; we bring them together\nand apply the figure ten to the several items. Or rather in that\ncase we say ten, but when the several items form a unity we say\ndecad. This would apply in the Intellectual as in the sensible.\n\nBut how then can number, observed upon things, rank among Real\nBeings?\n\nOne answer might be that whiteness is similarly observed upon\nthings and yet is real, just as movement is observed upon things and\nthere is still a real existence of movement. But movement is not on\na par with number: it is because movement is an entity that unity\ncan be observed upon it. Besides, the kind of real existence thus\nimplied annuls the reality of number, making it no more than an\nattribute; but that cannot be since an attribute must exist before\nit can be attributed; it may be inseparable from the subject\nbut still\nmust in itself be something, some entity as whiteness is; to be a\npredicate it must be that which is to be predicated. Thus if unity\nis observed in every subject, and \"one man\" says more than \"man's\noneness being different from the manness and common to all things-\nthen this oneness must be something prior to man and to all the\nrest: only so can the unity come to apply to each and to all: it\nmust therefore be prior also to even movement, prior to Being, since\nwithout unity these could not be each one thing: of course what is\nhere meant is not the unity postulated as transcending Being but the\nunity predicable of the Ideas which constitute each several thing.\nSo too there is a decad prior to the subject in which we affirm it;\nthis prior would be the decad absolute, for certainly the thing in\nwhich the decad is observed is not that absolute.\n\nIs this unity, then, connate and coexistent to the\nBeings? Suppose\nit coexistent merely as an accidental, like health in man, it still\nmust exist of itself; suppose it present as an element in a\ncompound, there must first exist unity and the unity\nabsolute that can\nthus enter into composition; moreover if it were compounded with an\nobject brought into being by its agency it would make that\nobject only\nspuriously a unity; its entry would produce a duality.\n\nBut what of the decad? Where lies the need of decad to a thing\nwhich, by totalling to that power, is decad already?\n\nThe need may be like that of Form to Matter; ten and decad may\nexist by its virtue; and, once more, the decad must previously\nexist of its own existence, decad unattached.\n\n\n## Section 6\n\n\n##### Section 6\n\n6. Granted, then, that there exist, apart from things, a unity\nabsolute and a decad absolute in other words, that the Intellectual\nbeings, together with their characteristic essence have also their\norder, Henads, Dyads, Triads, what is the nature of these numerical\nentities and how does it come into being? We cannot but think that\nsome reason accounts for their origin.\n\nAs a beginning, what is the origin of the Ideas in general? It\nis not that the thinking principle thought of each Idea and by that\nact of thought procured their several existences; not because\nJustice and Movement were thus thought did they come to be;\nthat would\nimply that while the thought is later than the thing- the concept of\nJustice must be later than Justice itself- yet the thought precedes\nwhat, as founded on the thinking, owes its existence to it. Besides,\nif justice is only a certain definite thought we have the absurdity\nthat Justice is nothing more than a definition of Justice.\nThinking of\nJustice or Movement is but grasping their nature; this would mean\ngrasping the non-existent, an impossibility.\n\nWe may be reminded that in immaterial objects the knowledge is\nidentical with the thing; but we must not misapply that statement;\nit does not say that the knowledge is the thing known, or that the\nreason surveying the thing is the thing, but that the immaterial\nthing, being an Intellectual object is also a thought; this does not\nimply a definition or conception of the object; the thing itself, as\nbelonging to the Intellectual, can be nothing else than Intellect or\nknowledge. This is not a case of knowledge self-directed; it is that\nthe thing in the Intellectual transmutes the knowledge, which is not\nfixed like the knowledge of material things; in other words it makes\nit true knowledge, that is to say no image of the thing but the\nthing directly.\n\nThus it is not the conception of movement that brings movement\nto be; movement absolute produces that conception; it produces\nitself as at once movement and the concept of movement, for movement\nas it exists There, bound up with Being, is a concept. It is\nmovement absolute because it is the first movement- there can be\nnone till this exist- and it is the authentic Movement since\nit is not\naccidental to something else but is the activity of actual Being in\nmotion. Thus it is a real existent, though the notion of Being is\ndifferent.\n\nJustice therefore is not the thought of Justice but, as\nwe may put\nit, a state of the Intellectual-Principle, or rather an activity of\nit- an appearance so lovely that neither evening nor dawn is so\nfair, nor anything else in all the realm of sense, an Intellectual\nmanifestation self-rising, self-seen, or, rather, self-being.