Andrea Araf

 

Aristotle in Plotinus’ Doctrine

of Extension

 

Abstract

This article examines the sources of Plotinus’ doctrine of extension, a central aspect of his Platonic dualism whose origins have received little scholarly attention. This doctrine entails a distinction between two central concepts: the notion of body as primarily divisible or extended ‘mass’ (ὄγκος) and that of immanent form as secondarily divisible or extended quality (ποιότης). The article argues that, although Plotinus presents this doctrine as an interpretation of Plato, Timaeus 35a, its philosophical content is irreducible to the Timaeus, and that Plotinus rather employs, adapts, and develops concepts drawn from Aristotle. First, Plotinus’ notion of ‘mass’ finds conceptual and textual parallels in Aristotle’s Physics, especially in the discussions of place and continuous magnitudes (Books IV and VI). Second, Plotinus’ distinction between bodies and qualities as primarily and secondarily divisible or extended represents a sophisticated development of chapter 6 of the Categories, where Aristotle discusses quantity and distinguishes per se and accidental quantities. Finally, the article shows that Middle Platonic authors (Ammonius Saccas, Numenius) had already employed Aristotle’s distinction between per se and accidental quantities in their anti-Stoic polemics, and that Plotinus’ engagement with Aristotle is far more sophisticated.

Keywords

Aristotle, Plotinus, Extension, Plato’s Timaeus, Middle Platonism

Author

Andrea Araf

Università Roma Tre

andrea.araf@gmail.com

ORCID: 0009-0008-3167-1727

 

 

 

 

 

 

 

 

 

Introduction

 

Extension plays a key role in Plotinus’ distinctive version of Platonic dualism. It distinguishes sensible and corporeal being from intelligible and incorporeal being. Roughly speaking, if something is neither quantitatively determined nor spatially extended, it is not a sensible being but an intelligible reality of one kind or another.[1] Furthermore, extension is an axiologically negative feature: it makes sensible being divisible, dispersed, and lacking in real unity and cohesion, which only belong to intelligible being.

Notably, Plotinus often argues against the Stoics, the Peripatetics, and even some Platonists that the soul is incorporeal and fully transcendent vis-à-vis the body. He does so precisely by pointing out that the soul is completely unextended. For this reason, the soul differs not only from bodies, but also from immanent forms or qualities such as colours and shapes. Indeed, Plotinus stresses that any other property belonging to a body is itself extended along with the body. In this sense, extension is something more than the property a thing must have to be a body or the characteristic feature of body as such. As E. Emilsson aptly remark, we might use Descartes’ terminology and say that “extension is a principal attribute of bodies, i.e. one which all the others presuppose”.[2] Furthermore, Plotinus describes bodies as primarily divisible and qualities as secondarily divisible. His point is that bodies and qualities have different internal structures and spatial behaviours. As we will see, only bodies possess a mereological structure wherein the part is less than the whole, whereas qualities are endowed with a sui generis kind of spatial extension that excludes such a mereological structure.[3] These are remarkable ideas and Plotinus consistently holds them across his writings, mainly in treatises on the soul such as IV.1, IV.2, IV.3, IV.7, and VI.4-5. Given the sophistication, consistency, and recurrence of these views, I think it is justified to speak of a proper ‘doctrine of extension’ in Plotinus’ philosophy.

The aim of this article is to illustrate Plotinus’ notions of extended body and extended quality, and trace their sources.[4] Specifically, I hope to show that Plotinus presupposes and develops notions drawn from Aristotle’s Physics and Categories. While the topic of extension also has several connections with Plotinus’ theory of matter, I shall leave these aside here.[5]

It should be stated at the outset that Plotinus often presents his doctrine of extension as an interpretation of Plato, Timaeus 35a – the celebrated passage on the World-Soul’s composition. However, it would be highly misleading to conclude that Plotinus simply draws this doctrine from the Timaeus. As Schwyzer, Jevons, and Chiaradonna have shown, Plotinus’ approach to this text, as to the whole dialogue, is idiosyncratic. He reinterprets this passage as referring to the individual soul rather than World-Soul, and systematically eliminates its mathematical dimension. This selective and purposive reading exemplifies his broader tendency towards a demathematised, metaphorical interpretation of the Timaeus.[6] For our goals, it is especially important that Plato defines corporeality through visibility and tangibility (31b) and appears to ascribe three-dimensional extension to the soul as well (36d-e). By contrast, as already noted, Plotinus considers extension to be a ‘principal attribute’ of bodies as such and regards the soul as completely unextended. More specifically, the Timaeus contains nothing remotely similar to Plotinus’ sophisticated doctrine of extension. To be sure, Plotinus’ distinction between a primary divisibility of bodies and a secondary divisibility of qualities reflects precisely the vocabulary Plato employs in Timaeus 35a. And yet Plotinus’ key notion of extended body or ‘mass’ (ὄγκος) significantly differs from the way Plato employs this term in the Timaeus. As we will see, Plotinus thinks of body as a spatially extended continuous magnitude, whereas Plato thinks of an aggregate of more fundamental constituents such as elementary solids or triangles.[7] Even Plotinus’ nuanced analysis of the difference between the extension and divisibility of bodies and qualities is completely absent from the dialogue.

