5.1 The Context of the Quest for the Notion of Number (V.5.4–5 and VI.6.1)

Plotinus also deals with the topic of unity and multiplicity in treatise VI.6 On Numbers, which is, as mentioned in the “Introduction”, a sort of supplement to the Großschrift elaborating on the discussion of number started in V.5.4–5. The main topic of treatise V.5 is the correct understanding of Intellect, its contents and its relation to the Good. Its focus is, however, explicitly on the question of unity and multiplicity. In V.5.1, Plotinus states that “we shall proceed to investigate how truth and the intelligible and Intellect are related [in this unity-in-duality; added by Armstrong]: are they together in one and the same reality, but also two and diverse, or how are they related?” (V.5.1.35–38). In V.5.4, he is thus concerned with specifying the goal of the ascent to the One, which must be truly one (ἓν ὄντως) rather than one to the same degree as it is many or one by participation. This is, however, also the case of Intellect, as we have seen in VI.2.10 (cf. section 4.3). Even the slightest departure from the stillness of the union with the One is a progression towards duality (δύο) derived from the One, i.e. towards multiplicity, although the monad also comes into existence prior to it. Since what comes after the One is Intellect, these two principles, the monad and the dyad, must somehow be related to it, but we do not learn how in this passage. Instead, Plotinus briefly sketches some of the problems that he will deal with in treatise VI.6. What is the relationship of the monad to the dyad? It is not present in the dyad as a unit, nor is it an essential number (οὐσιώδης ἀριθμός) which continually gives existence (ὁ τὸ εἶναι ἀεὶ παρέχων, scil. ἀριθμός; O.G.), nor is it a quantitative number (ὁ τοῦ ποσοῦ, scil. ἀριθμός; O.G.), which under certain circumstances gives quantity (ὁ τὸ ποσὸν, scil. ἀριθμός παρέχων; O.G.). The relationship between the quantitative numbers, essential numbers and the One is described as well, but only briefly and enigmatically. Plotinus says that the nature which belongs to the quantitative numbers imitates the relationship of essential number to the One. But how, then, is the dyad one and how are its units one? Plotinus’ short answer here is that they are one by participation in the first monad (μετέχειν τῆς πρώτης, scil. μονάδος). They participate in it in another way than the dyad itself does, just as different sensible things (e.g. an army or a house) are one in different ways. That said, are the units in various numbers then one in the same way or in a different way? And what about different numbers (cf. V.5.4.1–35)?

In V.5.5, Plotinus continues with his preliminary remarks on the topic of the generation of numbers and beings. The One, he claims, remains the same (μένει τὸ πρῶτον τὸ αὐτό) even if other things come into being from it. All beings participate (μεταλαμβάνω, μετάληψις) in the One, though in different ways, while it gives them being (οὐσία) and makes them a sort of trace of itself in being (ἴχνος τοῦ ἑνός; cf. V.5.5.12–14).¹ In a way analogous to how beings are generated from the One, there is another one which makes number (ποιοῦντος δὲ ἄλλου, scil. τοῦ ἑνός; H-S). Number comes into existence on the model of such a one (κατ’ αὐτό; cf. V.5.5.1–4). This other one is specified a few lines later to be the form (εἶδος) of number and called the monad (μονάς; cf. V.5.5.7–12). Plotinus himself, however, corrects this analogy. In contrast to the case of numbers, the One is sufficient to create beings, so that there is no need for the other one (cf. V.5.5.6–8), i.e. for the monad.² However, since V.5 precedes VI.6, and since, in VI.6.5.35–38, Plotinus does say that there is another one of this kind prior to forms, and that it is not the One, the direct participation model of all beings in the One might be challenged. Do they not rather participate in the One through the monad? One way of resolving this ambiguity might be to highlight the different contexts in which these claims are made in treatises V.5 and VI.6 (but also V.1), stressing the fact that Plotinus does not want to multiply the number of hypostases as the Gnostics do. Consequently, the direct participation model would be the only possibility. On the other hand, one could question the validity of the context argument, at least in the case of V.5 and VI.6, which are directly related both by their topic and by their chronological order. Moreover, the addition of a participated aspect of the One (like the monad) developed its own tradition in later Neoplatonism.³ But is the monad then a new hypostasis? Probably not. Rather, it must have some specific function within the Intellect, like that of a principle, as we already know from treatise VI.2. Does it, then, connect all beings to the One? We shall return to this question later (cf. section 5.3).

At this point, we can only speculate: the problem of whether all beings participate in the One directly or through a monad, seems analogous to the problem of the participation of sensibles in the forms of Intellect. As we have seen (cf. section 2.3), there are passages in the Enneads which support the model of direct participation, and others that situate soul as an intermediary between Intellect and sensibles. In discussing this topic, I have tried to present both versions as compatible, such that placing soul as an agent of participation represents a more developed version of the direct participation model, which, at the same time, more aptly captures the derivation of everything posterior to Intellect from it. Furthermore, when discussed in the context of other issues, the direct model may simply be more concise. Consequently, I would propose to adopt a similar attitude, i.e. to understand the version favouring the monad as a more developed account. At the same time, however, we ought to observe that the statements that support the idea of the direct activity of the One on the indefinite dyad better depict the derivation of Intellect from the One or may simply be used as a shortcut.

