I

The first lines of the surviving text of Alexander of Aphrodisias’ περὶ κράσεως καὶ αὐξήσεως (from now on De mixtione)Footnote ¹ present several challenges. For one thing, the original beginning of the treatise is lost. We do not know for certain the extent of the missing material, but Groisard plausibly suggested that it likely was not large and probably contained a synthetic overview of Chrysippus’ theory of total blending (κρᾶσις δι’ ὅλων), as the extant text opens in medias res with a critique of this theory.Footnote ² For another, the thrust of this initial, critical section—quite polemical in character—is not straightforward. Alexander expresses wonder that such a theory can be accepted in the face of its contradictory tenets and deems it worse than mythical narratives (De mixt. I, 1.1–9). To further hammer the point home, he then compares the Stoic position to two other, apparently paradoxical statements on blending, only to say that it is far more paradoxical (I, 1.9–16). This comparison is perplexing for several reasons, though, for both the relationship between these two statements and the possible identity of the philosopher(s) holding them are unclear. A look at the scholarly literature confirms the puzzlement.Footnote ³ Scholars have been mostly aware of these problems and have offered quite different solutions, some remaining at a purely interpretative level, others relying on textual conjectures.

None of the available interpretations convincingly reconstructs the comparison drawn by Alexander. At the same time, a different reading can be provided, which makes better sense of the text and need not pay the high price of emending it. This reading also sheds light on some interesting features of Alexander’s dialectical strategy, enabling us to better appreciate his position as part of a wider debate on mixture grounded in some common assumptions of a methodological and epistemological nature. Our aim is thus to argue for this alternative reading.

We first illustrate the initial section of the De mixtione, focussing on the main passage and highlighting the issues arising from the comparison drawn by Alexander (II). After having rehearsed the available interpretative options and assessed their strengths and weaknesses (III–IV), we put forth and defend our own reading of the passage (V–VI). We then take a closer look at the wider dialectical context of the treatise to show that it is in keeping with our reading (VII–VIII). Lastly, we summarize the main points and results of our discussion (IX).

II

At the outset of the preserved text of the De mixtione, Alexander brings up two major claims of the Stoic theory of total blending (which he probably introduced in the lost part of the text) about the state of blended bodies in a mixture: (a) they penetrate each other completely so that no part of them is separate (κεχωρισμένον) from the other body; (b) each of their parts retains the surface it possessed before the mixture.Footnote ⁴ Alexander rhetorically asks how it is possible to hold at once (a) and (b), clearly implying that they are incompatible and thus that Chrysippus’ position (a)+(b)Footnote ⁵ is inconsistent (I, 1.1–6). Indeed, he immediately judges (a)+(b) more paradoxical even than mythical narratives, briefly recalling Chrysippus’ meta-theoretical contention that only his position accounts for the fact that blended bodies can be separated again (I, 1.6–9).

At this point, Alexander further illustrates the paradoxicality of Chrysippus’ account by comparing it with two other statements on blending. This is the most perplexing passage. Here is Groisard’s Greek text:

As an initial reference, let us provide the translation given by R.B. Todd, though we shall later disagree on some of its key features and give our own translation.

As γάρ shows, the passage is intended to clarify the preceding point about Chrysippus’ position (a)+(b) being more paradoxical than mythical narratives. It is equally clear that, in Alexander’s view, Chrysippus’ position is more paradoxical than claims (i) and (ii). Claim (i) concerns, again, the separability of blended bodies, while claim (ii) concerns the impossibility of blending. Thus, there are four claims at stake in our passage: claim (i) about separability, claim (ii) about the impossibility of blending, and claims (a) and (b) constituting together Chrysippus’ position (a)+(b).

The precise meaning of both (i) and (ii), however, is disputed. Equally controversial is their relationship, namely whether they are separate theses or together constitute a single position on blending (i)+(ii). Lastly, whether we are dealing with two distinct theses (i) and (ii) or with just one position (i)+(ii), it is difficult to determine the identity of the philosopher(s) or philosophical school(s), if any, that might have held them, especially in the case of (ii). These problems are connected, for a different interpretation of the meanings of (i) and (ii) will result in a different stance on their unity and attribution; at the same time, if it can be determined independently whether (i) and (ii) must be taken together or not, this will pose some constraints on their interpretation.