Plotinus is by no means the first Platonist to have paid particular attention to Timaeus 35a. In antiquity this passage was considered the crucial Platonic text on the nature of the soul. In two recent contributions Jan Opsomer has thoroughly reconstructed the long history of the ancient interpretations of this crucial Platonic text. I refer to his study for a detailed assessment of Plotinus’ position within this tradition.[8] Here it should suffice to say that, as Opsomer’s analysis shows, certain elements of Plotinus’ syntactical understanding and metaphorical interpretation of Timaeus 35a are anticipated by previous authors, but the underlying doctrine of extension does not seem to find precedents in this tradition.

Section 1 analyses Plotinus’ notion of extended body or ‘mass’; section 2 focuses on its sources. Research on this concept has focused mainly on questions of translation and positioning within Plotinus’ broader metaphysics, without focusing on its philosophical precedents.[9] I will argue that this notion finds significant parallels in Aristotle’s discussions of place and continuous magnitudes in books IV and VI of the Physics, and, thus, that Plotinus employs Aristotle to interpret Timaeus 35a and its vocabulary of divisibility.

Section 3 analyses Plotinus’ notion of extended quality; section 4 focuses on its sources. Scholars have sought to trace this notion to Aristotle’s Categories or to Middle Platonic debates – suggestions that prove largely convincing. Building on these insights, I will highlight a further crucial parallel with Aristotle. In his discussion of the category of quantity in chapter 6 of the Categories, Aristotle distinguishes between per se and accidental quantities. I will argue that Plotinus’ distinction between primarily divisible bodies and secondarily divisible qualities is a sophisticated adaptation and development of this Aristotelian distinction, and, once again, that Aristotle provides important background for Plotinus’ interpretation of Timaeus 35a.

Section 5 uses these results to revisit a well-known parallel between Plotinus’ notion of extended quality and a report from Nemesius of Emesa on Ammonius Saccas and Numenius. I will argue that these authors had already appropriated Aristotle’s distinction between per se and accidental quantities in the context of a polemic against Stoic materialism, and that, as far as we can judge, Plotinus’ stance on the incorporeality of the soul and his use of Aristotle are more radical and sophisticated.

 

1. Plotinus’ Notion of Extended Body

 

The clearest presentation of Plotinus’ doctrine of extension is the early treatise IV.2 On the Essence of Soul I. Plotinus begins this inquiry by referring to the results of his previous work IV.7 On the Immortality of the Soul,[10] where he had examined the theories of soul proposed by different philosophical schools in a progression that increasingly approached the truth – from the most materialistic to Plato. After systematically refuting the Epicurean, Stoic, Pythagorean, and Aristotelian accounts,[11] he had established his conception of the soul as an incorporeal and incorruptible substance independent from the body through a synthesis of arguments from the Phaedrus and the Phaedo.

In IV.2 Plotinus announces a different kind of investigation. He no longer criticises his opponents, but rather takes as his starting point “what borders on the nature” of the soul (IV.2.1, 10: τὸ προσεχὲς τῆς φύσεως).[12] His strategy consists in characterising the soul by way of contrast with other realities. Furthermore, his key Platonic text is now Timaeus 35a: “in between the being that is indivisible and always changeless, and the one that is divisible and comes to be in the corporeal realm, he mixed a third, intermediate form of being, derived from the other two (τῆς ἀμερίστου καὶ ἀεὶ κατὰ ταὐτὰ ἐχούσης οὐσίας καὶ τῆς αὖ περὶ τὰ σώματα γιγνομένης μεριστῆς τρίτον ἐξ ἀμφοῖν ἐν μέσῳ συνεκεράσατο οὐσίας εἶδος)” (trans. Zeyl 2000).[13] Plotinus cites Timaeus 35a at the end of the treatise (cf. IV.2.2, 49-52), calling it Plato’s “divinely inspired riddling saying (τὸ θείως ᾐνιγμένον)” and clarifying that his preceding analysis represents an interpretation of this passage. Two crucial points must be underlined. First, unlike Zeyl, Plotinus understands the expression τῆς αὖ περὶ τὰ σώματα γιγνομένης μεριστῆς as “the one that becomes divisible among bodies”. Second, and consequently, Plotinus thinks that this expression refers to two distinct kinds of divisibility: the primary divisibility of bodies and the secondary divisibility of immanent forms or qualities, which become divisible among bodies. As a result, Plotinus identifies four natures in this passage: (1) the primary and completely indivisible nature of the Intellect; (2) the primary and completely divisible nature of bodies; (3) the secondary and completely divisible nature of qualities; (4) the at once divisible and indivisible nature of the soul.[14] We will focus exclusively on (2) bodies and (3) qualities.

Plotinus introduces bodies as follows:

 

λέγωμεν δὴ τὰ μὲν πρώτως εἶναι μεριστὰ καὶ τῇ αὑτῶν φύσει σκεδαστά· ταῦτα δὲ εἶναι, ὧν οὐδὲν μέρος ταὐτόν ἐστιν οὔτε ἄλλῳ μέρει οὔτε τῷ ὅλῳ, τό τε μέρος αὐτῶν ἔλαττον εἶναι δεῖ τοῦ παντὸς καὶ ὅλου. ταῦτα δέ ἐστι τὰ αἰσθητὰ μεγέθη καὶ ὄγκοι, ὧν ἕκαστον ἴδιον τόπον ἔχει, καὶ οὐχ οἷόν τε ἅμα ταὐτὸν ἐν πλείοσι τόποις εἶναι (Enn. IV.2.1, 11-17).