From these introductory remarks, we can see that much is at stake here: not only the question of the unity of different entities and the clarification of the still-cryptic notion of substantial number, which ought, in some sense, to be the giver of existence, but also the question of its relation to the One, to the monad and to quantitative number. Treatise VI.6 deals with these topics, but approaches them from a new perspective. It starts with the more general question of how multiplicity (πλῆθος) is to be understood and of whether innumerable multiplicity (πλῆθος ἀνάριθμον) or infinity (ἀπειρία) is a total falling away from the One (ἀπόστασις παντελής, scil. τοῦ ἑνός; O.G.) and evil (τὸ κακόν) and, if so, what consequences this has for our own value. Are we evil insofar as we are multiple (cf. VI.6.1.1–4)? Plotinus’ answer to this question involves making a distinction between: 1) multiplicity (πλῆθος), which designates the pouring out of a thing from itself, its extension in scattering (ἐκτείνηται σκιδνάμενον), its inability to tend to itself and its being utterly deprived of the one, and 2) magnitude (μέγεθος), which refers to the abiding of a thing in its outpouring (cf. VI.6.1.4–8). Magnitude might, in a sense, be considered dreadful (δεινὸν), because it is the product of a misguided seeking of itself outside itself or, as Plotinus puts it, of a desire (ἔφεσις) to be great (μέγα; cf. VI.6.1.8–16). Plotinus illustrates this with the dispersion of a whole, which gives rise to autonomous existence of its parts, but the whole itself perishes when its parts stop tending towards its one. In losing its one, a thing loses itself (cf. VI.6.1.17–23).

5.2 Defined Multiplicity, Form of Beauty and the Indefinite Dyad (VI.6.1–3)

An example of a defined multiplicity is the universe (τὸ πᾶν), which is both beautiful and large (μέγα καὶ καλόν), due to the fact that it has been circumscribed by one (περιελήφθη ἑνί) and not dispersed into infinity (cf. VI.6.1.23–25). At the same time, it is said to be beautiful through beauty (τῷ καλῷ) and not through its being large. On the contrary, its largeness would, on its own, be the source of ugliness and is itself quite disorderly and quite ugly (μᾶλλον ἄκοσμον, μᾶλλον αἰσχρόν). It is in need of beauty, because it is large and its largeness is, as Plotinus puts it, the matter of beauty which brings order (κόσμος) into what is many (πολύ; cf. VI.6.1.25–29). Plotinus brings this line of thought to a conclusion somewhat later when he says that multiplicity is not allowed to be altogether multiple (πάντη πλῆθος), but is always unified (ἥνωται) and, as such, both one and many (ἓν ὂν πλῆθος). It is worse than the One when compared to it, but because it turned back to the One and has one in itself, it preserves its majesty (σεμνόν; cf. VI.6.3.1–10).

These passages explicitly confirm what we have discovered about beauty so far. The universe is said to be beautiful on account of its being circumscribed by one, while its largeness, representing its multiplicity, is rather the source of its ugliness. Beauty is thus connected with the presence of unity in multiplicity, a unity which is itself worse than the One but has its own value and majesty when contrasted with utter multiplicity. At the same time, it is rather surprising that Plotinus uses beauty in the dative (τῷ καλῷ), which is standard in Plato for expressing the causation of an attribute of a sensible thing by a form (cf. locus classicus Phd. 100c–e). The impression that Plotinus is referring to the form of beauty is even strengthened by the statement that largeness is called the matter of beauty, once again implying that beauty is a form. Furthermore, later on in VI.6.8, Plotinus speaks in the same spirit about the absolutely righteous, beautiful and all other such things (δίκαιον αὐτὸ καὶ καλὸν καὶ ὅσα ἄλλα τοιαῦτα; cf. VI.6.8.3–4), and, in VI.6.14, he explicitly claims, that a beautiful thing is beautiful by the presence of beauty (καλὸν καλοῦ παρουσίᾳ, scil. ἐστι καλόν; O.G.) exactly as a thing that is white, one, two or just is that way on account of the presence of whiteness, the one, the dyad or the just (cf. VI.6.14.28–30).

In order to be able to evaluate these expressions for the purpose of reconstructing Plotinus’ notion of beauty, let me first lay out the possible explanations: 1) Plotinus changed his mind and in treatise VI.6, he considers beauty to be a form among other forms, like those of whiteness, justice, the one or the dyad; 2) He did not change his mind and what is said here is the same as what is said in treatises I.6 and V.8; 3) Plotinus is not speaking properly here and the presupposition of the existence of the form of beauty only serves dialectical purposes, but is not a claim to which he subscribes.

It seems to me that the first option can be dismissed right away, because even if we were to accept some form of developmental theory of Plotinus’ thought, it would still be strange that the existence of the form of beauty is not mentioned in treatise V.8, which is very closely connected to VI.6. I do not see how the elaboration of the doctrine of numbers could lead to such a substantial shift in Plotinus’ notion of beauty that we could argue in favour of a development between treatises V.8[32] and VI.6[34]. Moreover, many of Plotinus’ brief comments on the topic of number from much earlier treatises (like V.1[10] or V.4[7]) are compatible with those from VI.6, which seems to suggest that Plotinus had in mind at least the contours of the doctrine of number when he was writing treatise V.8. Moreover, the “forms” listed in VI.6.14 should attract our attention, even if we put beauty aside for a moment. First of all, both what we know about the one in Intellect and what we will learn about it later in VI.6 is not compatible with its being listed along with whiteness and the just, as if they functioned in the same way in Intellect. It seems rather that Plotinus here, as elsewhere, is attacking rival conceptions and using whatever arguments come to mind or, at least, allowing himself to speak imprecisely for the sake of the argument. Second, the just and the beautiful, at least, are typical Platonic examples of forms and Plotinus is perhaps “quoting” Plato from memory in order to take his ideas into account.

The second option for reconciling the passages at issue, that of interpreting the aforementioned statements about the form of beauty as being identical to what is said in the two treatises on beauty, does not seem convincing either. Plotinus clearly avoids talking about the existence of the form of beauty in I.6.2 and V.8.1, simply connecting beauty to the presence of a form (cf. sections 2.3 and 3.2). I can hardly believe that Plotinus is imprecise in his utterances about the existence of a form of beauty in treatises devoted to this very topic. That said, one could perhaps try to avoid the conflict between VI.6, on the one hand, and I.6 and V.8, on the other, by saying that, in the end, each form is all of the other forms in Intellect. In this sense, it would be possible to say that a thing becomes beautiful by partaking in any given form and, through this form, in the form of beauty. However, even this is to a great extent unpersuasive. Why, then, does a thing not become all things in the Intellect, if these are so easily interchangeable? The intelligibles do not form a complete, undifferentiated unity, but are “a richly variegated one keeping its many together in one” (VI.2.2.3), i.e. they are at the same time same and other, or as Proclus puts it, they are auto kai allo (Elem. Theol., Prop. 176). It is therefore impossible to deal with the problem of the existence of a form of beauty by placing the emphasis on the interchangeability of the forms, since it is not absolute. And even if this reasoning were correct, why would Plotinus keep silent about it in the two treatises devoted to beauty?