\n\n\n## Section 7\n\n\n##### Section 7\n\n7. It is inevitably necessary to think of all as contained\nwithin one nature; one nature must hold and encompass all; there\ncannot be as in the realm of sense thing apart from thing, here a\nsun and elsewhere something else; all must be mutually present\nwithin a unity. This is the very nature of the\nIntellectual-Principle as we may know from soul which reproduces it\nand from what we call Nature under which and by which the things of\nprocess are brought into their disjointed being while that Nature\nitself remains indissolubly one.\n\nBut within the unity There, the several entities have\neach its own\ndistinct existence; the all-embracing Intellect sees what is in it,\nwhat is within Being; it need not look out upon them since\nit contains\nthem, need not separate them since they stand for ever\ndistinct within\nit.\n\nAgainst doubters we cite the fact of participation; the\ngreatness and beauty of the Intellectual-Principle we know by the\nsoul's longing towards it; the longing of the rest towards\nsoul is set\nup by its likeness to its higher and to the possibility open to them\nof attaining resemblance through it.\n\nIt is surely inconceivable that any living thing be beautiful\nfailing a Life-Absolute of a wonderful, an ineffable, beauty: this\nmust be the Collective Life, made up of all living things, or\nembracing all, forming a unity coextensive with all, as our universe\nis a unity embracing all the visible.\n\n\n## Section 8\n\n\n##### Section 8\n\n8. As then there is a Life-Form primal- which therefore is the\nLife-Form Absolute- and there is Intellectual-Principle or Being,\nAuthentic Being, these, we affirm, contain all living things and all\nNumber, and Absolute Justice and Beauty and all of that order; for\nwe ascribe an existence of their own to Absolute Man,\nAbsolute Number,\nAbsolute Justice. It remains to discover, in so far as such\nknowledge is possible, how these distinct entities come to\nbe and what\nis the manner of their being.\n\nAt the outset we must lay aside all sense-perception; by\nIntellectual-Principle we know Intellectual-Principle. We reflect\nwithin ourselves there is life, there is intellect, not in extension\nbut as power without magnitude, issue of Authentic Being which is\npower self-existing, no vacuity but a thing most living and\nintellective- nothing more living, more intelligent, more real- and\nproducing its effect by contact and in the ratio of the contact,\nclosely to the close, more remotely to the remote. If Being is to be\nsought, then most be sought is Being at its intensest; so too the\nintensest of Intellect if the Intellectual act has worth;\nand so, too,\nof Life.\n\nFirst, then, we take Being as first in order; then\nIntellectual-Principle; then the Living-Form considered as\ncontaining all things: Intellectual-Principle, as the Act of Real\nBeing, is a second.\n\nThus it is clear that Number cannot be dependent upon the\nLiving-Form since unity and duality existed before that; nor does it\nrise in the Intellectual-Principle since before that there existed\nReal Being which is both one and numerous.\n\n\n## Section 9\n\n\n##### Section 9\n\n9. It remains then to consider whether Being by its distinction\nproduced Number or Number produced that distinction. It is certain\nthat either Number was the cause of Being, movement, rest, identity\nand difference, or these the cause of Number.\n\nThe first question is whether Number can exist in and of\nitself or\nis dependent upon things- Two being something observed in two\nthings, Three in three; and so of the arithmetical One, for if this\ncould exist apart from numbered objects it could exist also\nbefore the\ndivisions of Being.\n\nBut could it precede Being itself?\n\nFor the present we must take it that Being precedes\nNumber, is its\nsource. But if One means one being and the duality two beings, then\nunity precedes Being, and Number precedes the Beings.\n\nMentally, to our approach? Yes: and in reality of existence as\nwell.\n\nLet us consider: When we think of the existence and the fine\nappearance of a man as forming one thing, that unity is certainly\nthought of as subsequent to a precedent duality; when we\ngroup a horse\nwith a dog, the duality is obviously the subsequent. But\nthink of that\nwhich brings man or horse or dog into being or produces them, with\nfull intention, from where they lie latent within itself:\nthe producer\nmust say \"I begin with a first, I pass on to a second; that\nmakes two;\ncounting myself there are three.\" Of course there was no such\nnumbering even of Beings for their production, since the due number\nwas known from the very beginning; but this consideration serves to\nshow that all Number precedes the very Beings themselves.\n\nBut if Number thus preceded the Beings, then it is not included\namong them?\n\nThe truth is that it existed within the Authentic Being\nbut not as\napplying to it, for Being was still unparted; the potentiality of\nNumber existed and so produced the division within Being, put in\ntravail with multiplicity; Number must be either the substance of\nBeing or its Activity; the Life-Form as such and the\nIntellectual-Principle must be Number. Clearly Being is to\nbe, thought\nof as Number Collective, while the Beings are Number unfolded: the\nIntellectual-Principle is Number moving within itself, while the\nLiving-Form is Number container of the universe. Even Being is the\noutcome of the Unity, and, since the prior is unity, the secondary\nmust be Number.