 

Let us state that there are some things which are primarily divisible and by their very nature liable to dispersion: these are the things no part of which is the same as either another part or the whole, and the part of which must necessarily be less than the all and whole. These are the perceptible magnitudes and masses, which each have their own place, and it is not possible for the same one to be in several places at once.

 

Two elements of this passage merit attention. First, Plotinus employs ὄγκος and μέγεθος as synonyms: the ‘perceptible magnitudes’ and ‘masses’ are the same things, that is, bodies as such. Indeed, later in the treatise the synonymy extends also to ‘body’ (σῶμα) (cf., e.g., IV.2.1, 33), so that ὄγκος, μέγεθος and σῶμα can all three denote the extended body. This interpretation is confirmed by other passages in the Enneads. For example, Plotinus states that: “being divided, in fact, belongs to the body, and it is its affection in the primary sense, qua body (σώματος γὰρ καὶ τοῦτο καὶ πρώτως πάθος καὶ ᾗ σῶμα)” (VI.4.8, 15-19). It seems safe to conclude that Plotinus possesses a concept of the body qua body (ᾗ σῶμα), that is, of the extended body, and that he refers to it with ὄγκος, μέγεθος and σῶμα.

Second, Plotinus ascribes to the extended body four characteristics:

 

(i) Its parts are distinct from one another and from the whole.

(ii) Its parts are less than the whole.

(iii) It possesses its own place.

(iv) It cannot be at several places at once.

 

While characteristics (ii) and (iv) are rather clear, (i) and (iii) can be illustrated as follows.

Characteristic (i) should be understood in a spatial sense. Shortly after our main passage, Plotinus states: “body, in fact, is one by virtue of the continuous (συνεχεῖ), and each of its parts is different from the other and is somewhere else (ἄλλο, τὸ δ’ ἄλλο καὶ ἀλλαχοῦ)” (IV.2.1, 60-1). To be sure, the same kind of spatial otherness also characterises the relationship between the part and the whole, although between them there is partial overlap. The formula ἄλλο, τὸ δ’ ἄλλο is crucial in Plotinus’ doctrine of extension. It expresses the numerical distinctness resulting from spatial exteriority: as Plotinus says, the parts of a body are ἀλλαχοῦ with respect to one another, hence distinct. This formula recurs constantly in his writings and is also employed in the following passage from IV.7: “every magnitude, in fact, has one part different from another (τὸ μὲν ἄλλο, τὸ δὲ ἄλλο)” (25-26).^[15]

Characteristic (iii) asserts that each extended body possesses its own place (ἴδιον τόπον), namely, a place distinct from that of any other such body: two bodies cannot occupy the same place. Plotinus makes this clear in his polemic against the Stoic theory of total blending in IV.7.8², 7-22.

 

2. Plotinus’ Notion of Extended Body and Aristotle’s ‘Physics’

 

Aristotle provides a significant precedent for both this thematisation of the extended body and the interchangeable use of ‘mass’ (ὄγκος), ‘magnitude’ (μέγεθος), and ‘body’ (σῶμα). As Denis O’Brien observes: “l’ὄγκος, en effet, ne se distingue pas bien, chez Aristote, de la grandeur (μέγεθος) et du corps (σῶμα)”.^[16] Specifically, O’Brien refers to Phys. IV 8.216a26 ff., and Christian Pfeiffer has also recently observed that these three terms “seem to be used in the same sense here”.^[17] In this passage, an argument against the existence of void, we find the triple equivalence between ὄγκος, μέγεθος and σῶμα already found in Plotinus.

 

The cube, too, has a magnitude (μέγεθος) equal in amount to the void it occupies, and even if this – I mean the mass (τὸν ὄγκον) of the wooden cube – is hot or cold or heavy or light, yet nonetheless it is different in being from all its affections (πάντων τῶν παθημάτων) even if not separable [from them]. Hence – even if it were separated from all the other things and were neither heavy nor light – it will occupy an equal amount of void and will be in the same spot as the part of place and the part of void equal to itself. How then will the body of the cube (τὸ τοῦ κύβου σῶμα) differ from the equal amount of void and place? (Phys. IV 8.216b2-10. Trans. Hussey 1983, slightly modified).[18]

 

Magnitude, mass and body are one and the same aspect of the wooden cube, namely its extended body, which in fact is of the same size as the void it occupies. Furthermore, both Aristotle and Plotinus distinguish the extended body from its affections (παθήματα): indeed, Plotinus also refers to qualities as παθήματα (cf. IV.2.1, 53).

Earlier I emphasised that Plotinus describes the spatial exteriority between bodies and parts of bodies through the formula ἄλλο, τὸ δ’ ἄλλο. This formula, too, can be found in Aristotle: “that which is continuous has one part different from another, and these parts into which it is divisible are different in this way, i.e. spatially separate” (Phys. VI 1.231b 4-6: τὸ γὰρ συνεχὲς ἔχει τὸ μὲν ἄλλο τὸ δ’ ἄλλο μέρος, καὶ διαρεῖται εἰς οὕτως ἕτερα καὶ τόπῳ κεχωρισμένα. Trans. Hardie and Gaye 1930, slightly modified). The parallel is unmistakable. While the formula ἄλλο, τὸ δ’ ἄλλο and similar expressions appear frequently in Greek prose to indicate distinct entities in general (cf. Plato, Protagoras 330a; Alexander of Aphrodisias, De anima mantissa 3, p. 116, 13; and Plotinus himself at II.3.15, 28), Plotinus and Aristotle employ it in the same precise technical sense. Both mean that the parts, not only of body, but of any continuous magnitude (τῷ γὰρ συνεχεῖ τὸ σῶμα ἓν in Plotinus, τὸ γὰρ συνεχὲς in Aristotle) are spatially differentiated (ἀλλαχοῦ in Plotinus, τόπῳ κεχωρισμένα in Aristotle). In both cases, moreover, this spatial differentiation is explicitly connected to divisibility. The parallel is thus conceptual, not merely verbal.

