SEMINARI
E CONVEGNI
Universals in
Ancient Philosophy
edited by
Riccardo Chiaradonna
Gabriele Galluzzo
Introduction
Riccardo Chiaradonna, Gabriele Galluzzo 1
Universals before Universals: Some Remarks on Plato
in His Context
Mauro Bonazzi 23
Plato’s Conception of the Forms: Some Remarks
Francesco Ademollo 41
Plato’s Five Worlds Hypothesis (Ti. 55cd), Mathematics and Universals
Marwan Rashed 87
Plato and the One-over-Many Principle
David Sedley 113
Universals, Particulars and Aristotle’s Criticism of Plato’s Forms
Laura M. Castelli 139
Universals in Aristotle’s Logical Works
Mauro Mariani 185
Universals in Aristotle’s Metaphysics
Gabriele Galluzzo 209
Epicureans and Stoics on Universals
Ada Bronowski 255
Alexander, Boethus and the Other Peripatetics: The Theory of Universals in the Aristotelian Commentators
Universals, Education, and Philosophical Methodology in Later Neoplatonism
Michael Griffin 353
Universals in Ancient Medicine
Riccardo Chiaradonna 381
Universals in the Greek Church Fathers
Johannes Zachhuber 425
Bibliography 471
Index locorum 509
The Theory of Universals
in the Aristotelian Commentators
1. Dexippus, Simplicius and Peripatetic universals
his is how one must answer the arguments of the associates of Alexander and Boethus and the other Peripatetics [τοῖς περὶ Ἀλέξανδρον καὶ Βόηθον τοῖς τε ἄλλοις Περιπατητικοῖς ἐπιχειροῦσιν] and it is appropriate for those interpreting the Metaphysics to show that Aristotle gives priority to common items (τὰ κοινά) even when considering sensible things (Dexipp., In Cat., 45, 27-31 Busse)1.
hese lines from Dexippus provide signiicant evidence about the theory of universals developed in the Aristotelian commentary tradi-tion. he passage quoted above has a parallel in Simplicius (Simpl., In Cat., 82, 22 f. Kalbleisch), who also mentions the common source that lies behind both his report and that of Dexippus, i.e. Iamblichus’ lost Commentary on the Categories (Simpl., In Cat., 82, 10 and 83, 21 Kalbleisch). Unlike what happens elsewhere, however, here Dexip-pus provides a crucial detail which is missing in Simplicius. Whereas Simplicius only names Alexander of Aphrodisias, Dexippus provides a fuller list of Peripatetic opponents which includes Boethus, Alexan-der and the other Peripatetics2. hus, Dexippus makes an overt con-nection between Boethus of Sidon (irst century BCE) and Alexander of Aphrodisias (second-third century CE), the two main Aristotelian
1 English translations are generally adapted from those published in the series «he
Ancient Commentators on Aristotle». See, in particular, de Haas, Fleet 2001; Chase 2003 (for Simplicius’ Commentary on the Categories); Dillon 1990 (for Dexippus). I have also made use of the translations in Sharples 2010, pp. 75-89 (Ontology).
2 It is unclear to me whether in mentioning Boethus Dexippus was drawing from
Iamblichus or whether he added the name of Boethus to those found in his source. Dexippus does not usually name his predecessors: this may speak in support of the irst hypothesis. On Dexippus, see now the excellent discussion in Barnes 2009.
commentators in the post-Hellenistic age. Some recent studies have convincingly shown that Boethus and Alexander developed two difer-ent and alternative Peripatetic readings of Aristotle, which mirror two stages in the history of the reception of Aristotle’s school treatises3. In this contribution I aim to develop this point and show that Dexippus’ criticism sets out Boethus’ and Alexander’s positions misleadingly, since Dexippus (or his source Iamblichus) conlates the theories of his opponents without considering their mutual diferences within a com-mon Peripatetic philosophical background4.
It is worth quoting Dexippus’ passage in full:
SELEUCUS But what could we say to those who dispute this very point, claiming that in fact universals are not prior in nature to particulars, but posterior to them?
DEXIPPUS Well, if we were to consider the question carefully, we would ind that they actually take as agreed what is disputed. For when they say that the universals are prior in nature to each thing taken individually, but on the other hand absolutely5 posterior in nature, they are postulating that
particulars are prior also by nature6, and are proceeding invalidly in taking
as a irst principle that very thing that requires demonstration. Such attempts at proofs [ἐπιχειρήματα] as the following are also supericial: if the common item exists, it is necessary that an individual exists also (for individuals are comprehended in common items), but if an individual exists, it does not al-ways follow that a common item exists, if at least a common item belongs to many (instances). For it is obvious that a particular can be an individual only
3 See, irst and foremost, the illuminating discussion in Rashed 2007. Also, see
Chiaradonna, Rashed 2010 and the discussion of Rashed’s volume by Kupreeva 2010.
4 Signiicantly, Dexippus’ simplifying account was shared by such an eminent
scholar as Paul Moraux. See Moraux 1973, p. 156: «Für Boethos und Alexander […] ist das Gemeinsame nichts anderes als ein Produkt der abstrahierenden Fähigkeit des Geistes, das aus den enzig un allein in der Wirklichkeit vorhandenen Einzeldingen gewonnen wird; es besitzt nichts von der Selbständigkeit und von der Priorität der platonischen ideellen Wesenheiten» (my italics). Recent scholarship on Alexander has changed this picture radically.
5 At 45, 17 Busse Dillon reads πάντων instead of πάντως (MSS), but this seems
unnecessary to me.
6 καὶ τῇ φύσει (45, 17-18 Busse) and not only «with respect to us» (πρὸς ἡμᾶς) as
if a common item is immanent in it and completes its essence, for a particular human being is also Human Being. And it is also false to say that, when the common item is removed, the individual is not altogether removed; for if the being of the common item consists in extending to all the things ranked under it, the person who removes this immediately removes the whole existence of the individual7, his is how one must answer the arguments of the associates
of Alexander and Boethus and the other Peripatetics and it is appropriate for those interpreting the Metaphysics to show that Aristotle gives priority to the common items [τὰ κοινά] even when considering sensible things (Dexipp., In Cat., 45, 12-31 Busse)8.
According to Dexippus, the Peripatetics hold that universals or com-mon items are posterior in nature to particulars, because they are pos-terior to the extension of the particulars under them. Dexippus (see Simpl., In Cat., 82, 22-26 Kalbleisch) replies that his opponents sim-ply take it for granted that particulars are prior in nature, but do not provide any demonstration of this fact. Simplicius’ parallel discussion gives further details, since he remarks that Alexander of Aphrodisias claims – without any proof – that common items (τὰ κοινά) derive «their being and their essence» (τὸ εἶναι καὶ τὴν οὐσίαν) from particu-lars (παρὰ τῶν καθ’ ἕκαστα, Simpl., In Cat., 82, 24-25 Kalbleisch). Some lines above, Simplicius sets out this thesis as distinctively Peripa-tetic (82, 7-8 Kalbleisch): koina do not exist at all independently, but have their being in particulars (τὰ κοινὰ οὐδέ ἐστιν ὅλως καθ’ ἑαυτὰ ἐν ὑποστάσει, ἀλλ’ ἐν τοῖς ἀτόμοις ἔχει τὸ εἶναι).
he Peripatetic view rejected by Dexippus and Simplicius is not easy to assess. As a matter of fact, the claim that universals do not exist by themselves, independently of particulars, but are in particulars and depend on them for their existence is an ambiguous statement that can be interpreted in two diferent ways. (a) Universals do not possess any kind of existence distinct from that of particulars: they are in par-ticulars since nothing exists but particular entities; (b) universals are entities distinct from particulars, although they are not independent of particulars and could not exist without particulars. he reading (a)
7 At 45, 27 Busse I read τοῦ ἀτόμου instead of τοῦ κοινοῦ (MSS). As I see it, the
parallel with Simpl., In Cat., 82, 34-35 Kalbleisch is decisive. For discussion, see Dil-lon 1990, p. 83 note 34 (who, however, retains τοῦ κοινοῦ).
