Relativity, categories and principles in the diuisio aristotelea 67M/32DL

Abstract

The Diuisio Aristotelea 67M/32DL draws a distinction between two categories of beings, per se and relatives. I defend three main theses. First, that the relation of dependence characterizing the members of the latter category is modal and symmetrical in nature and, accordingly, the per se-relatives contrast cannot be equivalent to the substance-accidents contrast. Second, that the type of relativity relevant to this diuisio is both ontological and semantic in nature (but with different emphases depending on the version of the diuisio considered). Third, I argue, against a widespread opinion, that the last line of the DL version of the diuisio does not concern metaphysical principles. Here I also compare the diuisio to other Early Academic bicategorial schemes and show that they differ from one another significantly, especially as far as the alleged connection between categories and metaphysical principles is concerned.

I. Introduction

The Diuisiones quae dicuntur Aristoteleae (hereafter DA) is a text containing a corpus of ‘divisions’ (διαιρέσϵις), that is, brief and schematic classifications of philosophical concepts. The topics of these classifications are various (for example, soul, virtue, vice, justice, beings), but not in a way that makes the work completely heterogeneous, as all the divisions can be clearly grouped under five rubrics: logical/dialectical, ethical, physical, political and rhetorical. ¹ It has convincingly been suggested that the chief aim of this work was to provide a checklist of certain relevant philosophical concepts that would prove useful for dialectical discussions, scientific accounts or rhetorical discourses. ² Thus, the DA likely constituted a scholastic handbook compiled for students.

The DA is a ‘multiple-tradition text’: a text transmitted in different redactions, ³ even in different languages, for which a unique original model is supposed, albeit impossible to reconstruct. More precisely, the DA has been transmitted in Greek through Diogenes Laertius’ Lives of Eminent Philosophers (Recensio Laertiana) ⁴ and six Byzantine manuscripts, which transmit it as an independent text and, as Tiziano Dorandi has recently shown, in three different recensions (labelled by him the Recensio Marciana, Recensio Florentina and Recensio Leidensis, according to the place where the chief codex of each is preserved). These three recensions differ not only from Diogenes’ but also from one another. Thus, we have a total of four different redactions. ⁵ Finally, outside of the Greek tradition, the DA is also transmitted by one Syriac and two Arabic translations. All of these translations are supposedly based on a lost Greek exemplar presenting a redaction very similar to the Laertiana, although with significant differences likely due to multiple phases of rewriting, revision and manipulation. ⁶

Both the authorship and the historical origins of this text have been subject to intense debate for almost two centuries, that is, at least since the publication of Immanuel Bekker’s edition of Aristotle’s works, from which the DA was excluded, and Valentin Rose’s Aristoteles Pseudepigraphus, where it was first published. The hypotheses have been various: some have argued for an Aristotelian authorship; others have denied it; still others have proposed that the work comes from a text produced by a young Aristotle incorporating doctrines developed by Plato, Aristotle himself and other members of the Academy. ⁷ I will not engage with this controversy. Whatever the answer to the question may be, there is one main point that is shared by a substantial majority of scholars and is of genuine interest for the present study: whoever the author(s) of the DA may be, this text quite certainly contains material from the Early Academy. This opinion has been persuasively defended by Eduard Zeller, Wilhelm von Christ, Ernst Hambruch and several others, ⁸ and the remainder of this paper is founded on acceptance of the truth of their view.

My goal here is to provide a detailed examination and an overall interpretation of DA 67M/32DL. In all the versions in which it has come down to us, this diuisio draws an exhaustive and exclusive distinction between two categories of beings, dubbed by scholars per se (or absolutes) and relatives. I shall defend three main theses. First, that the relation of dependence characterizing the members of the category of relatives is modal and symmetrical in nature and, accordingly, the per se-relatives contrast cannot be equivalent to the substance-accidents contrast. Second, that the type of relativity relevant to this diuisio is both ontological and semantic in nature (but with different emphases depending on the version of the diuisio considered). Third, I argue, contrary to a common view, that the last line of the DL version of the diuisio does not concern metaphysical principles. In doing so, I also compare the diuisio to other Early Academic bicategorial schemes and show that they differ from one another significantly, especially as far as the alleged connection between categories and metaphysical principles is concerned.

