Plotinus’ views on concepts, as opposed to his views on ‘conceptions’ (ennoiai), have so far received very little attention in the literature.Footnote 1 This is mostly because Plotinus uses a bewildering variety of terms to refer to what seem to be mental states and/or objects that could, in principle, stand for what we might call a ‘concept’, however defined, as distinct from a conception of something or other, meaning some kind of thought.Footnote 2 There is, however, one place in the Enneads where he seems to deal precisely with what is at least one ancient account of concepts. This is Ennead 6.6.12–14, where Plotinus examines the Stoic account of one and numbers as ‘concepts’ (ennoēmata). It has long been acknowledged that this account is Stoic;Footnote 3 yet scarcely any attempt has been made at reconstructing either the account itself or Plotinus’ criticism of it.Footnote 4 This is probably for two reasons. The first is that Plotinus’ seems to be the only report we have on the Stoics’ account of numbers as concepts, and the lack of any term of comparison makes it harder for us to assess its reliability. The second reason is that Plotinus’ criticism of that account is very compressed and needs some unpacking. In this paper I will try to reconstruct both the views which Plotinus ascribes to the Stoics and his criticism of them. I will not, however, try to show that those views are genuinely Stoic, and that, therefore, Plotinus is a reliable source for the Stoic account of one and numbers as concepts. I will instead take Plotinus’ report at face value and use his criticism of the Stoics to understand his own views on concepts.
Roughly, a concept, for the Stoics, is an object of thought, which is distinct from the mental state – that is, the thought – it is the object of. We can say that it is the intentional object of a thought. It is widely agreed that the Stoic account of concepts goes back to the founder of the school, Zeno, who formulated it in the attempt to provide an alternative to Plato’s conception of universals as Forms (Stobaeus 1.136.21–137.6 = SVF 1.65 = LS 30A). I will take universals to be things whose nature is such that they can be predicated of more than one thing.Footnote 5 While Plato conceived of these things in terms of Forms, Zeno, in contrast, conceived of them in terms of concepts.
Zeno seems to have reached this view by reflecting on a specific Platonic text: Parmenides 132b–c, where Socrates suggests that Forms could be ‘thoughts’ (noēmata) in our soul (132b3–6). To this Parmenides replies:
T1 What do you mean? Is each thought one, but a thought of nothing? – That’s impossible – Of something, rather? (alla tinos?) – Yes – Of something which is or which is not? – Which is (ontos) – Is it not of some one thing (henos tinos), which that thought thinks is over all the particulars, being some single character? – Yes – Won’t this thing which is thought to be one, being always the same over all particulars, be a form? – This seems necessary.
Parmenides points out that a thought must be a thought of something, and of something which is, namely which exists. If what is thought of is some one thing which exists over a range of particulars, then that thing, Parmenides observes – that is, the object of the thought – will have a better claim to the status of Form than the thought itself.Footnote 6 Socrates agrees, while Zeno disagreed. Granted that there has to be an object that we think of, when we think of one character some particulars have in common, Zeno argued, this object does not have to be a Form, or a metaphysical being existing in its own right outside the mind, for it can be ‘an object in thought’, an en-noēma. Just as, for instance, generic ‘man’ is an ennoēma, Zeno said, so the corresponding mental state in which it is grasped is an ennoia or a ‘conception’ of this generic ‘man’ that spells out what it is, for example, a rational mortal animal. Pressing his polemical point, Zeno also argued that concepts, as distinct from mental states, far from being ‘beings’ of any sort, were mere ‘figments of the mind’ (Diogenes Laertius 7.60-1 = LS 30C). Just like mythological creatures, such as Centaurs, they had nothing corresponding to them in the world. We can think of the concept ‘man’, Zeno maintained, but there is no generic ‘man’ corresponding to it outside the mind, only particular human beings. Since Zeno granted that we could conceive of, that is, form an ennoia of, all sorts of things, it is unclear what things exactly he thought there were concepts of. However, in light of the important role he assigns to concepts in his epistemology, as subjects of definitions in particular, I will maintain here that concepts, for him, were the objects only of a particular class of ennoia, namely those formed naturally through our experience of sensible things.Footnote 7
Enn. 6.6.12–14 is the only place in the Enneads where Plotinus mentions the Stoic account of concepts.Footnote 8 Given his commitment to the existence of Forms, and the central role Forms have in his epistemology this is rather odd. Even more puzzling is the fact that he mentions that account in the context of a discussion about numbers rather than, for instance, Forms or universals. I will argue that, despite all appearances to the contrary, in Enn. 6.6.12–14 Plotinus criticizes not merely the Stoics’ account of one and numbers as concepts, but their account of concepts in general, and that, through this criticism, he aims to show that, rather than replacing Platonic Forms with concepts in the mind, as the Stoics did, one should replace concepts in the mind with Platonic Forms, and view these as the only proper objects of conceptions.
1 Plotinus’ Report: Enn. 6.6.12
Enn. 6.6 deals, in large part, with the problem of establishing the nature and the ontological status of numbers. Plotinus takes one and numbers to be intelligible things existing in their own right within the realm of Platonic Forms.Footnote 9 In chapter 12, he introduces an account of numbers which seems to raise a challenge for his view. The chapter begins abruptly with two objections against this account, the first of which runs as follows:
T2 But if one were to say that the one, i.e. the unit (tēn monada), has no reality – for there is no one which is not some one thing (ouden gar hen ho mē ti hen) – but is some kind of affection of the soul in respect to each being (pathēma de ti tēs psukhēs pros hekaston tōn ontōn), first why not say that, whenever one says ‘being’, this, too, is an affection of the soul, and there is no being? But if the reason is that this stabs and strikes and produces an impression (phantasian) about a being, we see that the soul is stabbed and takes an impression also about the one.