The connection with the Physics is further supported by Plotinus’ assertion that each body “has its own place” (IV.2.1, 16: ἴδιον τόπον ἔχει). This is characteristic (iii), which according to the analysis above means that two bodies cannot be co-located. Now, the expression “own place” is also drawn from the Physics:

 

[…] place may be either the ‘common’ place (τόπος ὁ μὲν κοινός), in which all bodies are; or the own place (ὁ δ’ ἴδιος), which is the first in which a body is (I mean, for example, that you are now in the heavens because you are in the earth and similarly in that because you are in this place which surrounds nothing more than you) (ὅτι ἐν τῷδε τῷ τόπῳ, ὃς περιέχει οὐδὲν πλέον ἢ σέ) (Phys. IV 2.209a32-b1. Trans. Hussey 1983, slightly modified).

 

Precisely like Plotinus, Aristotle too holds that it is impossible for two or more bodies to be co-located: indeed, a proper place is that which “surrounds nothing more than you”. This is also evident from Phys. IV 1.209a6-7, where co-location is considered an unacceptable consequence of the identification between place and body, and from IV 5.212b22-5, where Aristotle states that his own conception of place avoids this implication.^[19] Other passages from the Enneads confirm the plausibility of this parallel: on the rare occasions when Plotinus employs the notion of physical place (τόπος), he clearly draws on Aristotle’s discussion in Physics IV (cf. II.4.12).

We can now draw a first important conclusion. The parallels examined so far strongly suggest that Plotinus interprets his key Platonic passage (Timaeus 35a) through Aristotle’s Physics. Specifically, he understands Plato’s vocabulary of divisibility in light of Aristotle’s discussions of continuous magnitudes and place. To be sure, Plotinus does not offer any discussion of the continuous comparable to Physics VI. He simply draws these elements from the Physics and adapts them to his own anti-physicalistic framework. Where Aristotle provides a neutral analysis of continuous magnitude and spatial divisibility, Plotinus transforms these features into marks of ontological deficiency. In the description of extended bodies quoted above, he asserts that these, being primarily divisible, are “by their very nature liable to dispersion (σκεδαστά)” – a characteristically Plotinian move that imports axiological judgment into physical analysis. Extension is not only a feature of bodies, but also a sign of their inferior ontological status. Of course, such evaluation is completely absent from Aristotle’s discussion and can be understood only in light of Plotinus’ insistence on the absolute unity of transcendent intelligible realities like the soul. Thus, Plotinus borrows Aristotle’s conceptual apparatus and deploys it within a radically different philosophical framework.

 

3. Plotinus’ Notion of Extended Quality

 

Having focused on Plotinus’ notion of extended body and established its Aristotelian origins, we can now turn to his notion of extended quality. In this section, I will analyse Plotinus’ distinctive account of how qualities are spatially extended yet lack the mereological structure of bodies. Section 4 will then examine the Aristotelian roots of this doctrine.

Plotinus introduces qualities as follows:

 

[…] πρὸ μὲν τοῦ αἰσθητοῦ καὶ ἐγγύς τι τούτου καὶ ἐν τούτῳ ἄλλη ἐστὶ φύσις, μεριστὴ μὲν οὐ πρώτως, ὥσπερ τὰ σώματα, μεριστή γε μὴν γιγνομένη ἐν τοῖς σώμασιν· ὥστε διαιρουμένων τῶν σωμάτων μερίζεσθαι μὲν καὶ τὸ ἐν αὐτοῖς εἶδος, ὅλον γε μὴν ἐν ἑκάστῳ τῶν μερισθέντων εἶναι πολλὰ τὸ αὐτὸ γινόμενον, ὧν ἕκαστον πάντη ἄλλου ἀπέστη, ἅτε πάντη μεριστὸν γενόμενον· οἷα χροιαὶ καὶ ποιότητες πᾶσαι καὶ ἑκάστη μορφή, ἥτις δύναται ὅλη ἐν πολλοῖς ἅμα εἶναι διεστηκόσιν οὐδὲν μέρος ἔχουσα πάσχον τὸ αὐτὸ τῷ ἄλλο πάσχειν· διὸ δὴ μεριστὸν πάντη καὶ τοῦτο θετέον.

