Universals, Wholes, Logoi: Eustratios of Nicaea’s Response to Proclus’ Elements of Theology

ion from matter. In the passage from the Commentary on the Posterior Analytics, Eustratios makes three references to reason-principles in connection with the wholes or universals. First, he connects the whole in the part to the whole before the parts. Each of the monads from which the multiplicity arises is a whole in the part, for an individual man is a part of what is “man simpliciter” (ὁ ἁπλῶς ἄνθρωπος)—i.e. the whole before the parts—, since he embraces inhimself thewhole “reason-principle” (λόγος) of what is simplyman in an incomplete way. He is a whole in the part because he has in a part of the whole “the whole according to the reason-principle” (τὸ ὅλον κατὰ τὸν λόγον) as a whole. Second, Eustratios shows that the status of the whole of parts is determined according to a reason-principle. If a species is lacking, the genus as a whole is maimed, and if an individual is lacking, the species as a whole is maimed. This occurs not “according to their appropriate reason-principles” (κατὰ τοὺς οἰκείους λόγους) but in that “such universals as conceptual” (τὰ οὕτω καθόλου ὡς ἐννοηματικά) have their being or activity in embracing the things below and being predicated of them. Third, Eustratios connects the whole in the part to the whole of parts. Genus and species—i.e. the wholes of parts— are said to be wholes in the part for they “are seen” (θεωρούμενα) as wholes in the things below them “according to their appropriate reason-principles” (κατὰ τοὺς οἰκείους λόγους). It is not as foot or hand that the genus is thus in the species or the species in the individuals but as “imparting their own wholeness” (ὅλων ἑαυτῶν μεταδιδόντα) to things below them and being seen as a whole in them. There is one reference to logos in the materials quoted from the Byzantine commentator that tells a slightly different story. In the passage from the Commentary on the Nicomachean Ethics Eustratios observes in connection with the transcendent forms that thePlatonists here speak of certain “reason-principles, enhypostatic, divine, intellectual” (λόγοι... ἐνυπόστατοι θεῖοι νοεροί) “in relation” (πρός) to which all things “instantiated in matter” (ἔνυλα) exist and become. They call these reason-principles “forms, Ideas, wholes, and universal” (εἴδη, ἰδέαι, ὅλα, καθόλου). To some extent, this usage can be explained in terms of the Neoplatonic precedent whereby the notion of logos which is associated primarily with the levels of soul and nature can sometimes be applied to the level of intellect.54 However, Eustratios’ application of the term logos here to 54 See Früchtel 1970, p. 24–40. Stephen Gersh 9789004440685 Downloaded from Brill.com04/01/2021 05:39:53AM via free access eustratios of nicaea’s response to proclus 51 the transcendent forms situated within the divine Craftsman’s intellect may rather indicate a shift from the Proclean intellectual milieu to that of a more overtly Christian Platonism. Of course, both these explanations may be valid. Now if it is granted that an understanding of the function of logoi is necessary in order fully to grasp the theory of wholes and universals in Proclus and Eustratios, many obscurities still remain surrounding the notion of logos itself. As we have already argued, much of the difficulty in interpreting this notion results from themetaphysical ambiguities inherent in its relational nature and from the polysemy of the technical term logos itself. It is therefore perhaps not unconnected with this situation that Proclus himself can argue in the Commentary on Euclid’s Elements that the discursive part of the soul “has its substance in the reason-principles of mathematics” (ἐν τοῖς λόγοις οὐσίωται τῶν μαθημάτων) and pre-contains knowledge of those reason-principles “in a substantial and concealedmanner” (οὐσιωδῶς καὶ κρυφιῶς) even when it is not active in relation to them.55 But what precisely is the nature of this concealment? In twopassages of theCommentary on the First Alcibiades, Proclus contrasts the state in which the soul has its logoi concealed with the state in which they are brought forth in cognitive activity. In the former case, the soul with respect to the reason-principles “exhales knowledge of them, so to speak” (οἷον ἀποπνεῖν τὰς τούτων γνώσεις) and again56 “has the reason-principles as though palpitating” (οἱ λόγοι τῶν πραγμάτων οἷον σφύζοντες) within it.57 The nature of the concealmentof the logoi is here indicatedbymeansof metaphors. Since the latter are based on the notions of breathing or pulsation, this concealment of the logoi seems primarily to have the features of dynamism and unconsciousness. Given that the cognitive activity of soul as opposed to that of intellect is understood as taking place primarily in time, the question next arises whether the state in which the soul has its logoi concealed and unconscious and that in which they are brought forth in conscious cognitive activities are related as one temporal state to another or as an atemporal state to a temporal one. On the basis of Proclus’ fundamental tenets stated in the Elements of Theology that every participated soul has an eternal “substance” (οὐσία) but an activity in time,58 that the soul has its logoi in a “substantial” (οὐσιώδεις) mode,59 and that 55 Proclus, In Euclidem, 45. 18–46. 3. 56 Proclus, In Alcibiadem, 192. 1–5. 57 Proclus, In Alcibiadem, 189. 4–10. The importance of these metaphors was first noted by Steel 1997. 58 Proclus, Elements of Theology, prop. 191, proof 166. 26–27. 59 Proclus, Elements of Theology, prop. 194, proof 168. 33. Stephen Gersh 9789004440685 Downloaded from Brill.com04/01/2021 05:39:53AM via free access

gersh tonic commentators of late antiquity calling the former the universal "upon the many" (ἐπὶ τοῖς πολλοῖς)7 or the "later-born" (ὑστερογενές) universal and the latter the universal "before the many" (πρὸ τῶν πολλῶν). Throughout this passage he identifies a "universal" (καθόλου) with a "whole" (ὅλον). For the most part, he concentrates on describing the Platonic universal or whole, characterizing this as a reason-principle, form, or Idea which is enhypostatic, divine, transcendent, and intellectual-being in the reasoning of the divine Craftsman. This transcendent principle is called a "universal" because things come to be "according to" it;8 it is called a "whole" because things are referred to it as though to their own wholeness and according to a certain reason-principle. At the same time, Eustratios seems to assume an identification of the Aristotelian abstracted universal with a Platonic immanent form. Thus, he contrasts the transcendent form with a form instantiated in matter or an embodied form, the latter acquiring its subsistence "according to" (κατά) the former. He also explains the causal relation between the transcendent form and the embodied form by saying that the divine Craftsman imprints the latter "according to" (κατά) the former.