II. Symmetry and modality

We need a modicum of context first. The diuisio under consideration is found only in the Marciana and Laertiana recensions (so neither in the Florentina nor in the Leidensis). ⁹ As regards the internal structure of the DA corpus, this diuisio appears to belong to two subgroups. On the one hand, it is one of the divisions concerned with beings (τὰ ὄντα). Besides DA 67M/32DL, this subgroup includes DA 25M, 26M/31DL and 55M/24DL. DA 25M, only attested in the codex Marcianus, presents a threefold classification of beings, by distinguishing those by essence (κατ’ οὐσίαν), by accident (κατὰ συμβϵβηκός) and by affection (κατὰ πάθος). DA 26M/31DL divides beings into indivisible (ἀμϵρῆ) and divisible (μϵριστά), and subdivides the latter into homeomers (ὁμοιομϵρῆ) and anhomeomers (ἀνομοιομϵρῆ). DA 55M/24DL distinguishes beings good (ἀγαθόν), bad (κακόν) and those that are neither (οὐδέτϵρον). On the other hand, only in the Recensio Marciana, DA 67 is also part of another subgroup including DA 64–69 M. These six diuisiones (concerning genus/species, prior/posterior, the whole, beings, opposites and affirmation/negation) constitute a unified cluster, as they explicitly recall one another. ¹⁰

I shall examine DA 67M/32DL by considering first the version of Recensio Laertiana and then that of the Marciana. Here is text of the Recensio Laertiana:

T1: τῶν ὄντων τὰ μέν ἐστι καθ’ ἑαυτά, τὰ δὲ πρός τι λέγϵται. τὰ μὲν οὖν καθ’ ἑαυτὰ λϵγόμϵνά ἐστιν ὅσα ἐν τῇ ἑρμηνϵίᾳ μηδϵνὸς προσδϵῖται· ταῦτα δ’ ἂν ϵἴη οἷον ἄνθρωπος, ἵππος καὶ τἆλλα ζῷα. τούτων γὰρ οὐδὲν δι’ ἑρμηνϵίας χωρϵῖ. τῶν δὲ πρός τι λϵγομένων ὅσα προσδϵῖταί τινος ἑρμηνϵίας, οἷον τὸ μϵῖζόν τινος καὶ τὸ θᾶττόν τινος καὶ τὸ κάλλιον καὶ τὰ τοιαῦτα· τό τϵ γὰρ μϵῖζον ἐλάττονός ἐστι μϵῖζον καὶ τὸ θᾶττον <θᾶττόν> τινός ἐστι. τῶν ὄντων ἄρα τὰ μὲν αὐτὰ καθ’ αὑτὰ λέγϵται, τὰ δὲ πρός τι.

ὧδϵ καὶ τὰ πρῶτα διῄρϵι κατὰ τὸν Ἀριστοτέλη. ¹¹

Among beings, some are spoken of per se, others relatively to something. The things which are spoken of per se need nothing in the expression. These might be, for example, a human being, a horse and other animals. For none of these proceeds in virtue of an expression. The things which are spoken of relatively to something are such that they need a certain expression, for example, what is larger than something or faster than something or more beautiful and alike. ¹² For the larger is larger than the smaller, and the faster is faster than something. Among beings, then, some are spoken of per se, others relatively to something.

In this way, according to Aristotle, <Plato> also divided the primary things.

T1 draws a dichotomous distinction between two classes of beings or categories. ¹³ Arguably, the author(s) took the distinction to be exhaustive, as the use of the τὰ μέν … τὰ δέ construction throughout the DA seems consistently to suggest. ¹⁴ So, the whole domain of beings is here divided into two jointly exhaustive classes: on the one hand, that of beings spoken of by themselves, or simply per se (τὰ μέν καθ’ ἑαυτά); on the other, that of beings spoken of relatively to another (τὰ δὲ πρός τι).

One attractive way of understanding the philosophical import of this bicategorial distinction focuses on the examples of per se beings mentioned by Diogenes. These examples are ἄνθρωπος, ἵππος and τἆλλα ζῷα, that is, items one would tend to recognize as Aristotelian substances. In Aristotle’s doctrine of the categories, substances are contrasted with the other nine categories, in that the former are prior to all of the latter λόγῳ καὶ γνώσϵι καὶ χρόνῳ (Metaph. Z 1.10128a31–1028b7), such priority being the main grounds for the so-called doctrine of πρὸς ἕν homonymy defended in Metaph. Γ 2. Thus, the relation of dependence of non-substances to substances is asymmetrical. For it cannot be the case that if, say, a quality is dependent upon a substance, then a substance is also dependent upon a quality. One might suggest that a similar type of relation is operative in T1 and that the examples of per se beings mentioned in the diuisio suggest that T1 draws a distinction between a class of metaphysically fundamental beings and one of metaphysically dependent beings (i.e. dependent on the fundamental ones). Hence, on this reading, the τι to which a πρός τι being is relative is a per se being; and a πρός τι being exists because there is a per se being that exists and is metaphysically explanatory of the existence of a πρός τι being. A reading along these lines is proposed for example by Gail Fine, ¹⁵ who argues that our diuisio ‘distinguishes between substances and non-substances, for we have independent evidence that the distinction was of central concern in the Academy’. ¹⁶