\n\nHence it is that the Forms have been described as Henads and\nNumbers. This is the authentic Number; the other, the\n\"monadic\" is its\nimage. The Authentic is that made manifest in the Forms and\nhelping to\nbring them to be; primally it is the Number in the Authentic Being,\ninherent to it and preceding the Beings, serving to them as root,\nfount, first principle.\n\nFor the Unity is source to Being; Being's Being is\nstayed upon the\nUnity as its safeguard from dissolution; the Unity cannot rest upon\nBeing which at that would be a unity before possessing unity; and so\nwith the decad before possessing decadhood.\n\n\n## Section 10\n\n\n##### Section 10\n\n10. When it takes lot with multiplicity, Being becomes Number by\nthe fact of awakening to manifoldness;- before, it was a\npreparation, so to speak, of the Beings, their fore-promise, a total\nof henads offering a stay for what was to be based upon them.\n\nHere with us a man will say \"I wish I had such and such\na quantity\nof gold\"- or \"such and such a number of houses.\" Gold is one thing:\nthe wish is not to bring the numerical quantity into gold\nbut to bring\nthe gold to quantity; the quantity, already present in the\nmind, is to\nbe passed on to the gold so that it acquire that numerical value.\n\nIf the Beings preceded the number and this were discerned upon\nthem at the stirring, to such and such a total, of the numbering\nprinciple, then the actual number of the Beings would be a chance\nnot a choice; since that total is not a matter of chance, Number is\na causing principle preceding that determined total.\n\nNumber then pre-exists and is the cause by which produced things\nparticipate in quantity.\n\nThe single thing derives its unity by participation in\nUnity-Absolute; its being it derives from Being-Absolute, which\nholds its Being from itself alone; a unity is a unity in virtue of\nBeing; the particular unity- where the unity is a multiple unity- is\none thing only as the Triad is; the collective Being is a unity of\nthis kind, the unity not of the monad but of the myriad or any such\ncollective number.\n\nTake a man affirming the presence of ten thousand\nthings; it is he\nthat produces the number; he does not tell us that the ten thousand\nhave uttered it; they merely exhibit their several forms; the\nenumerator's mind supplies the total which would never be\nknown if the\nmind kept still.\n\nHow does the mind pronounce?\n\nBy being able to enumerate; that is by knowing Number: but in\norder to this, Number must be in existence, and that that Principle\nshould not know its own total content is absurd, impossible.\n\nIt is with Number as with Good. When we pronounce things to be\ngood either we mean that they are in their own nature so or we\naffirm goodness as an accidental in them. Dealing with the primals,\nthe goodness we have in mind is that First Hypostasis; where the\ngoodness is an accidental we imply the existence of a Principle of\nGood as a necessary condition of the accidental presence; there must\nbe some source of that good which is observed elsewhere, whether\nthis source be an Absolute Good or something that of its own nature\nproduces the good. Similarly with number; in attributing the decad to\nthings we affirm either the truly existent decad or, where the\ndecadhood is accidental, we necessarily posit the self-subsistent\ndecad, decad not associated; if things are to be described as\nforming a decad, then either they must be of themselves the decad or\nbe preceded by that which has no other being than that of decadhood.\n\nIt must be urged as a general truth that anything affirmed of a\nsubject not itself either found its way in from outside or is the\ncharacteristic Act of that subject; and supposing the predicated\nattribute to show no variation of presence and absence but to be\nalways present, then, if the subject is a Real Being so also is the\naccidental in an equal degree; or, failing Real Being, it at least\nbelongs to the existents, it exists. In the case when the subject\ncan be thought of as remaining without its Act, yet that Act is\ninbound with it even though to our minds it appears as a later; when\non the contrary the subject cannot be conceived without the\nattribute-man, for example, without unity- then the attribute is\neither not later but concomitant or, being essential to the\nexistence,\nis precedent. In our view, Unity and Number are precedent.\n\n\n## Section 11\n\n\n##### Section 11\n\n11. It may be suggested that the decad is nothing more than so\nmany henads; admitting the one henad why should we reject the ten?\nAs the one is a real existence why not the rest? We are certainly\nnot compelled to attach that one henad to some one thing and so\ndeprive all the rest of the means to unity: since every existent\nmust be one thing, the unity is obviously common to all. This means\none principle applying to many, the principle whose existence within\nitself we affirmed to be presupposed by its manifestation outside.\n\nBut if a henad exists in some given object and further\nis observed\nin something else, then that first henad being real, there cannot be\nonly one henad in existence; there must be a multiplicity of henads.