In the course of describing the transcendent and embodied forms and the relation between them, Eustratios introduces some further important ideas by way of contrast. Thus, the transcendent form relates to the embodied form not "conceptually" (ἐννοηματικῶς)-that is, as an Aristotelian abstracted universal relates to a particular-but "intellectually" (νοερῶς)-presumably, as the divine Craftsmen pre-contains his effects. Moreover, the "whole" represented by the transcendent form relates to things called its "parts" not as conceived "upon" (ἐπί) a number of items-that is, in the manner of an Aristotelian abstracted universal-nor as assembled "from" (ἐξ) a number of parts. In order to understand this last point, Eustratios now introduces an important conceptual distinction.9 7 The translation of the Greek preposition ἐπί is problematic in this context. The present author's reasons for settling upon the sense of "upon" will emerge in the discussion below. 8 An etymological connection κατὰ + καθόλου is implied. 9 Eustratios,In Ethica Nicomachea,I. 4,[40][41]: "They say that "whole" is referred to in three ways: as "before the parts," as "of the parts," and as "in the parts." The much-discussed forms are said to be wholes before the parts because each of them has been established before the many things that have come to be in accordance with it, these forms being most simple and immaterial. Composite things and things divided into many are said to be wholes of the parts, whether they are homoeomerous as a stone in relation to stones is a whole in relation to the parts into which the stone is divided-each part taking up the name and the reason-principle of the whole-, or whether they are anomoeomerous as a man is divided into hands, feet, and head-none of the man's parts being similar to the whole, inasmuch as it receives neither the name nor the reason-principle of the whole. Those things that are also said to be "upon the many" and "later-born," as are conceptual things, are said to be wholes in the parts. These are According to the Platonists, there are three kinds of whole. The first kind of whole is the whole before the parts and corresponds to the transcendent Platonic form which has already been described in detail. The second kind of whole is the whole of parts. Here, Eustratios gives two illustrations that are, at first sight, easy enough to understand: namely, a homoeomerous whole whose parts have the same reason-principle as the whole (for instance, stone with parts that are stones) and an anomoeomerous whole whose parts do not have the same reason-principle as the whole (for instance, man with parts that are head and hand). The third kind of whole is the whole in the parts. It is here that the problems of interpretation arise because of Eustratios' apparent identification of the whole in the parts with the universal upon the many discussed in the previous paragraph, the former seeming to correspond more to the Platonic embodied form and the latter more to the Aristotelian abstracted universal. Undoubtedly, the explanation of the phrase "upon the many" as referring to things that are substantialized in the soul with reference to the subsistence of the many, of the phrase "later-born" as denoting the process in which the soul contemplates particulars that are identical or similar in form and have been previously10 established in bodies, and of the phrase "conceptual" as referring "later-born" because the soul which has contemplated particular things that have the same or similar forms previously established in bodies, and which has in itself given substance to that reason-principle that has been contemplated in its generality according to an abstraction from matter, then refers this reason-principle suitably to itself: that is to say, in a rational and cognitive manner. These wholes in the parts are "conceptual" because such wholenesses have their substance up to the limit of conceptuality and are in no way existent in actuality aside from the particulars from which they have been taken. They are "in the parts" because the things said about them appear in the particulars in relation to which they are also said to be wholenesses. They are "upon the many" because the soul has in itself given substance to them after the subsistence of the many." (τριχῶς γάρ φασι λέγεσθαι τὸ ὅλον, πρὸ τῶν μερῶν ἐκ τῶν μερῶν καὶ ἐν τοῖς μέρεσι. πρὸ τῶν μερῶν μὲν ἐκεῖνα τὰ εἴδη, ὅτι πρὸ τῶν πολλῶν ἕκαστον ἐκείνων ὑφέστηκεν ἃ πρὸς ἐκεῖνο γέγονεν, ἁπλούστατα ὄντα καὶ ἄυλα· ἐκ τῶν μερῶν δὲ τὰ σύνθετα καὶ εἰς πολλὰ μεριζόμενα, εἴθ' ὁμοιομερῆ ὡς λίθος εἰς λίθους ὅλον ὂν πρὸς μέρη εἰς ἃ καὶ διαιρετός ἐστιν, ὧν ἕκαστον τό τε ὄνομα καὶ τὸν λόγον τοῦ ὅλου ἐπιδέχεται, εἴτ' ἀνομοιομερῆ ὡς ἄνθρωπος εἰς χεῖρας πόδας κεφαλήν· οὐδὲν γὰρ τῶν μερῶν τοῦ ἀνθρώπου ὅμοιον τῷ ὅλῳ, ὡς μήτε τοὔνομα μήτε τὸν λόγον τοῦ ὅλου δεχόμενον· ἐν τοῖς μέρεσι δέ, ὡς τὰ ἐννοηματικά, ἃ καὶ ἐπὶ τοῖς πόλλοις καὶ ὑστερογενῆ λέγεται· ὑστερογενῆ μὲν ὃτι τὰ καθ' ἕκαστα ὁμοειδῆ ἢ ὁμογενῆ ἡ ψυχὴ θεωρήσασα πρότερον ὑφεστηκότα ἐν σώμασι καὶ τὸ ἐν αὐτοῖς κοινῶς θεωρούμενον λόγον κατὰ ἀφαίρεσιν τὴν ἀπὸ τῆς ὕλης ἐν ἑαυτῇ ὑποστήσασα, ἐπιφέρεται τοῦτον οἰκείως ἑαυτῇ, ἤγουν λογικῶς καὶ ἐπιστημονικῶς· ἐννοηματικὰ δέ, ὅτι μέχρις ἐννοίας τἠν ὑπόστασιν αἱ τοιαῦται ὁλότητες ἔχουσι, μηδαμῇ χωρὶς τῶν καθ' ἕκαστα ἐξ ὧν καὶ ἐλήφθησαν ἐνεργείᾳ οὖσαι· ἐν τοῖς μέρεσι δέ, ὅτι ἐν τοῖς καθ' ἕκαστα, πρὸς ἃ καὶ ὁλότητες λέγονται, τὰ περὶ αὐτῶν λεγόμενα ἀναφαίνεται· ἐπὶ τοῖς πολλοῖς δέ, ὅτι μετὰ τὴν ὕπαρξιν τῶν πολλῶν αὐτὰ ἐν ἑαυτῇ ἡ ψυχὴ ὑπεστήσατο.) 10 The temporal connotation of course emerges in the prefix of the term ὑστερογενές. gersh to things that are substantialized to the extent that they are thought-all these are consistent with the understanding of this whole as an Aristotelian abstracted universal. The suggestion that this whole is in no way actual aside from the particulars from which it is taken perhaps indicates a nominalist shift in the understanding of Aristotle. By contrast, the suggestion that the common element substantialized by the soul is a reason-principle that can be brought into agreement with the soul points-as we shall see below-to a kind of realism. It is presumably because of Eustratios' apparent combination of the Platonic embodied form with the Aristotelian abstracted universal that this epistemological ambiguity or flexibility becomes possible. We now turn from the Commentary on the Nicomachean Ethics to the Commentary on the Posterior Analytics where there is another discussion of the three kinds of whole.11 According to Eustratios' explanation here the whole 11 Eustratios, In Analyticorum posteriorum librum secundum, B. 13, 195. 