Divergences on these issues have given rise to at least four different accounts of the passage, advanced by Todd, Montanari, Groisard and Betegh respectively. We can divide these four interpretations into two camps. Todd, Groisard and Betegh take (i) and (ii) as a unitary position (i)+(ii), which, as a whole, is less paradoxical than Chrysippus’ position. Montanari, by contrast, understands them as two distinct theses, each less paradoxical than Chrysippus’ position; but he believes that the text requires emendation to make sense. In our view, (i) and (ii) constitute two different positions, but no emendation is needed. Let us address the two camps in this order.

III

According to Todd,Footnote ⁸ Alexander says that Chrysippus’ position (a)+(b) is more paradoxical than (i)+(ii), that is, the conjunction of claim (i) about separability and claim (ii) about the impossibility of blending. Claim (i) means that bodies which have been blended can be separated from the mixture. As for (ii), Todd takes ὅλως to qualify κιρνᾶσθαι and separates it from the negation μηδ’, which he then understands as negating δύνασθαι. As a result, claim (ii) expresses a restriction on the possibility of mixture: certain bodies cannot blend completely, others can (‘certain bodies cannot be completely blended’). The unitary position (i)+(ii) would then represent the correct, Peripatetic stance, according to which the ingredients can be recovered from the blend, and genuine blends are possible only between bodies of certain types.

GroisardFootnote ⁹ challenges Todd’s reading of (ii) and, consequently, his overall assessment of the passage. He argues that (ii) is a complete negation of the possibility of mixture: μηδ’ ὅλως is a unitary expression, meaning ‘not at all’ and denying the whole phrase κιρνᾶσθαί τινα δύνασθαι (‘it is not at all possible that some bodies blend’). This is a frequent meaning of ὅλως when accompanied by a negation.Footnote ¹⁰ As Groisard reports in his commentary, manuscript A even has the variant μηδόλως, frequently attested too.Footnote ¹¹ He also argues, in terms of content, that (ii) would be paradoxical only if read this way, which seems required by the context: since Alexander charges the Stoic position with being ‘far more paradoxical’ than other positions, these other positions must also be deemed paradoxical in some sense to act as terms of comparison. Groisard also raises a similar problem about claim (i), which asserts that blended bodies can be separated again; since this is one of the most common assumptions in the debate about mixture, it cannot be regarded as paradoxical. He solves this problem by understanding (i) and (ii) as a unitary position (i)+(ii) which is paradoxical as a whole and represents the Democritean stance: ingredients can be recovered from (apparent) blends and blending is not possible at all. He further supports this interpretation by noting a parallel between claim (ii) on the impossibility of blending and II, 3.16–17, where Alexander says of Democritus οὐδὲ τὴν ἀρχήν φησιν εἶναι πρὸς ἀλήθειάν τινα κεκραμένα (‘he says that in reality there are no blended bodies at all’). So, according to Groisard, Alexander compares Chrysippus’ position not to the correct, Peripatetic position, but to the less paradoxical, even though still wrong, position of Democritus.

BeteghFootnote ¹² returns to Todd’s reading of (ii) as asserting that certain bodies cannot blend completely, while others can: against Groisard, he argues that it would be strange to maintain at once that (i) blended bodies can be separated again and that (ii) bodies cannot blend. He also questions whether Alexander would have attributed to Democritus the talk of ‘blended bodies’ (τὰ κεκραμένα) present in (i), given the latter’s account of mixture as mere juxtaposition. Still, Betegh differs from Todd in his assessment of the passage, noting that not only Alexander, but also Chrysippus accepts the conjunction (i)+(ii). Therefore, Betegh claims that Alexander does not compare the wrong position of Chrysippus to the correct, Peripatetic position, nor to the wrong Democritean position: rather, he discriminates between the acceptable and unacceptable elements of Chrysippus’ position—(i)+(ii) and (a)+(b) respectively.

Groisard’s arguments about (ii) are convincing: this claim is not a restriction of the possibility of mixture (as Todd and Betegh have it). Rather, (ii) expresses a complete negation of the possibility of genuine mixture, and thus it can only reflect Democritus’ position, the only philosopher discussed by Alexander who denies the reality of mixture (II, 3.13–26). Against Groisard, however, we do not concede that (i) (‘blended bodies can be separated’) reflects Democritus’ position. As Betegh rightly notes, it is problematic to ascribe to him talk of ‘blended bodies’ (τὰ κεκραμένα), given that Alexander reports him as saying that ‘in reality there are no blended bodies at all’ (II, 3.16–17).