\n\nSupposing that first henad alone to exist, it must obviously be\nlodged either in the thing of completest Being or at all\nevents in the\nthing most completely a unity. If in the thing of completest Being,\nthen the other henads are but nominal and cannot be ranked with the\nfirst henad, or else Number becomes a collection of unlike monads\nand there are differences among monads [an impossibility]. If that\nfirst henad is to be taken as lodged in the thing of\ncompletest unity,\nthere is the question why that most perfect unity should require the\nfirst henad to give it unity.\n\nSince all this is impossible, then, before any particular can be\nthought of as a unit, there must exist a unity bare,\nunrelated by very\nessence. If in that realm also there must be a unity apart from\nanything that can be called one thing, why should there not exist\nanother unity as well?\n\nEach particular, considered in itself, would be a manifold of\nmonads, totalling to a collective unity. If however Nature produces\ncontinuously- or rather has produced once for all- not halting at\nthe first production but bringing a sort of continuous unity into\nbeing, then it produces the minor numbers by the sheer fact\nof setting\nan early limit to its advance: outgoing to a greater extent- not in\nthe sense of moving from point to point but in its inner changes- it\nwould produce the larger numbers; to each number so emerging it\nwould attach the due quantities and the appropriate thing, knowing\nthat without this adaptation to Number the thing could not exist or\nwould be a stray, something outside, at once, of both Number and\nReason.\n\n\n## Section 12\n\n\n##### Section 12\n\n12. We may be told that unity and monad have no real existence,\nthat the only unity is some definite object that is one\nthing, so that\nall comes to an attitude of the mind towards things\nconsidered singly.\n\nBut, to begin with, why at this should not the affirmation of\nBeing pass equally as an attitude of mind so that Being too must\ndisappear? No doubt Being strikes and stings and gives the\nimpression of reality; but we find ourselves just as vividly struck\nand impressed in the presence of unity. Besides, is this attitude,\nthis concept itself, a unity or a manifold? When we deny the unity\nof an object, clearly the unity mentioned is not supplied by the\nobject, since we are saying it has none; the unity therefore\nis within\nourselves, something latent in our minds independently of\nany concrete\none thing.\n\n[An objector speaks-] \"But the unity we thus possess comes by\nour acceptance of a certain idea or impression from things external;\nit is a notion derived from an object. Those that take the notion of\nnumbers and of unity to be but one species of the notions held to be\ninherent in the mind must allow to numbers and to unity the reality\nthey ascribe to any of the others, and upon occasion they\nmust be met;\nbut no such real existence can be posited when the concept\nis taken to\nbe an attitude or notion rising in us as a by-product of the\nobjects; this happens when we say \"This,\" \"What,\" and still more\nobviously in the affirmations \"Crowd,\" \"Festival,\" \"Army,\"\n\"Multiplicity.\" As multiplicity is nothing apart from certain\nconstituent items and the festival nothing apart from the people\ngathered happily at the rites, so when we affirm unity we are not\nthinking of some Oneness self-standing, unrelated. And there are\nmany other such cases; for instance \"on the right,\" \"Above\" and\ntheir opposites; what is there of reality about this\n\"On-the-right-ness\" but the fact that two different positions are\noccupied? So with \"Above\": \"Above\" and \"Below\" are a mere matter of\nposition and have no significance outside of this sphere.\n\nNow in answer to this series of objections our first remark is\nthat there does exist an actuality implicit in each one of the\nrelations cited; though this is not the same for all or the same for\ncorrelatives or the same for every reference to unity.\n\nBut these objections must be taken singly.\n\n\n## Section 13\n\n\n##### Section 13\n\n13. It cannot reasonably be thought that the notion of unity is\nderived from the object since this is physical- man, animal, even\nstone, a presentation of that order is something very different from\nunity [which must be a thing of the Intellectual]; if that\npresentation were unity, the mind could never affirm unity unless of\nthat given thing, man, for example.\n\nThen again, just as in the case of \"On the right\" or other such\naffirmation of relation, the mind does not affirm in some caprice\nbut from observation of contrasted position, so here it affirms\nunity in virtue of perceiving something real; assuredly the\nassertion of unity is not a bare attitude towards something\nnon-existent. It is not enough that a thing be alone and be\nitself and\nnot something else: and that very \"something else\" tells of another\nunity. Besides Otherness and Difference are later; unless\nthe mind has\nfirst rested upon unity it cannot affirm Otherness or\nDifference; when\nit affirms Aloneness it affirms unity-with-aloneness; thus unity is\npresupposed in Aloneness.\n\nBesides, that in us which asserts unity of some object is first\na unity, itself; and the object is a unity before any outside\naffirmation or conception.