 

[…] bordering on the perceptible, and rather near it, and in it, there is another nature which is not primarily divisible, like bodies, but all the same does become divisible in bodies; so that when bodies are divided, the form in them is divided too, but is a whole in each of the divided parts, becoming many and remaining the same, when each of the parts is completely separated from another part, since it is completely divisible: like colours and all qualities and every figure, which can be at the same time in many separate things, while having no part which is affected in the same way in which another is affected. And therefore this, too, must be affirmed to be in every way divisible (Enn. IV 2 [4] 1, 31-41).^[20]

 

As evidenced by the expression τὸ ἐν αὐτοῖς εἶδος and the repeated use of the preposition ἐν, these are immanent forms – that is, qualitative and formal features that inhere in bodies. Plotinus mentions colours and every figure (ἑκάστη μορφή), but the expression ποιότητες πᾶσαι shows that he thinks of every qualitative feature: elsewhere, besides the colour white (VI.4.1; IV.3.2), he also mentions the sweetness of honey (IV.7.8¹; VI.4.1), pairs of opposite qualities such as hot/cold, hard/soft, liquid/solid, light/heavy, dense/rarefied (IV.7.4), and shape (σχῆμα) (II.4.8). In Plotinus’ time, the relationship between bodies and qualities was the center of a heated debate focused on the Stoic thesis that qualities are bodies (SVF II 376-398). This anti-Stoic polemic is attested in Plutarch (De comm. not. 50, 1085 e), Alcinous (Didaskalikos XI), Alexander of Aphrodisias (De anima mantissa 6, pp. 122-125; in Top. IV p. 181), and in the pseudo-Galenic treatise Quod qualitates incorporeae sint. Plotinus himself takes part in this debate (IV.7.8¹; II.7.2; VI.1.29), and sides with the anti-Stoic front of Platonists and Peripatetics, according to whom qualities are incorporeal. In this context, however, he simply presupposes this thesis and seeks to show that, although qualities are incorporeal, they are spatially extended and thus completely divisible like bodies. For this reason, the soul’s status cannot be assimilated to that of a quality.

Plotinus ascribes to qualities the following characteristics (designated with letters to distinguish them from those of bodies):

 

(a) They are in bodies.

(b) They are whole in multiple places and in each part of the body in which they inhere.

(c) No exemplification of a quality undergoes an affection because another one does.

 

Characteristic (a) is roughly analogous to (iii). Just as bodies are in a place, qualities too are localised – that is, they are in the bodies of which they are properties.

Characteristic (b) shows that this analogy is only partial. Unlike a body, a particular shade of white can be found as whole in multiple places at once. Think of two sheets of white paper. The quality ‘white’ is present as whole in both sheets: both exemplifications fully satisfy the same definition – they are the same particular shade of white. Note that, in the same way, a quality can also be whole in each part of the single body in which it inheres. As Plotinus states in a famous passage, “the whiteness in a portion of milk is not a part of the whiteness of the whole milk but is the whiteness of a portion, but not a portion of whiteness” (IV.3.2, 16-19). The same argument is used in IV.7.8¹, 18-23 to demonstrate that qualities are incorporeal: the sweetness of honey is no less sweetness in any part of the honey, but remains whole. This is a crucial point. According to Plotinus, qualities are just like bodies in the sense that they are spatially extended and therefore divisible. However, they are unlike bodies because they possess a sui generis type of spatial extension that does not include a mereological structure: qualities are indeed divisible, but they are not divisible into parts. If divided, they remain whole – that is, the division produces a plurality of exemplifications of the same quality, but these exemplifications are in no way ‘less’ than the original whole. I invoke the process of actual division here merely as an illustration: this structural feature – being spatially extended without having parts – belongs to immanent forms as such, independently of whether any process of actual division occurs. This characteristic, (b), should be contrasted with characteristic (ii) of bodies: in the case of qualities, there simply are no parts less than the whole.

Now, characteristic (b) might suggest that, in the case of qualities, spatial and ontological distinction do not correspond, and that two exemplifications of ‘white’, though spatially distinct, are actually just one thing: ‘white’. But characteristic (c) blocks such a conclusion. Plotinus observes that, just like bodies, exemplifications of the same quality do not undergo co-affection: should one of the two exemplifications undergo a change and cease to exist (e.g., because the sheet of paper changes from white to black), the other exemplification will not therefore cease to exist as well. According to Plotinus, this shows that immanent forms are not unitary beings, and on these grounds he will argue that soul cannot be assimilated to them (cf. IV.2.2).[21]

 

4. Plotinus’ Notion of Extended Quality and Aristotle’s ‘Categories’

 

Emilsson, Kalligas, and Chiaradonna have convincingly connected Plotinus’ notion of extended quality to the traditional interpretation of Aristotle’s particular properties in the Categories.[22] In the second chapter of this work (2.1a20-b6), Aristotle advances a fourfold division of being based on the fundamental notions of “being said of a subject” (predication) and “being in a subject” (inherence). The second class resulting from this division is that of particular properties: items which are in a subject but are not said of any subject (e.g., a certain grammatical doctrine in the soul and a certain white in the body). According to the traditional interpretation, these are non-substantial and non-recurrent individuals: individuals belonging to categories other than substance and necessarily instantiated by a single subject. Let us come back to the colour ‘white’. Aristotle’s particular property is not a maximally determinate shade of white, exemplified by a plurality of subjects. Rather, it is a certain exemplification of it in a certain subject. This traditional interpretation is based on a plausible reading^[23] of the second condition posited by Aristotle for something to be ‘in a subject’: “by ‘in a subject’ I mean what is in something, not as a part, and cannot exist separately from what it is in (ἀδύνατον χωρὶς εἰναι τοῦ ἐν ᾧ ἐστίν)” (2.1a24-25. Trans. Ackrill 1963).