Since (i) cannot be ascribed to Democritus, while (ii) can only be ascribed to him, it follows that the assumption shared by Todd, Groisard and Betegh is flawed: (i) and (ii) do not form a unitary position (i)+(ii) but are separate claims. This conclusion is further supported by two textual observations. As Betegh notes, Alexander twice presents Chrysippus’ coordinate theses (a) and (b) through the parallel construction ὁμοῦ … ὁμοῦ … (I, 1.3–6 and 12–14),Footnote ¹³ which signals that (a) and (b) constitute together the unitary position (a)+(b). Alexander, however, does not employ the same construction in the case of (i) and (ii), which suggests that they are separate claims. Moreover, as Groisard observes, (i) and (ii) function syntactically as distinct complements to the comparative adjective παραδοξότερον.Footnote ¹⁴ Alexander presents (i) and (ii) separately, using an instance of the genitive articular infinitive τοῦ … λέγειν for each, thus making it clear that he is comparing Chrysippus’ position to two separate theses: τοῦ τε γὰρ λέγειν δύνασθαι χωρίζεσθαι τὰ κεκραμένα, ἀλλὰ καὶ τοῦ μηδ’ ὅλως κιρνᾶσθαί τινα δύνασθαι λέγειν κτλ. Betegh’s and Groisard’s remarks strongly speak against their view that (i) and (ii) constitute a unitary position. Having thus established that (i) and (ii) are distinct positions, we can also endorse Groisard’s reading of (ii) as a complete denial of the possibility of mixture without being affected by Betegh’s objection regarding its awkward combination with (i).

This analysis leads to three conclusions. First, (i) and (ii) represent two distinct stances. Second, only (ii) represents the Democritean position, which denies the existence of genuine blends. Third, while both (i) and (ii) are judged less paradoxical than the Chrysippan position, each is paradoxical to some extent. One difficulty remains, however: while the Democritean position (ii) is clearly paradoxical to some degree, the same is less obvious for claim (i). This is one of the most widely shared assumptions about mixture and therefore seems far from paradoxical. This led Groisard to conclude that there is nothing paradoxical about it and that only its combination with claim (ii) provides a paradoxical position. In section IV, we first consider the interpretation proposed by Montanari, who, like us, understands (i) and (ii) as distinct positions but raises a concern similar to Groisard’s. Then, in section V, we show that claim (i) is to some extent paradoxical too.

IV

Our critique of Todd, Groisard and Betegh entails a strong departure from Todd’s translation of the passage. Let us now present our own version (De mixtione I, 1.9–16):

This translation aligns with Montanari’s understanding of the transmitted text:Footnote ¹⁵ (i) and (ii) represent different positions, (ii) expresses the Democritean stance, and both claims are deemed by Alexander paradoxical to a certain extent, though less so that Chrysippus’ position. However, Montanari also notes that Alexander actually endorses (i) and that, for this reason, he cannot regard it as paradoxical to any degree. Given that (i) and (ii) are distinct positions, and therefore the former must be paradoxical in its own right, he concludes that, as far as (i) is concerned, the transmitted text is corrupted and proposes to emend it as follows: <μὴ> δύνασθαι χωρίζεσθαι τὰ κεκραμένα. So understood, (i) reads that bodies that have been blended cannot be separated (‘it is not possible that bodies which have been blended get separated’). This is a claim that Alexander would deem paradoxical, for he endorses its unemended version. To sum up Montanari’s interpretation, neither (i) nor (ii) represents the correct, Peripatetic position, although both are better than Chrysippus’ position, with (i) the denial of separability being less paradoxical than (ii) the denial of genuine mixture.

We reject Montanari’s emendation. First, however, let us consider a second argument which he advances. He points to a parallel between our passage and the following text from Alexander’s later refutation of Chrysippus (VII, 14. 9–12):

Montanari understands this passage as a report of the following meta-theoretical claim put forth by Chrysippus.Footnote ¹⁶ In Montanari’s reading, according to Chrysippus, the impossibility of total blending would entail the impossibility either of a genuine unification between ingredientsFootnote ¹⁷ or of separability. Montanari builds on this reconstruction to support his emendation in Chapter I. He argues that in Chapter I Alexander responds to Chrysippus’ meta-theoretical claim as follows: saying that total blending is possible is more paradoxical both than (i) maintaining that separability is impossible (hence Montanari’s emendation with a negation) and (ii) maintaining that genuine unification is impossible.