It seems to me that this leaves us with the third option, which, however, is perhaps not merely a default solution, but one that has its own rationale. None of the three passages that imply the existence of a form of beauty deals with this topic, but only mention it in passing. In VI.6.1, Plotinus focuses on the elaboration of the opposition between defined multiplicity (μέγεθος) and infinite multiplicity (πλῆθος), in order to emphasise the ethical dimension of his enquiry. In VI.6.8, he is trying to express the fact that Intellect, as the living being, contains all that is and that beauty is something existent. Moreover, this testimony in favour of the existence of a form of beauty might be further weakened, given that Plotinus immediately adds that it remains to be considered how all of the contents of Intellect that have been named exist and what they are (cf. VI.6.8.6–7 and my comments in section 5.3). Finally, in VI.6.14, Plotinus is interested in freeing the notion of number from being understood as a relation, treating number here (i.e. the one and the dyad) as forms similar to those of white, beautiful or just, for the sake of the argument. As we shall see, however, numbers are not, in fact, simply forms, but rather designate the limited nature of each form. Number is, in this sense, the structural principle of Intellect as a whole (see section 5.3). The three passages from VI.6 that seem to suggest the existence of a form of beauty might each be interpreted as advocating it only for dialectical purposes. It therefore seems reasonable to ignore these implications and to refuse to posit a form of beauty.⁴

But let me return to the analysis of VI.6. In what follows, Plotinus turns to the problem of the number of the infinite (ἀριθμός τῆς ἀπειρίας; cf. VI.6.2) and the existence of the infinite as such (τὸ ἄπειρον; cf. VI.6.3), and expounds on it as the great and the small (μέγα καὶ σμικρόν, cf. VI.6.3.29), i.e. as what is known in the Platonic tradition as the indefinite dyad (ἀόριστος δυάς).⁵ As Slaveva-Griffin points out, Plotinus needs to “address Aristotle’s misconception of Plato’s reference to the Indefinite Dyad and infinite number”, which he does in sections VI.6.2–3 in order to show “how multiplicity, as number, unfolds into the universe”, because “numbers originate from the Indefinite Dyad” (Slaveva-Griffin 2009, p. 56). The notion of the infinite is, from the very beginning, contrasted with that which is limited (ὁρίζω) and as something which requires limit from outside, it is revealed as precisely unlimited or infinite (cf. VI.6.3.10–15). In itself, it could be depicted as an escape (φεύγει, scil. τὸ ἄπειρον; O.G.) from limit, but this flight is “caught by being surrounded externally” (VI.6.3.16–17). In trying to delimit it, we always miss its elusive nature (cf. VI.6.3.33–35 and the use of the verb ὑπεκφεύγω) and it always emerges as its opposite. Thus, it is to be understood as the simultaneity of opposites, which are also not opposites (cf. VI.6.3.28–29), i.e. precisely insofar as they are the indefinite dyad. As such, it plays the role of the principle of multiplicity, which receives limit and is defined by number, thus becoming all of the forms of the Intellect (cf. the above-mentioned V.1.5, Nikulin 1998a, p. 92, and Slaveva-Griffin 2009, p. 71).

5.3 Number in the Intelligible (VI.6.4–8)

Plotinus then turns to the main topic of the treatise, which is how the numbers exist in the intelligible. Basically, he considers three options: 1) Number is posterior to the forms (ὡς ἐπιγινομένων τοῖς ἄλλοις εἴδεσιν; cf. VI.6.4.1–2); 2) Number is simultaneous with the forms (συνεγεννήθη; παρακολουθούντων; cf. VI.6.4.1–3 and 6–9); 3) It is possible to think number itself in itself (αὐτὸς ἐφ’ ἑαυτοῦ; cf. VI.6.4.9–11). Plotinus dismisses the hypothesis of the posteriority of numbers based on what Plato says about true numbers (ἐν τῷ ἀληθινῷ ἀριθμῷ; cf. Rep. 529c–530c) or number in substance (ἀριθμὸν ἐν οὐσίᾳ; cf. VI.6.4.20–25), as well as due to the fact that number itself has substantial unity and not the unity of numbered quantity, as the Pythagoreans had already noted (cf. VI.6.5.1–16). The simultaneity of number and forms is also rejected, because all forms, including being and movement—which Plotinus mentions here—are one, such that one must be prior to each form, and number (here represented by a decad) must be prior to all forms. This one, however, is not the One itself, but the other one (cf. VI.6.5.16–52), which we touched upon in V.5.5 (cf. section 5.1). Therefore, number is to be found in the Intellect, where all is intellect (νοῦς) and knowledge (ἐπιστήμη; cf. VI.6.6.18–27).

Nevertheless, all forms in the Intellect are one nature (μία φύσις) and are not separated (χωρίς) from each other. Rather, we must think of them—as Plotinus claims, paraphrasing Anaxagoras—as being all things together in one (ὁμοῦ ἐν ἑνὶ πάντα; cf. VI.6.7.1–5). At the same time, Intellect thinks them as already eternally separated (κεχώρισται ἐν αὐτῷ ἀεί), because it thinks them as defined forms that are distinct from each other (cf. VI.6.7.7–10). In thinking them as separate, Intellect unwinds into multiplicity. In thinking them as one nature, this multiplicity is circumscribed by one (cf. VI.6.1.25). Plotinus presents a very interesting argument for this specific nature of Intellect, i.e. for the fact that it is the paradigm of unified multiplicity. He says that this situation can be confirmed with reference to the participants who are attracted by the beauty (τὸ κάλλος) and greatness (τὸ μέγεθος) of Intellect, i.e. who fall in love with it (ἔρωτι πρὸς αὐτό, scil. νοῦν; O.G.). To the extent that soul is similar to Intellect, the same phenomenon can be seen in the love of other things for soul (cf. VI.6.7.10–14). If there is a beautiful living being here, i.e. the whole sensible cosmos, there must be an absolute living being of wonderful and inexplicable beauty there (θαυμαστοῦ τὸ κάλλος καὶ ἀφαύστου ὄντος, scil. αὐτοζῴου; O.G.). Or rather, Intellect is this complete living being (παντελὲς ζῷον), encompassing (περιέχον) all beings in itself (cf. VI.6.7.14–19 and Tim. 30a8–31b3 and 37c6–d4).