Plotinus does seem to be thinking along the lines of the traditional interpretation of Aristotle’s particular properties. He regards occurrences of the same quality as numerically distinct from one another, and points to the absence of co-affection between them as proof of this. I would add a further element that points to the connection established by Emilsson, Kalligas, and Chiaradonna. When focusing on the extended nature of qualities at the beginning of VI.4, Plotinus appears to invoke Aristotle’s second condition for something to be ‘in a subject’, though with slightly different phrasing:

 

These [qualities like whiteness and sweetness] are affections of body, so that the whole of what is affected has the affection, and the affection is nothing of itself since it is something belonging to a body (καὶ μηδὲν εἶναι ἐφ’ ἐαυτοῦ σώματος ὄν τι) and known as such when the body is affected; for this reason it is necessarily of a certain size (διὸ καὶ ἐξ ἀνάγκης τοσοῦτον) (VI.4.1, 19-22).

 

In what follows, I will argue that the connection between Plotinus and the Categories can be further developed. In particular, important background for Plotinus’ distinction between primarily divisible bodies and secondarily divisible qualities can be found in Aristotle’s treatment of quantity in chapter 6 of the Categories, especially in his distinction between per se and accidental quantities. Once again I suggest that Plotinus understands Plato’s vocabulary of divisibility from Timaeus 35a through Aristotelian concepts.

According to Aristotle, only number, speech, line, surface, body, time, and place are properly quantitative (κυρίως), while all other quantitative items are such only accidentally (κατὰ συμβεβηκός):

 

for it is to these [i.e. to per se quantities] we look when we call the others quantities. For example, we speak of a large amount of white because the surface is large (οἷον πολὺ τὸ λευκὸν λέγεται τῷ τὴν ἐπιφάνειαν πολλὴν εἶναι), and an action or a change is called long because the time is long. For it is not in its own right that each of these others is called a quantity […] in saying how much white one will determine it by the surface – whatever the size of the surface one will say that the white too is that size (καὶ τὸ λευκὸν ποσόν τι ἀποδιδοὺς τῇ ἐπιφανείᾳ ὁριεῖ, - ὅση γὰρ ἂν ἡ ἐπιφάνεια ᾖ, τοσοῦτον καὶ τὸ λευκὸν φήσει εἶναι) (Cat. 6.5a39-5b8. Trans. Ackrill 1963).[24]

 

Just as Aristotle places body among per se quantities and a quality like the colour white among accidental quantities, Plotinus ascribes primary divisibility to bodies and secondary divisibility to qualities. Like Aristotle, Plotinus uses colours, and white specifically, as a main example of qualities (VI.4.1; IV.3.2). Aristotle also says that we determine the quantity of the colour white only accidentally, that is, by reference to the quantity of the surface in which it inheres. This recalls the passage from VI.4.1 we have just read: Plotinus affirms that white has a certain size, namely the size of the body of which it is a property, and this precisely because (διό) it is its property (σώματος ὄν τι). Some lines above, Plotinus had even adopted Aristotle’s terminology, clearly implying that qualities possess magnitude accidentally (κατὰ συμβεβηκός): “[…] one could reasonably inquire how the soul acquires magnitude accidentally. For soul is certainly not in the whole body in the same way as quality, sweetness or colour for instance” (VI.4.1.16-19). Further support for this interpretation comes from treatise IV.7. As we have seen, here Plotinus illustrates the sui generis kind of extension proper to quality through the example of the sweetness of honey. Aristotle employs this very example as an illustration of the third species of quality, affective qualities (Cat. 8.9a28-b2). Note that colours are affective qualities too, and in the passage just quoted Aristotle explicitly classes colours as accidental quantities.

If this interpretation is on the right track, we can identify a further element of Aristotle’s discussion of quantity that may have inspired Plotinus:

 

Most distinctive of quantity is its being called both equal and unequal. For each of the quantities we spoke of [i.e., per se quantities] is called both equal and unequal. For example, a body is called both equal and unequal, and a number is called both equal and unequal, and so is a time […]. But anything else – whatever is not a quantity – is certainly not, it would seem, called equal and unequal. For example, a condition is certainly not called equal and unequal, but, rather, similar; and white is certainly not equal and unequal, but similar (καὶ τὸ λευκὸν ἴσον τε καὶ ἄνισον οὐ πάνυ, ἀλλ’ ὅμοιον) (Cat. 6.6a26-34. Trans. Ackrill 1963).

 

Aristotle affirms that ‘equal’ and ‘unequal’ are proper predicates of per se quantities. As such, they do not apply to items that fall under other categories. I suggest that Plotinus draws on and innovates this Aristotelian idea when distinguishing bodies from qualities on mereological grounds. Characteristic (ii) states that the parts of a body “must necessarily be less than the all and whole (ἔλαττον εἶναι δεῖ τοῦ παντὸς καὶ ὅλου)”. This characteristic can be understood as an application of that Aristotelian idea. After all, the predicate ‘less’ is a quantitative predicate just like ‘equal’ and ‘unequal’. Plotinus can be understood as saying that bodies are necessarily characterised by an internal inequality: that of their mereological structure, wherein the part is less than the whole. Conversely, characteristic (b) states that qualities, as secondarily divisible, lack such mereological structure: they are whole, not ‘less’, in each part of the body in which they inhere. This characteristic can be seen as an application of Aristotle’s idea that quantitative predicates do not apply to qualities. Picking up Plotinus’ example: the reason why the whiteness in a portion of milk is not ‘a part’ of the whiteness of the whole milk is that the ordinary notion of ‘part’ necessarily implies the quantitative predicate ‘less’, and quantitative predicates do not apply to qualities like colours. As Aristotle states in the passage above, ‘white’ is neither ‘equal’ nor ‘unequal’, but rather ‘similar’ or ‘dissimilar’. If this reading is correct, Plotinus does not merely employ Aristotle’s analysis of quantitative items and predicates, but develops it in an original philosophical direction. His key innovation lies in the different perspective he adopts on quantitative items and predicates. Aristotle focuses on comparative relations between distinct items: per se quantities are ‘equal’ or ‘unequal’ with respect to each other (while accidental quantities cannot be ‘equal’ or ‘unequal’ to each other). By contrast, Plotinus focuses on the very internal structure of extended items: bodies are characterised by an internal inequality, that between part and whole (which does not apply to qualities).