8 καὶ ἐν τῇ τῶν αἰσθητῶν θεωρίᾳ: on Dexippus’ καὶ at 45, 30 Busse, see the last
of the Peripatetic thesis is equivalent to an extensional position which would lead us to equate universals with mere collections of particulars. he reading (b) is instead equivalent to a moderate kind of realism according to which universals are entities that can be determined in themselves and are not identical to collections of particulars; however, these entities only exist insofar as there is some particular that instan-tiates them. According to (a), deinitions ultimately refer to the par-ticulars that belong to the extension of a certain predicate. According to (b), deinitions refer to a feature proper to each particular; such a feature satisies the intension of the deinitional account and is an en-tity in some sense of the word9. As I aim to show, the view (a) is that held by Boethus, whereas the view (b) is that held by Alexander. Fur-thermore, both (a) and (b) are diferent from (c), Iamblichus’ strong realism about universals, according to which universals are universalia ante rem, i.e. self-subsistent paradigmatic entities that are prior, met-aphysically separate and independent with respect to particulars. At the level of the sensible world Iamblichus and his followers posit im-manent common entities (universalia in re), which are lower than the universalia ante rem and partake in them, but are nevertheless prior to particulars.
Ater outlining the Peripatetic view on the priority of particulars, both Dexippus and Simplicius focus on the arguments (ἐπιχειρήματα, Dexipp., In Cat., 45, 19 Busse; ἀποδείξεις, Simpl., In Cat., 82, 26 Ka-lbleisch) developed by the Peripatetics in support of their theory. Dexippus and Simplicius (who follow their common source Iambli-chus) discard these arguments as unsatisfying (ἐπιπόλαια, Dexipp., In Cat., 45, 19 Busse; σαθραί, Simpl., In Cat., 82, 26 Kalbleisch). he two arguments rejected by Dexippus and Simplicius can be seen as complementary parts of the same demonstration, since they adopt two canonical rules of natural priority that were taken to be equivalent by the commentators:
(1) Fs are prior to Gs if and only if F co-removes but is not co-re-moved by G;
(2) Fs are prior to Gs if and only if F is co-introduced by but does not co-introduce G10.
9 For the distinction between the extensional and the intensional reading, see
Rashed 2007, p. 168 and passim. Also, see Kupreeva 2010, p. 225.
he Peripatetics apply both rules to the relation between particulars and universals, since (2) individuals are co-introduced by but do not introduce universals and (1) individuals remove but are not co-removed by universals. Interestingly, however, these rules of priority are compatible with both the reading (a) and the reading (b) outlined above. According to (a), i.e. the extensional reading of the Peripatetic position, individuals are co-introduced by universals since universals are nothing but collections of particulars: thus, given a certain collec-tion, the particulars that belong to this collection are also given. Fur-thermore, particulars co-remove universals, since when all particulars are removed, their collection is also removed. he opposite does not hold: one could well consider a species, for instance, with a unique par-ticular member (e.g. the sun and the moon, according to the examples given in Arist., Met. Ζ 15)11. In such cases, the unique member of the species exists but does not belong to any universal collection: hence the individual does not co-introduce the universal and the universal does not co-remove the particular. One may indeed remark that the collection composed by one single individual is still an entity diferent from the single individual member that belongs to it. To the best of my knowledge, however, the ancient commentators do not develop any argument of this kind. Furthermore, the collection with one single member would still not be ‘universal’ in the sense of ‘being composed by several members’12. he two rules of priority are also compatible with reading (b), i.e. the ‘intensional’ reading of the Peripatetic posi-tion. In this case, individuals are co-introduced by universals, since universals are deinable entities that exist only insofar as they are in-stantiated by some individual. When all individuals are removed, the universal deinable nature is also removed. he opposite does not hold, as is shown again by the example of a species with one single particu-lar instantiation. he situation, however, is more complicated here. In fact, one could well consider a deinable entity corresponding to the sun (the nature ‘sun’) which exists only insofar as it is instantiated by a unique individual. his deinable nature would not be universal, but would nevertheless be diferent from the unique particular that instantiates it (the deinable nature would be the same even if it were
11 See on this Adamson, this volume.
12 I consciously avoid talking of «classes» and of their members, but rather adopt
the term «collection», which is more neutral and does not suggest any direct parallel between these ancient views and modern logic.
instantiated by several particulars). As we shall see below, Alexander of Aphrodisias develops an argument of this kind and treats the deinable nature (e.g. the genus ‘animal’, the species ‘human being’ or ‘sun’) as something separate from its being universal (see Alex. Aphr., Quaest. I.11a, 22, 3-6 and I.11b, 23, 26-27 Bruns).
2. Boethus of Sidon: the extensional position
Unfortunately, the commentaries on the Categories by Boethus and Alexander are lost. he situation is extremely diicult with Boethus since, unlike what happens with Alexander, none of his works are ex-tant. In order to assess his views, we depend completely on later second or third-hand accounts furnished by Neoplatonist commentators13. It is actually very unlikely that Dexippus and Simplicius read Boethus di-rectly. Probably they based their accounts on Iamblichus, who in turn had relied on Porphyry’s lost commentary Ad Gedalium for
informa-tion about Boethus14. his should indeed recommend prudence. For
example, Martin Tweedale has convincingly shown that Simplicius sometimes provides a misleading account of Alexander’s position: the same might well be the case with Boethus, but, unlike what happens with Alexander, we cannot check Dexippus and Simplicius’ outlines against Boethus’ own writings. Furthermore, the testimonia are oten obscure: for instance, it is very diicult to separate Simplicius’ report from his assessment of Boethus’ position. hat said, we should not simply give in to desperation, since what we can ind in Dexippus and Simplicius is enough to draw a suiciently clear and consistent outline of Boethus’ position15.
13 On Boethus, see Moraux 1973, pp. 143-79. More recently, Reinhardt 2007;
Rashed 2007, who provides an in-depth discussion of Boethus in relation to Alex-ander; Rashed 2013a. Sharples 2008a focuses on Boethus’ position within the early reception of Aristotle’s Categories; on this, see also Chiaradonna 2009b. Several tes-timonia on Boethus have now been translated and commented upon in Sharples 2010. Griffin forthcoming provides an extensive discussion of Boethus’ interpreta-tion of the Categories.
14 It is controversial whether Simplicius read Porphyry’s Ad Gedalium directly.
Chase 2003, p. 109 note 194 and passim suggests that Simplicius only relied on Iam-blichus.
As noted above, Dexippus’ reference to Boethus and Alexander is open to diferent interpretations. he most we can say is that the Peri-patetic position about the priority of individuals was diferent from the Neoplatonist realism about universals held by Iamblichus and his followers. However, two diferent interpretations are possible within the same Peripatetic philosophical background, i.e. the extensional and the intensional. Our testimonia on Boethus strongly suggest he held an extensional view of the universals. First it is worth focusing on Simpl., In Cat., 78, 4-20 Kalbleisch. Here Simplicius famously ex-pounds Boethus’ views on sensible substance16. As Simplicius reports, Boethus compared Aristotle’s theory of substance in the Categories, ac-cording to which ousia is a single category (μίαν […] κατηγορίαν), to the division of substance into form, matter and composite which Aris-totle expounds «elsewhere» (ἐν ἄλλοις). Boethus’ conclusion is radical to say the least: while matter and composite substance satisfy the crite-ria of substantiality established in the Categories, form is in matter as «in something else» and is therefore cut of from substance. hus, form should be seen as belonging to non-substantial categories such as qual-ity, or quantqual-ity, or some other. Signiicantly, Boethus comes to this conclusion by noting that Aristotle’s deinition of primary substance (τὸν τῆς πρώτης οὐσίας λόγον, Simpl., In Cat., 78, 10 Kalbleisch) in the Categories can only be applied to matter and composite substance, since the property of ‘not being said of any subject and not being in any subject’ belongs to them (In Cat., 78, 11-12 Kalbleisch, see Arist., Cat., 5, 2a11-13 and 3a8-9). From these remarks, Boethus infers that form is outside the category of substance. Boethus, then, equates ‘sub-stance’ with ‘primary sub‘sub-stance’ without any further qualiication; apparently, he does not focus on the status of Aristotle’s secondary substances (species and genera) that are ‘said of a subject’ without ‘be-ing in a subject’ (Cat., 5, 2a37-b2). Hence, he does not consider the hypothesis according to which form may be substance since it is ‘said of a subject’ with respect to matter without being, in consequence of this, ‘in a subject’ in relation to matter. Accordingly, if Simplicius’ par-Archimedes palimpsest (probably a section of Porphyry’s Ad Gedalium) provides some crucial new testimonia on Boethus, which lend further support to the present interpretation. Here I will leave out these passages. For further discussion, see Chi-aradonna, Rashed, Sedley 2013.