\n\nA thing must be either one thing or more than one, manifold: and\nif there is to be a manifold there must be a precedent unity. To\ntalk of a manifold is to talk of what has something added to\nunity; to\nthink of an army is to think of a multitude under arms and brought\nto unity. In refusing to allow the manifold to remain manifold, the\nmind makes the truth clear; it draws a separate many into one,\neither supplying a unity not present or keen to perceive the unity\nbrought about by the ordering of the parts; in an army, even, the\nunity is not a fiction but as real as that of a building erected\nfrom many stones, though of course the unity of the house is more\ncompact.\n\nIf, then, unity is more pronounced in the continuous, and more\nagain where there is no separation by part, this is clearly because\nthere exists, in real existence, something which is a Nature or\nPrinciple of Unity. There cannot be a greater and less in the\nnon-existent: as we predicate Substance of everything in sense, but\npredicate it also of the Intellectual order and more strictly there-\nsince we hold that the greater and more sovereign substantiality\nbelongs to the Real Beings and that Being is more marked in\nSubstance,\neven sensible Substance, than in the other Kinds- so,\nfinding unity to\nexhibit degree of more and less, differing in sense-things as well\nas in the Intellectual, we must similarly admit that Unity exists\nunder all forms though still by reference, only, to that\nprimal Unity.\n\nAs Substance and Real Being, despite the participation of the\nsensible, are still of the Intellectual and not the sensible\norder, so\ntoo the unity observed present in things of sense by participation\nremains still an Intellectual and to be grasped by an Intellectual\nAct. The mind, from a thing present to it, comes to knowledge of\nsomething else, a thing not presented; that is, it has a prior\nknowledge. By this prior knowledge it recognises Being in a\nparticular\nbeing; similarly when a thing is one it can affirm unity as it can\naffirm also duality and multiplicity.\n\nIt is impossible to name or conceive anything not making one or\ntwo or some number; equally impossible that the thing should\nnot exist\nwithout which nothing can possibly be named or conceived; impossible\nto deny the reality of that whose existence is a necessary condition\nof naming or affirming anything; what is a first need,\nuniversally, to\nthe formation of every concept and every proposition must\nexist before\nreasoning and thinking; only as an existent can it be cited\nto account\nfor the stirring of thought. If Unity is necessary to the\nsubstantial existence of all that really is- and nothing exists\nwhich is not one- Unity must precede Reality and be its author. It\nis therefore, an existent Unity, not an existent that develops\nUnity; considered as Being-with-Unity it would be a manifold,\nwhereas in the pure Unity there is no Being save in so far as Unity\nattends to producing it. As regards the word \"This,\" it is nat a\nbare word; it affirms an indicated existence without using the name,\nit tells of a certain presence, whether a substance or some other\nexistent; any This must be significant; it is no attitude of the\nmind applying itself to a non-existent; the This shows a thing\npresent, as much as if we used the strict name of the object.\n\n\n## Section 14\n\n\n##### Section 14\n\n14. To the argument touching relation we have an answer surely\nlegitimate:\n\nThe Unity is not of a nature to lose its own manner of being\nonly because something else stands in a state which it does\nnot itself\nshare; to stray from its unity it must itself suffer division into\nduality or the still wider plurality.\n\nIf by division the one identical mass can become a\nduality without\nloss of quantity, clearly the unity it possessed and by this\ndestructive division lost was something distinct. What may be\nalternatively present and absent to the same subject must be classed\namong Real-Beings, regardless of position; an accidental\nelsewhere, it\nmust have reality in itself whether it be manifested in things of\nsense or in the Intellectual- an accidental in the Laters but\nself-existent in the higher, especially in the First in its aspect\nof Unity developing into Being. We may be told that Unity may lose\nthat character without change in itself, becoming duality by\nassociation with something else; but this is not true; unity does\nnot become two things; neither the added nor what takes the addition\nbecomes two; each remains the one thing it was; the duality is\npredicable of the group only, the unity remaining unchanged\nin each of\nthose unchanged constituents.\n\nTwo and the Dyad are not essentially relative: if the only\ncondition to the construction of duality were meeting and\nassociation such a relation might perhaps constitute Twoness and\nDuality; but in fact we see Duality produced by the very opposite\nprocess, by the splitting apart of a unity. This shows that duality-\nor any other such numerical form- is no relation produced either by\nscission or association. If one configuration produces a certain\nthing it is impossible that the opposite should produce the same so\nthat the thing may be identified with the relation.\n\nWhat then is the actual cause?\n\nUnity is due to the presence of Unity; duality to that\nof Duality;\nit is precisely as things are white by Whiteness, just by Justice,\nbeautiful by Beauty. Otherwise we must reject these universals and\ncall in relation here also: justice would arise from a certain\nattitude in a given situation, Beauty from a certain pattern of the\nperson with nothing present able to produce the beauty,\nnothing coming\nfrom without to effect that agreeable appearance.