Plotinus does not explicitly mention the Stoics here – he never does – but we can be sure that they are his target because he mentions a view he ascribes to them elsewhere (e.g., Enn. 3.6.6.33–6), namely the view that ‘beings’ (onta) – that is, on Stoic ontology, bodies – produce impressions which ‘strike’ and ‘stab’ us. Plotinus, then, says that, for the Stoics, the one (i.e. the unit) has no reality by itself outside the mind, but is merely a way in which our mind is impressed in respect to each and every being. This is because, in their view, ‘there is no one which is not some one thing’. What he means by this can be inferred from the objection he moves against the Stoic conception of the one, and from what he thinks the Stoics themselves would reply to him. Plotinus argues, polemically, that their account of the one should commit the Stoics to an analogous account of ‘being’. Presumably, this is because, like many contemporary scholars, Plotinus takes the Stoics to be particularists, and thus reasons as follows. If, on the grounds that there is no ‘one’ which is not some one thing, the Stoics conclude that the one has no reality by itself, then why, on the grounds of their particularist thesis that there is no ‘being’ which is not some being, are they not concluding that ‘being’ has no reality by itself, and that, therefore, there is nothing which truly ‘is’ outside the mind? The Stoics, he suggests, would reply that the case of ‘being’ differs from that of the one in that there is something which makes a thing a ‘being’. This is its capacity to act (see SVF 1.90 = LS 45A and SVF 2.363 = LS 45B), in virtue of which that thing ‘strikes’ our mind and produces an impression on it. To this Plotinus retorts that, since they admit that ‘some one thing’, too, produces an impression on us, they should concede that there is something which makes it ‘one’, and that this something is a being. In light of these preliminary remarks, we can say that what Plotinus means when he claims that, for the Stoics, ‘there is no one which is not some one thing’ is that they denied the extra-mental reality of both a ‘one itself’ and a property ‘unity’ responsible for making this or that thing ‘one thing’. Since the Stoics denied any extra-mental existence to the one, Plotinus says, polemically, that they conceived of it as being merely some kind of mental affection.
Let us pass to Plotinus’ second objection:
T3 Then do we see the affection, i.e., the thought (to noēma), of the soul to be one or a plurality? But if we say ‘not one’ (mē hen), we do not have the one from the thing itself – for we say that the one is not in it – so we do have ‘one’, and it is in the soul without the ‘some one’ (ti hen).
Now Plotinus identifies the affection of the soul he mentioned in T2 with a ‘thought’ (noēma) and treats this thought as if it were something analogous to an object outside the mind. Let us grant the Stoics that when we encounter some one thing in the world we form the thought that it is ‘one’ without there being any unity present in it, he argues. Let us now consider this very thought: were we as if ‘to look at it’, would we say that it is ‘one’ or ‘not one’? Presumably because a thought is something articulated into at least a subject and a predicate, Plotinus suggests that anybody would say that this thought is ‘not one’. From this Plotinus infers that the notion of ‘one’ or ‘unity’ should be something our mind has access to before any encounter with ‘some one thing’. In saying that the thought of some one thing is ‘not one’, he argues, what we say, in fact, is that the notion of ‘one’, that is unity, does not apply to it. But, he goes on, the very fact that we can say that the notion of ‘one’ does not apply to our thought shows that we have access to that notion before and independently of that thought. In other words, even granting that we could derive our notion of ‘one’ from ‘some one thing’, Plotinus says, our ability to deny that this notion applies when we encounter something which is not ‘some one thing’ shows that our mind has access to it independently of any ‘some one thing’.
Note that Plotinus’ first objection aims to press the Stoics into acknowledging that the one must have some extra-mental existence, while the second objection aims to force them into acknowledging that some notion of the one must be available to our mind before we encounter some one thing and we think of it as being ‘one’. Plotinus introduces what he takes to be the actual Stoic account of one and numbers as concepts as their answer to these objections. Thus, right after T3, he observes that the Stoics would answer the second objection in this way:
T4 ‘But we have the one by having taken from the things outside some kind of thought and some kind of imprint, as if an ‘object in thought’ (hoion ennoēma)’, [they would say]. For those who posit the numbers and the one as one kind of what they call ‘concepts’ (οἱ μὲν γὰρ τῶν λεγομένων παρ’ αὐτοῖς ἐννοημάτων ἓν εἶδος τὸ τῶν ἀριθμῶν καὶ τοῦ ἑνὸς τιθέντες) would posit them as realities of this kind [scil. as objects in thought], if indeed any such thing is real; and it would be the right time to speak against these people about them.
Plotinus remarks that, to answer his second objection, the Stoics would invoke their account of the one as concept. They would grant that speaking or thinking of what is ‘not one’ requires access to the notion of ‘one’, but would argue that this notion is the empirically derived concept ‘one’.