16 On this passage, see now Reinhardt 2007; Sharples 2010, pp. 86 f.; Rashed
aphrase is trustworthy, Boethus makes a selection within Aristotle’s criteria of substantiality in the Categories: he accepts Aristotle’s stricter notion of substance (as the particular bearer of properties) and passes over in silence the reasons that may lead us to regard genera and spe-cies as secondary substances.
Indeed, Simplicius’ second or third-hand paraphrase could well be inaccurate17. Yet, further testimonia suggest similar conclusions and it is tempting to infer from the extant evidence that according to Boethus universals have no reality at all by themselves and are nothing but mere collections of particulars. Simpl., In Cat., 50, 2-9 Kalbleisch contains Boethus’ answer to the aporia according to which individual substances are ‘in a subject’ with reference to the place and time in which they are situated. First Boethus denies that particular substances are ‘in a subject’ in relation to a particular place and a particular time: the reason for this fact is that substances in motion change place and time lows continu-ally. One may say, however, that particulars are in universal time (ἐν τῷ καθόλου χρόνῳ, In Cat., 50, 5-6 Kalbleisch). Boethus answers that
he universal does not even exist [οὐδὲ εἶναι ἐν ὑποστάσει]18 according to
Aristotle, and if it did exist, it would not be ‘something’ [οὐ τὶ εἶναι]; but Aristotle said ‘in something’ [ἔν τινι]. So what is in something cannot be in what is universal (Simpl., In Cat., 50, 6-9)19.
Again, an opinionated reading of the Categories is detectable in these lines. In order to counter the view that particulars are in universal time
17 Signiicantly, Simplicius’ paraphrase of Boethus is followed immediately by
Por-phyry’s response (p. 78, 20 f. Kalbleisch = Porph. 58F. Smith), which Simplicius read either directly (if he had access to Porphyry’s Ad Gedalium) or via Iamblichus.
18 he translation of ὑπόστασις is famously controversial. In what follows I will
variously render this term as «reality», «existence» or «real existence». A clear-cut dis-tinction between essence and existence is actually diicult to ind in the Greek com-mentators (as well as in all ancient philosophers). Neither should we assume that an extremely common term such as ὑπόστασις always possesses the technical Stoic mean-ing of «subsistence». See on this Burnyeat 2003, pp. 20 f.
19 Dexipp., In Cat., 22, 30 f. Busse provides a slightly diferent version of this
argu-ment and does not name Boethus. Luna 2001, pp. 279 f. compares the two versions extensively. She concludes that, their diferences notwithstanding, «[l]es éléments uti-lisés dans les deux textes sont donc les mêmes; ce qui change, ce sont leur disposition et leur valeur» (Luna 2011, p. 281).
as ‘in a subject’, Boethus argues that time as a universal cannot in any way be conceived of as a subject in the relation of ‘being in a subject’ (ἐν ὑποκειμένῳ εἶναι). From Boethus’ remark one may legitimately in-fer that nothing can be related to a universal subject according to the relation of esse in subiecto, since (i) what is universal has no reality (ὑπόστασις) and (ii) even if universals had some kind of reality, they would, in any case, not be ‘something determinate’ (οὐ τὶ εἶναι).he relation between (i) and (ii) is not completely clear to me. I would pro-pose that Boethus aims to separate the status of what is universal from both the status of substances and that of qualities. Both substances and qualities are, in fact, real entities, whereas universals are not. However, he might have added (ii) as sort of ad hominen remark: even if we grant that universals are real, they cannot however in any way be regarded as subjects of inherence. His explanation is ultimately based on Cat., 2, 1a24-25, where Aristotle deines what is in a subject as that which «is in something, not as a part [ὃ ἔν τινι μὴ ὡς μέρος ἐνυπάρχον], and cannot exist separately from what it is in». Apparently, Boethus leaves out Aristotle’s remark on the notion of ‘part’ and develops the idea that what is ‘in a subject’ should exist ‘in something’ (ἔν τινι). Even if we grant that what is universal has some kind of existence, it cannot in any way be taken to be a τι; accordingly, nothing can exist ἔν τινι in relation to a universal subject.
he parallel passage from Dexippus’ commentary (οὐδὲν τῶν κοινῶν οὔτε τόδε οὔτε τὶ ὑπάρχει, Dexipp., In Cat., 22, 32-33 Busse) suggests that Boethus used τι as a designation for Aristotles’ τόδε τι. In fact, both in the Categories and in the Metaphysics Aristotle denies that what is universal (secondary substances, according to the jargon of Aristotle’s Categories) has the status of a τόδε τι. Rather, Aristotle is inclined to conceive of universals as quasi-qualitative entities (ποιόν τι, Cat., 5, 3b17; τοιόνδε, Met., Ζ 13, 1039a2). hat said, it is worth noting that Aristotle does not suggest that universals cannot have the position of subjects in the relation of ‘being in a subject’ (ἐν ὑποκειμένῳ εἶναι). As he argues in Cat., 5, 3a1-6, nothing prevents non-substantial items from being ‘in a subject’ with regard to substantial species and gen-era. Probably Boethus gave full emphasis to Aristotle’s remarks on the quasi-qualitative status of universal items and (unlike Aristotle) came to regard universals as incapable of being subjects in the relation of ἐν ὑποκειμένῳ εἶναι.
As noted above, Simplicius’ account of Boethus’ theory of substance suggests that Boethus simply took the ‘category of substance’ to be identical with Aristotle’s primary substance in the Categories and ruled
out Aristotle’s secondary substances. In a similar way, Simplicius’ ac-count of universal time suggests that Boethus used the (genuine Aris-totelian) remark that a universal item is not a tode ti in order to argue that universals have no reality and that even if they did, they could not in any way be conceived of as subjects of inherence. Further passages conirm these provisional conclusions. Boethus’ view about the tode ti is referred to again in Simpl., In Cat., 104, 27 Kalbleisch (Simplicius’ discussion is paralleled in Dexipp., In Cat., 51, 15-22 Busse, but Dex-ippus’ account is cursory and Boethus is not named). Simplicius asks in which respect we shall say that the individual substance is a tode ti: in respect of the form, the matter or the composite? In his answer, he explains that the individual can be seen as a tode ti on account of all of these. He mentions Boethus when he explains why the individual can be called a tode ti on account of its form: «[…] in respect of the form, insofar as it is determinate and one in number, for Boethus too deter-mines unity by means of “this”»20.