\n\nYou see something which you pronounce to be a unity; that thing\npossesses also size, form, and a host of other characteristics you\nmight name; size, bulk, sweetness, bitterness and other Ideas are\nactually present in the thing; it surely cannot be thought\nthat, while\nevery conceivable quality has Real-Being, quantity [Number] has not\nand that while continuous quantity exists, discrete quantity does\nnot and this though continuous quantity is measured by the discrete.\nNo: as size by the presence of Magnitude, and Oneness by the\npresence of Unity, so with Duality and all the other numerical modes.\n\nAs to the How of participation, the enquiry is that of all\nparticipation in Ideal Forms; we must note, however, that\nthe presence\nof the Decad in the looser totals is different from its presence in\nthe continuous; there is difference again in its presence within\nmany powers where multiplicity is concentred in unity; arrived at\nthe Intellectuals, there too we discover Number, the\nAuthentic Number,\nno longer entering the alien, Decad-Absolute not Decad of some\nparticular Intellectual group.\n\n\n## Section 15\n\n\n##### Section 15\n\n15. We must repeat: The Collective Being, the Authentic,\nThere, is\nat once Being and Intellectual-Principle and the Complete\nLiving Form;\nthus it includes the total of living things; the Unity There is\nreproduced by the unity of this living universe in the\ndegree possible\nto it- for the sense-nature as such cannot compass that\ntranscendental\nunity- thus that Living-All is inevitably Number-Entire: if\nthe Number\nwere not complete, the All would be deficient to the extent of some\nnumber, and if every number applicable to living things were not\ncontained in it, it would not be the all-comprehending Life-Form.\nTherefore, Number exists before every living thing, before the\ncollective Life-Form.\n\nAgain: Man exists in the Intellectual and with him all other\nliving things, both by possession of Real-Being and because that is\nthe Life-Form Complete. Even the man of this sphere is a\nmember of the\nIntellectual since that is the Life-Form Complete; every living\nthing by virtue of having life, is There, There in the Life-form,\nand man is There also, in the Intellectual, in so far as he is\nintellect, for all intelligences are severally members of That. Now\nall this means Number There. Yet even in Intellect Number is not\npresent primally; its presence There is the reckoning of the Acts of\nIntellectual-Principle; it tallies with the justice in\nIntellectual-Principle, its moral wisdom, its virtues, its\nknowledge, all whose possession makes That Principle what it is.\n\nBut knowledge- must not this imply presence to the alien? No;\nknowledge, known and knower are an identity; so with all the rest;\nevery member of Intellectual-Principle is therefore present to it\nprimally; justice, for example, is not accidental to it as to soul\nin its character as soul, where these virtues are mainly potential\nbecoming actual by the intention towards Intellectual-Principle and\nassociation with it.\n\nNext we come to Being, fully realized, and this is the seat of\nNumber; by Number, Being brings forth the Beings; its movement is\nplanned to Number; it establishes the numbers of its offspring\nbefore bringing them to be, in the same way as it establishes its\nown unity by linking pure Being to the First: the numbers do not\nlink the lower to the First; it suffices that Being is so linked;\nfor Being, in taking form as Number, binds its members to\nitself. As a\nunity, it suffers no division, remaining self-constant; as a thing\nof division, containing its chosen total of members, it knows that\ntotal and so brings forth Number, a phase therefore of its content:\nits development of part is ruled by the powers of Number, and the\nBeings it produces sum to that Number. Thus Number, the primal and\ntrue, is Principle and source of actuality to the Beings.\n\nHence it is that in our sphere, also, Number accompanies the\ncoming to be of particular things and to suppose another number than\nthe actual is to suppose the production of something else or of\nnothing.\n\nThese then are the primal numbers; they are numerable;\nthe numbers\nof the other order are of a double character; as derived from the\nfirst numbers they are themselves numerable but as acting for those\nfirst they are measures of the rest of things, numbering numbers and\nnumerables. For how could they declare a Decad save in the light of\nnumbers within themselves?\n\n\n## Section 16\n\n\n##### Section 16\n\n16. But here we may be questioned about these numbers which we\ndescribe as the primal and authentic:\n\n\"Where do you place these numbers, in what genus among Beings?\nTo everyone they seem to come under Quantity and you have certainly\nbrought Quantity in, where you say that discrete Quantity\nequally with\nthe continuous holds place among Beings; but you go on to say that\nthere are the numbers belonging to the Firsts and then talk of other\nnumbers quite distinct, those of reckoning; tell us how you arrange\nall this, for there is difficulty here. And then, the unity in\nsense-things- is that a quantity or is quantity here just so many\nunits brought together, the unity being the starting-point\nof quantity\nbut not quantity itself? And, if the starting-point, is it a kindred\nthing or of another genus? All this you owe it to us to make clear.