27-196. 16: "And the whole is referred to in three ways: either as "before the parts" or as "of the parts" or as "in the part." The wholes that are before the parts, as the Platonists say, are the primal monads from each of which the number coordinate with it is generated, the monad itself being unparticipated, the many being generated from it according to a procession. These many are also said to be parts of the monad in the sense that the latter is a cause prior to them. They are said in their totality to divide up the subsistence derived from the monad through its extension into multiplicity and in their totality to refer back to the subsistence as to something monadic, primal, and transcendent with respect to the things derived from it. The collection of all these is a whole of parts as though assembled part by part from those monads. Moreover, each of these monads from which the multiplicity arises is a whole in the part, for a particular man being a part of man simpliciter, carries around in himself the whole and integral reason-principle of man simpliciter, and is a whole in the part as having the whole as a whole in the part of the whole according to the reasonprinciple. A species is a whole as though compounded from the parts ranged under it, and again the genus a whole as compounded from its species in the sense that, if a species is lacking, the whole that is the genus is maimed, and if any of the particulars is lacking, the whole that is the species is maimed. This will not occur according to its own proper reason-principles, for "living creature" will not be maimed according to its being a substance, ensouled, and sensitive, if horse, ox, or some other of the species ranged under it is missing, just as "man" will not be maimed according to his being a living creature, terrestrial, and bipedal, if Socrates or Plato is missing. Rather, the genus or species is maimed because the things that are universal in this way-that is, as conceptual-have their being and their actuality in embracing the things ranged under them and being predicated of them. If any of the things ranged under them is missing, the conceptual universals are maimed according to the missing component, for they do not embrace it and are not predicated of it. Such wholes are also said to be in the parts as being contemplated as wholes in the things ranged under them according to their own proper reason-principles. For the genus is a whole in relation to the species and the species a whole in relation to the particulars not as a foot or a hand is a whole, but as imparting themselves as wholes to the things ranged below them and as being contemplated as wholes in the latter." (λέγεται δὲ καὶ τὸ before the parts is not the Platonic transcendent form as described in the earlier passage but something apparently equivalent to it: namely, an originative monad or an unparticipated term. The nature of the "parts" with respect to which this transcendent monad or form can be called a "whole" is explained in the next stage of Eustratios' explanation. Thus, the whole of parts is the entire collection of the monads which proceed from the originative monad, stretch out its subsistence, and are referred back to it whereas the whole in the part is each individual monad within the entire collection proceeding from the originative monad.12 The commentator provides as convenient examples of the whole before the parts and whole in the part "man simpliciter" and "a particular man" respectively. However, it is when he shifts his attention from collections of monads to genera and species that the passage becomes harder to interpret. According to Eustratios, genera and species are both wholes of parts in that these universals as conceptual have their being and activity in being predicated of the things below them, and also wholes in the part in that they are contemplated as wholes according to a reason-principle in the things below them. As in the earlier passage, the commentator is clearly thinking of genera and species first in terms of the Aristotelian abstracted universals and then secondly in terms of a Platonic embodied form. ὅλον τριχῶς, ἢ ὡς πρὸ τῶν μερῶν ἢ ὡς ἐκ τῶν μερῶν ἢ ὡς ἐν τῷ μέρει. αἰ μὲν οὖν πρὸ τῶν μερῶν ὀλοτήτες, ὡς οἰ περὶ Πλάτωνα λέγουσιν, αἰ ἀρχικαὶ μονάδες εἰσίν, ἐχ ὧν ἐκάστης ὁ σύστοιχος αὐτῇ ἀριθμὸς ἀπογεννᾶται, μονάδος μἐν οὔσης αὐτῆς ἀμεθέκτου, πολλῶν δ' ἐξ αὐτῆς κατὰ πρόοδον γεννωμένων, αἳ καὶ μέρη ἐκείνης λέγονται, ὡς ἐκείνης μὲν οὔσης αἰτίας πρὸ αὐτῶν. τούτων δἐ πασῶν μεριζομένων τἠν ἐξ αὐτῆς ὕπαρξιν διὰ τὸ εἰς πλῆθος ἐκτείνεσθαι, καὶ πασῶν ἀναφερομένων εἰς ἐκείνην ὡς εἰς μοναδικήν τε καὶ ἀρχικὴν καὶ ὑπερκειμένην τῶν ἐξ αὐτῆς. τὸ δὲ ἐκ πάντων ἄθροισμα ὅλον ἐστὶν ὡς ἐκ μερῶν τῶν κατὰ μέρος τούτων μονάδων συντεθειμένον. ἑκάστη δὲ τῶν μονάδων τούτων, ἐξ ὧν τὸ πλῆθος, ὄλον ἐν τῷ μέρει ἐστίν· ὁ γάρ τις ἄνθρωπος, μέρος ὢν τοῦ ἁπλῶς ἀνθρώπου, ὅλον ἐν ἑαυτῷ καὶ ἀνελλιπῆ τὸν ἐκείνου περιφέρει λόγον, καὶ ὅλον ἐν τῷ μέρει ἐστίν ὡς ἐν τῷ μέρει τοῦ ὅλου ὅλον ἔχων τὸ ὅλον κατὰ τὸν λόγον. τὸ δὲ εἶδος ὅλον ὡς ἐκ μερῶν τῶν ὑπ' αὐτο συγκείμενον, καὶ τὸ γένος αὖθις ἐκ τῶν εἰδῶν· ὡς εἰ εἰδος ἐπιλείπει, κολοβοῡσθαι τὸ ὡς γένος ὅλον, καὶ εἰ τῶν καθ' ἕκαστά τι, κολοβοῦσθαι τὸ ὡς εἶδος ὅλον οὐ κατὰ τοὺς οἰκείους λὀγους (οὐ γὰρ καθὸ οὐσία ἔμψυχος αἰσθητικὴ τὸ ζῷον κολοβωθήσεται, εἰ ἵππος ἐπιλείποι ἢ βοῦς ἤ τι τῶν ὑπ' αὐτὸ εἰδῶν ἕτερον, ὥσπερ οὐδὲ ᾖ ζῷον πεζὸν δίπουν ὁ ἄνθρωπος, Σωκράτους ἐπιλείποντος ἢ Πλάτωνος), ἀλλ' ἐπεὶ τἀ οὕτω καθόλου ὡς ἐννοηματικὰ ἐν τούτῳ ἔχει τὸ εἶναι καὶ ἐνεργεῖν, ἐν τῷ περιέχειν τὰ ὑπ' αὐτὸ καὶ κατηγορεῖσθαι αὐτῶν, εἴ τι ἐπιλείποι τῶν ὑπ' αὐτά, κεκολόβωται κατὰ τὸ λεῖψαν, ἐκεῖνο μὴ περιέχοντα μήτε μὴν ἐκείνου κατηγορούμενα. λέγονται δὲ τὰ τοιαῦτα ὅλα καὶ ἐν τοῖς μέρεσιν ὡς ἐν τοῖς ὑπ'αὐτὰ θεωρούμενα ὅλα κατὰ τοὺς οἰκείους αὐτῶν λόγους· οὐ γὰρ ὡς ποὺς ἢ χείρ, οὕτω τὸ γένος ὅλον πρὸς τὸ εἶδος, ἤ τὸ εἶδος πρὸς τὰ καθ' ἕκαστα, ἀλλ' ὥς ὅλων ἑαυτῶν μεταδιδόντα τοῖς ὑπ' αὐτὰ καὶ ὅλα ἐν αὐτοῖς θεωρούμενα).