he reference is cursory to say the least and Simplicius seems to mention Boethus’ view outside of its original context (signiicantly, Boethus’ name appears immediately ater a reference to Plato’s theory of matter in Ti. 50b: see In Cat., 104, 25 Kalbleisch). hus, Simplicius’ discussion in these lines probably cannot be used in order to explain the sense of Boethus’ original remark. hat said, we can nevertheless assume with some certainty that Boethus determined (ἀφορίζει) unity according to the tode ti. Prudence is necessary, but the parallel with the passages discussed above suggests that Boethus regarded the tode ti (i.e. the individual substance) as the only kind of reality provided with genuine unity, whereas on his account genera and species do not
20 I follow the translation by de Haas in de Haas, Fleet 2001, p. 48. he Greek text
is καὶ γὰρ ὁ Βόηθος τὸ ἒν κατὰ τόδε ἀφορίζει and it seems to me necessary to sup-ply τὸ before τόδε (κατὰ <τὸ> τόδε: this suggestion was already made by Kalbleisch 1907, p. 559; see below, 104, 30-31 Kalbleisch: τὸ δὲ σύνθετον […] ἐπιδέχεται τὸ τόδε). Sharples’ translation is diferent and closer to the received text: «for Boethus too deines in this respect [κατὰ τόδε] what is one» (Sharples 2010, p. 79). As I see it, however, this interpretation is less convincing, because Simplicius does not focus on the deinition of what is one, but on the deinition of what can be regarded as a tode ti. Simplicius irst points out that an individual substance can be seen as a tode ti on account of its form, since form makes the individual determinate and one in number. hen, in support of his point, Simplicius mentions Boethus’ view that being one is the same as being tode ti.
correspond to any determinate entity provided with unity (since, if the present interpretation is correct, Boethus regarded genera and species as mere collections of particulars). his is simply an hypothesis, but it is nevertheless interesting that the cursory reference to Boethus ap. Simpl., In Cat., 104, 25 Kalbleisch may be read according to the con-clusions reached so far.
he same holds for a passage from Syrianus’ Commentary on the Metaphysics (In Met., 105, 19 f. Kroll) where he critically discusses some erroneous interpretations of Plato’s Ideas. According to Syri-anus, Boethus the Peripatetic «goes astray as a result of Aristotle’s teaching, identifying the Forms with generic items» (εἰς ταὐτὸν ἄγων τοῖς γενικοῖς τὰς ἰδέας, 106, 6-7 Kroll). Syrianus speciies further that the Stoic Cornutus is not far from this position. he reference is again cursory and not very perspicuous. In particular, the status of Boethus’ genika needs further scrutiny. Syrianus (In Met., 106, 7-13 Kroll) op-poses genika and particulars and equates genika and universals. his passage may plausibly be read in connection to Simplicius’ discussion on the universal time ap. Simpl., In Cat., 50, 6-9 Kalbleisch. Presum-ably, Boethus conlated ideas and universal items in order to criticize and undermine Plato’s Ideas. hus, he probably argued that Ideas, as well as universal items, do not exist. he parallel between Boethus and the Stoic Cornutus is obviously interesting in this respect21. Signii-cantly, according to Syrianus Boethus is led astray by Aristotle’s teach-ing: his position is set out as an interpretation of Aristotle and Syrianus does not point to any direct Stoic inluence on Boethus. It is notewor-thy however that Syrianus regards Boethus’ distinctive reading of Ar-istotle as convergent with Stoicism. hus, even without postulating a direct inluence of the Stoic view, we can reasonably assume that Boe-thus developed an opinionated reading of the Categories in which uni-versal items were conceived of as beret of any existence. Predictably enough, Boethus’ position was perceived as close to that of the Stoics.
Here the dossier ‘Boethus and the Stoa’ cannot be discussed exten-sively. Certainly Boethus was very well aware of the Stoic theories. Simplicius (In Cat., 163, 6 Kalbleisch) says that Boethus devoted a whole book (ὅλον βιβλίον)22 to the relative, in which he critically
dis-21 On universals in Stoicism, see Bronowski, this volume.
22 Presumably, this book was part of his Commentary on the Categories, whatever its
cussed the Stoic views (see Simpl., In Cat., 167, 22 f. Kalbleisch)23. Furthermore, some of his views are indeed similar to those of the Sto-ics: this is the case with his theory of the immanent form as an ‘acci-dent’ of matter (ap. Simpl., In Cat., 78, 11-20 Kalbleisch), which has been connected to the Stoic theory of quality24, and with his theory of the universals, whose ainities with the Stoic theory did not escape Syrianus. Robert Sharples remarks that «Boethus’ position is closer to that of the Stoics than to Aristotle»25, hese conclusions need some qualiication, however, since Boethus’ position can also be seen as a systematic reading of Aristotle which gives full weight to some aspects of Aristotle’s thought and treats other aspects as secondary. Marwan Rashed has interestingly presented that of Boethus as one among sev-eral «possible Aristotelianisms». According to Rashed, Boethus devel-ops his systematic Aristotelianism by giving full weight to the ontic priority of individuals established in the Categories. As a consequence of this fact, Boethus regards the status of the hylomorphic form as sec-ondary. hus, no speciic Stoic inluence would be necessary to explain Boethus’ position, which would only be based on a selection of works and themes internal to Aristotle’s corpus. Other Aristotelian commen-tators in the irst century BCE, such as Andronicus, shared this atti-tude and their reading of Aristotle was mostly based on the Categories (as Rashed aptly remarks, their Aristotelianism was «Catégories-cent-rique»), whereas works such as the Physics and the Metaphysics played a minor role. As Rashed takes it, Alexander of Aphrodisias’ essentialist reading of Aristotle was a reaction against the reading of his ancient colleagues26.
Rashed’s reading sheds new light on the development of the ancient Aristotelian tradition. Yet I would perhaps qualify his interpretation with some further remarks. In my view, it is crucial to note that Aris-totle’s Categories do not suice to explain the genesis of Boethus’ read-ing of Aristotle27, Boethus’ rejection of the universals outside substance goes in fact far beyond Aristotle’s views on species and genera as ‘sec-ondary substances’. Boethus radicalizes the sec‘sec-ondary status of genera
23 See Sharples 2010, pp. 62 f.; Rashed 2013a. 24 See Reinhardt 2007, pp. 526 f.
25 Sharples 2010, p. 87.
26 See Rashed 2007, pp. 1-31 and p. 42; Rashed 2004.
27 Here I am inclined to disagree with Rashed 2007, p. 42: «Boéthos et consorts
and species, to the extent that they are conceived of as beret of real existence. hus, according to Boethus Aristotle’s substance is simply identical with the primary substance in the Categories, whereas sec-ondary substances are not substances at all. Probably Boethus does not even take the status of universal items to be the same as that of non-substantial qualities or quantities. Rather, he is likely to be assuming that universal items simply do not exist as distinct from individuals. As we shall see below, Alexander follows a diferent path and does his best to give full emphasis to the substantial status of secondary substances. Certainly, they are secondary, since they are not independent of indi-viduals and could not exist without any instantiation. Yet in Alexan-der’s view genera and species are not mere collections of particulars, but deinable natures that exist in particulars. Boethus’ view about the unqualiied ontic priority of individual substances may well be read in connection with the philosophical climate of his time, which was de-termined by the Hellenistic schools and by Stoicism in particular. I also suspect that the selection of Aristotle’s esoteric works among the early commentators was heavily inluenced by late Hellenistic philosophical debates (this holds for Aristotle’s Categories and On the Heaven, the two ‘star treatises’ of the early commentators)28. hese remarks are by no means intended to reject Rashed’s systematic reading of Boethus. In my view, however, it is philosophically very interesting to situate the genesis of Boethus’ reading of Aristotle within the philosophical climate of his time. his may help to explain why the early commen-tators developed an opinionated reading of Aristotle, which could be seen (and indeed later was seen) as convergent with Stoicism.