Plotinus then turns to the enquiry about the absolute or complete living being. It is called the primary living being (ζῷον πρώτως ἐστι) and identified with Intellect (νοῦς) and real being (οὐσία ἡ ὄντως), and it is said to contain not only all living things, but also the whole number (ἀριθμός σύμπας), righteousness itself, beauty (“itself” is here implied by the context: δίκαιον αὐτὸ καὶ καλὸν καὶ ὅσα ἄλλα τοιαῦτα) and all other such things (cf. VI.6.8.1–7). However, Plotinus adds as an afterthought, how each of these things exist and what they are is yet to be discovered, signifying perhaps that he has not spoken with total precision (cf. VI.6.8.6–7). The surprising implication of the presence of beauty itself may thus be qualified in this passage. If then, he continues, one assumes a succession of being (τὸ ὄν), intellect (νοῦς) and living being (ζῷον), number is prior to all of them. It must be prior to the living being and to intellect, since they are the third and the second respectively, and consequently they presuppose number. However, number is also prior to being (οὐσία), because being is itself one and many as we know from treatise VI.2 (cf. VI.6.8.17–24).

5.4 The Role of Number in the Generation of Beings (VI.6.9–10)

We then come to the crucial section of treatise VI.6 where Plotinus considers “if being generated number by its own division, or number divided being” (ποτέρα ἡ οὐσία τὸν ἀριθμὸν ἐγέννησε τῷ αὐτῆς μερισμῷ, ἢ ὁ ἀριθμὸς ἐμέρισε τὴν οὐσίαν; VI.6.9.1–3, translation modified). This question, he explains, does not only concern being, but also the rest of the highest kinds—Movement, Rest, the Same and the Other—which either generated number or were generated by number (cf. VI.6.9.3–5). From what comes next, it is obvious that the question in fact relates to all forms or, as Plotinus puts it in this section, to all beings (ὄντα; cf. VI.6.9.9, 14, 22–24 and 36–39). Moreover, Plotinus recalls the question he raised in VI.6.4 of whether number exists by itself (ἐφ’ ἑαυτοῦ) or is only observed in a number of things. This time, however, he supplements this question with an additional one: is this true also for the one among numbers (τὸ ἓν τὸ ἐν τοῖς ἀριθμοῖς)? Is this one also prior to beings? If so, is it also prior to being (cf. VI.6.9.5–10)?

Plotinus sketches two possible answers: 1) Being⁶ is before number (τοῦτο πρὸ ἀριθμοῦ, scil. τὸ ὄν; O.G.) and number comes to exist from being (δοτέον ἀριθμὸν ἐξ ὄντος γίνεσθαι; cf. VI.6.9.10–12); 2) One is before being (προηγήσεται τοῦ ὄντος τὸ ἕν) and number before beings (ὁ ἀριθμὸς τῶν ὄντων, scil. προηγήσεται; O.G.; cf. VI.6.9.12–14). We are familiar with the first option from our experiences counting things (cf. VI.6.9.15–18). However, Plotinus objects that, in the very process of generating beings, it must have been clear how many beings there had to be, if they were not generated arbitrarily (κατὰ τὸ ἐπελθόν; cf. VI.6.9.15–23). Thus, he concludes, the whole of number existed before the beings themselves did (πρὸ αὐτῶν τῶν ὄντων) and, as such, number itself is not any of the beings (cf. VI.6.9.23–24).

What is number, then, and how is it related to being and to beings? Plotinus’ answer is that number existed in being (ἐν τῷ ὄντι), but not as its number (οὐκ ἀριθμὸς ὢν τοῦ ὄντος), because at the beginning of the generation of beings, which is of course not to be understood temporally, being was still one (ἓν γὰρ ἦν ἔτι τὸ ὄν; cf. VI.6.9.24–26). Rather, he says, the power of number (ἡ τοῦ ἀριθμοῦ δύναμις) divided being (ἐμέρισε τὸ ὄν) and “made it, so to speak, in labour to give birth to multiplicity” (οἷον ὠδίνειν ἐποίησεν αὐτὸν τὸ πλῆθος; VI.6.9.27). Obviously, the δύναμις here is not to be understood as potentiality, but rather as productive power, since it was able to produce multiplicity (cf. Slaveva-Griffin 2009, p. 86). Number itself is said to be either the very being of being (ἡ οὐσία αὐτοῦ, scil. τοῦ ὄντος; O.G.) or its actuality (ἐνέργεια). Consequently, the absolute living being (τὸ ζῷον αὐτό) and Intellect (νοῦς) are number (cf. VI.6.9.27–29). In the most enigmatic passage of this treatise, Plotinus explains that Being is to be understood as unified number (ἀριθμὸς ἡνωμένος), beings as unfolded number (ἀριθμὸς ἐξεληλιγμένος), Intellect as number moving in itself (ἀριθμὸς ἐν ἑαυτῷ κινούμενος) and the living being as inclusive number (ἀριθμὸς περιέχων; cf. VI.6.9.29–32). Because it comes from the One, Being must be number, and the forms are henads and numbers (cf. VI.6.9.32–34). Without the One, Being itself would be scattered (cf. VI.6.9.39–44). This number, which is in Being (ἐν τῷ ὄντι) and with Being (μετὰ τοῦ ὄντος), but before beings (πρὸ τῶν ὄντων), and which can be contemplated in the forms (ἐπιθεωρούμενος τοῖς εἴδεσι) and has a share in their generation (συγγεννῶν αὐτά), is to be called substantial (οὐσιώδης; cf. VI.6.9.36–38). Beings are based on substantial number (βάσιν δὲ ἔχει τὰ ὄντα ἐν αὐτῷ) and have their source (πηγή), root (ῥίζα) and principle (ἀρχή) in it (cf. VI.6.9.38–39). At the same time, monadic number, with which we count, is but an image of substantial number (cf. VI.6.9.35–36). Plotinus concludes his exposition with the following:

Being, therefore, standing firm in multiplicity (ἐν πλήθει) was number, when it woke as many (πολύ), and was a kind of preparation for the beings (παρασκευὴ πρὸς τὰ ὄντα) and a preliminary sketch (προτύπωσις), and like unities (ἑνάδες) keeping a place (τόπον ἔχουσαι) for the beings which are going to be founded on them (τοῖς ἐπ’ αὐτὰς ἱδρυθησομένοις).

VI.6.10.1–4

These passages require some comment. Let me start by paraphrasing what Plotinus says here. Number is to be found in Being as its limit, i.e. as that which defines it as if it were its form. Being is unified number, because Being entails, as it were, all of the other highest kinds—or rather they unfold from it—and because all other forms are derived from these (cf. section 3.4.4, point 2). In this sense, at the very beginning of the process of generation of Intellect (which is, once again, not to be thought temporally) when Being was still one, it was unified number (cf. section 3.4.4, point 5). However, it never really is one, since being is always to be thought along with and among the other highest kinds. Only “afterwards” do they unfold into all of the other forms. For this reason, Being is unified number, because it must be thought as multiple or rather as limited or defined multiplicity (cf. section 3.4.4, point 2). Plotinus tries to capture this moment in the process of the generation of Intellect by comparing it to waking up to multiplicity, but waking up from a sleep that always already stands in multiplicity. Intellect, which is Being, becomes aware, as it were, of its multiplicity by grasping it through the act of intellection. However, multiplicity—i.e. the rest of the highest kinds, as well as the forms of Intellect as a whole—were already there during this sleep. Plotinus once again tries to express this inchoate “state of being” of all of the forms and the highest kinds before they came to be thought by Intellect. They were in Being or rather they were Being, but only as preparations or preliminary sketches, keeping a place for themselves until they came to be conscious or grasped intellectually. Once they have been grasped, they can be called “unfolded number”, where “unfolded” refers to the process of their generation, while “number” refers to their defined or limited multiplicity (cf. section 3.4.4, point 5).⁷

The designation of Intellect as number moving in itself (cf. DA 408b32–33) once again combines several features of the second hypostasis. As moving number, it is thinking or intellective activity, and this activity implies multiplicity, because thinking is self-relation and because Intellect thinks a variety of intelligible objects (cf. section 3.4.4, point 3). Intellect is therefore moving number. Moreover, this intellective activity is directed towards itself, because the intelligibles are not outside the Intellect (cf. treatise V.5), so that it is number moving in itself. From a different perspective, the self-containedness of Intellect is alluded to in the denomination of the Living Being as inclusive number. As we know from VI.6.7–8, the complete or primary Living Being refers to Intellect and its contents, i.e. to all of the intelligible forms. The Living Being may therefore also be called inclusive number, but this time with the emphasis laid on inclusive since it contains all of the forms. Therefore, the entire multiplicity is circumscribed by one, as Plotinus claims in the very first section of VI.6. The contents of Intellect are, as we know (cf. section 3.4.4, point 1), of such a kind that all of the forms are all the other forms and the whole of them. For this reason, inclusive number brings limit to all forms and to the whole of them, i.e. to the Living Being, and may therefore be identified with it.

As Slaveva-Griffin (2009, p. 109) aptly puts it, “the absolute unified number in Being, when contemplated by Intellect (the number moving in itself), divides substance and becomes the unfolded number of beings, enclosed by the finite number of the Complete Living Being.” As can be observed, the identification of different aspects of Intellect with number (unified, unfolded, moving in itself and inclusive) functions as a shorthand for the different perspectives from which Plotinus describes the utmost unified multiplicity of Intellect.⁸ Designating different aspects of Intellect as unified and unfolded number captures its unity and multiplicity in the process of its generation (cf. section 3.4.4, point 5), including the unifying role of the highest kinds (cf. section 3.4.4, point 2). Referring to an aspect of Intellect as number moving in itself reminds us of the unifying and multiplying role of its intelligible activity (cf. section 3.4.4, point 3). The fact that, from a different perspective, Intellect is also inclusive number can be read as a reference to the interconnectedness of all intelligible forms with each other and with the intelligible forms as a whole, which, at the same time, expresses their unity and multiplicity (cf. section 3.4.4, point 1). Finally, in all of these cases Plotinus identifies aspects of Intellect with number. By doing so, he highlights the results of the enquiry carried out in VI.6, according to which Intellect is a limited multiplicity on the grounds of its “arithmetical structure”, understood as the activity of number in Intellect (cf. section 3.4.4, point 4). In this sense, Plotinus later claims that number “is in Intellect as the sum of the active actualities of Intellect” (VI.6.15.16).

A rather difficult question that arises from what I have discussed so far is that of the exact relation of the highest kinds, as interpreted in VI.2, to the doctrine of numbers in VI.6.9–10. Let me begin by saying that we must be very careful here. Slaveva-Griffin, for example, connects Rest with unified number, Motion with number moving in itself, unfolded number with the Other and the Same with encompassing number (cf. Slaveva-Griffin 2009, p. 109, and 2014, p. 205). The obvious problem is that there are five highest kinds, but only four numbers mentioned in VI.6.9, such that if one tries to identify the highest kinds with these numbers, it is necessary to come up with a solution to explain the missing one. In the case of Slaveva-Griffin, it is Being which must be grafted onto the numbers: “When put together, all activities of substantial number bring together the different aspects of the same whole. This same whole, in turn, corresponds to the fifth primary kind of being” (Slaveva-Griffin 2009, p. 109). But, in reality, things are even more complicated, since for example the assumed correspondence of Rest to unified number, is mediated through Being because “the unified substantial number simply defines Being as stasis” (Slaveva-Griffin 2009, p. 102).