Then Plotinus goes on to explain what the Stoics would say in response to his first objection:
T5 But, then, 1) if one were to say that this affection or thought has come to be in us from the things [outside] as something which is posterior in the way in which ‘this’ (to touto) is, and ‘something’ (to ti), and, for that matter, also ‘crowd’, ‘feast’, ‘army’, and ‘multitude’ – for just as the multitude is nothing apart from the things which are said to be many (ὥσπερ τὸ πλῆθος παρὰ τὰ πράγματα τὰ πολλὰ λεγόμενα οὐδέν ἐστιν), and the feast is nothing apart from those people who came together and are enjoying themselves at the rites, thus even when we say ‘one’ we do not do so because we think the one to be something alone and isolated from any other thing (οὕτως οὐδὲ τὸ ἓν μόνον τι καὶ ἀπηρημωμένον τῶν ἄλλων νοοῦντες, ὅταν λέγωμεν ἕν) – and 2) if one were to say that there are many other things of this sort, for instance ‘right’, ‘above’, and their opposites – for what could the reality of ‘right’ amount to other than the fact that one stands or sits here and another there? And indeed the same holds in the case of above: one thing has this position and is more in that region of the universe which we call ‘above’ [scil ‘above us’], while another is in the so-called ‘below’ – in answer to these things one must say that there is some kind of reality of the things we mentioned present in each of them […].
There is no need to postulate that the one has some extra-mental existence and that there is some unity in things in order to explain how we can receive an impression from, and think of, ‘some one thing’, the Stoics would reply. For, they would say, when we think of something as being ‘one’, we do not think of it as a special thing set apart from the rest by its ‘oneness’ or ‘unity’, just as we do not think of ‘this thing’ (touto) or simply of ‘something’ (ti) as things set apart from the rest by, respectively, their ‘thisness’ and their ‘somethingness’. According to Plotinus, the Stoics would support these ontological considerations about the one by appealing to an analogy. Just as an army, they would say, is nothing apart from the individuals who constitute it and are disposed in a certain way, and just as ‘on the right of’ is nothing apart from a thing standing in a certain relation in respect to another thing, so the one is nothing apart from the thing which is said to be ‘one’. The examples used in this analogy – crowd, army, on the right of – reveal that, on Plotinus’ reading, the Stoics appealed to their theory of the categories to explain what being ‘one’ consisted in for something or other. This theory provided a classification of the many ways a thing can be or exist. A thing, the Stoics argued, is basically an ‘object’ (hupokeimenon), namely some lump of matter, but an object can be either some ‘qualified object’ (poion) or some ‘object so disposed’ (pōs ekhon) or, finally, some ‘object so disposed in relation to something’ (pros ti pōs ekhon). They held that ‘qualified objects’ and ‘objects so disposed’, that is, objects in the second and the third category respectively, were intrinsically differentiated – the former by a quality, the latter by the disposition of their parts – while objects in the fourth category were merely extrinsically differentiated by standing in some relation or other in respect to other objects. In the second category they included things like human beings, which, in their view, owed their being the sort of things they were to a quality (i.e. ‘humanity’); in the third category they included things like ships and armies; in the fourth things like ‘father’ or ‘on the right of’. Precisely as Plotinus suggests, they held that – since they were not what they were in virtue of an intrinsic quality – objects in the third and the fourth category – that is, things like armies and objects standing ‘on the right of’ – were nothing ‘apart from’ (παρά + gen.) their constituent parts or the objects standing in the relevant relations. In T5 Plotinus certainly alludes to the third and the fourth categories. Note, however, that he does not say that, for the Stoics, to be ‘one’ was to be an object in one of these categories. What he says, rather, is that, on his interpretation, the Stoics invoked the third and the fourth categories to support their claim that something or other could be ‘one’ without having any unity in it. As Plotinus claims in T2, the Stoics, for him, thought that ‘one’ could be said ‘in respect of each being’, that is, they thought that any being, i.e. any object, could be ‘one’ (more on this, see Section 2).
To see how the Stoics argued for this view on Plotinus’ interpretation, consider the way in which he phrases their reply to his first objection in T5: ‘Just as the multitude is nothing apart from the things which are said to be many […], thus even when we say ‘one’ we do not do so because we think the one to be something alone and isolated from any other thing (οὐδὲ τὸ ἓν μόνον τι καὶ ἀπηρημωμένον τῶν ἄλλων νοοῦντες)’. This is a rough quotation from Plato’s Sophist, 237d1–4. There the Visitor wonders what the name ‘that which is not’ (to mē on) could be applied to (237b–c). He concludes that, since it cannot be applied to ‘that which is’ (to on), it cannot be applied to ‘something’ (to ti) either. This is because:
T6 Presumably it is clear to us that on each occasion we say also this ‘something’ of a being (τὸ ‘τὶ’ τοῦτο ἐπ’ ὄντι λέγομεν); for it is impossible to say it alone, as if it were naked and isolated from all the things that are (μόνον γὰρ αὐτὸ λέγειν, ὥσπερ γυμνὸν καὶ ἀπηρημωμένον ἀπὸ τῶν ὄντων ἁπάντων, ἀδύνατον). Is it not?
Having obtained Theaetetus’ agreement, the Visitor remarks the following:
T7 Are you agreeing because you consider that one who says something must be saying some one thing (τόν τι λέγοντα ἕν γέ τι λέγειν)? […] For you will certainly say that ‘something’ is a sign of one, and ‘some couple’ is a sign of two, and ‘some’ is a sign of many (ἑνὸς γὰρ δὴ τό γε ‘τὶ’ φήσεις σημεῖον εἶναι, τὸ δὲ ‘τινὲ’ δυοῖν, τὸ δὲ ‘τινὲς’ πολλῶν). […] Indeed it seems that one who says ‘not something’ says nothing at all.