Admittedly, the two passages are similar: both connect Chrysippus’ position with the issues of (i) separability and (ii) reductionism. The passage from Chapter VII, however, does not speak in favour of Montanari’s emendation in Chapter I. First, the context strongly suggests that this passage is not a report on a claim advanced by Chrysippus, but the first outline of a dialectical objection moved by Alexander against him. For one thing, the expression κατ’ αὐτούς, though compatible with Montanari’s interpretation, is often used by Alexander to set his opponents against their own standards.Footnote ¹⁸ Moreover, the following lines start with the particle γάρ, which shows that Alexander is clarifying the preceding point, and advance a dilemmatic objection against Chrysippus picking up the alternative outlined in the passage quoted above (first horn: VII, 14.13–33; second horn: 14.22–15.2).Footnote ¹⁹ If the quoted passage from Chapter VII is not a report on Chrysippus, but an objection by Alexander against him, Montanari’s assessment of the relationship between Chapter I and VII is flawed. Furthermore, it is doubtful that Chrysippus could advance that meta-theoretical claim. While he certainly regards total blending as the only possible explanation of separability (cf. I, 1.8–9 and VII, 14.8–9), there is no evidence that he also considers it the only possible explanation of genuine unification. In fact, Chrysippus is committed to the existence of fusion—a kind of mixture distinct from total blending which nonetheless involves genuine unification (cf. III, 6.20–25). Hence he could hardly advance the first part of the meta-theoretical claim, which derives the impossibility of genuine unification from that of total blending. In sum, Montanari’s reconstruction of Chapter VII is highly speculative at best, if not actually untenable, and certainly cannot bear the weight of an emendation in Chapter I. But there is a second reason why Chapter VII does not support Montanari’s emendation. Chapter VII formulates claim (i) about separability exactly as Chapter I, that is, without the supplied negation μή: compare τὸ δύνασθαι χωρίζεσθαι τὰ κεκραμένα (VII, 14.11–12) with δύνασθαι χωρίζεσθαι τὰ κεκραμένα (I, 1.9–10). Hence on a textual level too Chapter VII does not invite any emendation in Chapter I.

It then remains Montanari’s and Groisard’s contention that (i) cannot be deemed paradoxical by Alexander because he endorses it.

V

As noted, Alexander presents both (i) and (ii) as, at least to a certain extent, paradoxical, despite endorsing (i) himself. Pace Montanari and Groisard, we do not think this is a real problem. To address their concerns, let us first clarify what ‘paradoxical’ (παράδοξος) exactly means, to then show why (i) is in some sense paradoxical too.

Alexander says that Chrysippus’ position (a)+(b) is ‘by far more paradoxical and against everybody’s conceptions’ (μακρῷ παραδοξότερον καὶ παρὰ τὰς ἁπάντων ἐννοίας) than statements (i) and (ii). The καί is epexegetic, telling us that to be paradoxical means to clash with conceptions held by everybody. Alexander alludes to the doctrine of κοιναὶ ἔννοιαι (for the precise phrase, cf. III, 7.10 and V, 9.14–15), probably originating in the Stoic school and later developed by Epicureans, Platonists and Peripatetics, too.Footnote ²⁰ In his commentary on Aristotle’s Topics, Alexander explains that a παράδοξος obtains ‘due to the clash with the common preconceptions’ (in Top. 78.27 Wallies: διὰ τὴν πρὸς τὰς κοινὰς προλήψεις μάχην).Footnote ²¹ So by declaring the Chrysippan account ‘by far more paradoxical and against everybody’s conceptions’, Alexander suggests that it conflicts with common conceptions more severely than (i) and (ii). This implies that (i) and (ii) conflict with some common conception as well. We shall specify the precise content of these common conceptions later (section VII). For now, it is easy to see why (ii) Democritus’ reductionism conflicts with common conceptions: it altogether denies the reality of genuine blending. But could (i) separability, too, be deemed paradoxical?