12
As the threefold classification of wholes is generally applied, there does not seem to be any significant conceptual distinction between "whole in the parts" (plural)-as in the earlier text-and "whole in the part" (singular)-as in the present instance.

gersh
The threefold division of wholes into wholes before the parts, wholes of the parts, and wholes in the parts that is foregrounded in Eustratios' discussions and the twofold division of universals into universals before the many and universals in the many that is also suggested there can perhaps be usefully compared with the classifications of wholes and universals proposed in certain propositions of Proclus'Elements of Theology and in the two-part prologue to Proclus' Commentary on the First Book of Euclid's Elements that may strike the reader as being quite similar. Comparison with the first text will provide a more detailed account of the three kinds of whole and comparison with the second the addition of a third kind of universal to the earlier two, both comparisons allowing us to envisage the possibility of merging the threefold divisions of wholes and universals.
A proposition13 in the Elements of Theology states that every "wholeness" (ὁλότης) is either a whole "before the parts" (πρὸ τῶν μερῶν), a whole "of parts" (ἐκ τῶν μερῶν), or a whole "in the part" (ἐν τῷ μέρει). The proof adds that the whole before the parts is the form of each thing "contemplated" (θεωρεῖσθαι) in its cause or alternatively the form "pre-established" (προυποστάν) in its cause; the whole of parts is the form contemplated in all the parts "together" (ὁμοῦ)withdrawal of any part diminishes the whole-whereas the whole in the part is the form contemplated in each part-where even the part becomes a whole "in a partial way" (μερικῶς). In the cases of both the whole of parts and the whole in the part the parts participate in the whole before the parts. Further, the whole before the parts is a whole "according to cause" (κατ'αἰτίαν), the whole of parts is a whole "according to existence" (καθ'ὕπαρξιν), and the whole in the part is a whole "according to participation" (κατὰ μέθεξιν). Finally, the whole in the part "at the lowest level" (κατ'ἐσχάτην ὕφεσιν) is still a whole because it "imitates" (μιμεῖται) the whole of parts. Although Eustratios in citing the same doctrine only makes a vague attribution to Greek philosophy with the phrase "they say" (φασι) and could therefore be referring to Proclus, an Aristotelian commentator, or some other authority, there are good reasons for thinking that he is depending directly on the first-mentioned.14 Apart from certain peculiar phraseology that explicitly recalls the Athenian Successor, a more explicit connection with Proclus' Elements is made in a somewhat similar context by his teacher John Italos.15 13 Proclus Now it must be admitted that Proclus does not in the quoted proposition and proof identify the threefold division of wholes with the threefold division of universals. However, the propositions which immediately follow the propositions dealing with the threefold division of wholes in the Elements of Theology do connect wholes with universals in a general way. Here, Proclus draws a series of distinctions with respect to causality between higher and lower principles and with respect to participations between lower and higher principles by speaking of terms that are "more whole / universal" (ὁλικώτερα) and "more partial / particular" (μερικώτερα),16 and then goes on to show on the assumption that every "form / species" (εἶδος) is a whole but not every whole is a form/species that whole is a broader category within which universal is to be placed.17 Moreover, in the prologue to his Commentary on Euclid's Elements, 18 Proclus explicitly invokes a threefold division of universals. Here, he states that every "universal" (καθόλου)-defined as "a one that includes a many" (ἕν … τῶν πολλῶν περιληπτικόν)-is either "in particulars" (ἐν τοῖς καθ'ἕκαστα), having a "subsistence inseparable" (ὕπαρξις … ἀχώριστος) from them, and moving or at rest together with them; or else "prior to the many" (πρὸ τῶν πολλῶν), producing the latter by "offering its appearances" (ἔμφασεις … παρέχον) to them and "being causal with respect to their participations" (μεθέξεις … χορηγοῦν); or else formed from the many "according to thought" (κατ'ἐπίνοιαν), having "subsistence generated upon them" (ὕπαρξις ἐπιγενηματική), and "gaining consistency upon the many in a later-born manner" (ὑστερογενῶς ἐπισυνίστασθαι τοῖς πόλλοις).19 16 Proclus, Elements of Theology, props. 70-72. 17 Proclus,Elements of Theology,prop. 74,In Euclidem,[50][51]. In addition, the proof includes definitions of both "whole" and of "form / species." 19 The threefold division suggested in this passage seems to lie behind a standard gloss on Now, by combining these texts we can conclude that Proclus has shown that there are three kinds of whole: before the parts, of the parts, and in the parts; that the theory of wholes is closely related to the theory of universals; and that there are three kinds of universals: before the many, upon the many, and in the many.20 However, it is clearly not possible on this basis and without more ado to combine the three kinds of wholes with the three kinds of universals and present this combination as part of an interpretation of Eustratios' doctrine in the commentaries on the Nicomachean Ethics and the Posterior Analytics. In Eustratios, although the whole before the parts is identifiable with the universal before the many, the whole of the parts does not correspond exactly to any of the types of universal but rather to a relation-that of genus to speciesbetween different instances of one type of universal that is otherwise unspecified, while the whole in the parts is identifiable with both the universal upon the many (as an Aristotelian abstracted universal) and the universal in the many (as a Platonic immanent form).
However, given that Eustratios' arguments do exhibit striking similarities with those of Proclus, is it possible to resolve some of the interpretative problems that we have seen in connection with the former by appealing to this late antique antecedent? The remainder of this paper will be devoted to arguing that this is the case and will thereby attempt to break some new ground in the scholarly debate.
However, it is worth prefacing this discussion with some observations regarding the epistemological basis of Proclus' treatment of universals in his understanding of psychology in the Commentary on the Timaeus. This is set out in his lengthy explanation of the lemma dealing with Timaeus' statement that the realm of becoming is grasped by a combination of opinion and sensation,21 and especially in the passage explaining the application of the phrase: "by opinion together with irrational sensation" (δόξῃ μετ' αἰσθήσεως ἀλόγου). According to Proclus, there is a "series" (σειρά) of cognitive faculties containing three terms in descending metaphysical order: 1. intellection, which is "above logos" (ὑπὲρ λόγον), 2. logos itself or discursive reason, and 3. opinion, which is "knowledge of sensible things in accordance with logos" (κατὰ λόγον … γνῶσις τῶν αἰσθητῶν).22 The further characterization of the last member of this series is particularly important, for Proclus here explains that opinion is partly accordaccount of the Aristotelian abstracted universal is already shifted in the direction of Platonism. In other words, it implies the application of logos theory to be discussed below. 20 Or at least words to that effect. 21 Proclus,In Timaeum, For now, we will leave the word logos untranslated. See further below.