By inserting this quotation in T5 Plotinus suggests that what motivated the Stoics to deny that the one was something apart from some object or other which happened to be one was their reading of the Visitor’s remarks in T6 and T7. Starting from T6, they reasoned, in his view, that, if ‘something’ is never ‘naked’ and ‘isolated’, this is because it is nothing apart from some being or other, as there is no ‘something itself’ out there in the world nor is there anything set apart from other things by the presence of some ‘somethingness’ in it. Then, on the grounds of T7, they concluded that the same had to hold of ‘one’. Just like ‘something’, they argued, ‘one’ is never ‘naked’ and ‘isolated’ because it is nothing apart from ‘some one being’ or other, as there is no ‘one itself’ nor is there anything set apart from other things by the presence of some ‘oneness’ or unity in it.
According to Plotinus, then, any being, for the Stoics, was ‘one’, just as any being was ‘something’, so that, for them, ‘something’ and ‘one’ were co-extensive or, at least, were equally said of each and every being. As they were said of each and every being, neither of them was itself a ‘being’, either by being a distinct object, that is, a ‘one itself’ or a ‘something itself’, or by being a distinct property, that is, unity or ‘somethingness’, present in some objects but absent from others.Footnote 10
In light of T5 we can already draw some preliminary conclusions about Plotinus’ reading of the Stoics’ account of one and numbers as concepts. It is often said that Locke’s ideas are the closest approximation to what the Stoics meant by ‘concepts’. T5 reveals that, on Plotinus’ reading, this is true also of their concept ‘one’ and, in general, of the concepts they identified numbers with. As for Locke, so for the Stoics, numbers were merely notions in the mind, and the concept ‘one’ was, as Locke puts it, ‘suggested to the understanding by every object without us, and every idea within’ (Essay 2.7.7).
2 Plotinus’ Criticism
2.1 Enn. 6.6.13
In chapters 13 and 14, Plotinus provides more details about the Stoic account of one and numbers and, while articulating more fully his two objections against it, he begins to introduce his own views on what one and numbers are. ‘We need to know specifically, Frege says in The Foundations of Arithmetic (42): is the dog conscious, however dimly, of that common element in the two situations which we express by the word ‘one’, when, for example, it first is bitten by one larger dog and then chases one cat? This seems to me unlikely. I infer, therefore, that the notion of unity is not, as Locke holds, ‘suggested to the understanding by every object without us, and every idea within’, but becomes known to us through the exercise of those higher intellectual powers which distinguish men from brutes. Consequently, such properties of things as being undivided or being isolated, which animals perceive quite as well as we do, cannot be what is essential in our concept’.Footnote 11 This quotation from Frege will help us to see the two main points Plotinus aims to establish in chapter 13. The first point, which is related to his second objection against the Stoics in chapter 12, is that the one must be an intelligible object existing in its own right that the mind must grasp before forming a thought. The second point, which is related to his first objection against the Stoics in chapter 12, is that unity must be a distinct and intrinsic property of any being. It is with the discussion of this first objection that chapter 13 begins.
Right at the beginning of the chapter, Plotinus observes (2. 1–6) that we cannot form ‘the thought of the one’ (tēn noēsin tou henos) in the way the Stoics suggest we do, namely just by thinking of ‘some one thing’, one human being, for instance, or one animal. This is because, he says, in that case, ‘the thought of the one’ would not differ in any way from the thought of a human being or of an animal, and we could not explain how we can think of many different things, for example, humans, animals, but also stones, and so forth, as being equally ‘one’. To understand the full impact of his criticism we need to consider a passage from Simplicius’ commentary on Aristotle’s Categories (in Cat. 214, 24–37 = SVF 2.391 = LS 28M).
Simplicius reports that the Stoics spoke of ‘qualified objects’ – that is, assigned an object to the second category – only ‘in the case of unified objects’ (epi tōn hēnomenōn). This was because they thought that, if an object was unified, it had to be so in virtue of an intrinsic quality, namely, a single bit of ‘binding’ pneuma, holding it together. This quality was not, on Simplicius’ account, a special property ‘unity’, but rather the very quality which made that object the sort of object it was, for example, in the case of a human being, ‘humanity’. In light of Simplicius’ report, we can explain Plotinus’ criticism as follows: the Stoics maintain that objects in the second category, such as human beings, are ‘one’ in the sense that they are unified. Since, however, they do not distinguish their unity from the quality which makes them the sort of things they are, they are unable to explain what it is that makes them ‘one’ as opposed to just humans, for instance. Hence, they are unable to explain how thinking of something as being ‘one’ differs from thinking of it as being such and such an object, for example, a human being.
Then Plotinus introduces a possible Stoic reply to his criticism (2. 9–10). The Stoics, he says, would argue that, even if an object is indeed unified by the quality which makes it the sort of thing it is, when they say of it that it is ‘one’, they do not mean that it has that quality, but ‘that it is alone and there is no other thing’ (ὅτι μόνον καὶ οὐκ ἄλλο), which is something distinct from its having a certain quality. Plotinus retorts that, to be able to tell whether an object is ‘other than’, or ‘different from’, this or that thing, so as to isolate it from its surroundings, we need, first, to be able to see it as ‘one’ (2. 10–14).