It is worth focusing on two further diicult testimonia from Sim-plicius. he irst passage is about the theory of speciic diferentia:
Boethus, however, says that the diferentia is properly placed with the spe-cies, not with the genus [ὁ μέντοι Βόηθος πρὸς τὸ εἶδος κυρίως συντάττεσθαί φησιν τὴν διαφοράν, ἀλλ’ οὐ πρὸς τὸ γένος], because the diferentiae are oten substituted for the species [ἀντὶ τοῦ εἷδους παραλαμβάνονται] (Simpl., In Cat., 97, 28-30 Kalbleisch)29.
In his discussion, Simplicius irst reports the view of some exegetes who regard the diferentia as something which by nature separates
28 See Chiaradonna 2013; Chiaradonna 2011c.
items under the same genus (In Cat., 97, 25-26 Kalbleisch). his deinition is an ancient one: it occurs in Porphryry’s Isagoge and its ultimate source is the Topics (Z 3, 140a27-29)30. According to Sim-plicius, Boethus disagrees, since he claims that the diferentia should properly be placed with the species, not with the genus. Ater the lines quoted above, Simplicius makes some further remarks, but it is un-clear whether he is still reporting Boethus’ view or critically discuss-ing it (Simpl., In Cat., 97, 31-34 Kalbleisch)31: for this reason, I will not consider these lines in the present discussion. Simplicius’ remark against Boethus at In Cat., 97, 34-35 Kalbleisch (cf. Dexipp., In Cat., 48, 6-9 Busse) is however very interesting and can be used as a start-ing point in order to outline Boethus’ position. Simplicius says that the diferentia is diferent from the species (Dexippus remarks that the diferentia is diferent from the species as the part is diferent from the whole) and it is a kind of form (μορφή) of the genus, while the genus is like a subject (ὑποκείμενον).
It has been suggested that Boethus echoes Met. Ζ 12, where Aristotle identiies the ultimate diferentia with the eidos32. his is not impossi-ble, but I would be prudent about Boethus’ use of Met. Ζ, since Aristo-tle’s hylomorphism plays virtually no role in Boethus’ philosophy. As I see it, Boethus’ silence about the genus, and his equation between the species and the diferentia can well be read as relecting the extensional interpretation developed so far. If, in fact, we conceive of universals in an extensional way, i.e. as collections of individuals, any generic en-tity or nature will simply be suppressed. Accordingly, the genus can-not be like a subject that is determined by the diferentia: this explains Simplicius’ critical remark. In Boethus’ view, the genus simply does not exist as such (i.e. as a nature determined in an intensional way): this explains Boethus’ parallel between the genera and Plato’s Ideas. If this is the case, the diferentia must be placed with the species, because the species is identical with the diferentia. he species cannot in fact be composed of the genus and the diferentia, since the genus in itself simply does not exist.
Unfortunately, we do not know how Boethus conceived of the dif-ferentia and its ontic status (we do not know, in particular, whether
30 See. Porph., Isag., 11, 18-19 Busse and the excellent commentary ad loc. in Bar-
nes 2003, p. 197, with further parallels.
31 See de Haas in de Haas, Fleet 2001, p. 74 note 115. 32 De Haas in de Haas, Fleet 2001, p. 74 note 114.
he regarded diferentiae as tropes, something which would indeed it very well with the interpretation developed so far); neither do we know what kind of relation Boethus established between the diferen-tia and the (in his view non-substandiferen-tial) hylomorphic form. So, the present discussion cannot but be partial and speculative. It is how-ever at least possible to propose some hypotheses about Boethus’ view, which try to combine the information drawn from the passages discussed above. According to Boethus, matter and individuals are the only existing substantial subjects, whereas diferentiae are mere non-substantial qualities (diferentiae cannot be substantial, since they cannot be regarded as subjects of inherence). Species are mere collections of particulars grouped according to their diferentiae and these diferentiae are somehow equivalent to the non-substantial ‘for-mal’ properties inhering in matter mentioned ap. Simpl., In Cat., 78, 19-20 Kalbleisch. hus, diferentiae make it possible to class individu-als according to speciic collections. For an individual, belonging to a species means belonging to a speciic collection on account of the non-substantial qualities inhering in it. According to this theory, a genus would be nothing but the sum (or rather the logical product) of several speciic collections (see also Simpl., In Cat., 58, 29-59.4 Kalbleisch). Boethus’ overall attitude can aptly be characterized as ‘nominalist’ and, as noted above, his position goes beyond what Aris-totle says in the Categories. In Met., Ζ 12, 1038a5-6 ArisAris-totle famously provides the following alternative: either the genus absolutely does not exist apart (παρά) from the species, or – if it does exist – exists as matter. If Boethus ever considered this text, he must have opted for the irst horn of the alternative. In his view, the genus has in itself simply no kind of existence and cannot be seen as the subject of any possible ‘information’ of the part of the diferentia.
If general concepts have no real correlate apart from particulars, one might well wonder just what their status is. Did Boethus regard gen-eral concepts as mere mental ictions? Again, all we can do is draw some hypotheses. Possibly in his discussion about universals Boethus made use of his semantic view that propositions are «about» things (περὶ […] πράγματος), but their meaning is composed of concepts or «thoughts» (νοήσεις, see Simpl., In Cat., 41, 14-19 and 41, 28-42, 2 Kalbleisch), since according to Boethus there are no ‘propositional objects’ which can be the meaning of statements. Boethus’ remarks are perhaps (and very interestingly) reminiscent of Plato’s distinc-tion between saying something and saying something about some-thing (Pl., Sph. 262e-263d), and may well be directed against the Stoic
λεκτόν33. hus, we cannot directly refer these remarks to the status of general concepts. hat said, the diference between being τοῦ πράγματος and being περὶ πράγματος (Simpl., In Cat., 41, 18-19 Kalbleisch) can plausibly be applied to the meaning of statements such as «Socrates is man» or «Socrates is animal». Boethus could easily argue that the predicate in these judgements does not stand for any general entity. So general terms only mean mental concepts. his, however, does not entail that species and genera are mere igmenta, since their real cor-relate is given by the particular members of their extension. According to this overall view, general terms would have the status of common names: again, such a theory can aptly be characterized as ‘nominalist’.
hese diiculties notwithstanding, the passages discussed above pro-vide a suiciently consistent picture of Boethus’ position about univer-sals. he same is not the case with Simpl., In Cat., 65, 19-24 Kalb-leisch. Here Simplicius focuses on some objections against the alleged completeness of Aristotle’s list of categories. Among these objections, he mentions the one concerning the categorial status of the monad and the point. Ater mentioning Alexander’s solution (the monad and the point should be placed among the relative), Simplicius says:
If, however, number is twofold – one incorporeal, the other corporeal – then, as Boethus too would say the monad will also be twofold: one which is substance, and is in intelligible number – Aristotle also thinks that this one exists – and one which is a relative or quantiied item. Later, however, Boethus says that perhaps it is better to call it a quantiied item, for as whiteness is to white, so the dyad is to two. If, therefore, the former are both quantiied, the latter are also quantiied (Simpl., In Cat., 65, 19-24 Kalbleisch)34.
Paul Moraux had already remarked that this passage is troublesome to say the least35. Boethus’ criticism of Plato’s Ideas and his view about
33 Boethus was certainly familiar with Plato’s Sophist: see below. On Boethus’
criti-cism of the Stoic lekton, see Rashed 2013a.