Groisard’s remark that separability is the most widely accepted assumption regarding mixture is perfectly correct. Before Alexander, Aristotle considered separability a given fact that must be accommodated and accounted for in a satisfying theory of mixture (Gen. corr. 1.10, 327b27–29 φαίνεται δὲ τὰ μιγνύμενα πρότερόν τε ἐκ κεχωρισμένων συνιόντα καὶ δυνάμενα χωρίζεσθαι πάλιν, ‘It is evident that the ingredients of a mixture come together from previously having been separate and can be separated again’). Alexander himself insists that separability is part of the common preconceptions on mixture (see section VII below) and he clearly considers it an empirical fact (VII, 14.14–15). This suggests not only that separability is one of the most common assumptions regarding mixture, but also that it is acknowledged by every participant in the debate. Peripatetics and Stoics alike did this. Upon reflection, it is plausible that even philosophers like Democritus, who reduce mixture to juxtaposition, would do so. Separability is easily explained in the framework of such reductionist accounts: ingredients can be separated from a blend precisely because they were never blended in the first place, but only juxtaposed (cf. the expression δοκοῦσαν κρᾶσιν attributed to Democritus at II, 3.17–8). In this regard, it is relevant that Alexander’s critique of Democritus omits any discussion of separability. Reductionists could even consider separability a confirmation of their own theory, though we lack direct evidence to confirm this interpretation.

These considerations show why Groisard’s concern is unjustified. One must distinguish between separability as an empirical fact (acknowledged by every participant in the debate) and separability as a theoretical element, as such embedded in a specific explanatory framework. More precisely, certain explanatory frameworks (as the reductionist one) can account for separability more easily than others. Conversely, separability becomes paradoxical when combined with theoretical assumptions which are seemingly incompatible with it. This is the case with the realist framework, according to which ingredients genuinely blend with one another. Both Peripatetics and Stoics shared such a realist framework, and their theories are further developments of its fundamental tenets. Within this framework, though, it is hard to see how ingredients can be recovered. Therefore, unlike the reductionist framework, this one risks conflicting with the common conception that ingredients are separable. By implying that (i) is to a certain extent paradoxical, Alexander acknowledges that the realist framework, which he himself shares with the Stoics, seems in tension with the common notion––and the underlying empirical fact––of separability. This interpretation is suggested by τὰ κεκραμένα (‘the bodies which have been blended’), used to phrase sentence (i). Above we argued with Betegh that talk of blended bodies cannot be ascribed to a reductionist like Democritus. Now we argue that this term must be taken in a strong sense, as referring specifically to the realist framework according to which the ingredients of a mixture are not only juxtaposed, but genuinely unified. Since ingredients are genuinely unified, it is hard to see how they could be recovered. Thus the framework that allows for such unification is to some extent paradoxical.

This line of reasoning allows us to overcome Montanari’s concern as well, and, consequently, to reject his emendation. Note that in this reading Alexander does not deem his own full-fledged theory as paradoxical, not even in a prima facie sense. Rather, he highlights the challenge that someone starting from a realist framework must face. That realists themselves perceived this challenge is also suggested by Alexander’s report of Chrysippus’ claim that separability can only be explained through (a)+(b) (I, 1.8–9): this shows that in Chrysippus’ view, the theory of total blending, that is, position (a)+(b), was intended among other things to address the challenge that separability poses to realists about mixture. In our passage, Alexander is thus arguing that, while separability is a problem for realists, the Stoic solution is far more paradoxical than the paradox it means to address.

VI

Having shown that claim (i) can be deemed paradoxical and thus that no emendation is needed, we can review the argumentative structure of the passage.

Alexander raises a complex objection against Chrysippus’ claim that the account of mixture (a)+(b) is the only possible explanation of separability (cf. I, 1.8–9). First, this account is much more paradoxical than the paradox it is supposed to solve, namely claim (i) in our passage that genuinely unified ingredients can be separated. The reason why this claim is to a certain extent paradoxical, as highlighted, is that, if the ingredients of a mixture are genuinely unified, it should be impossible to separate them. Second, and remarkably, Alexander objects that Chrysippus’ account (a)+(b) is even more paradoxical than Democritus’ reductionist theory of mixture as juxtaposition—a theory that denies the reality of blending. Reductionism is paradoxical because it conflicts with a common notion grounded in empirical evidence: we see that certain bodies combine to form homogeneous substances different from them (cf. I, 3.2–3). The remarkable aspect of this conclusion is conveyed by the words ἀλλὰ καί (‘but even’): while both Alexander and Chrysippus aim to preserve the reality of blending, Chrysippus’ account proves even less satisfactory than that of Democritus, who dismisses blending altogether. In sum, Alexander not only argues that Chrysippus’ solution is more paradoxical than the initial paradox it was supposed to solve, but that rather than accepting Chrysippus’ account it would be preferable to abandon realism altogether and accept Democritus’ view that mixtures are really just juxtapositions.