Having dealt with the Stoics’ account of how objects in the second category are ‘one’, Plotinus turns to their account of how objects in the third category are ‘one’ and draws a general conclusion:
T8 For it [scil. an object] is either one or more than one, i.e. many, and, if many, one must exist before it. Since also when it [scil. reason] says ‘multitude’ it says ‘more than one’, and it thinks of an army as many armed men and gathered together into one order, and although it is a multitude, it does not let it be a multitude. Reason which gives the one, which the multitude does not have, presumably makes this clear also in this case; [reason] whichFootnote 12, having sharply seen the one which derives from the order, collected together the nature of the many into one (ὀξέως τὸ ἓν τὸ ἐκ τῆς τάξεως ἰδοῦσα τὴν τοῦ πολλοῦ φύσιν συνήγαγεν εἰς ἕν). For not even in that case [scil. That of the multitude] ‘one’ is falsely predicated, just as also in the case of a house the one which is derived from many stones [is not falsely predicated either], though, in the case of the house, the one is present in a higher degree (μᾶλλον μέντοι τὸ ἓν ἐπ’ οἰκίας). If, then, it is present in a higher degree in the case of what is continuous and in a [still] higher degree in the case of what is indivisible, this is clearly because the one is some particular and real nature. For it is not possible for there to be ‘a higher degree’ in non-beings (οὐ γὰρ οἷόν τε ἐν τοῖς μὴ οὖσι τὸ μᾶλλον εἶναι) […].
To understand Plotinus’ point, we must turn, once again, to the passage from Simplicius mentioned above. Having said that, for the Stoics, unified objects were such in virtue of the quality that made them the sort of objects they were, Simplicius remarks that this, for them, did not imply that objects in the third category, such as ships, armies, or choirs, were not unified at all.Footnote 13 All objects in both the second and the third category, he says, were intrinsically unified for the Stoics, though the latter were less so, because they were unified only in virtue of their ‘co-operation towards the fulfillment of a single task’ (τὴν πρὸς ἑνὸς ἔργου συνεργίαν), that is, only in virtue of the function-oriented structure of their parts, with continuous parts – as in ships (or houses) – accounting for a tighter structure and, thus, for a higher degree of unity.
It seems clear to me that, in T8, Plotinus has in mind this Stoic account of how things are unified. The Stoics, he argues, hold that some objects – those in the second and the third categories – are ‘one’ in different degrees. This is because, though all intrinsically unified, some of them are so in virtue of a ‘binding’ quality, while others are so only in virtue of the structure of their parts, which in some cases (e.g., a house) are continuous, while in others (e.g., a multitude) are separate. Yet, Plotinus objects, if the Stoics want to maintain that these objects are unified in different degrees, they must posit in each of them a property ‘unity’. For (see 2. 27–36), if the unity of a human being, say, consisted merely in its having the quality ‘humanity’, and the unity of a house and of a multitude consisted merely in a house having this kind of structure and the multitude having that kind of structure, then each of them – human being, house, and multitude – would be unified in its own way, and, thus, could not be ‘more’ or ‘less unified’ in respect to the others. Some things can be said to be ‘more unified’ than others only on the assumption that all unified things share one and the same property ‘unity’ in respect of which they are comparable. Thus, if the Stoics want to maintain that some things are more unified than others, Plotinus concludes, they must posit in each of them a distinct property ‘unity’ and conclude that this property is present in them in different degrees.
Plotinus goes on to observe that, as sensible things cannot have perfect unity, unity in the highest degree, or ‘unity itself’, must be an intelligible thing (2.27–36), and this leads him to the following conclusion:
T9 Just as substance and being are intelligible and not sensible, even if the sensible participates in them, so also the one might be observed in the sensible according to participation, but is nonetheless intelligible, and reason grasps it in an intelligible manner; thus, starting from one thing, it thinks of something else, which it does not see: so it knew it before. But if it knew it before as being ‘some this’ (tode ti), it is the same as being. And whenever it [scil. reason] says ‘something’, it says in turn ‘one’, just as whenever it says ‘a couple’, it says ‘two’, and whenever it says ‘some’, it says ‘many’ (καὶ ὅταν τι, ἓν αὖ λέγει· ὥσπερ ὅταν τινέ, δύο· καὶ ὅταν τινάς, πολλούς). If then it is not possible to think of anything without one or two or some number, how can that without which it is not possible to either think or say anything not exist? For it is impossible to say of that which, when it is not existent, you cannot think or say anything that it does not exist. But that which is needed in all cases for every thought or statement to come about, must pre-exist both statement and thought (προϋπάρχειν δεῖ καὶ λόγου καὶ νοήσεως); for this is how it can contribute to their coming to be.
Having argued that the Stoics should grant that unified things are unified in virtue of their unity, and that the one has, therefore, some extra-mental existence, Plotinus turns to the topic of his second objection: the priority of the notion of the one in respect to our thoughts about some one thing or other.