\"\n\nBe it so; we begin by pointing out a distinction:\n\nYou take one thing with another- for we must first deal with\nobjects of sense- a dog and a man, or two men; or you take a\ngroup and\naffirm ten, a decad of men: in this case the number affirmed is not a\nReality, even as Reality goes in the sphere of sense, but is purely\nQuantity: similarly when you resolve into units, breaking up the\ndecad, those units are your principle of Quantity since the single\nindividual is not a unity absolute.\n\nBut the case is different when you consider one man in\nhimself and\naffirm a certain number, duality, for example, in that he is at once\nliving and reasoning.\n\nBy this analysis and totalling, you get quantity; but there are\ntwo objects under consideration and each of these is one; each of\nthe unities contributes to the complete being and the oneness is\ninherent in each; this is another kind of number; number essential;\neven the duality so formed is no posterior; it does not signify a\nquantity apart from the thing but the quantity in the essence which\nholds the thing together. The number here is no mere result of your\ndetailing; the things exist of themselves and are not\nbrought together\nby your reckoning, but what has it to do with essential reality that\nyou count one man in with another? There is here no resultant unity\nsuch as that of a choir- the decad is real only to you who count\nthe ten; in the ten of your reckoning there cannot be a decad without\na unitary basis; it is you that make the ten by your counting, by\nfixing that tenness down to quantity; in choir and army there is\nsomething more than that, something not of your placing.\n\nBut how do you come to have a number to place?\n\nThe Number inherent apart from any enumeration has its own\nmanner of being, but the other, that resulting upon the appearance\nof an external to be appraised by the Number within yourself, is\neither an Act of these inherent numbers or an Act in accordance with\nthem; in counting we produce number and so bring quantity into being\njust as in walking we bring a certain movement into being.\n\nBut what of that \"Number within us having its own manner of\nbeing\"?\n\nIt is the Number of our essence. \"Our essence\" we read \"partakes\nof Number and harmony and, also, is Number and harmony.\"\n\"Neither body\nnor magnitude,\" someone says: soul, then, is Number since it is\nessence. The number belonging to body is an essence of the order of\nbody; the number belonging to soul constitutes the essences of souls.\n\nIn the Intellectuals, all, if the Absolute Living-Form,\nthere is a\nmultiple- a triad, let us say- that Triad of the Living-Form\nis of the\nnature of essence: and the Triad prior to any living thing, Triad in\nthe realm of Being, is a principle of essence.\n\nWhen you enumerate two things- say, animal and beauty- each of\nthese remains one thing; the number is your production; it lay\nwithin yourself; it is you that elaborate quantity, here the\ndyad. But\nwhen you declare virtue to be a Tetrad, you are affirming a Tetrad\nwhich does actually exist; the parts, so to speak, make one\nthing; you\nare taking as the object of your act a Unity- Tetrad to which you\naccommodate the Tetrad within yourself.\n\n\n## Section 17\n\n\n##### Section 17\n\n17. But what of the Infinite Number we hear of; does not all\nthis reasoning set it under limit?\n\nAnd rightly so if the thing is to be a number; limitlessness and\nnumber are in contradiction.\n\nHow, then, do we come to use the term? Is it that we think of\nNumber as we think of an infinite line, not with the idea that any\nsuch lire exists but that even the very greatest- that of\nthe [path of\nthe] universe, for example- may be thought of as still greater? So\nit might be with number; let it be fixed, yet we still are free to\nthink of its double, though not of course to produce the doubled\nquantity since it is impossible to join to the actual what is no\nmore than a conception, a phantasm, private to ourselves.\n\nIt is our view that there does exist an infinite line, among the\nIntellectual Beings: for There a line would not be quantitative and\nbeing without quantity could be numerically infinite. This however\nwould be in another mode than that of limitless extension. In what\nmode then? In that the conception of the Absolute Line does not\ninclude the conception of limit.\n\nBut what sort of thing is the Line in the Intellectual and what\nplace does it hold?\n\nIt is later than Number since unity is observed in it;\nit rises at\none point and traverses one course and simply lacks the quantity\nthat would be the measure of the distance.\n\nBut where does this thing lie? Is it existent only in\nthe defining\nthought, so to speak?