He also contrasts this last cognitive faculty with the lower non-cognitive faculty of sensation. Whereas each of the five senses constituting the latter grasps "one aspect of its object" (ἕν τι τῶν περὶ αὐτό)-and even the common sense merely distinguishes between these features-, opinion knows that "the whole object has a substance of such and such a kind" (τοιάνδε ἔχον ἐστὶν οὐσίαν τὸ ὅλον) and also knows "the whole as though before the parts" (τὸ ὅλον … πρὸ τῶν οἱονεὶ μερῶν).23 From this description, we can conclude that it is with the faculty of opinion that the soul's apprehension of the wholes or universals discussed in the texts considered earlier really begins. Given that he states with careful qualification that opinion knows the whole-as opposed to merely disconnected sensory affections-as though before the parts, it is probably safe to assume that Proclus is not rejecting the more obvious assumption that perception of wholes and universals by the faculty of opinion would begin with wholes in the part, but is rather attempting to delineate the fundamental difference between partial and holistic approaches to the external objects of perception as such.

Proclus' Theory of Universals and Logoi
To return to the philosophical problems that appeared in connection with Eustratios' account of wholes and universals, we can leave aside the relatively unproblematic identification of the whole before the parts with the universal before the many as representing the Platonic transcendent forms. However, the problems of interpretation with respect to the second and third terms in the threefold schema of wholes clearly need further investigation.24 Here, the main difficulties are that, although the two types of whole are ostensibly to be associated simply with the two types of universal, Eustratios in the passage from the Commentary on the Nicomachean Ethics apparently identified both the Aristotelian abstracted universal and the Platonic embodied form with the whole in the part and the universal upon the many, whereas in the passage from the Commentary on the Posterior Analytics he identified the Aristotelian abstracted universal-in the sense of genera and species-with both the whole of 23 Proclus,In Timaeum, Later we will turn to an analogous problem with the (metaphysically) higher part of the threefold schema. gersh parts and the whole in the parts while at the same time identifying a collection of Platonic monads with the whole of parts and an individual monad with a whole in the parts. Reading these two texts in conjunction leads to even greater difficulties, since we now realize that the universal upon the many-the Aristotelian abstracted universal in the first instance-is to be identified with both the whole of parts and the whole in the parts and further that the whole in the parts-the Platonic embodied form in the first instance-is to be identified with both the universal upon the many and the universal in the many. The relations between the two kinds of universal and the two kinds of whole might be represented by the following schema: However, the approach of Eustratios can perhaps be justified on the basis of Proclus' own treatment of wholes and universals which seems to make three important moves: first, it treats the universal in the many-Eustratios' whole in the parts-as the embodied Platonic form; second, it treats the universal upon the many-still Eustratios' whole in the parts-as a mediation of the embodied Platonic form with an element not so far considered: an internal reason-principle of the soul; third, it treats the universal upon the many-now Eustratios' whole of parts-as the "projection" of the reason-principle itself-, thereby turning what would become for the Byzantine commentator a twofold division of whole in the parts and whole of parts into a threefold division of whole in the parts, whole in the parts plus universal upon the many, and whole of parts.25 The insertion of a mediating term is not only typical of the Proclean metaphysical approach in general but also in this specific context changes the Aristotelian later-born universal-which he henceforth treats as a mere phantasm-into a Platonic later-born universal-now underpinned by the reality of a psychic reason-principle. These developments are set out most clearly in Proclus' Commentary on the Parmenides where he comments on the lemma26 dealing with Socrates' suggestion that a form is a "thought" (νόημα) coming to be in the soul. Proclus notes initially that this agrees with the Peripatetics' notion of a form as "later-born" 25 On Proclus' epistemology one may now consult the studies by Helmig 2004Helmig , 2006Helmig , 2008Helmig , 2011 Proclus, In Parmenidem, IV. 891-897.
(τὸ ὑστερογενές) but that there is a difference between this and that which he terms the "psychic reason-principle" (ὁ ψυχικὸς λόγος). This reason-principle resides substantially in souls. By looking towards this the soul is all the forms and is the place of the forms, is present not only potentially but actually (in the first meaning of actuality), and is "substantial" (οὐσιῶδες) and "more substantial" than the many (μᾶλλον). On the other hand, the later-born is dimmer than the many inasmuch as it "arises from them" (ἐπ'αὐτοῖς), and is "less substantial than the many" (ἧττον οὐσία τῶν πολλῶν).
Having stated the fundamental difference between Aristotelian and Platonic approaches to universals, Proclus proceeds to expand the threefold division of wholes or universals first, by tracing back the Platonic embodied form to the notion of reason-principle. He does this by contrasting the manner in which a physical reason-principle is a "basis of coherence of the many" (συνεκτικὸν τῶν πόλλων) and that in which the later-born is "upon the many" (ἐπὶ τοῖς πόλλοις), noting in the process that the former underlies the "form residing in matter" (τὸ ἐν ὕλῃ κείμενον εἶδος) and that it is the latter which knows things on a general level (κοινῶς). Thus, the embodied Platonic form is replaced by an internal principle of coherence based on a reason-principle. In the course of the same discussion, Proclus now treats the universal upon the many as the mediation of the embodied Platonic form with the soul's internal reason-principles. His approach can be seen by noting his remark that the "universal in the many" (τὸ καθόλου τὸ ἐν τοῖς πόλλοις) is less than each of the individuals since the latter are amplified by accidents, whereas the later-born-as the universal upon the many is here characterized-must comprehend each of the many in being predicated of them. This remark should be combined with his further comment that the psychic generality just mentioned must be derived not from the common quality in the many but from some other source of which it is an "image" (εἰκὠν), coming into existence through "recollection of the causal principle aroused within" (ἀνάμνησις … τῆς ἔνδον ἀνακινουμενης αἰτίας) on the basis of things appearing. In commenting on the same lemma, Proclus finally treats the universal upon the many as the "projection" of the soul's internal reason-principles themselves. Here, he notes that rational souls "generate these universals" (γεννῶσι ταῦτα τὰ καθόλου) and progress from sensible things to opinable things by having reason-principles of things, and that those who know things "on a general level" (κοινῶς) contemplate their "generalities" (κοινότητες) through "preembracing" (προειληφέναι) these reason-principles.27 Thus, prior to the so-gersh called later-born there must be "substantial reason-principles" (οὐσιώδεις λόγοι) which are "eternally projected" (ἀεὶ προβεβλημένοι) and efficacious in the divine souls superior to us but are "sometimes" (ποτέ) obscured and sometimes active in us.