The reason why we can think of something as being ‘one’, he says in T9, is that there is a metaphysical unit, which is a particular object (i.e., tode ti) in which sensible things participate, and which the mind grasps whenever it thinks of them. Say that we see a cat: we recognize the unity in it in virtue of our natural ability to grasp ‘the unit itself’, and so we think of that cat as ‘one’; the same happens when we see a dog. Our grasp of ‘the unit itself’ is what enables us to think of different things, one cat and one dog, say, as being both ‘one’, that is, as being equally units. Having said this, Plotinus examines the passage which, in his view, inspired the Stoics to conclude that there is no ‘one’ apart from ‘some one thing’: Soph. 237d1–e2 (T6 and T7 above). That passage, he argues, does not say, as the Stoics maintain, that ‘one’, just like ‘something’, is said of each and every being as opposed to being itself a being. What it says, rather, is that any statement and any thought, insofar as it is of ‘something’, must be of ‘one’ or some number, because just by saying ‘something’ one says ‘one’, as just by saying ‘some couple’ one says ‘two’. If to speak, or think, of ‘something’ is to speak, or think, of ‘one’ or a number, Plotinus argues, then one and numbers must not only be beings (i.e., exist in their own right) so as to be the proper objects of statements and thoughts, but they must also exist before any statement or thought, so as to make the formulation of statements and thoughts possible.Footnote 14 In light of his interpretation of Soph. 237d1–e2, Plotinus leads the Stoics into a self-refutation. The Stoics, he observes, maintain that one and numbers, far from being ‘beings’ which are prior to statements and thoughts, are merely mental constructs derived from, and so posterior to, our thoughts about sensible things. Yet, he concludes, the very fact that they can formulate the statement that one and numbers do not exist proves that they do, for that statement could not have been formulated without them.
2.2 Enn. 6.6.14
Chapter 14 starts almost mid-sentence:
T10 One could reasonably reply to what has been said of relation (πρὸς δὲ τὰ κατὰ τὸ πρός τι λεχθέντα) that the one is not the sort of thing whose nature is destroyed without it suffering anything when something else suffers something, but must, if it is going to depart from the one, suffer the privation of the one by being divided into two or more. If therefore the same mass (ho autos onkos), having been divided, becomes two without having been destroyed as mass, it is clear that the one, which it [scil. the mass] lost when the division destroyed it, was present in it apart from the object (para ton hupokeimenon).
Plotinus returns to the topic of his first objection, the extra-mental existence of the one, and he assumes his readers to be familiar with a Stoic view he has not mentioned so far. The Stoics, Plotinus suggests, maintain that some objects, namely those in their second and third categories, are ‘one’ by being intrinsically unified in some way or other. But they think that even objects which are not so unified, such as masses, can be ‘one’. They are ‘one’ (or more), they hold, in the sense that they are countable, and they are so simply because, just like things in the fourth category, they stand in a particular relation to other objects rather than in virtue of some intrinsic differentiation accounting for their unity. Take some lump of mud (or a heap), for instance, it certainly has some intrinsic qualities, but none of them accounts for its being one, unified, lump of mud, the way ‘humanity’, for instance, accounts for this thing being one, unified, human being, or the way a certain intrinsic structure accounts for this other thing being one ship. Against this view Plotinus argues the following: assume that a mass, such as a lump of mud, is ‘one’ without being intrinsically unified, but only insofar as it stands in a particular relation in respect to other masses, for example, in relation to some other lump of mud. When the mass is cut, both it and its ‘oneness’ should be affected in the same way. Yet we can see that the mass remains unaffected, for it remains the mass it is (e.g., some mud) while its ‘oneness’ is destroyed, because it is no longer one mass but two. This, Plotinus concludes, suggests that the ‘oneness’ of the mass was all along a distinct property in it.
Then Plotinus anticipates an objection from his opponents:
T11 But if one were to say that the one also, without being affected at all, will no longer be one but two when something else has come to it (προσελθόντος ἄλλου αὐτῷ), one will not be speaking correctly. For it is not the case that the one has become two, neither that to which it was added nor that which was added, but each remains one, just as it was. Two is predicated of both, but one [is predicated] separately of each, each remaining [what it is]. Hence the two and the dyad do not by nature consist in a relation (en skesei).
Plotinus explains that his Stoic opponents would not agree with his claim (in T10) that the ‘oneness’ of the mass is destroyed when the mass is cut. They would say, rather, that it ‘becomes’ (γίνεται) ‘two’, and this without suffering anything, but merely because ‘something else has come to it’ (προσελθόντος ἄλλου αὐτῷ), so that, from ‘one’ that it was, it is now ‘two’. This strange expression ‘something else has come to it’ reveals that, for Plotinus, the Stoics argued that even beings which were not intrinsically unified could be ‘one’ by appealing to Plato’s puzzles about growth at Phaedo 96c–101e. For it is an expression Plato uses there in the context of his discussion of the so-called battlefield of the opposites (102d5–103a2). In the Phaedo, Socrates argues that a human being cannot be or become large, and thus grow, by the addition of some flesh to their body, just as ‘one’ cannot be or become ‘two’ by the addition of another ‘one’. Why exactly he rejects this possibility is a matter of controversy, but, it seems, the Stoics found nothing objectionable in it. Something can indeed become ‘two’, they argued, just because something else is added to it, which is why even beings which are not unified in themselves can be ‘one’, ‘two’, or many. Plotinus, too, invokes the Phaedo in his reply (2.19–27). Thus, immediately after T11, he says that being ‘two’ could consist in a relation only if a particular relation could be held responsible for making something or other ‘two’. But, appealing to Phd. 97a5–b3, he observes that a thing becomes ‘two’ not just by ‘the coming together’ of what was previously separated, but also by ‘the splitting’ of one thing into two. If both ‘splitting’ and ‘coming together’ (i.e., two opposite relations) can make a thing ‘two’, he infers, then any relation could make a thing be or become ‘two’, with the result that nothing would be more ‘two’ than ‘not-two’. Starting from these polemical remarks Plotinus argues in support of his Platonist account of how objects are one or many (2.27–33). Objects are ‘one’, he concludes, by the presence in them of ‘the one’ and two by the presence of the ‘the dyad’, that is, they are one, two, or some number by participating in the one itself and in numbers themselves.