A different option, advocated by Nikulin is to split the highest kinds into two groups and connect (Nikulin 2002, pp. 78–79) or even identify (Nikulin 1998b, pp. 331–332) the Same and Rest with the monad, and the Other and Movement with the dyad. The interaction between the monad and the dyad could then be understood as the constitution of beings from Being, such that unified number, number moving in itself, unfolded number and encompassing number are descriptions of such a genesis of beings (Nikulin 2002, p. 80), i.e. the genesis of being as Intellect (Nikulin 2002, pp. 76 and 80).

Although these speculations may be based on reasonable assumptions, they remain speculations. That said, we should not make the opposite mistake and deny the connection between these two topics, since Plotinus explicitly identifies the highest kinds with numbers in VI.2.10 and brings them into play at the very beginning of VI.6.9. The solution that I propose is, therefore, not to try to connect individual kinds to particular types of number or to the monad and the dyad, but to understand them as being related through the mediation of the problem of unity and multiplicity. As indicated above, I read the crucial passage VI.6.9.29–32 as capturing the utter unified multiplicity of Intellect, which is otherwise described from several different perspectives (cf. section 3.4.4). The highest kinds are only one aspect of this topic, albeit an important one. I believe that apart from the oft-repeated statement that the highest kinds are numbers (cf. VI.2.2 and 10), we cannot really say much more on the basis of the textual evidence and perhaps there is little more to be said anyway. The designation “number” indicates that a thing is a limited multiplicity, which is precisely the case of the highest kinds. I see no need to specify what kind of number it is, because it is only a question of how we express ourselves. Plotinus has a lot to say about what kind of unified multiplicity the highest kinds are, without having to use an analogy from the realm of numbers.

Another controversial topic related to the discussion in VI.6.9 is the answer to Plotinus’ question from VI.6.9.8–10 of whether number (including the one among numbers) exists before beings or even before Being itself. As we have seen, Plotinus suggests two options: 1) Being is before number and number comes from being; 2) One is before being and number is before beings (see above, p. 99). Slaveva-Griffin’s answer is ambivalent. First, she claims that number and being are “ontologically equal and inseparable” (Slaveva-Griffin 2009, p. 90). However, later she asserts that “number has priority even over Being and if number is prior to Being, then the unified substantial number is the closest to the source of all” (p. 100). On my reading, Plotinus argues for the second option (which corresponds rather to Slaveva-Griffin’s first statement): one is before Being and number before beings, so that number, as such, is in Being and with Being (cf. VI.6.9.24–26 and 36–38). Beings, on the other hand, are clearly derived from number (cf. VI.6.9.38–39). But how does number itself come into existence and what is the one which is, according to VI.6.9.12–14, before Being?

As we have seen, even the slightest departure from the One is a progression towards multiplicity, which is the indefinite dyad⁹ (cf. V.5.1.8–11), or infinite, manifold, unbounded (πολὺς καὶ ἄπειρος; cf. VI.7.17.20) and unlimited (ἀόριστος; cf. VI.7.17.15) life (ζωή; cf. VI.7.17.11 ff. and my discussion of these passages in section 6.3).¹⁰ But with it or rather prior to it, the monad comes to existence (cf. V.1.5.6–8). These two principles interact, i.e. the monad limits the dyad and Intellect is born (cf. V.1.5.7–9, V.4.2.7–8). Their interaction is described, from one perspective, as an attempt by Intellect which does not yet see (ὄψις οὔπω ἰδοῦσα; cf. V.3.11.5–6 and also V.4.2.7), or—as Emilsson (2007, p. 70) puts it—of the inchoate Intellect, to attain the One in its simplicity (ἐπιβάλλειν ὡς ἁπλῷ; cf. V.3.11.2–3). Similarly, Plotinus sometimes speaks of an unintellectual looking at the One (ἔβλεπεν ἀνοήτως) that in fact never sees the One (cf. VI.7.16.13–19 and my discussion of these passages in section 6.3). From a similar perspective, the interaction of the monad and the dyad results in a vague (ἀόριστος; cf. V.3.11.7) presence of an image (φάντασμά τι; cf V.3.11.7) or a trace (ἴχνος; cf. V.5.5.12–14, III.8.11.22–24, VI.7.17.39, VI.8.18.16) of the One in Intellect.

The monad itself is not essential number (cf. V.5.5 but also VI.2.10.13–16), but rather makes number, which comes into existence on the model of it and through it on the model of the One (cf. V.5.5.1–4). The one in being (i.e. the monad), as it were, falls out of the One with Being (VI.2.9.39–43), so that they always come together. However, the “coming together” of Being and the monad does not refer to the generative process of Being itself. Rather, it reflects the fact that, in Intellect, Being and the one are closely connected—or even connected to the highest degree possible in multiplicity. The monad and Being are connected in the sense that number is the very being or actuality of Being (cf. VI.6.9.27–29), or again that Being is unified number. Therefore, there is always number in Being or with Being (cf. VI.6.9.36–38). Since the monad is a trace of the One in Being, it functions, in turn, as a connecting element with the One (cf. συνάπτω in VI.6.15), whereas numbers are said not to do this, because it suffices for Being to be linked to it via the monad (cf. VI.6.15.24–29 and Horn 1995, pp. 257–261). Nevertheless, because all numbers participate in the monad in some way, everything that is shaped by number can also be said to be a sort of trace of the One in Being (cf. V.5.5.12–14).

Since what unfolds from Being and the rest of the highest kinds are all of the forms of Intellect (cf. VI.6.11.24–34), and since they all participate in the unity of the principle, which is the monad, they are all henads. Slaveva-Griffin (2009, p. 102) aptly summarises the role of henads in the constitution of Intellect: “the henads represent the multiplicity of beings that retain a trace of the unified number of Being in themselves to impart onto their beings. Thus, each henad, as a holding place for being, is an individual version of the unified number of Being.” However, the use of the words “henad” and “monad” is to a certain extent confusing in VI.6 and Plotinus does not seem to consistently apply the systematically defined meanings I am trying to use here (cf. a similar observation by Slaveva-Griffin 2009, pp. 92–93).