Attractive as this interpretation may be, I believe it does not have the cogency claimed for it. The text posits that the two classes of beings are distinguished on the basis of two different predicative behaviours of the terms that signify them: per se beings are such that the terms that signify them do not need any ἑρμηνϵία, whereas those signifying relative beings do. ¹⁷ A proper understanding of the notion of ἑρμηνϵία is therefore important for a correct interpretation. The meaning of this word in the ancient Greek philosophical vocabulary, notably with regard to the title and σκοπός of Aristotle’s De interpretatione, is notoriously controversial. ¹⁸ However, I do not think this proves particularly puzzling as far as the translation and interpretation of T1 is concerned. LSJ and standard Greek etymological dictionaries list as the main meanings of ἑρμηνϵία ‘interpretation’, ‘explanation’ and ‘expression’, especially of thoughts by words. ¹⁹ The term ἑρμηνϵία and its cognates are found with these meanings, which I do not regard as technical, in several places of the Platonic, Aristotelian and Xenophontean corpora. ²⁰ My sense is that ‘expression’ is the preferable translation of ἑρμηνϵία in T1. ²¹ I take ἑρμηνϵία here to designate a semantic or syntactic supplement (as LSJ puts it: ‘an expression of thoughts by words’), of the form of a complement of specification, here indicated by the indefinite pronoun τινός at l. 109.1196. Without such a syntactic supplement (explicitly stated or implicitly presupposed in an elliptical sentence) a given predicate cannot be meaningful (i.e. cannot form a well-formed sentence when predicated of a given subject). This is the case of a predicate that stands for a relative being. By contrast, a per se being is signified by a predicate which does not ‘proceed in virtue of an expression’ (οὐδὲν δι’ ἑρμηνϵίας χωρϵῖ), that is, one that does not need such a syntactic supplement. ²²

The text lends support to this reading. As previously mentioned, the diuisio posits that the two classes of beings are distinguished on the basis of two different predicative behaviours of the terms that signify them: per se beings do not need any ἑρμηνϵία, whereas relative beings do. It follows that the two categories, in addition to being jointly exhaustive, are mutually exclusive (it is not the case that a single predicate can have both predicative behaviors). When it comes to explaining what it means to need an ἑρμηνϵία, the text offers no explicit clarification of this notion, but provides some examples (οἷον). These examples are all comparatives (τὸ μϵῖζόν καὶ τὸ θᾶττόν καὶ τὸ κάλλιον καὶ τὰ τοιαῦτα) whose counterparts (i.e. the τι to which a πρός τι entity is relative) are first each referred to with an indefinite pronoun (τινος), but then one of them, that of τό μϵῖζον, is unequivocally identified as a correlative (ἐλάττονος). Comparatives are relatives in that they need the expression or syntactic supplement of a complement of specification in order, when predicated of a subject x, to make a well-formed sentence. Thus, if I predicate ‘larger’ (μϵῖζον) of a subject x, I must add a complement like ‘than y’ (explicitly stated or implicitly presupposed in an elliptical sentence), otherwise the sentence ‘x is larger’ is not well-formed and does not constitute a meaningful grammatical unit. ²³ The y variable here stands for a correlative (or an item qua correlative), ²⁴ which must be ‘smaller’ (ἐλάττονός) than x.

If this reading is correct, two further remarks are in order. First, Diogenes’ text draws a distinction between categories of beings, as signified by complete and incomplete predicates . ²⁵ This is a classification of items in the attribute mode (i.e. qua attributes of subjects). ²⁶ A per se being is signified by a semantically or syntactically complete predicate. A relative being is signified by a semantically or syntactically incomplete predicate. A syntactically incomplete predicate is a predicate that needs to be supplied with an additional linguistic expression, namely a complement, in order to constitute a well-formed sentence, when it is predicated of a certain subject (for example, ‘Four is the double of…’). A syntactically complete predicate, by contrast, does not need such a supplement (for example, ‘Paul is a human being’). A semantically incomplete predicate is one that may not be syntactically incomplete, but whose semantics suggests an implicit reference to another item (for example, ‘Mathematics is a science’, which is a syntactically complete expression, but suggests that mathematics is the science of something, namely numbers, as being a science is always said in relation to something, i.e. to the object of that science). Semantically complete predicates do not suggest so (for example, ‘Humans are bipedal’).