It should be apparent by now that a major component in Proclus' strategy of handling the threefold division of wholes and universals (together with the expansion suggested) is the introduction of something distinct from both the wholes and the universals themselves: namely, the reason-principles. What precisely are these reason-principles and how do they function? These questions are far too complicated to deal with adequately under the present restrictions of space. However, it is at least possible to summarize the main points of Proclus' doctrine of the reason-principle that are relevant to the present discussion of the theory of universals on the basis of some passages from the Elements of Theology and the Commentary on Euclid.28 These two texts have not only already provided some essential background to the discussion of wholes and universals in Eustratios but also most clearly exemplify the mathematical understanding of the reason-principle which is probably its most important feature. Indeed, Eustratios' explanation of the three wholes in terms of monads and numbers in the Commentary on the Posterior Analytics shows that mathematical and dialectical notions are inextricably linked in his mind. Now considered on its most fundamental level, logos is conceived by the Neoplatonists as almost synonymous with relation: a fact which in itself helps to explain the difficulty of coming to grips with it. Relation in its turn has a peculiar status in their philosophy being conceived in different contexts both as a hypostasis and not a hypostasis.29 This second problem might be summarized as follows: Given the existence of two existent principles x and y and the relation between them R, we have to ask about the nature of R. If it is an existent, then there were really three principles to begin with. If it is not an existent, then there was really no relation between the two original principles. This kind of conundrum about relation explains why it is difficult to say whether the world's Logos in Plotinus' Third Ennead is a hypostasis or not, and why Proclus' theological system seems like an endless multiplication of triads. At any rate, from Plotinus onwards the notion of logos is predominantly associated if not identified with the hypostasis of soul and especially with the nature that selves, Proclus has here passed from considering the level of opinion to considering the level of logos or discursive reason. 28 In this essay, we will discuss only certain features of the epistemology in Proclus' Commentary on Euclid. For a more general overview see MacIsaac 2010. 29 On the peculiarly Neoplatonic treatment of relation see Gersh 1996, p. 45-56. represents the lower phase of soul.30 It is against this background that Proclus elaborates the notion of logos that we see in the two treatises named.31 Aside from this metaphysical ambivalence, the notion of logos is difficult to grasp because of the polysemy of the word itself. Taking our cue from Porphyry who at one point stops to map the range of meanings implicit in the term logos,32 we might perhaps here briefly sketch the semantic unfolding of the term as it emerges from Proclus' usage in the Commentary on Euclid's Elements, taking account of the fact that there is no single English translation that captures all the senses of the original Greek term.33 Thus, logos appears (1.) as form. At one point, Proclus invites us to think of the universal in the manythe example being the reason-principles of circularity, triangularity, or figure as such-as being twofold: in the objects of sense and in the objects of imagination. Prior to these are the reason-principle in the discursive reasoning and the reason-principle in nature, the former giving substance to imagined circles and the single form in them and the latter giving support to sensory circles and the single form in them.34 Turning to the various types of relation in which logos manifests itself, of particular importance are (2.) mediation. Reason-principles can mediate between intellect and soul, for example when Proclus explains that the totality of forms in the soul is derived both from the prior intellect and from the soul itself, and that the soul is therefore not a writing-tablet "empty of logoi" (τῶν λόγῶν κενόν) but is itself always written upon by intellect and writing itself;35 and likewise reason-principles can mediate between understanding and imagination, for example when he argues that the circle in the understanding is simple and unextended whereas that in the imagination is divisible and extended-both being instances of reason-principles36-and that thinking in geometry takes place through the "projection" (προβολή) of the various figures and their parts from understanding to the imagination.37 Also among the vari- 30 On the status of Logos in Plotinus see Armstrong 1940, p. 98-108;Rist 1967, p. 84-102;Früchtel 1970;Turlot 1985;Couloubaritsis 1992;and Fattal 1998. 31 Also more extensively in his Commentary on the Timaeus which we will not discuss here. 32 For discussion of this passage see Gersh 1992, p. 152-153. For a more general discussion of logos in Porphyry see Gersh 2017. 33 Accordingly, during the next few paragraphs we will employ-in addition to simple transliteration and the neutral expression "reason-principle"-the more specialized renderings "ratio," "proposition," "reasoning," etc. as required by the context. 34 Proclus,In Euclidem,In Euclidem,. 36 Proclus,In Euclidem, Proclus, In Euclidem, 13. 6-11. On the important role of imagination in Proclus' theory of geometry see Nikulin 2010. gersh ous types of relation represented by logos is (3.) proportion. In commenting on Euclid's geometry Proclus also takes the opportunity of summarizing Plato's teaching in the Timaeus where the latter authority constructs the soul out of all the mathematical forms, then divides it according to numbers, and finally binds it with "analogies and harmonic proportions" (ἀναλογίαι … ἁρμονικοὶ λόγοι).38 Of equal importance among the types of relation in which logos manifests itself are (4.) that between the one and the many and (5.) that between the whole and the part: two types of relation that are perhaps better exemplified in some passages of the Elements of Theology to be discussed below. Last but not least, logos appears (6.) as thinking.