The designation “substantial number” is also a Plotinian innovation, although it is partially derived from what is said about true numbers (ἀληθινὸς ἀριθμός) in Plato’s Republic (529c–530c) and about true being (οὐσία ὄντως οὖσα) in the Phaedrus (247a–248a). Because various forms are different multiplicities that are unified in different ways (i.e. they participate differently in the monad), or in other words, because each of them is a particular henad, they all have their source, root and principle in substantial number (cf. VI.6.9.38–39). Slaveva-Griffin once again accurately paraphrases Plotinus, stating “substantial number is the mold into which the Forms slip to exist” (Slaveva-Griffin 2009, p. 87) and also “the rational principle (logos), described in V.1.5.13, which orders substance (ousia) and constitutes being (to on)” (Slaveva-Griffin 2009, p. 89). As such, substantial number is not only the limit imposed through the monad on every single form by the One, but also the structuring principle of Intellect as a whole. Substantial number is the product of the interaction between the indefinite dyad and the monad, i.e. it is the very limited nature of the intelligible forms and of the whole of Intellect. Therefore, this term captures both the fact that they are a defined multiplicity, and the fact that the monad rules over this multiplicity, i.e. that it is a unified multiplicity.

5.5 Number and Beauty (VI.6.18)

A crucial question remains to be answered: what does all this have to do with beauty? First of all, the enquiry into the highest kinds and into the account of number was elicited by the connection of beauty to Intellect on the grounds of its utter unity in multiplicity. My enquiry was guided by the desire to further specify this unity from two important perspectives: 1) the generic and principal role of the highest kinds and 2) the structural role of number in the intelligible. I have already succeeded in specifying the unity of the Intellect by determining the one as a principle in it, I have discussed why beauty is not one of the highest kinds and I have been able to identify Being as the most beautiful “part” of Intellect. A closer reading of treatise VI.6 On Numbers was of considerable importance for this topic. I have tried to show that number may function as a shorthand for the utter unified multiplicity of Intellect, derived from the nature of its intelligible activity and from the nature of its objects of thought, from the atemporal process of Intellect’s genesis including the role played by the highest kinds in it, and finally from the structural unity and multiplicity of each of its parts and the whole of it. Also, multiplicity of Intellect was identified as a limited one, because, as inclusive number, it was circumscribed by one, both as a whole and as each part. Further implications of this account of number for the question of beauty are listed by Plotinus himself in the last section of the treatise. These passages explicitly address the relationship between beauty and number and may lend further support to my conclusions.

In VI.6.18, Plotinus describes how number is in Intellect from the perspective of limit. All numbers there are limited (ὥρισται) and in no way deficient, in the sense that they cannot be in any way greater than they are. One could say that they are unlimited (ἄπειρον) only in the sense that they cannot be measured by something else, because they themselves are measures (μέτρα; cf. VI.6.18.1–12). That which requires an external limit is precisely that which is not limited in itself, but needs to be measured in order to be prevented from carrying on into indefiniteness. Real beings, i.e. intelligible forms, as numbers, do not need such an external limit. They are bound by their own agency in being what they are. Additionally, Plotinus claims that these forms or numbers are beautiful, because they are self-limiting measures of this sort, but also because they are living beings—or rather because they constitute a single Living Being living a divine life (i.e. the first, clearest and best one, that is in no way deficient or weak, unmixed with death and possessing the pure essence of life). Moreover, this life, which is derived from the One and directed towards it, is an intelligent life or, as Plotinus puts it, it is accompanied by the thinking of all beings (ἡ πάντων φρόνησις) and by universal Intellect (ὁ πᾶς νοῦς). By mixing thought (συγκερασάμενος φρόνησιν) into this divine life and giving it the colour of greater goodness (ἀγαθώτερον αὐτὸ ἐπιχρώσας), the beauty (τὸ κάλλος) of Intellect comes to be even more majestic (σεμνότερον), for even here below a thoughtful life is majesty and beauty in conformity with truth (τὸ σεμνὸν καὶ τὸ καλὸν κατὰ ἀλήθειάν; cf. VI.6.18.7–25). This is all the more true of Intellect, where life flashes out of everything, where there is no contradiction and nothing external to it, but only eternal being in and by itself everywhere, i.e. where being is one. Because Intellect eternally gives being to everything, it is great in power and in beauty (ἐν δυνάμει καὶ κάλλει μέγα) and, as such, charming (θέλγω), such that all seek (ζητέω) the Good with it (μετ’ αὐτοῦ τὸ ἀγαθόν; cf. VI.6.18.25–53).

The relevance of the treatise On Numbers for the enquiry into the beautiful should now be much more obvious. Beauty is identified with measure, i.e. something limited or number, but also something that does not acquire its limit from something external, since it is limited by itself. Because number was previously identified with the actuality of each form, it is precisely the being itself of a form which is number. Number is therefore a suitable notion for capturing both of the requisite aspects of beauty: the fact that it is limited and the fact that this limit is not external to it. Otherwise, a beautiful thing would be a mere decorated corpse, because Plotinus understands the external limitation of a thing as, in a way, emphasising its own unlimited nature (cf. II.4.16). Moreover, the fact that Plotinus connects number and beauty provides further support for what was already observed in V.8.13 (cf. section 3.5): Intellect is beautiful, since it is what is primarily differentiated and bound, i.e. differentiated and bound to the maximum degree possible. Number stands for precisely these two aspects. As number, Intellect is multiple, but limited. From a structural perspective, treatise VI.6 therefore supports the claim that beauty is unitas multiplex, and it even more vigorously emphasises the self-determination of beauty, i.e. the fact that a thing is beautiful when it is bound by its own limit. In this respect, the existence of the form of beauty (cf. section 5.2) makes even less sense, because what makes a form beautiful is precisely something that is characteristic of each form, or rather of Intellect as a whole.