34 εἰ δὲ διττὸς ὁ ἀριθμός, ὁ μὲν ἀσώματος, ὁ δὲ σωματικός, ἔσται, ὡς καὶ ὁ Βόηθος ἂν
φαίη, καὶ ἡ μονὰς διττή, ἡ μὲν οὐσία, ἡ ἐν τῷ νοητῷ ἀριθμῷ (τοῦτο δὲ καὶ Ἀριστοτέλει δοκεῖ), ἡ δὲ πρός τι ἢ ποσόν. ὕστερον δέ φησιν ὁ Βόηθος μήποτε ἄμεινον εἶναι ποσὸν φάναι· ὡς γὰρ λευκότης ἔχει πρὸς λευκόν, οὕτως καὶ ἡ δυὰς πρὸς τὰ δύο· εἰ οὖν ἐκεῖνα ἄμφω ποιόν, καὶ ταῦτα ποσόν. Parallel in Dexipp., In Cat., 33, 23-27 Busse. On these passages, see the extensive commentary in Luna 2001, pp. 673-96.
the unqualiied priority of particulars cannot easily be reconciled with a theory of ideal numbers such as that which Simplicius seems to at-tribute to Boethus in these lines. Moraux, however, regards Simplicius’ report as trustworthy and suggests that Boethus followed Speusippus on this issue, since Boethus was certainly interested in Speusippus and referred to his theory of polyonyms (ap. Simpl., In Cat., 36, 28-30 Kalbleisch). Unfortunately, Simplicius’ words (ὡς καὶ Βόηθος ἂν φαίη, 65, 20 Kalbleisch) do not help to settle the issue and it remains uncertain whether his paraphrase can be trusted completely or not36.
Here I will propose a tentative explanation of this controversial pas-sage. Simplicius’ outline of Boethus’ theory of sensible substance opens with these words: Ὁ μέντοι Βόηθος ταῦτα μὲν παρέλκειν τὰ ζητήματα βούλεται· μὴ γὰρ εἷναι περὶ τῆς νοητῆς οὐσίας τὸν λόγον (Simpl., In Cat., 78, 4-5 Kalbleisch). he questions (zêtêmata) rejected by Boe-thus are those set out in Simplicius’ previous pages, where he focuses on Nicostratus’ and Plotinus’ criticisms against substance. To make a long story short, according to Simplicius Nicostratus and Plotinus claim that Aristotle’s theory of substance in the Categories is unsatis-fying and incomplete, since Aristotle leaves out intelligible substance (Simpl., In Cat., 76, 13-17)37. Simplicius’ account misleadingly lends the impression that Boethus countered these objections raised by later exegetes, arguing that their criticism was redundant since Aristotle’s discussion of substance in the Categories simply does not focus on the intelligible ousia. Perhaps Boethus was addressing objections devel-oped by an early anti-Aristotelian exegete and similar to those later raised by Nicostratus and Plotinus. Perhaps Simplicius (or Iamblichus) incorporated Boethus in his account in order to counter Nicostratus’ and Plotinus’ later objections. It is also possible that Boethus was react-ing to an early Platonizreact-ing readreact-ing of the Categories: by his remark, he might be warning that one should not read Plato’s Ideas into Aristo-tle’s ousia. Be that as it may38, Boethus certainly mentioned Aristotle’s irst mover in his discussion of ποιεῖν and πάσχειν (Simpl., In Cat., 302, 17 Kalbleisch). Accordingly, if Boethus really claimed that one should not consider the νοητὴ οὐσία when interpreting Cat. 5, by this he did not intend to rule out intelligible beings from the interpretation
36 See the critical remarks against Moraux in Tarán 1981, p. 745 f. Griffin
forth-coming provides a full discussion.
37 On Plotinus and Nicostratus, see Chiaradonna 2005. 38 For further discussion, see Chiaradonna 2009b.
of Aristotle’s Categories, nor suggest that intelligible beings do not ex-ist at all. Rather, he was probably claiming that a discussion about in-telligible substances is redundant in the framework of Cat. 5 (whereas in his view talking of the unmoved mover was certainly not redundant in the discussion on ποιεῖν and πάσχειν). Accordingly, nothing rules out the possibility that Boethus might have referred to the theory of intelligible numbers where he thought this to be relevant to his reading of Aristotle.
his is all the more likely, since Boethus was possibly reacting against the Pythagorizing reading of Aristotle’s Categories developed by Eu-dorus of Alexandria, a reading which is detectable in Ps.-Archytas’ treatise Περὶ τῶ καθόλου λόγω, as well in Philo and Plutarch. Perhaps Boethus’ remark about the irrelevance of the sensible substance for the interpretation of Cat. 5 was originally directed against Eudorus39. Given such premises, Boethus’ mention of the intelligible monad is not really surprising: he might well have referred to this theory when discussing the views of his rival Platonic-Pythagorean readers of Aris-totle (and this could explain why he would seem to ascribe the theory of intelligible numbers to Aristotle: this would in fact be an allusion to the exegesis developed by his opponents)40. Moraux’s parallel with Speusippus is plausible too, for the early commentators were certainly willing to recall and possibly incorporate the views of Plato and the Ancient Academy. As noted above, Boethus mentions Speusippus’ polyonyms and refers to Plato (Simpl., In Cat., 159, 12 f.). Andronicus mentions Xenocrates when discussing the categorial bi-partition per se/relative and the theory of the soul41. his attitude is easily justiiable within the philosophical climate of the irst century BCE, which was still rather luid and marked by the renaissance of ancient dogmatic philosophies within a philosophical debate dominated by the Hellen-istic schools. Perhaps Boethus and Andronicus’ appeal to the Academy was directed against the Stoics. Be that as it may, Boethus’ mention of the intelligible monad can plausibly be placed within this picture.
hese remarks, however, still do not answer to the main question
39 See Chiaradonna 2009b; Griffin forthcoming.
40 his, however, is not completely sure, since the words τοῦτο δὲ καὶ Ἀριστοτέλει
δοκεῖ at 65, 21 Kalbleisch might well be a remark by Simplicius. According to Chase 2003, p. 147 note 734 Simplicius’ reference may be to Aristotle’s lost On the Good.
41 Ap. Simpl. In Cat., 63, 22-24 Kalbleisch; Them. In De An., 32, 19-31 Heinze. See
raised by the passage quoted above: given Boethus’ nominalist posi-tion about substance and universals, is it plausible that he developed a Platonizing theory of ideal numbers and that he ascribed this view to Aristotle? Certainty cannot be attained, and Simplicius’ passage is obscure. Actually Simplicius refers to two diferent solutions proposed by Boethus. According to the irst solution, Boethus distinguished be-tween a substantial monad, which is in the realm of intelligible number, and a relative or quantiied monad (which should obviously be placed in the sensible world). According to a second solution set out «later», however, Boethus says that perhaps it is better to call «it» a quantiied item, for the dyad is to two as whiteness is to white. Accordingly, if both whiteness and white are qualiied, then both the dyad and the two are quantiied. he Greek text at 65, 14 Kalbleisch runs as follows: ὕστερον δέ φησιν ὁ Βόηθος μήποτε ἄμεινον εἶναι ποσὸν φάναι. he subect of einai poson can plausibly be identiied with the monad. If this is the case, according to Boethus’ second solution both the monad and the dyad are quantiied items. hus, given a couple of particulars, the dyad is the quantity which corresponds to the quantiied predicate ‘two’. his view is not incompatible with those on the status of sub-stances and generic items and does not point to any metaphysics of ideal numbers.
According to Simplicius, however, Boethus’ irst solution recognized the existence of intelligible numbers (among which we should place the substantial monad). If Simplicius does not misleadingly ascribe to Boethus the Platonist-Pythagorean view that he aimed to reject through his second solution (although this may well be the case, as noted above), then we are forced to admit that Boethus acknowledged the existence not only of the unmoved mover, but also of ideal num-bers. While I would not endorse this reading without some hesitation, it is crucial to note that even in this case Boethus would not be conceiv-ing of ideal numbers as causal principles, nor takconceiv-ing them to be generic of universal entities. Rather, essential numbers would have the status of intelligible individuals, and thus be diferent from Plato’s Forms (which Boethus regarded as non-substantial genika).