It is here that we must complete the semantic unfolding of the term logos in the Commentary on Euclid by considering various conceptual combinations in Proclus of the types of logos-form, mediation, proportion, whole-part, onemany, and thinking-enumerated above. Thus, logos appears as a combination of form (1) + mediation (2) where it corresponds to mathematical form as mediating between intelligible and sensible form. In one passage, Proclus explains that the "mathematical entities" (τὰ μαθηματικά) are the offspring of limit and infinity and hence there are "ratios proceeding to infinity but controlled by the causal principle of limit" (προέρχονται μὲν εἰς ἄπειρον οἱ λόγοι, κρατοῦνται δὲ ὑπὸ τῆς πέρατος αἰτίας).39 Logos also occurs as a combination of thinking (6) + the one and the many (5) in various cases of cognitive synthesis ranging from simple abstraction-for example, where he considers whether mathematical genera and species are derived from sensible things either according to "abstraction from materiate things" (ἀφαίρεσις τῶν ἐνύλων) or by "collection from particulars to one common definition" (κατὰ ἄθροισιν τῶν μερικῶν εἰς ἕνα τὸν κοινὸν λόγον)40-to the complexities of syllogistic deduction-for example, where he explains how our knowledge of the common theorems in geometry is the prior science from which the other sciences "receive their common propositions" (τοὺς κοίνους ὑποδέχονται λόγους).41 Logos appears as a combination of thinking (6) + mediation (2) in various accounts of psychic faculties where logos is situ- 38 Proclus, In Euclidem, 16. 16-19. Cf. 6. 7-15 (similar interpretation of the Philebus). 39 Proclus,In Euclidem,[6][7][8][9][10][11][12][13][14][15] Proclus, In Euclidem, 12. 2-7 + 15. 16-18. As we have already seen in connection with the Commentary on the Parmenides, Proclus considers these processes to represent only half of the process of acquiring knowledge. In order to achieve the latter, it is necessary for the logos of "definition" mentioned here to turn into / be combined with the logos projected on the basis of intellect. Proclus thus speaks of recollection and awakening of logoi. See In Eucl. 18. 17-20 and 45. 2-15. Of course, the duality of this process is a quintessential illustration of logos as mediation. 41 Proclus,In Euclidem,[9][10][11][12][13][14][15][16][17][18][19] ated on the level of the discursive thinking that operates between intellect and sense-for example where Proclus discusses the reasons why the Pythagoreans introduced the term mathematics in order to characterize "the science of discursive reasonings" (ἐπιστήμη τῶν διανοητικῶν λὀγων)42-or on the level of the imagination operating between discursive resoning and sense-for example in the passage considered above where the reason-principles of the psychological faculties of discursive reasoning, imagination, and sense are arranged in a hierarchy.43 Logos also appears as a combination of form (1) + the one and the many (5) where it corresponds to the unfolding of the simplicity of intelligible form into discursive multiplicity. At one point, Proclus explains that the discursive reasoning is not motionless like the activity of intellect but "unfolds and traverses the incorporeal world of the reason-principles" (ἀνελίσσεται καὶ διέξεισι τὸν ἀσώματον τῶν λόγων διάκοσμον) now moving from first principles to conclusions and now moving in the reverse direction.44 The term logos appears only occasionally in the Elements of Theology. However, the relative infrequency of the term itself should not lead us to conclude that the notions underlying the term are less important in that text. On the contrary, the entire work consists of propositions and proofs which exemplify the sense of logos as a combination of thinking + the one and the many in syllogistic argument as described earlier.45 Moreover, the senses of logos as proportion and as the relations between the whole and the part and between the one and the many are indicated in the accounts of the numerous orders and series of hypostases contained in the work's propositions and proofs.46 The most important points regarding these latter senses of logos may perhaps be stated briefly as follows: 1. Logoi govern simple relations between parts and wholes. Proclus argues that in each order or causal chain there exists a single monad prior to the manifold which determines for the members of the order their "unique 42 Proclus,In Euclidem,In Euclidem,In Euclidem,[18][19][11][12][13][14][15][16][17][18][19][20][21][22]etc. 45 For logos as argument see Proclus,Elements of Theology,props. 59,proof 58. 2;62,proof 58. 32;145,proof. 128. 16; for logos as demonstration: prop. 111, proof 98. 31-32. Proclus also restates his general view that logos is an aspect of cognition. As such it is a real thing and relates to real things in prop. 123, proof 108. 29-31. All "knowledge through a reasonprinciple" (διὰ λόγου γνῶσις), inasmuch as it grasps intelligible notions and subsists in acts of intellections, is knowledge "of real existents" (τῶν ὄντων). Its power of apprehending truth is "among real things" (ἐν τοῖς οὖσιν).

46
For the general structuring function of logos see Proclus,Elements of Theology,prop. 18, gersh proportional relation to one another and to the whole" (ἕνα λόγον πρός τε ἀλλήλα καὶ πρὸς τὸ ὅλον).47 2. Logoi are multiple relations. They govern sets of relations between one part and another. One proposition states that every particular soul with respect to the divine soul under which it is ranked "has the same proportional relation" (τοῦτον ἔχει τὸν λόγον) as does its vehicle to the vehicle of the divine soul.48 3. Logoi are multiple relations. They govern sets of relations not only between one part and another but between parts and the whole [monad]. Within the proof of another proposition, stating that the first members of a monadic series are conjoined by community of nature with the members of the supra-jacent series, whereas the last members of the series have no contact with it, Proclus observes: "Such terms are not identical in their proportional relation but in the relation whereby they are derived from and referred back to a single term" (οὐδὲ γὰρ εἶς ὀ λόγος, ἀλλ'ὡς ἀφ'ἐνὸς καὶ πρὸς ἕν).49 4. Logoi are more universal and less universal + determine the status "according to participation." Another proposition states that all those characters "having the proportional relation of a substratum in participants" (ἐν τοῖς μετέχουσιν ὑποκέιμενον ἔχοντα λόγον) proceed from more perfect and more universal causes.50 5. Logoi are more universal and less universal + they determine the status "according to causality." Within another proof, we read that fathers differ as "more universal or less universal" (ὁλικώτεροι … μερικώτεροι)-as do the divine orders themselves-according to the "proportional relation of their causality" (κατὰ τὀν τῆς αἰτίας λόγον).51 6. A Logos determines the status of a monadic term as "monadic". Within the proof of a proposition stating that there are series of terms beginning with a monad and proceeding to a coordinate multiplicity, Proclus introduces the words: "For the monad, having the proportional relation of an originative principle …" (ὁ μὲν γὰρ μονάς, ἄρχῆς ἔχουσα λόγον …)52

A logos determines the status of an unparticipated term as "unparticipated."
Within the proof of a proposition stating that the first term in each series must be unique, Proclus includes the words: "For the unparticipated, having the relative status of a monad (…)" (τὸ μὲν γὰρ ἀμέθεκτον, μονάδος ἔχον λόγον (…)).53 Now the apparent concentration on a relatively limited selection of the senses of logos in the Elements of Theology does not indicate that Proclus does not also assume there the full range of meanings set out in the Commentary on Euclid, any seeming difference of approach resulting from the fact that the latter work theorizes regarding the methodology of geometry whereas the former exemplifies the application of this geometry to theology.