The situation is more complicated when it comes to the second reason given for the beauty of Intellect: the fact that it is a living being. It seems that there are several motives that come together here. The first motive is, once again, the connection of beauty to unity in multiplicity, because the life of Intellect is distinctive precisely in being a life in and by itself that is present everywhere, such that life flashes out of everything, i.e. in being a single life that is also many (cf. VI.6.18.25–44).

Second, life was associated earlier in VI.6.9 with the completeness of the unfolded Intellect, i.e. with the fact that it encompasses every form. This connection of life with such an unfolded multiplicity could be understood as not being restricted to a merely “arithmetical” perspective, encompassing number. It could also be taken to have “biological” connotations with generative or reproductive power. As we know from III.8, the life of Intellect is productive contemplation. In living or contemplating, Intellect unfolds itself. The connection of beauty to life, in the sense of an unfolded but defined multiplicity, has implications for the interpretation of Being as the most beautiful “part” of Intellect, which was derived from parts of treatise VI.2 (cf. section 4.4). It seems that Plotinus adopts a much more positive attitude here towards defined multiplicity, when he makes life one of the causes of beauty. Even from these passages, it seems that if Intellect were not all forms, but only some of them, it would be less beautiful (cf. VI.6.18.20–25 and see further below). In this sense, Intellect, as unified number, would not be as beautiful as encompassing number, because it would “not yet” be the fullness of its contents. At the same time, this enriching role played by multiplicity is not to be overestimated, as Plotinus himself urges in VI.6.1.8–22, in part because the reason for its having such a positive function is the fact that Intellect does not lose any of its unity as a result of this unfolding. In the stages of Intellect’s constitution, it is one to the same degree in the moment “when” it is only the highest genera as it is in the moment “after” it has unfolded down into the last of the forms. Moreover, because Intellect never is and never was in an undeveloped state, this issue is merely the result of an inaccurate description. Nevertheless, the motivation for designating the highest kinds, Being or unified number as the most beautiful “part” of Intellect was the fact that these are closest to the One and, in this sense, more fully one. Perhaps, however, the passages from VI.6 currently under discussion show that the metaphor of closeness starts to break down here.¹¹

Let us return, however, to Plotinus’ motives for making life the cause of beauty. There might be a third motive, which in a way comprises both of the previous ones.¹² To quote Armstrong (1960, p. 403), “It seems to me most unlikely that a philosopher who knew something about Aristotelian theology could have written this without intending an explicit reference to the discussion of divine thought in Metaphysics.”¹³ I too think that Plotinus is actually trying to correct Aristotle’s account of νόησις νοήσεως here (cf. Met. 1074b15–1075a11). Aristotle devotes this passage to specifying the object of god’s thought and he does so, among other things, in the context of the god’s necessary majesty (τὸ σεμνόν; cf. Met. 1074b17–18). The god must think that which is most divine (τὸ θειότατον) and precious (τιμιώτατον; cf. Met. 1074b25–26) in order to be beautiful (τὸ καλόν; cf. Met. 1074b23–24), meaning it must think its own thinking (ἔστιν ἡ νόησις νοήσεως νόησις; cf. Met. 1074b33–35). This activity of the god was moreover previously identified with the god’s life (cf. Met. 1072b28–31). It is striking that not only beauty, but also majesty come into play, when Aristotle more closely defines the divine life of the god, which is the thinking of its own thinking. Plotinus obviously alludes to these passages and, to some extent, presents a similar picture. The life of the god, which is Intellect, is also intelligent life accompanied by the thought of all beings (ἡ πάντων φρόνησις) and universal Intellect (ὁ πᾶς νοῦς; cf. VI.6.18.20–23) and it lives a divine life (cf. VI.6.18.12–18). Moreover, Intellect’s thought is reflexive, but it does not simply think its own thinking. Rather, it thinks itself as the plurality of all forms. From Aristotle’s perspective, this would threaten the beauty and majesty of god, but Plotinus forestalls this objection with two considerations: 1) Intellect does not think something external, but rather itself as all of the forms; 2) The object of thought is beautiful, because all of the forms are measures or numbers. As previously noted, the connection of Intellect with the plurality of forms seems even to make its beauty grander, for it does not become more majestic until the life of Intellect is mixed with thought and until it is given the colour of greater goodness (cf. VI.6.18.20–25).

That said, it is not clear what this “colour of greater goodness” refers to exactly and how it makes Intellect more beautiful. Plotinus does not provide any answers here, since his thoughts are focused rather on defining beauty more precisely with respect to what is both prior and posterior to Intellect. Intellect is said to give being to everything (cf. VI.6.18.46–47) and, with it, beauty. Even soul is number, if it is a substance (cf. VI.6.16.44–45), and everything that comes into being is, in the end, determined by the first numbers (cf. VI.6.15.35–42 and Magi 2013). In an earlier passage, however, the multiplicity of the sensible world was not considered to be as positive as the multiplicity of Intellect. It was said to be the source of its ugliness—or, more precisely, it was said that the world would be ugly if it were not circumscribed by one, as by something external (cf. VI.6.1.23–29). Plotinus describes the productive and paradigmatic status of Intellect with respect to what comes after it as its being great in power and beauty (ἐν δυνάμει καὶ κάλλει μέγα; cf. VI.6.18.47–50): in power, because it has the ability to do so and, indeed, does so; in beauty, because it is the primarily beautiful, the paradigm of beauty. For this reason, Plotinus even calls the Intellect charming, placing it as an intermediary between all beings and the One, through which they all seek the One (cf. VI.6.18.46–53). This ability of the beautiful Intellect is, of course, grounded in the fact that it is derived from and directed towards the One (cf. VI.6.18.18–20). Nevertheless, as something charming—or, more precisely, because of its majesty (cf. VI.6.3.1–10), its wonderful and inexplicable beauty and its greatness (cf. VI.6.7.10–16)—it may also hinder our ascent to the One and bind to itself those who admire it.¹⁴