We can thus draw a second conclusion. Plotinus deploys Aristotle’s analysis of quantitative items and predicates into a novel reflection on the internal structure of bodies and qualities as spatially extended realities. This novel reflection on the internal structure of bodies and qualities provides the conceptual foundation for his interpretation of the nature ‘that becomes divisible among bodies’ from Timaeus 35a. Plotinus identifies two natures in this expression: bodies, which are primarily divisible and endowed with a mereological structure wherein the part is less than the whole, and qualities, which are secondarily divisible and lack such structure. Thus, the doctrine Plotinus presents as Platonic exegesis rests on an original and sophisticated development of Aristotelian notions.

 

5. Some Remarks on Plotinus’ Notion of Extended Quality

and Middle Platonism

 

The conclusion we have just reached conflicts with an hypothesis advanced by Heinrich Dörrie. One of Plotinus’ examples of quality – sweetness, which is whole in every part of honey (IV.7.8¹) – appears in similar terms in Calcidius (In Tim. 242.19-22 Waszink). For this and other reasons, Dörrie believed that both Plotinus and Calcidius drew this example from a lost Middle Platonic handbook.[25] Against this interpretation, Cristina D’Ancona has already observed that Calcidius may have drawn the example from Plotinus himself.[26] I would add that, if my interpretation is correct, there is no need to suppose the existence of a lost handbook to explain the presence of this example in Plotinus. As we have seen in the previous section, Aristotle himself employs it at Cat. 8.9a28-b2. Now, it is true that Aristotle mentions the sweetness of honey only to illustrate the third species of quality, and, unlike Plotinus and Calcidius, does not connect this example to the idea that qualities lack parts. However, it is unnecessary to suppose that Plotinus found this idea in a lost Middle Platonic handbook. It is more economical and plausible to think that Plotinus found the example of the sweetness of honey in Aristotle (or even in commentaries on the Categories, although I view this latter hypothesis as unnecessary as well), and that he himself introduced the idea that sweetness, being a quality, is a whole in every part of honey. He did so by developing the Aristotelian analysis of quantitative items and predicates in an original direction, as argued in section 4 above. Plotinus certainly possessed the philosophical talent and originality to make such an advance. He even had a compelling reason to do this: his account of qualities as wholes in every part of body plays a central role in his theory of the soul, which was itself quite original and represented a fundamental priority of his philosophical agenda. Calcidius, as D’Ancona suggests, may have followed his lead.

To be sure, this does not exclude Middle Platonic mediations. Tornau and Emilsson have plausibly suggested that Plotinus’ insistence on the distinction between qualities and soul constitutes a critique of previous Platonists. In particular, this suggestion is based on a convincing parallel between VI.4.1 and a report by Nemesius of Emesa on Ammonius Saccas’ and Numenius’ anti-Stoic polemic regarding the incorporeality of the soul.[27] We can now revisit this parallel in light of the results obtained thus far. The passage from Nemesius reads as follows:

 

What Ammonius, the teacher of Plotinus, and Numenius the Pythagorean said is satisfactory in reply to all those together who say that the soul is a body. […] If they were to say that bodies are three-dimensional and the soul which penetrates the whole body is three-dimensional and therefore must be a body, we shall say that while every body is three-dimensional, not everything three-dimensional is body. For both quantity and quality are incorporeal in themselves but are incidentally quantified in a bulk (καὶ γὰρ τὸ ποσὸν καὶ τὸ ποιὸν ἀσώματα ὄντα καθ’ ἑαυτὰ κατὰ συμβεβηκὸς ἐν ὄγκῳ ποσοῦται). So in the same way the soul as such has no dimensions, but incidentally is viewed together with the three-dimensional thing in which it is, and is itself three-dimensional (οὕτως οὖν καὶ τῇ ψυχῇ καθ’ ἑαυτὴν μὲν πρόσεστι τὸ ἀδιάστατον, κατὰ συμβεβηκὸς δὲ τῷ ἐν ᾧ ἐστι τριχῇ διαστατῷ ὄντι συνθεωρεῖται καὶ αὐτὴ τριχῇ διαστατή) (De nat. hom. pp. 17, 16-18, 22 Morani. Trans. Sharples and van der Eijk 2008).

 

According to Nemesius, Ammonius and Numenius argued against the Stoics that the soul, while three-dimensional, is not a body, because not everything that is three-dimensional is a body: several three-dimensional things are incorporeal. According to them, while incorporeal and unextended in itself, the soul possesses accidental magnitude by virtue of its presence in the three-dimensional body. This line of reasoning assimilates the soul to quantity and quality, which are themselves incorporeal but “are incidentally quantified in a bulk (κατὰ συμβεβηκὸς ἐν ὄγκῳ ποσοῦται)”.