3 Plotinus vs the Stoics on Concepts
A proper assessment of Plotinus’ interpretation of the Stoic account of one and numbers as concepts would require a complete reconsideration of the evidence we have concerning the Stoic theory of concepts, and this is not a task I can undertake here. What I want to draw attention to is the remarkable fact that, after having said that it would be the right time to speak against the Stoics on the subject of concepts (T4 above), throughout Enn. 6.6.12–14, Plotinus speaks almost exclusively of the concept ‘one’. He does not say anything about other concepts, such as, for instance, the concept ‘man’. As I have said in my introductory remarks, this is rather strange, given that Stoic concepts were meant to provide an alternative to Plato’s account of universals, and that Plotinus endorses Plato’s account. I want to suggest that the reason why Plotinus does not provide a separate, distinct criticism of Stoic concepts in general is that he thinks that, by having established that one and numbers must be beings, he has, thereby, already shown that all those things the Stoics call ‘concepts’ must be beings as well, and that, as generic beings, they must be Forms.
We have seen that, for Plotinus, the Stoics hold that the one is not itself a being, as it is neither an object – a ‘one itself’ – nor an intrinsic property of objects – some ‘oneness’ or unity. We have also seen that he takes the Stoics to have reached this conclusion on the grounds of their interpretation of Soph. 237d. But why, we should ask, were the Stoics so committed to denying any extra-mental existence to one and numbers? And, furthermore, why, according to Plotinus at least, did they appeal to Plato’s Sophist to build their argument for this conclusion? Let us go back to Parm. 232b–c (T1), the passage which seems to have inspired Zeno’s account of universals as concepts. There Parmenides says that a thought cannot be a thought of ‘nothing’ (oudenos), for a thought must be a thought ‘of something’ (tinos), and of something ‘which is’ (ontos) and is ‘some one thing’ (henos tinos). As I have said, Zeno rejected the conclusion that a thought must be a thought of something ‘which is’. This, right away, committed him to the view that a thought could be of something ‘which is not’; a view he readily endorsed, since he stressed that concepts were in fact not ‘beings’ but mere ‘figments of the mind’ corresponding to no object in the world. Yet, Zeno must have been reluctant to give up the idea that a thought had to be a thought of ‘some one thing’. For to say that a thought is not of ‘some one thing’ (or more), that is, of something that can be individuated and counted, is just to say that it is a thought of nothing and, thus, presumably, no thought at all.Footnote 15 Zeno, then, had to explain how a thought could be a thought of ‘that which is not’ and still be a thought of ‘some one thing’. According to my reconstruction of Enn. 6.6.12–14, Plotinus suggests that, to solve this problem, he or the Stoics after him looked at the Sophist, where in fact Plato struggles precisely with the issue of how we can speak, or think, of ‘that which is not’.
While aiming to explain how we can speak, or think, of ‘that which is not’, the Visitor in the Sophist acknowledges that some serious difficulties stand in the way of this task. T6 and T7 above are indeed the two central passages of what is generally taken to be the first difficulty, or first aporia, about not-being introduced by the Visitor. Roughly, this aporia runs as follows: to speak, or think, of ‘that which is not’ is impossible, because to say something is to say one thing or more and thus some being or some beings. The reason why to say ‘one thing’ amounts to saying one ‘being’ is left unclear in the text, but it seems that the Stoics, according to Plotinus, had no interest in solving this first aporia. They instead used the Visitor’s remarks on ‘one’ and ‘something’ to argue that ‘one’ and ‘something’ were not themselves beings, but merely things said of any being whatsoever. Almost immediately after T7, however, the Visitor introduces a second aporia about not-being:
T12 There are still more confusions to come, including the primary and most fundamental one, which actually happens to be at the source of the whole problem – What do you mean? Don’t hold back. Tell me – To that which is there might belong some other of those which are – Of course – But shall we say that any of those which are can ever belong to that which is not? – How could they? – Now then, we take all the numbers to be beings – yes, if we take anything else to be – Then let’s not even try to apply either plurality of number or one to that which is not – Our way of speaking itself tells us that it would be wrong to try to – Then how would anyone try either to say those things which are not or that which is not out loud, or even grasp them in thought, apart from number? (πῶς οὖν ἂν ἢ διὰ τοῦ στόματος φθέγξαιτο ἄν τις ἢ καὶ τῇ διανοίᾳ τὸ παράπαν λάβοι τὰ μὴ ὄντα ἢ τὸ μὴ ὂν χωρὶς ἀριθμοῦ;) – Tell me – Whenever we speak of that which is not aren’t we applying one to it? – Obviously – But we say it isn’t either right or correct to try to attach that which is to that which is not – That’s absolutely true – Do you understand, then, that it’s impossible to say, speak, or think, that which is not itself correctly by itself? It’s unthinkable, unsayable, unutterable, and unformulable in speech (ἀδιανόητόν τε καὶ ἄρρητον καὶ ἄφθεγκτον καὶ ἄλογον).