Eustratios' Theory of Universals Revisited
The passage quoted earlier from the Commentary on the Parmenides showed the role of logoi specifically in Proclus' theory of universals and we have now seen applications of the notion of logoi in a wide range of contexts by the same author. Given that our initial review of Eustratios' arguments in the Commentary on the Nicomachean Ethics and the Commentary on the Posterior Analytics had indicated that his approach paralleled that of Proclus, is it possible now to find traces of the same logos theory in the Byzantine commentator's discussion of wholes and universals? If the answer to this question is affirmative, then it will be reasonable to conclude more decisively that Eustratios' approach to these doctrines is in agreement with that of Proclus, and at the same time to resolve some of the interpretative problems that originally arose in connection with that theory. In fact, both passages drawn from Eustratios' commentaries refer to the notion of logoi, and it is worth revisiting them briefly in order to bring these references into greater relief. In the passage from the Commentary on the Nicomachean Ethics, Eustratios notes concerning the whole of the parts that the notion of wholeness here refers to "compound things" (σύνθετα) and things divided into many parts. When these compound things are homoeomerous, he adds, the whole is related to the parts in such a way that each part has "the reason-principle and name" (τό τε ὄνομα καὶ ὁ λόγος) of the whole, as stone is divided into stones. The commentator also notes concerning the whole in the parts-which replaces, as we have seen, the Platonic embodied form-gersh that these wholenesses are called "later-born" because the soul contemplates "particulars" (καθ'ἕκαστα) identical or similar in form which have been previously established in bodies and "substantializes in itself the reason-principle" (λόγον … ἐν ἑαυτῇ ὑποστήσασα) seen in them as a common element through abstraction from matter. In the passage from the Commentary on the Posterior Analytics, Eustratios makes three references to reason-principles in connection with the wholes or universals. First, he connects the whole in the part to the whole before the parts. Each of the monads from which the multiplicity arises is a whole in the part, for an individual man is a part of what is "man simpliciter" (ὁ ἁπλῶς ἄνθρωπος)-i.e. the whole before the parts-, since he embraces in himself the whole "reason-principle" (λόγος) of what is simply man in an incomplete way. He is a whole in the part because he has in a part of the whole "the whole according to the reason-principle" (τὸ ὅλον κατὰ τὸν λόγον) as a whole. Second, Eustratios shows that the status of the whole of parts is determined according to a reason-principle. If a species is lacking, the genus as a whole is maimed, and if an individual is lacking, the species as a whole is maimed. This occurs not "according to their appropriate reason-principles" (κατὰ τοὺς οἰκείους λόγους) but in that "such universals as conceptual" (τὰ οὕτω καθόλου ὡς ἐννοηματικά) have their being or activity in embracing the things below and being predicated of them. Third, Eustratios connects the whole in the part to the whole of parts. Genus and species-i.e. the wholes of partsare said to be wholes in the part for they "are seen" (θεωρούμενα) as wholes in the things below them "according to their appropriate reason-principles" (κατὰ τοὺς οἰκείους λόγους). It is not as foot or hand that the genus is thus in the species or the species in the individuals but as "imparting their own wholeness" (ὅλων ἑαυτῶν μεταδιδόντα) to things below them and being seen as a whole in them.
There is one reference to logos in the materials quoted from the Byzantine commentator that tells a slightly different story. In the passage from the Commentary on the Nicomachean Ethics Eustratios observes in connection with the transcendent forms that the Platonists here speak of certain "reason-principles, enhypostatic, divine, intellectual" (λόγοι … ἐνυπόστατοι θεῖοι νοεροί) "in relation" (πρός) to which all things "instantiated in matter" (ἔνυλα) exist and become. They call these reason-principles "forms, Ideas, wholes, and universal" (εἴδη, ἰδέαι, ὅλα, καθόλου). To some extent, this usage can be explained in terms of the Neoplatonic precedent whereby the notion of logos which is associated primarily with the levels of soul and nature can sometimes be applied to the level of intellect.54 However, Eustratios' application of the term logos here to 54 See Früchtel 1970, p. 24-40. the transcendent forms situated within the divine Craftsman's intellect may rather indicate a shift from the Proclean intellectual milieu to that of a more overtly Christian Platonism. Of course, both these explanations may be valid. Now if it is granted that an understanding of the function of logoi is necessary in order fully to grasp the theory of wholes and universals in Proclus and Eustratios, many obscurities still remain surrounding the notion of logos itself. As we have already argued, much of the difficulty in interpreting this notion results from the metaphysical ambiguities inherent in its relational nature and from the polysemy of the technical term logos itself. It is therefore perhaps not unconnected with this situation that Proclus himself can argue in the Commentary on Euclid's Elements that the discursive part of the soul "has its substance in the reason-principles of mathematics" (ἐν τοῖς λόγοις οὐσίωται τῶν μαθημάτων) and pre-contains knowledge of those reason-principles "in a substantial and concealed manner" (οὐσιωδῶς καὶ κρυφιῶς) even when it is not active in relation to them.55 But what precisely is the nature of this concealment? In two passages of the Commentary on the First Alcibiades, Proclus contrasts the state in which the soul has its logoi concealed with the state in which they are brought forth in cognitive activity. In the former case, the soul with respect to the reason-principles "exhales knowledge of them, so to speak" (οἷον ἀποπνεῖν τὰς τούτων γνώσεις) and again56 "has the reason-principles as though palpitating" (οἱ λόγοι τῶν πραγμάτων οἷον σφύζοντες) within it.57 The nature of the concealment of the logoi is here indicated by means of metaphors. Since the latter are based on the notions of breathing or pulsation, this concealment of the logoi seems primarily to have the features of dynamism and unconsciousness.
Given that the cognitive activity of soul as opposed to that of intellect is understood as taking place primarily in time, the question next arises whether the state in which the soul has its logoi concealed and unconscious and that in which they are brought forth in conscious cognitive activities are related as one temporal state to another or as an atemporal state to a temporal one. On the basis of Proclus' fundamental tenets stated in the Elements of Theology that every participated soul has an eternal "substance" (οὐσία) but an activity in time,58 that the soul has its logoi in a "substantial" (οὐσιώδεις) mode,59 and that gersh any effect which proceeds must also remain,60 it is necessary for the second answer to be the correct one. However, this in its turn implies that the conscious cognitive activities of the soul that do take place in time are inseparable from and simultaneous with the unconscious cognitive activities of the soul's internal logoi.
We can take the first steps in pursuing the implications of this last point for an understanding of the role performed by the logoi in the structuring and processing of the world of forms if we return briefly to the semantic unfolding of the term logos sketched earlier. It is therefore now possible to argue that the reason why logos is treated often as though it were simply equivalent to form and often treated as though it were simply equivalent to thinking is not because it is metaphysically identifiable with either of these in the strict sense-this would be impossible both because Proclus explicitly distinguishes logos from form in certain contexts61 and because the notion of an unconscious thinking is obviously self-contradictory. Rather, the logos functions as a kind of concealed complement to the structuring and processing of the world of forms by thinking and therefore does not need to be named and indeed cannot be named independently. In different contexts, logos can represent the mediating relation between forms thought as x, y, z, etc., or the proportional relation between given forms as thought determinately; it can also represent the relation between the one and the many with respect to forms thought as x, y, z, etc., or the relation between whole and the part with respect to given forms. Most importantly for the theory of universals, it represents the relations signified by the prepositions "before" (πρό), "of" (ἐξ), "upon" (ἐπί), and "in" (ἐν) rather than the meanings of the substantives to which the prepositions are attached.
If this interpretation is correct, then some light has indeed been shed on the obscurities surrounding Proclus' and Eustratios' accounts of wholes and universals. Our close analysis of the most relevant texts selected from the two authors has perhaps been sufficient to show that some of the problems can be resolved. However, the most important lesson to be taken away is undoubtedly that the non-resolution of certain other problems has at least the justification of methodological consistency.62 60 Proclus, Elements of Theology, prop. 35 and proof 38. 9-13. 61 For instance, there are logoi but not forms of artificial objects. See Proclus,In Parmenidem, The author would like to thank members of the audience at the colloquium on the Elements of Theology for making insightful comments at the oral presentation of the first draft of this paper in November 2015. A particular debt is owed to Michael Chase for alerting the writer to some of the irregularities in published English translations of the Neoplatonic Aristotelian commentaries.