We ind a similar situation in Alexander (ap. Simpl., In Cat., 82, 7-10 Kalbleisch), who – according to Iamblichus/Simplicius – claims that the intelligible and separate form (τὸ νοητὸν καὶ χωριστὸν εἶδος) is called individual substance (ἄτομον οὐσίαν). Simplicius explains that this view is probably characteristic of the Peripatus, since according to the members of this school common items have no independent exist-ence (οὐδέ ἐστιν ὅλως καθ’ ἑαυτὰ ἐν ὑποστάσει), but rather only have
their being in individuals. his passage is indeed somewhat surprising and might suggest that Alexander held some version of Plato’s theory of separate forms. his is certainly not the case, however, and Simpli-cius later explains (In Cat., 90, 21 f. Kalbleisch) that Alexander was referring to what he took to be a separate form, i.e. the irst mover42. Possibly Alexander was replying to Nicostratus, who regarded Aristo-tle’s discussion in the Categories as partial, since Aristotle leaves out intelligible substances. Against Nicostratus, Alexander was perhaps attempting to show that the accounts of substance in Cat. 5 and Met. Λ are compatible, since Aristotle’s deinition of primary substance in the Categories can also be referred to the unmoved mover, which is not a universal but an individual, and is not in subiecto. If Simpli-cius’ paraphrase of Boethus’ irst solution is trustworthy, the passage about the intelligible monad could be interpreted along similar lines, and Boethus’ view on the monad would in no way be opposed to his nominalist view of generic items. In fact, whether he really admitted an intelligible monad or not, nothing suggests that he conceived of it as a universal.
his hypothesis might suggest further (indeed very speculative) conclusions. Alexander was probably inclined to equate the status of mathematical objects and that of universals43. In both cases, he devel-oped an abstractionist view according to which these items are im-manent in sensible particulars and our soul is able to separate them from matter, thus conceiving them ‘in themselves’. his view should carefully be distinguished from that according to which mathemati-cal objects are mere mental constructions. In fact, both universals and mathematical objects are perfectly real entities that can be determined objectively. Our soul simply separates them from matter and con-ceives of in itself what de facto only exists insofar as it is instantiated by material objects. As noted above, Boethus’ view on universals is radi-cally diferent from Alexader’s abstractionist essentialism and we can plausibly suppose that Alexander was reacting against his predecessor. According to Boethus, universals are mere collections of individuals, they are beret of existence and there is no entity that corresponds to
42 See on this Guyomarc’h 2008. On Alexander’s approach to Plato’s forms, see
Lefebvre 2008.
43 See Mueller 1990, pp. 467-70 with the supplementary remarks in Rashed 2011,
pp. 59-64, who convincingly rejects Mueller’s mentalistic interpretation of Alexan-der’s abstractionism.
(e.g.) the general concept ‘human being’ and is immanent in particular human beings. It is at least possible that Boethus regarded ‘human be-ing’ as a mere mental concept without any direct general real correlate, whereas the expression ‘human being’ actually denotes the particular human beings classed according to their proper qualities. Given such premises, if Boethus was inclined to conceive of mathematical objects as real independent entities, he could not have regarded their status as parallel to that of the genika. Hence, it is not completely unlikely that he held some (perhaps Speusippean) theory according to which ideal numbers are individual and intelligible substances. If this is true, Boethus’ distinguished real individual and substantial numbers from those in the sensible world, which are mere quantiied and collective predicates of particular items. his would explain the relation between Boethus’ irst and second solution, without making the two incompat-ible. If this is the case, Alexander’s essentialism was toto caelo opposed to Boethus’ ontology, both on the status of universals and on that of mathematical objects.
To sum up: either Simplicius’ paraphrase is misleading and Boethus’ irst solution does not express Boethus’ own view, but rather that of his Pythagorean opponents, or Simplicius’ paraphrase is correct, and Boe-thus’ irst solution provides a realist view about mathematical objects, which is compatible with Boethus’ nominalism about universals. he second solution expresses either Boethus’ own position (as opposed to that of the Pythagoreans), or his view about sensible and quantiied numbers (as opposed to substantial and intelligible numbers).
3. Alexander of Aphrodisias’ essentialism and his views on universals his ‘nominalist’ view on universals is repeatedly criticized by Alex-ander of Aphrodisias, whose own Peripatetic view is basically equiva-lent to the ‘intensional’ position set out above44. Even if Alexander does not mention Boethus by name in these contexts (indeed, Alexander rarely mentions the names of his adversaries), it is more than plausi-ble that Boethus was his polemical target. Against Boethus’ nominal-ism, Alexander develops a kind of moderate realism about universals,
44 he literature on Alexander’s views on universals is abundant. I would only refer
to Lloyd 1981; Tweedale 1984; Sharples 2005; Rashed 2007, pp. 254-60. Sorabji 2004, pp. 149-56 provides an excellent survey.
which is part of his overall systematic essentialist reading of Aristotle’s logic, physics and ontology. Here I will only cursorily recall some as-pects of Alexander’s position.
Quaestio I.3 probably provides the clearest way to approach all as-pects of Alexander’s sophisticated realism45. In this short work, Alex-ander aims to establish what kind of things are those referred to by deinitions. he Quaestio opens by outlining two opposite theories that Alexander rejects. According to the irst position (7, 20-24 Bruns), deinitions refer to particulars. Alexander rejects this view because particulars are what they are in conjunction with accidents; they are not always self-identical, but are subject to change; and in addition to that, particulars are the object of perception rather than deinition. According to the second position (7, 24-27 Bruns), deinitions refer to a common entity separated from particulars, an entity that is in-corporeal and eternal. Alexander rejects this theory too. His remark is rather cursory and he simply asks how ‘biped’ could be something incorporeal and ‘mortal’ something eternal. his remark is actually not very convincing: for instance, one may well conceive of the separate form ‘biped’ as an incorporeal entity, which is the principle that ex-plains why the quality ‘biped’ is present in corporeal things. Signii-cantly, Alexander himself regards qualities inhering to sensible par-ticulars as incorporeal (see De An., 18, 5-7 Bruns), since they do not include matter in their nature even if they exist only in conjunction with matter46. So his polemical remark against self-subsisting separate incorporeal forms could in principle also be addressed against his own views on qualities. However, Alexander’s remark can perhaps better be understood in connection to what he says against the nominalist position in the immediately preceding lines. According to Alexander, deinitions should refer to stable objects that only reason can grasp adequately. his prevents deinitions from referring to particulars that exist in conjunction with accidents and are beret of stability. hat said, one should not assume that there are deinable entities independent of particulars: such entities would in fact be beret of any connection with particulars. His remark about the status of ‘biped’ and ‘mortal’ can be read as an emphatic statement of this point. Deinitions must in some way be connected to sensible particulars: using notions such as that of ‘biped’ or ‘mortal’ in order to refer to entities separate from and
45 See now the commentated translation of this work in Rashed 2007, pp. 257 f. 46 See on this Kupreeva 2003.
independent of particular biped and mortal living beings would make little (if any) sense.
his issue comes up at 7, 27-28 Bruns, where Alexander says that deinitions refer to (a) common entities that exist in particulars, or (vel) (b) to those particulars insofar as they are determined by the com-mon entities that are present in them (ἀλλ’ εἰσὶν οἱ ὁρισμοὶ τῶν ἐν τοῖς καθέκαστα κοινῶν, ἣ τῶν καθέκαστα κατὰ τὰ ἐν αὐτοῖς κοινά). In his view, (a) and (b) are not mutually exclusive hypotheses, but diferent ways of expressing the same fact. We can now clearly understand why Alexander rejects both the nominalist and the realist Platonic posi-tions. Since deinitions refer to entities that are common and difer-ent from particulars, the nominalist view must be rejected. Particulars, however, cannot merely be cut of from the object of deinition: if this were the case, we could well deine the universal Human Being, but this deinition could in no way be applied to particular human beings. Alexander takes a sort of middle path between Boethus’ nominalism and a kind of Platonic realism47.