Second, the relation of dependence this diuisio draws upon, unlike that between Aristotelian substances and non-substances, is symmetrical. For the relation between correlatives must be symmetrical: what is faster is always said of something slower, and what is slower is always said of something faster. Further, as well as being symmetrical, this relation of dependence is also modally qualified in the text, ²⁷ by two occurrences of the compound verb προσδϵῖται (ll. 1193, 1195). This verb is a composite of the preposition πρός plus the verb δέομαι, which obviously has a modal semantic colour, notably in the third person singular and in impersonal constructions. In other words, the verb προσδϵῖταί establishes that an expression must be provided (i.e. is a necessary condition) for a πρός τι predicate to constitute a meaningful grammatical unit. Thus, in T1 the relation of dependence between a πρός τι predicate and its ‘expression’ (ἑρμηνϵία) is symmetrical and modal in nature.

One might object that the fact remains that the examples of per se beings are items that we would recognize as Aristotelian substances. Undoubtedly. But this is outweighed by two pieces of evidence. First, the examples of relative beings include only relatives, not members of any of the other nine non-substantial categories. Second, the specification of the criterion of distinction between the two classes of beings in terms of ἑρμηνϵία cannot fit the substance-accidents contrast. In other words, the need of an ἑρμηνϵία cannot be identical or comparable to the πρὸς ἕν relation explored in Metaph. Γ 2 or the ‘being-in-a-subject’ relation described in Cat. 2. ²⁸ Hence, the rest of the division suggests that the αὐτὰ καθ’ ἑαυτά class should include all the items denoted by syntactically or semantically complete predicates: thus even predicates which in the Aristotelian categorial scheme stand for qualities, quantities and so on (i.e. all nine non-relative categories). Interestingly enough, this seems to be how Clement of Alexandria (Strom. VIII 24.1 Stählin–Früchtel–Treu), as well as Simplicius (in Cat. 174.16–20 Kalbfleisch) and Galen (Dig. Puls. II 2.839,13–16 Kuhn) conceived of the καθ᾽αὑτά-πρός τι contrast. ²⁹

Now, the version of the Recensio Marciana:

T2: τῶν ὄντων τὰ μὲν αὐτὰ καθ’ ἑαυτά ἐστι, τὰ δὲ πρός τι. αὐτὰ μὲν οὖν καθ’ ἑαυτά ταῦτά ἐστιν, οἶον ἄνθρωπος οἰκία ἱμάτιον χρυσίον καὶ πάντα ὅσα ἁπλῶς, μὴ τῷ ἕτϵρόν τι ϵἶναι ἐi ἀνάγκης ἐστι, τὰ δὲ πρός τι τοιαῦτα ἐστὶν οἶον τὸ διπλάσιον καὶ ἡ ἐπιστήμη. τό τϵ γὰρ διπλάσιον πρὸς τὸ ἥμισυ λέγϵται καὶ ἡ ἐπιστήμη πρὸς ἄλλο τι.

Among beings, some are per se, others are relative to something. Per se are those, for example, a human being, a house, a dress, a coin and all such things which are in an absolute way, and do not necessarily exist accompanied by the existence of something else. Those which are relative to something, instead, are of such kind, for example, double and science; for double is said relatively to half and science relatively to something else.

Just as in T1, this text too proposes a dichotomous division into two jointly exhaustive classes: on the one hand, that of beings in themselves by themselves, or simply per se (τὰ μὲν αὐτὰ καθ’ ἑαυτά); on the other, that of relative beings (τὰ δὲ πρός τι). Yet, unlike T1, T2 does not make any reference to the notion of ἑρμηνϵία to explain the difference between these two classes. Rather, it posits that per se beings exist in an absolute way (ἁπλῶς). This adverbial qualification would not in itself be very illuminating if it were not in turn clarified by a further explanatory remark: things that are ἁπλῶς are such that they do not necessarily need, for their own existence, something different to exist as well. By contrast, this is the distinctive status of relative beings. Such a characterization suggests that a relation of dependence is at play here.