The reason why Chrysippus’ theory of total blending is so disappointing, as evidenced in our passage, seems to be twofold. First, it clashes with the common preconceptions about mixture more than the other theories. This is clearly articulated in the statement that (a)+(b) is ‘by far more paradoxical and against everybody’s conception’. Furthermore, beyond this conflict, Chrysippus faces an internal contradiction, namely one between (a) and (b). Alexander had already pointed out this inner tension in the preceding lines (I, 1.1–6), and now he emphasizes it through the construction ὁμοῦ … ὁμοῦ …, highlighting a lack of logical coherence on Chrysippus’ part. These two reasons do not appear strictly connected at first, and only the former seems to point to a conflict with common notions (and thus to yield a paradoxical position). Yet later chapters of the treatise develop the connection between these points more fully. Αs we shall see in section VIII, claim (a) contradicts both a general common notion about bodies and (b), which represents a specific version of a common notion about separability of the ingredients. If we then recall that the concept of ‘common notion’ is an important piece of Stoic epistemology, we can see that Alexander, by charging Chrysippus with departing more severely from common preconceptions than others, also stresses that he violates his own epistemological standards.Footnote ²² In light of all this, Alexander’s dialectical strategy in this passage is clear: on Chrysippus’ own standards, total blending does not qualify as a viable account, let alone as the only possible explanation of separability, and is even more inconsistent with common notions than the notoriously paradoxical position of Democritus.

VII

The larger framework of the De mixtione sheds considerable light on our passage. In this and the next sections, we shall examine it briefly, showing that it provides confirmation for our interpretation both of Alexander’s dialectical strategy in our passage and of his assessment of the paradoxicality of the Stoic position.

Before focussing on Democritus’ and Epicurus’ reductive accounts, Alexander provides a bird’s-eye view of the opposite camps of the debate on mixture (I, 2.1–3.8): he registers not only the opposition between philosophers who conceive matter as unified (Peripatetics and Stoics) and those who conceive it as discrete (Democritus, Epicurus, Anaxagoras and the Platonists), but also the internal dissent within each camp.Footnote ²³ The following text explains the reasons for such disagreements (De mixtione I, 3.1–8):

The key sentence is ‘for each of the offered explanations peculiar difficulties follow (ἕπεσθαι)’. The verb ἕπεσθαι must be emphasized, for it plays a central function in Alexander’s reasoning. The reason why every explanation of blending entails peculiar difficulties is an inherent tension in the following three common preconceptions on blending, aptly summarized by de Haas (reference to the De mixtione passages in brackets):Footnote ²⁴

1. cn1 blending consists in the unification of the ingredients (4.16–17); and

2. cn2 blending implies the preservation of the ingredients (4.20–21; 7.15–16), since

3. cn3 the ingredients can be retrieved from the blend (7.5–8)

The tension consists in the fact that the common preconceptions ‘at the same time suppose both, a complete unification of the ingredient substances and their preservation’, as Corcilius notes in providing a similar list.Footnote ²⁵ Hence the exceptional difficulty of the research-field on mixture, namely, to accommodate these common conceptions within a coherent framework.

This background illuminates the rationale behind Alexander’s evaluation of the theories of mixture as paradoxical to lesser or greater degrees. Both (i) the realist perspective and (ii) the reductionist perspective struggle with at least one of the mentioned common conceptions; consequently, a peculiar challenge ensues that makes it appear paradoxical. While strongly relying on complete unification (cn1), realists struggle to account for the equally attested empirical fact of separability (cn3). Reductionists, on the other hand, can easily account for separability (cn3) because they explain blending as a case of juxtaposition, but do not accommodate complete unification (cn1) (cf. II, 4.19: οὔτε δὲ ἡ παράθεσις ἕνωσις). At first glance, both realists and reductionists seem unable to integrate certain empirical evidence: separability and unification, respectively. Thus both must either accept to live with a defect in their account of blending or overcome it somehow.

Alexander acknowledges that separability, while leaving reductionism untouched, poses a serious challenge for the realist framework. This is what motivates point (i) of our passage. As Alexander will argue later in the treatise, however, his own full-fledged theory (that is, his version of Aristotle’s theory of mixture) possesses the resources to tackle this problem adequately, namely the concepts of actuality and potentiality, and the distinction between numerical and specific identity. Alexander’s solution in Chapters XIII to XV will be that blended ingredients are preserved only in potentiality and recovered ingredients are only specifically identical to the original ingredients, not numerically (cf. XV, 33.17–34.10). Therefore Alexander believes that his theory is ultimately able to overcome the challenge separability poses to realists.Footnote ²⁶