\n\nNo; it is also a thing, though a thing of the Intellectual. All\nthat belongs to that order is at once an Intellectual and in some\ndegree the concrete thing. There is a position, as well as a\nmanner of\nbeing, for all configurations, for surface, for solid. And certainly\nthe configurations are not of our devising; for example, the\nconfigurations of the universe are obviously antecedent to\nourselves; so it must be with all the configurations of the things\nof nature; before the bodily reproductions all must exist There,\nwithout configuration, primal configurations. For these primals are\nnot shapes in something; self-belonging, they are perfect without\nextension; only the extended needs the external. In the sphere of\nReal-Being the configuration is always a unity; it becomes discrete\neither in the Living-Form or immediately before: I say \"becomes\ndiscrete\" not in the sense that it takes magnitude There but that it\nis broken apart for the purpose of the Living-Form and is allotted\nto the bodies within that Form- for instance, to Fire There, the\nIntellectual Pyramid. And because the Ideal-Form is There,\nthe fire of\nthis sphere seeks to produce that configuration against the check of\nMatter: and so of all the rest as we read in the account of the\nrealm of sense.\n\nBut does the Life-Form contain the configurations by the\nmere fact\nof its life?\n\nThey are in the Intellectual-Principle previously but they also\nexist in the Living-Form; if this be considered as including the\nIntellectual-Principle, then they are primally in the Life-Form, but\nif that Principle comes first then they are previously in\nthat. And if\nthe Life-Form entire contains also souls, it must certainly be\nsubsequent to the Intellectual-Principle.\n\nNo doubt there is the passage \"Whatever Intellect sees in the\nentire Life-Form\"; thus seeing, must not the\nIntellectual-Principle be\nthe later?\n\nNo; the seeing may imply merely that the reality comes into being\nby the fact of that seeing; the Intellectual-Principle is\nnot external\nto the Life-Form; all is one; the Act of the Intellectual-Principle\npossesses itself of bare sphere, while the Life-Form holds the\nsphere as sphere of a living total.\n\n\n## Section 18\n\n\n##### Section 18\n\n18. It appears then that Number in that realm is definite; it is\nwe that can conceive the \"More than is present\"; the infinity lies\nin our counting: in the Real is no conceiving more than has been\nconceived; all stands entire; no number has been or could be omitted\nto make addition possible. It might be described as infinite in the\nsense that it has not been measured- who is there to measure it?-\nbut it is solely its own, a concentrated unit, entire, not ringed\nround by any boundary; its manner of being is settled for it\nby itself\nalone. None of the Real-Beings is under limit; what is limited,\nmeasured, is what needs measure to prevent it running away into the\nunbounded. There every being is Measure; and therefore it is that\nall is beautiful. Because that is a living thing it is beautiful,\nholding the highest life, the complete, a life not tainted towards\ndeath, nothing mortal there, nothing dying. Nor is the life of that\nAbsolute Living-Form some feeble flickering; it is primal, the\nbrightest, holding all that life has of radiance; it is that first\nlight which the souls There draw upon for their life and bring with\nthem when they come here. It knows for what purpose it lives,\ntowards What it lives, from Whence it lives; for the Whence of its\nlife is the Whither... and close above it stands the wisdom of all,\nthe collective Intellectual-Principle, knit into it, one with it,\ncolouring it to a higher goodness, by kneading wisdom into it,\nmaking its beauty still more august. Even here the august and\nveritably beautiful life is the life in wisdom, here dimly\nseen, There\npurely. For There wisdom gives sight to the seer and power for the\nfuller living and in that tenser life both to see and to become what\nis seen.\n\nHere attention is set for the most part upon the unliving and,\nin the living, upon what is lifeless in them; the inner life is\ntaken only with alloy: There, all are Living Beings, living wholly,\nunalloyed; however you may choose to study one of them apart from\nits life, in a moment that life is flashed out upon you:\nonce you have\nknown the Essence that pervades them, conferring that unchangeable\nlife upon them, once you perceive the judgement and wisdom and\nknowledge that are theirs, you can but smile at all the lower nature\nwith its pretention to Reality.\n\nIn virtue of this Essence it is that life endures, that the\nIntellectual-Principle endures, that the Beings stand in their\neternity; nothing alters it, turns it, moves it; nothing, indeed, is\nin being besides it to touch it; anything that is must be\nits product;\nanything opposed to it could not affect it. Being itself could not\nmake such an opposite into Being; that would require a prior to both\nand that prior would then be Being; so that Parmenides was right\nwhen he taught the identity of Being and Unity. Being is thus beyond\ncontact not because it stands alone but because it is Being.\nFor Being\nalone has Being in its own right.\n\nHow then can we deny to it either Being or anything at all that\nmay exist effectively, anything that may derive from it?\n\nAs long as it exists it produces: but it exists for ever; so,\ntherefore, do its products. And so great is it in power and beauty\nthat it remains the allurer, all things of the universe\ndepending from\nit and rejoicing to hold their trace of it and through that to seek\ntheir good. To us, existence is before the good; all this world\ndesires life and wisdom in order to Being; every soul and every\nintellect seeks to be its Being, but Being is sufficient to itself.",
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