Two relevant details clarify how the notion of dependence is conceived of in this context. First, the phrase ἐi ἀνάγκης, which, I submit, stands for a modal operator (analogous to προσδϵῖταί in T1) and thus suggests once again a modal analysis of the relation of dependence. The second detail is the crucial phrase τῷ ἕτϵρόν τι ϵἶναι. One attractive interpretation of this phrase is that the article in the dative case stands for a phrase such as ‘in virtue of’ or ‘because’ and thus imposes a modification of the modal relation of dependence that makes it asymmetrical. This would mark a major difference from the relation of dependence characterizing the πρός τι class in T1, as it was accounted for earlier in this section. For the diuisio would be drawing a distinction between a class of metaphysically fundamental beings and another of metaphysically dependent beings (i.e. dependent on the fundamental ones: a πρός τι being exists because there exists a per se being that is metaphysically explanatory of the existence of that πρός τι being). Once again, the resulting relation of dependence displayed here would be very close to that between Aristotelian substances and non-substances. One might even go so far as to say that, if this reading is correct, it would also constitute indirect evidence against the proposed interpretation of T1.

Yet, just as for T1, this interpretation is unpersuasive. First, the examples used by the author(s) of the diuisio seem to restrict membership to the πρός τι class only to items denoted by syntactically or semantically incomplete predicates, such as ‘double’ or ‘science’. However, this would mean that the τι to which a πρός τι entity is relative (i.e. the τι whose existence is required for the existence of a πρός τι entity) is not a per se being, but a correlative. The explanation of the examples provided in the last line of the diuisio supports this reading: what a double is, is always said in relation to a half (i.e. its correlative); and what a science is, is always said in relation to its object (again, its correlative). ³⁰ Accordingly, the article in the dative case cannot stand for an expression such as ‘in virtue of’ or ‘because’, which would make the modal relation of dependence asymmetrical, too. The relation between correlatives, once again, must be symmetrical. ³¹ For this reason, I translated the dative articular infinitive as ‘accompanied by the existence of something else’. Hence, for both T1 and T2, the relation of dependence characterizing the members of the πρός τι category is modal and symmetrical in nature and, thus, the per se-relatives contrast cannot be equivalent to the substance-accidents contrast.

III. Types of relativity

Commenting on the eighth sceptical mode, Julia Annas and Jonathan Barnes make the following remark:

the notion of relativity is itself a complex one. The Greeks speak frequently of ta pros ti, ‘things relative to something’; but behind that uniform nomenclature there stand several different accounts or theories of relativity. Different philosophical schools offered different analyses of ta pros ti. ³²

This is certainly true and we should therefore ask which notion of relativity is operative in DA 67M/32DL. In their analysis of the eighth mode Annas and Barnes single out three types of relativity: epistemic, ontological and semantic. For x to be epistemically relative to y, x is not recognizable or knowable without y. For x to be ontologically relative to y, x cannot exist without y. For F to be semantically relative to y, sentences of the form ‘x is F’ need a syntactic or semantic supplement such that they can make sense only if they are elliptical for sentences of the form ‘x is F in relation to y’. ³³

It is perhaps natural to suggest that the notion of relativity operative in T1 is semantic in nature. The most telling textual signposts in this regard are, on the one hand, the several occurrences of forms of the verb λέγϵιν (λέγϵται (ll. 1191, 1199), λϵγόμϵνα (l. 1192) and λϵγομένων (l. 1195)) and, on the other, the very notion of ἑρμηνϵία, which, as I argued, here means ‘expression’. Thus, the linguistic and semantic dimensions are certainly prominent in the Recensio Laertiana. And yet, I suggest that the text is not concerned solely with semantics. For the subject of the diuisio is τὰ ὄντα: DA 32DL is and is intended to be a bicategorial distinction of beings. Beings, and not words or concepts, are here divided. The modality of their division appeals to semantics, however. And one might well suppose that, far from excluding every notion of ontological relativity, the author(s) of this scholastic handbook of divisions simply found it explanatorily or didactically more perspicuous to present the per se-relatives contrast in terms of syntax and semantics. In other words, a double cannot exist without a half, both in the sense that a sentence of the form ‘four is double’ needs the supplement ‘of two’ (which is the half of four) and in the sense that the property of being double and that of being a half necessarily do or do not exist together. Accordingly, the dominant notion of relativity operative in T1 is certainly the semantic one, but the opening genitive τῶν ὄντων suggests an ontological nuance. ³⁴

It is likewise natural to suggest that the notion of relativity operative in T2 is ontological in nature. The most telling textual signposts in this regard are the multiple occurrences of forms of the verb ϵἶναι: ἐστι(ν) (ll. 11, 12, 13), ϵἶναι (l. 12). So, the ontological aspect is certainly prominent in the Recensio Marciana. Yet again, I submit that the text is not concerned solely with ontology. For at l. 14 the verb λέγϵται suggests that the per se-relatives contrast concerns both beings and their linguistic correlates (i.e. predicates). The ‘double-half’ example also fits this remark perfectly well. ³⁵