This expression strongly suggests that, before Plotinus, Ammonius and Numenius had already appropriated Aristotle’s distinction between per se and accidental quantities in their anti-Stoic polemic. They classified body as a per se quantity and both soul and qualities as mere accidental quantities. However, as far as we can judge from this brief report, Plotinus’ position represents a significant advance beyond his predecessors in two respects. First, his stance on the incorporeality of the soul is more radical. While Plotinus agrees that qualities are incorporeal and possess only accidental magnitude, he finds the assimilation of soul to quality inadequate. For him, the soul differs fundamentally from qualities: it is completely unextended and thus independent from the body, whereas qualities are divisible and spatially extended, though only secondarily. Thus, Plotinus restricts the application of accidental quantity to qualities alone, conceiving the soul as entirely unextended. Second, Plotinus’ engagement with Aristotelian concepts is considerably more sophisticated. Whereas Ammonius and Numenius merely invoke the distinction between per se and accidental quantities, Plotinus supplements this distinction with a detailed account of the different modes of extended being proper to bodies and qualities. Furthermore, if my analysis of this account is correct, Plotinus employs Aristotle’s idea that quantitative predicates apply only to per se quantities, and innovates by transposing this principle from comparative relations between quantitative items to their internal structure. There is absolutely nothing in Nemesius’ report to suggest that Ammonius and Numenius engaged with Aristotle’s Categories in a comparable way.

 

Conclusion

 

In this article I have examined Plotinus’ account of the extended mode of being of bodies and qualities. I have argued that, while he presents this doctrine as an interpretation of the celebrated passage on the World-Soul’s composition (Timaeus 35a), its underlying concepts are drawn from Aristotle’s physical and logical treatises.

First, Plotinus’ notion of extended body or ‘mass’ exhibits significant parallels with Aristotle’s discussions of continuous magnitudes and place in books IV and VI of the Physics: the triple terminological equivalence between ‘mass’ (ὄγκος), ‘magnitude’ (μέγεθος), and ‘body’ (σῶμα); the formula ἄλλο, τὸ δ’ ἄλλο to indicate the spatial differentiation and numerical distinctness of the parts of continuous quantities; and the concept of ‘proper place’ (ἴδιος τόπος). While Plotinus draws his notion of extended body from Aristotle, he attaches to it a negative axiological judgment that is completely absent in Aristotle’s neutral analysis, and thus makes extension a mark of the ontological deficiency of bodies vis-à-vis the absolute unity of intelligible realities. Hence, Plotinus employs Aristotelian means to interpret Plato and the vocabulary of divisibility employed in Timaeus 35a.

Second, Plotinus’ notion of extended quality likewise presupposes Aristotelian concepts, in this case from the Categories. Building on the connection to Aristotle’s particular properties (Cat. 2) already established in scholarship, I have argued that Plotinus’ distinction between primarily divisible bodies and secondarily divisible qualities is a sophisticated development of Aristotle’s discussion of quantity in Categories 6 and, more specifically, of the distinction between per se and accidental quantities. A further important element is Aristotle’s observation that ‘equal’ and ‘unequal’ are proper predicates of per se quantities and do not apply to accidental quantities. Plotinus innovates this Aristotelian idea by shifting perspective from comparative relations (one body is equal or unequal to another body) to a focus on internal structure. He asserts that bodies, as primarily divisible, are necessarily characterised by an internal inequality – the mereological structure wherein parts are less than the whole. Conversely, qualities lack mereological structure precisely because, as accidental quantities, they do not admit quantitative predicates. Again, these ideas provide the conceptual foundation through which Plotinus interprets Plato’s vocabulary of divisibility from Timaeus 35a.

Third, I revisited from this perspective a well-known report from Nemesius on Ammonius Saccas and Numenius. This passage indicates that, before Plotinus, these authors had already appropriated Aristotle’s distinction between per se and accidental quantities in their anti-Stoic arguments about the soul’s incorporeality. Yet Plotinus’ position on the incorporeality of the soul is more radical and his engagement with Aristotle more sophisticated. This represents a significant philosophical advance within the Platonic tradition.

These results reveal Plotinus’ sophisticated exegetical method: he does not extract doctrines directly from Platonic texts, but reads Plato through carefully selected Aristotelian concepts that he significantly develops to articulate positions nowhere explicit in the dialogues themselves. Furthermore, his doctrine of extension plays a crucial systematic role in his ontology. It enables him to draw a clear-cut divide between sensible and intelligible reality: by describing in detail the precise status of qualities as extended beings, he differentiates them from the soul and thereby secures the latter’s position on the intelligible side.

 

Acknowledgments: This text is based on part of my doctoral research, carried out at the University of Roma Tre, University of Roma Tor Vergata, and University of Würzburg, and funded by the University of Roma Tor Vergata. Previous versions were presented in Vercelli and Athens as part of the panel Aristotle among the Neoplatonists at the 22nd conference of the International Society for Neoplatonic Studies. I would like to thank Aristotelica’s anonymous reviewers and all those who provided comments on the ideas presented here: Riccardo Chiaradonna, Daniela Taormina, Christian Tornau, Christoph Horn, Alexandra Michalewski, Leonida Vanni, Jan Opsomer, Paolo Maffezioli, and Bruce McCuskey. All remaining errors, of course, are mine.

 

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