According to Alexander, the fact that several individuals are ‘such and such’ is grounded on another more primitive fact, i.e. the existence of a common entity according to which (cf. κατά, 7, 28 Bruns) those particulars are ‘such and such’. As far as we can judge from the extant evidence, Boethus held a very diferent view and regarded the fact that several particulars are ‘such and such’ (in his jargon: that several par-ticulars have certain diferences) as primitive: this primitive fact does not require any further explanation. Alexander’s objection, however, points to an interesting problem. A radically anti-essentialistic view should address the issue of how to establish a suicient criterion in order to select those aspects of particular beings which make it pos-sible to rank them under the same species. In other words, a philo-sophical position that suppresses the existence of generic or speciic es-sences should nonetheless somehow account for our classiications of the natural world. Indeed, one may well argue that natural species are nothing but pragmatic arbitrary classiications with no ontic import. Alexander, however, would probably have regarded this conclusion as simply nonsensical (and all ancient non-sceptic philosophers would share such an attitude).
his explains Alexander’s remark at 7, 21-22 Bruns that particulars
47 As Rashed 2007, p. 259 aptly remarks, «[l]es Aristotéliciens ne doivent pas
are ‘such and such’ (τοιαῦτα) in conjunction with accidents. In his view, a deinition entails that we select its object and isolate it from the other features which inhere to particulars. Alexander, therefore, demands a suicient criterion for establishing this selection and his essentialism actually provides an answer to the problem (indeed, an answer that could easily be criticized as circular), whereas Boethus’ radical anti-realist position is much more problematic from this perspective. Sig-niicantly, Simplicius reports that Porphyry raised a similar objection: according to Porphyry, Boethus envisaged enmattered form (what Aristotle himself conceived of as substance) as nothing but a quality or some other among the accidents (ap. In Cat., 78, 21-22 Kalbleisch = 58F. Smith). hus, he was not able to isolate essential features from qualitative aspects in the structure of sensible particulars. Porphyry’s objections against Boethus recall Alexander’s views and it is more than likely that Porphyry based his criticism on previous objections raised
by Alexander48. his is not enough to demonstrate beyond all doubt
that Boethus is polemically targeted at the beginning of Alexander’s Quaestio I.3 (although this is a plausible hypothesis); be that as it may, the philosophical parallel between Boethus’ position and Alexander’s nominalist polemical target remains interesting.
In the remaining part of the Quaestio, Alexander focuses on the ontic status of immanent deinable entities. As he explains at 7, 32 f. Bruns, the deinition «rational mortal animal»49 can be taken in conjunction with the «material circumstances and diferences» accompanying its concrete existence: in this case, the deinable entity produces (ποιεῖ, 8, 2) Socrates, Callias and all other individuals. herefore, we should not suppose that particular beings and their deinable natures are mutually separated. Each deinable nature (e.g. ‘human being’) only exists inso-far as it is instantiated by the particular material beings determined by it. If all particulars were suppressed, the deinable nature would be sup-pressed with them (see also Quaest. I.11b, 24, 11-15 and 19-22 Bruns). his, however, does not entail that particular beings are all that exists. Indeed, objects of deinition are immanent to particulars and exist in actuality only insofar as they determine particular beings. hat said, it is crucial to regard each object of deinition as an entity irreducible to particulars, an entity that we can grasp through our mind in isolation
48 See Chiaradonna, Rashed 2010, pp. 272 f.
49 Here Alexander calls ‘deinition’ the deinable nature which is the real correlate
from the particulars which it is in. When grasped by our mind, the object of deinition becomes common (κοινὸν γίνοιτο, 8, 3-4 Bruns). his is a key aspect of Alexander’s abstractionist realism, according to which deinitions refer to real natures that exist in individuals. hese are natures that are not universal as such, but only insofar as our soul isolates them from matter and conceives of them by themselves (see De An., 85, 14-20 Bruns).
If we come back to the parallel between Boethus and Alexander es-tablished by Dexippus, we can easily see how Alexander’s essential-ist thesis about the ontic priority of individuals toto caelo difers from Boethus’ extensional theory. According to Alexander, what is common is a nature that is deinable and irreducible to particulars, a nature that exists «in each particular as a whole», the same in all (8, 9-10 Bruns). Alexander conceives of both the speciic (human being: see. Quaest. I.3) and the generic (animal: see Quaest. I.11 a and b) deinable natures in this way50. In both cases, he aims to rule out all possible extensional conclusions in the theory of universals. hus, universals are connected to formal natures that are deinable in themselves and are the proper object of rational knowledge. Alexander’s famous and controversial thesis according to which what we call a universal is an «accident» of a given «thing» (πρᾶγμα, Quaest. I.11a, 22, 3-6; I.11b, 23, 26-27; see I.3, 8, 12-13 Bruns) is part of this theory. As noted by M. Tweedale, the «thing» which the universal is an accident of should not be equated with a particular being, but with a deinable nature (animal or human being)51. Alexander’s terminology is not completely consistent, but a general theory is clearly at work in his writings. Formal natures can be determined and deined by themselves and are not necessarily univer-sal as such. If, for example, there were only one human being, his dein-able nature would not be universal (at least de facto), since it would be instantiated by only one particular being. Nonetheless, it would equally be possible to isolate the deinable nature human being from the unique human being determined by this nature (Quaest. I.3, 8, 13-16 Bruns). Hence it is an accident that the deinable nature is universal, while it
50 Here I ignore Alexander’s sophisticated and somewhat ambivalent ontology of
the genus: see Rashed 2007, pp. 94-104. I only focus on what Rashed would call «la teneur formelle» of the genus.
51 See Tweedale 1984. Alexander’s view that what is universal is an accident of the
deinable nature should not be conlated with the view that existence is an accident of the deinable nature: see Chiaradonna, Rashed 2010, p. 288.
not accidental that this nature is intensionally determined as it is. As reported by Simpl., In Cat., 85, 13-14 Kalbleisch, Alexander applied this line of argument to some canonical examples of species instantiat-ed by only one particular, such as the sun, the moon and the cosmos52. As noted above, at the beginning of Quaestio I.3 Alexander raises a quasi-Platonist criticism against the nominalist position: deinitions cannot refer to particulars, since particulars change and deinitions should refer to permanent objects. he concluding part of this short work explains how Alexander regards deinable natures as permanent objects without conceiving of them as separate quasi-Platonic forms. As he notes, common natures are incorruptible in virtue of the «eter-nity by succession» (ἐκ τῆς διαδοχῆς αἰδιότητι, 8, 23 Bruns) of the particulars in which they exist. hus, the logico-epistemological real-ist analysis of deinable natures is ultimately grounded in the Peripa-tetic hylomorphic analysis of generation. As noted by Marwan Rashed, the hylomorphic form provides objective content for the species and makes it diferent from any arbitrary classiication53. he close connec-tion between universality, the eternity of the species and hylomorphic form emerges in Alexander’s On Providence (87, 5-91, 4 Ruland)54. Here Alexander relies on Aristotle’s GC Β 10 and explains that the eternal and universal species is the primary object of providence. Eternity and universality come to be taken as equivalent characters. As Rashed re-marks, the eidos is unique in the chain of generation: its continual and eternal realization directly entails that it is universal55.
A succinct comparison between Boethus’ and Alexander’s views may help to summarize our conclusions. According to Boethus, universals are mere collections of individuals, whereas according to Alexander universals are deinable entities that happen to be universals insofar as they are instantiated by several particulars. As far as we can judge, according to Boethus deinitions are simply based on the primitive fact that particulars are ‘such and such’, whereas according to Alexander the actual structure of sensible particulars depends on immanent de-inable natures. Boethus’ general view makes it very diicult to isolate those essential aspects that allow us to rank several particulars under
52 Tweedale 1984, p. 293 shows that Simplicius does not understand Alexander’s
point correctly.
53 See Rashed 2007, pp. 253 f.
54 his text is preserved in Arab. Translation in Rashed 2007, p. 253. 55 See Rashed 2007, p. 255.