I shall conclude this brief section by suggesting that, rather than striving to single out one particular notion of relativity operative in each of the two recensions, it seems more advisable to talk about different, but not exclusive, emphases. T1 insists more on the linguistic aspect of the division, whereas T2 stresses the ontological aspect. In other words, I take both divisions to be concerned with beings as they are signified by the appropriate predicates, ³⁶ with T1 focusing more on the semantic features of those predicates, and T2 focusing more on the ontological features of the beings those predicates signify. ³⁷

IV. Principles?

I shall devote the last section of my paper to the final sentence of T1: ὧδϵ καὶ τὰ πρῶτα διῄρϵι κατὰ τὸν Ἀριστοτέλη. A question arises from the outset: what exactly are τὰ πρῶτα? Several commentators have taken this phrase to indicate the first ‘principles’ of Plato’s unwritten metaphysics, shared and developed by some members of the Academy, notably Xenocrates. These principles are traditionally called the One and the Indefinite Dyad. According to this reading, the diuisio would be establishing a relationship between two distinctions, one concerning categories and the other concerning metaphysical principles. These commentators take this relationship to be explanatory in nature (the explanation in question being metaphysical, i.e. dependence). I will call this interpretation the “Categories-Principles Interpretation”. ³⁸

To understand better the grounds of this reading, it should first be recalled that DA 67M/32DL is only one of several examples of bicategorial distinction in the Early Academy. ³⁹ There are at least three other relevant texts: Simpl. in Cat. 63.21–24 Kalbfleisch = Xenocrates F 15 IP²; Alexander Aphrodisiensis. in Metaph. 56.13–21 Hayduck = Arist. De bono fr. 2 Ross; Simpl. in Phys. 247.30–248.15 Diels = Hermodorus F 5 IP². ⁴⁰ Supporters of the Categories-Principles Interpretation think that these texts report, with some variations, an identical basic doctrine, in that they divide beings into two categories, and then trace them back to the two first principles.

More precisely, it has been suggested that the bicategorial scheme constituted the basis for a ‘categorial reduction argument’, which was meant to support the very postulation of those metaphysical principles. The argument goes roughly as follows: once the whole domain of beings is divided up into two categories, one will be in a position to see the general distinctive ontological features of each category (i.e. to be per se and to be relative to something else) and, finally, to recognize the pair of supreme metaphysical principles upon which those categories depend and which ultimately explain those ontological features.

Further, so the exegetical hypothesis continues, some of these texts, namely our T1, Arist. De bono fr. 2 Ross, and Hermodorus F 5 IP², are consistent in attributing this doctrine to Plato himself; but since there is no clear trace of such a tenet in the dialogues, this must have been part of Plato’s unwritten teachings. ⁴¹ Thus, according to the Categories-Principles Interpretation, there is a common and persistent doctrinal scheme shared by all these Early Academic texts, according to which there is a relation of dependence between the two categories and the two metaphysical principles. In what follows, I will try to show that the Categories-Principles Interpretation is misleading, both as an exegesis of the last line of T1 and, more generally, as a reconstruction of an alleged ‘Academic doctrine of the categories’.

We should bear in mind that the last line of T1 constitutes the end of the entire corpus of divisions reported by Diogenes. This corpus begins as follows: διῄρϵι δέ, φησὶν Ἀριστοτέλης, καὶ τὰ πράγματα τοῦτον τὸν τρόπον (Diog. Laert. 3 80.864–65). Clearly, this initial statement symmetrically corresponds with the last line of T1 (ὧδϵ καὶ τὰ πρῶτα διῄρϵι κατὰ τὸν Ἀριστοτέλη). Apart from the occurrence of the same verb (διῄρϵι) and a parallel structuring of the formula, the explicit reference to Aristotle’s name, which does not appear in any diuisio in between, makes the correspondence unequivocal. It follows that, just as the opening sentence does not belong to any diuisio, it has no relevant doctrinal content and is nothing but an introductory clause to the corpus, so too the last line, I submit, does not belong to any diuisio, has no relevant doctrinal content and is nothing but a concluding clause to the corpus. In other words, the last line of T1 is not part of DA 32DL. ⁴² It does not matter for my present purposes whether Diogenes himself inserted these clauses in the text or whether he found them in the source he copied, and I would rather suspend my judgement on this question, although I am inclined to believe that the latter was the case. What does matter, instead, is that no philosophical point is made in the final line of T1. ⁴³