The interpretation of this passage is very controversial, but, basically, the Visitor claims that, if you grant that one and numbers are beings, then you cannot speak, or think, of ‘that which is not’. For, just by saying ‘that which is not’ (in the singular), that is, just by mentioning it, you are applying ‘one’ to it, and, just by saying ‘those which are not’ (plural), you are applying ‘many’. Assuming that one and numbers are beings, and that we cannot apply beings to non-beings, as the Visitor remarks, it follows that we cannot either mention ‘that which is not’ or even conceive of it, for ‘that which is not’ is not a being.Footnote 16
I suggest that, according to Plotinus, the Stoics found this second aporia to be the crucial aporia about not-being, and the one they needed to solve in order to defend their account of concepts. They noticed that the aporia rested on a prima facie unjustified assumption, namely the assumption that one and numbers are beings. They argued that, in light of their interpretation of the Visitor’s remarks in the context of the first aporia (i.e., T6 and T7) that assumption was simply false. When we mention, or conceive of, ‘that which is not’, they argued, we are mentioning, or conceiving of, ‘something’, and we are indeed applying ‘one’ to it; however, since neither ‘something’ nor ‘one’ are beings, we are not thinking of a being, and we are not applying a being to it. From these remarks they concluded that ‘that which is not’ could be mentioned and conceived without absurdity, and that, therefore, we could think of something which is not, such as the concept ‘man’, for instance, and yet think of ‘some one thing’, just as required by Parmenides in Plato’s Parmenides.Footnote 17
If these remarks are correct, then Plotinus’ defense of his conception of numbers as extra-mental intelligible entities in Enn. 6.6.12–14 turns out to be also a defense of Plato’s universals. Let us go back to T9. As I have said in Section 2.1, Plotinus there criticizes the Stoics by using the same passage from the Sophist they invoked, in his view, to defend their claim that ‘one’ is not a being, but is merely something said of any being whatsoever, namely T7. Note how Plotinus phrases the Visitor’s point in T9: ‘Whenever it [scil. reason] says ‘something’, it says in turn ‘one’, just as whenever it says ‘a couple’, it says ‘two’, and whenever it says ‘some’, it says ‘many’. If then it is not possible to think of anything without one or two or some number, how can that without which it is not possible to either think or say anything not exist?’Plotinus uses T7 to explain why one and numbers must exist, that is, to explain why, in T12 (the second aporia), the Visitor assumes that one and numbers are beings. This is a complete reversal of what I have suggested was, in his view, the Stoic reading of the relation between the first and the second aporiai about not-being in the Sophist. For him, I have argued, the Stoics read T7 as saying the same thing as T6, that is, as saying that ‘one’, just like ‘something’ in T6, is said of any being, but is not itself a being. Then they used T7 to show that the second aporia contained a false assumption, namely the assumption that one and numbers are beings. Plotinus, in contrast, takes T7 to provide the second aporia with the grounds for that assumption. Thus, in light of his interpretation of T7, he concludes that the Stoic solution of the second aporia is no solution at all. To say ‘something’, he argues, is to say ‘one’, but ‘one’ is a being, which is why, just as the Visitor says, we cannot speak, or think, of ‘that which is not’; for, just by mentioning, or conceiving of, ‘that which is not’, we are applying ‘one’, and therefore a being, to it. Having explained why one and numbers must be beings, and why, therefore, the Stoics, in his view, failed to prove that we can speak, or think, of ‘that which is not’, Plotinus concludes that Stoic concepts do not provide a viable alternative to Plato’s Forms. When we think of (generic) ‘man’, he argues, we must think of a being, because it impossible to think of ‘man’ (in the singular) without applying ‘one’ to it. Thus, either ‘man’ is a being, and, as a generic being, a Form, or we cannot think of it at all.
4 Conclusion
To conclude, then, Plotinus’ analysis of the Stoic account of concepts shaped his reflections concerning the nature of universals.Footnote 18 While the Stoics conceived of universals in terms of concepts, that is, in terms of mental objects, Plotinus, following Plato, conceives of them in terms of Forms, that is metaphysical objects existing outside, and independently of, the mind. The Stoics tried to replace Forms with concepts, Plotinus argues, but they failed, which is why, rather than try to replace Forms with concepts, one should replace concepts with Forms, and view Forms as the only proper objects of conceptions. To be sure, as is well known, Plotinus is committed to the view that Forms are thoughts which, as such, are within intellect, both the Intellect that corresponds to one of his metaphysical principles and our intellect. But the crucial point here is that, for him, Forms are a very special sort of thoughts, insofar as they are both thoughts and real beings.
It is worth noting that, while Plotinus uses the term ‘concept’ (ennoēma) only sparingly, and only in polemical contexts, he regularly uses the term ‘conception’ (ennoia) to refer to our grasp of some abstract thing or other. This is what he does, for instance, at Enn. 6.6.4.24, where he wonders how we might come to acquire our ‘conception’ of number. There are discrepancies between what Plotinus means by a ‘conception’ and what the Stoics meant by it, which have been interpreted in different ways in the literature.Footnote 19 For my present purpose, however, all that matters is to notice that he speaks of ‘conceptions’ in a way the Stoics never did; for he speaks of them as if they were something dynamic and ‘moving’ towards a target. Thus, at Enn. 6.6.4.24, he remarks that our conception of number might be ‘stirred up’ by our experience of sensible things, and at Enn. 3.7.6.46 he claims that our conception of eternity ‘stretches out’ (eporegetai) to reach its object. While the claim that our conceptions are ‘stirred up’ by our experiences is not uncommon among Plotinus’ Platonist predecessors, the claim that they ‘stretch out’ towards their objects is, as far as I know, entirely peculiar to him. It is undoubtedly a strange claim, but considering his criticism of the Stoic account of concepts we can see that he uses it to signal something important about the objects of conceptions, namely that, for him, they are not concepts in our mind, as the Stoics argued, but Forms to be approached by and reached only outside of our mind.
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