On the other hand, as his critical assessment of Democritus and Epicurus shows, Alexander thinks that reductionists do not possess the resources to overcome their own prima facie difficulty. Democritus expressly endorses the denial of the reality of mixture as a natural consequence of his account based on juxtaposition. Remarkably, Alexander praises him for not hiding the undesirable outcome of his explanation: ‘a lover of truth and philosopher, not shrinking from stating the consequence (τὸ ἑπόμενον) for those who say that blends occur in this way’ (II, 3.22–4). Democritus’ theory, albeit unsuccessful, is still a respectable account because it explicitly accepts the partial denial of common conceptions on mixture and endorses its logical outcome.Footnote ²⁷ In this respect, Epicurus does not meet the standards set by his predecessor. While adhering to the explanation of blending through juxtaposition, he elaborates Democritus’ account in order to ‘avoid what, according to Democritus, follows (ἕπεσθαι) for those who argue that blending occurs through the juxtaposition of the blended bodies’ (II, 3.27–4.1). To preserve the reality of blending, he introduces the process of reduction to the elements, that is, the atoms, and explains blending as a corruption of the ingredients and a juxtaposition of the atoms into which they are reduced (II, 3.1–13). Epicurus’ attempt fails not only because it still resorts to juxtaposition and is thus incapable of accounting for real unification (conflicting with cn1), but also because, if the ingredients are corrupted in the process, then even their preservation (cn2) is no longer respected (II, 4.20–2). Therefore he is unsuccessful in evading the consequence lucidly articulated by Democritus. More generally, we see that reductionism (not only as a general framework, but also as a full-fledged theory) is paradoxical in view of its clash with part of the common conceptions on mixture, no matter whether it accepts the complete denial of mixture’s reality (Democritus) or unsuccessfully attempts to avoid this inevitable conclusion (Epicurus). This accounts for the fact, noted by Montanari, that our passage presents Democritus’ position (ii) as more paradoxical than the realist framework (i):Footnote ²⁸ such a denial contradicts evident phenomena, since ‘it is evident (ἐναργὲς εἶναι) that some bodies blend with one another’ (I, 3.2–3).

VIII

The way in which Alexander frames his confrontation with the Stoics is in keeping with this dialectical setting. According to his report, they claim to accommodate the common conceptions with success. They distinguish between mixture through juxtaposition (παραθέσει), which complies only with cn2 and cn3, mixture through fusion (συγχύσει), in which the ingredients are destructed and thus complies only with cn1, and blending (κρᾶσις), whose nature is described by (a)+(b) in our passage and, in their view, is in accordance with all three common conceptions (III, 6.10–7.8). Furthermore, they believe this difference between three types of μίξις to be ultimately grounded in some representation (φαντασία) that shows their reality: accordingly, they produce a full list of phenomena that would specifically illustrate blending (III, 7.9–23). By providing this taxonomy and its empirical justification, the Stoics probably wanted to show awareness that not everything that is called μίξις actually complies with the common conceptions of what a mixture is (juxtaposition and fusion do not), and introduce their notion of total blending as the result of an investigation that respects common notions and has full legitimacy in front of them.

In the face of all this, Alexander considers their attempt a complete failure, for the two reasons first hinted at in our passage (see section VI). First of all, while they say that ‘one should make use of the common notions (κοιναῖς ἐννοίαις)’ (V, 9.14–5), still (V, 9.18–24):

Alexander reproaches the Stoics for a methodological inconsistency: they claim to base their account on common notions (differing from Democritus, who was willing to renounce some of them), but their account is in blatant conflict with them. More specifically, Alexander first notes that one element of the Stoic theory of total blending, namely claim (a) in our passage (the complete interpenetration of bodies), is incompatible with another common notion, which is not specific of mixture only but more general: what is full cannot receive in itself something else (cn4 on de Haas’s count). Chapters V and VI of the De mixtione are devoted to show in detail why the theory of total interpenetration directly conflicts with cn4 and thus cannot be used to build a good theory of mixture.Footnote ²⁹ For Alexander, this results in a situation far worse than the initial position of realists about mixture (as the Stoics themselves are), worse even than both the starting point and final position of the reductionists. The problem of the Stoic theory is not just a conflict with some common conceptions about mixture, nor a conscious negation thereof. Rather, total interpenetration of bodies itself is preconceived as impossible, because it conflicts with a general common notion about the basic structure of the physical world. Worse than the reductionists, who deny that mixture really is as it appears to the senses, the Stoics put forth an impossible scenario.