I foresee two possible objections. First, the fact remains that the last line of T1 invokes τὰ πρῶτα. What else could they designate other than metaphysical principles? I answer that the pendant between the introductory and the concluding clauses rather suggests that τὰ πρῶτα is more naturally read in relation to the initial τὰ πράγματα. ⁴⁴ After all, there is only one other occurrence of the adjective πρῶτος, η, ον, in Diogenes Laertes’ DA (l. 1106) and it has nothing to do with metaphysical principles. But if this is the case, one might reply, it is unclear in what sense the divisions listed by Diogenes might be ‘first’. One speculative hypothesis is that the reference is to those of the other recensions that have been transmitted to us and are missing from the Laertiana. But this hypothesis will not do, as Diogenes does not appear to be aware of any other group of divisions, nor is there any mention of an integration of the provided list. More reasonably, τὰ πρῶτα means ‘the chief things’ or ‘the primary things’, and we can speculate that since the DA was a scholastic handbook, Diogenes or (more likely) his source compiled a selection of (the main) divisions for didactic purposes.

The second objection concerns the phrase ὧδϵ καὶ. Does this not clearly indicate a connection with DA 32 (‘in this way too’) and suggest that Diogenes is proposing an analogy between a distinction concerning categories and another concerning metaphysical principles? It does not. For one thing, there is a καὶ in the introductory clause as well (καὶ τὰ πράγματα κτλ.), which of course has no connection whatsoever with what precedes it. For another, nothing compels us to think that the demonstrative ὧδϵ refers precisely to the bicategorial distinction just drawn and not to the divisional procedure implemented throughout the corpus. Again, the introductory clause is most helpful for a sober exegesis: ὧδϵ is more naturally interpreted as the concluding counterpart of the initial τοῦτον τὸν τρόπον (ll. 864–65). In other words, ὧδϵ καὶ is an expository formula with no doctrinal bearing.

Accordingly, the Categories-Principles Interpretation is untenable as a reading of T1. But I would also like to show that it is not a consistent interpretative proposal in itself. The contents of the other testimonies reporting Early Academic bicategorial schemes, I submit, differ significantly from one another and can hardly be reduced to a single coherent doctrine, especially as far as the putative connection between categories and principles is concerned.

The text of Xenocrates’ F 15 IP² is the following:

T4: ἄλλοι δὲ κατ’ ἄλλον τρόπον αἰτιῶνται τὴν πϵριττότητα. οἰ γὰρ πϵρὶ Ξϵνοκράτη καὶ Ἀνδρόνικον πάντα τῷ καθ᾽ αὑτὸ καὶ τῷ πρός τι πϵριλαμβάνϵιν δοκοῦσιν, ὥστϵ πϵριττὸν ϵἶναι κατ’ αὐτοὺς τὸ τοσοῦτον τῶν γϵνῶν πλῆθος.

Others raise the accusation of superfluity in another way. Xenocrates and Andronicus and their followers seem to include all things in [the opposition] per se and relative, so that, according to them, so large a multitude of genera is superfluous. ⁴⁵

The text reports that Xenocrates defended a bicategorial doctrine (against Aristotle’s tenfold scheme), but it makes no reference whatsoever to first principles. ⁴⁶ So, one would naturally conclude that it should be regarded as uninformative about the categories-principles relation. Still, it has been speculated, for example by Margherita Isnardi Parente, ⁴⁷ that since Xenocrates had a doctrine of principles, he too might have posited a connection between categories and principles. In other words, the speculative argument would be that since (1) in other sources, such as T1, Arist. De bono fr. 2 Ross and Hermodorus F 5 IP², the bicategorial distinction is somehow connected to the metaphysics of principles, and since (2) Xenocrates defended both a bicategorial distinction and a metaphysics of principles, it follows that (3) for Xenocrates, too, the two theories were connected. But there are two serious problems with this reconstruction. For one thing, this speculation simply has no support in the texts. There is no trace in the extant Xenocratean fragments of an alleged connection between the bicategorial distinction and the metaphysics of principles.

It is also impossible to illuminate how exactly the two theories might have been connected for Xenocrates. The only putative (indirect) evidence to illuminate this point is found in the very Early Academic texts I am presently examining, as is clear from premise (1) in the previous argument. But not only do these texts differ from one another significantly, as we will see shortly, it would also be arbitrary to ascribe their doctrines to Xenocrates. Further, since one would need to supply claims and arguments from other Early Academic sources to interpret Xenocrates’ alleged view about the categories-principles connection, it would be methodologically circular to use Xenocrates’ fragment in turn to interpret any of them, including T1. Hence, Xenocrates’ F 15 IP² is also of no use to illuminate the categories-principles relation in T1.