The second and even more serious source of failure emerges in Chapter VII. There, we read that for Alexander it is ‘yet far more’ (πολὺ μᾶλλον ἔτι) incompatible with common notions to say that bodies which are ‘altogether extended with one another and mixed through and through can themselves be preserved with respect to what they had from the beginning and retain the proper qualities’ (VII, 13.26–14.1). This last formulation (‘can … be preserved … and retain the proper qualities’) represents a more general version of claim (b) in our passage and corresponds to cn2. Here, Alexander argues that the Stoics violate this common notion because they hold simultaneously also claim (a) of our passage, namely the total interpenetration of bodies (VII, 13.26: ‘altogether extended with one another and mixed through and through’). In Chapters VII–VIII, Alexander argues that these two claims are incompatible with one another and refutes the Stoic attempt to solve this tension by way of the theory of the infinite division of bodies.Footnote ³⁰ What is remarkable is that the Stoics contradict a common notion about mixture (cn2) by virtue of a claim that is impossible in itself, namely (a). So, the Stoic theory is not just incompatible with common notions (again, despite their professed adherence to them), but contradicts them through an intrinsically impossible thesis, resulting in a self-contradictory account of blending. Note, in this connection, the parallel with our passage, where what is deemed ‘by far more paradoxical’ is to hold ‘at once’ (ὁμοῦ μὲν … ὁμοῦ δ’ …) claim (a) and (b). The progression from Chapter V to VIII reveals precisely what Alexander had in mind when raising this charge.

IX

This review of the larger dialectical context of the De mixtione enables us to highlight the following points.

First of all, it confirms our interpretation of (i) and (ii) as expressing the realist framework and Democritus’ position respectively. Both of them face some challenge, because both seem to conflict with some common notions shared by everybody: (i) is in tension with the recoverability of the ingredients (cn3), while (ii) with their unification (cn1). Thus it is plausible to regard (i) as well as (ii) as, to some extent, paradoxical.

Second, this review helps explain why (ii) Democritus’ position is more paradoxical than (i) the realist framework. This greater paradoxicality does not stem from Alexander’s factionalism, but rather from the reductionist perspective itself: while the realist framework can be made coherent through Alexander’s full-fledged theory (or so he argues in the treatise), the reductionist perspective, articulated most rigorously by Democritus, must ultimately renounce common notions and deny the reality of mixture, despite contrary appearances and Epicurus’ unsuccessful attempt to prove otherwise.

Last, this review explains why the Stoic theory is the most paradoxical. Notwithstanding their claim to adhere strictly to the common notions, they are in sharp contrast with them in a double way. On the one hand, they put forth thesis (a) of the total interpenetration of bodies, which contradicts a common notion about bodies in general (cn4) and is thus in itself impossible. On the other, and due to this very thesis, they contradict another common notion, which they also claim to hold, namely the preservation of the ingredients of the blend (cn2). This double contrast with the common notions makes the Stoic position ‘by far more paradoxical’ even than the reductionist one. Note the parallel with the assessment of Epicurus, who is charged with a similar inconsistency: he tried to eschew Democritus’ consequent denial of the reality of mixture, but without success (breaking with cn1 and, as Chrysippus, with cn2). As a consequence, only Democritus is regarded as a worthy opponent, while Epicurus is overshadowed by his predecessor. Now, Alexander does not aim at a full comparison between all positions, ultimately because he is not interested in making ‘a display of a historical record and of great knowledge’ (II, 5.15), and he does not tell us whether or not Epicurus might be better than Chrysippus. All caution notwithstanding, it is likely that in Alexander’s eyes Epicurus fares better. His inconsistency results from his attempt at solving a real and important problem afflicting the reductionist framework and is thus more excusable than Chrysippus’ incoherence of declaring his account the least paradoxical while falling short of adhering to the common notions. Moreover, Epicurus’ account does not involve any actual impossibility, while Chrysippus advances two (interpenetration and its co-occurrence with preservation). Be that as it may, the Stoics remain Alexander’s main opponents, in part because they endorse a realist account like him, and in part because of the great reputation of Chrysippus himself, which for Alexander ‘could be a reason to take even a paradoxical view seriously’.Footnote ³¹ And as far as they are concerned, his judgement is clear: they propose an impossible, self-contradictory account that breaks with common notions both concerning mixture in itself and bodies more generally. This makes the Stoic theory, among all, the most paradoxical.