In Arist. De bono fr. 2 Ross, it is said that, according to Plato, ‘the equal and the unequal are the principles of all things, both of those per se and of the opposites’ (τὸ ἴσον καὶ τὸ ἄνισον ἀρχὰς ἁπἁντων τῶν τϵ καθ’ αὑτὰ ὄντων καὶ τῶν ἀντικϵιμένων). Leaving aside the significant fact that the second category is named differently from all the other texts, it should be observed that the grammar of this sentence demands that each category must depend upon both principles. ⁴⁸ Aristotle does not say that per se beings are traced back to the One and ἀντικϵίμϵνα to the Dyad. Instead, each category derives from the ‘cooperation’ of both principles.

Finally, I shall briefly consider Hermodorus’ F 5 IP². This fragment is certainly too complex to be explored here in any detail. ⁴⁹ But for the present purposes it is crucial to stress that Hermodorus recognized only one supreme principle. What other members of the Academy recognized as a second principle Hermodorus describes as essentially privative, passive and deprived of causal efficacy. Accordingly, it is for Hermodorus not a substance and not a principle. Here is the relevant passage of F 5 IP² which corroborates this point:

T5: ὥστϵ ἄστατον καὶ ἄμορφον καὶ ἄπϵιρον καὶ οὐκ ὂν τὸ τοιοῦτον λέγϵσθαι κατὰ ἀπόφασιν τοῦ ὄντος. τῷ τοιούτῳ δὲ οὐ προσήκϵιν οὔτϵ ἀρχῆς οὔτϵ οὐσίας, ἀλλ’ ϵ̓ν ἀκρισίᾳ τινὶ φέρϵσθαι. δηλοῖ γὰρ ὡς ὃν τρόπον τὸ αἴτιον κυρίως καὶ διαφέροντι τρόπῳ τὸ ποιοῦν ϵ̓στιν, οὕτως καὶ ἀρχή, ἡ δὲ ὕλη οὐκ ἀρχή. διὸ καὶ τοῖς πϵρὶ Πλἁτωνα ϵ̓λέγϵτο μία, ὅτι ἡ ἀρχή.

Consequently, such a thing, being unstable and formless and unlimited and a not-being, is described by negation of being, and to such a thing neither principle nor substance is appropriate, but it is driven into confusion. For [Plato] makes clear that just as in one way what acts is the cause in the strict sense and distinctively, so too it is a principle. But matter is not a principle, and therefore also it was said by those around Plato that there is one principle. ⁵⁰

Hermodorus is therefore a monist about metaphysical principles. He does not accept the correspondence between categories and principles, as it is proposed by the Categories-Principles Interpretation for the very simple reason that there is place for only one principle in his metaphysics.

The three texts I have just discussed invite us to resist the Categories-Principles Interpretation. They show that neither the relata of the connection between categories and principles nor the nature of the connection itself are identical across all these testimonies. The only thing that these texts seem to share is the basic scheme of a twofold division of beings. Accordingly, they can hardly be reduced to a single, persistent, doctrinal body. In other words, there seems to have been nothing like an ‘Academic doctrine of the categories’ or a ‘categorial reduction argument’. The evidence attests little more than a series of modest attempts to divide beings into two categories (sometimes with different names) that are occasionally connected, in different ways, to the doctrine of principles.

V. Conclusions

The study of the meagre remnants attesting bicategorial distinctions in the Early Academy may make (and has made) it tempting to downplay the originality of Aristotle’s contrast between substances and accidents by tracing it back to the doctrines of other members of Plato’s schools or to a purported ‘Academic doctrine of the categories’ shared by several of Plato’s disciples. In this paper, my aim has been to show that, as far as Diuisio Aristotelea 67M/32DL is concerned, such a reconstruction is unconvincing. I have shown that the relation of dependence characterizing the members of the πρός τι category is modal and symmetrical in nature and, thus, the per se-relatives contrast cannot be equivalent to the substance-accidents contrast.

In addition, I have defended two further theses. The first is that the type of relativity relevant to this diuisio is both ontological and semantic in nature (but with different emphases depending on the version of the diuisio considered). Second, I have argued that the last line of the DL version of the diuisio does not concern metaphysical principles. In so doing, I also compared the diuisio to other Early Academic bicategorial schemes and showed that they differ significantly, especially as far as the alleged connection between categories and metaphysical principles is concerned. Accordingly, not only is the Aristotelian contrast between substances and accidents different from that between per se and relatives that we find in some Early Academic categorial accounts, but these very accounts in turn differ significantly. Thus, I think it is inaccurate to speak of an ‘Academic doctrine of the categories’, as if it were a uniform view shared by the members of the Early Academy.