FOCAL DEPENDENCE, LOGICAL PRIORITY AND THE UNITY OF ARISTOTLE’S METAPHYSICS*

A long-standing problem in Aristotelian scholarship concerns the question of how to reconcile Aristotle’s twofold description of metaphysics as ontology (the universal science of being qua being) and theology (the science of the changeless and separate substance). An important attempt to answer this question (advanced first by G. Patzig) consists in saying that the changeless and separate substance is focally prior to (or the focal meaning of) substance and therefore to being in general (since substance is focally prior to being in general). This article aims to refute this kind of approach to the problem of the unity of Aristotle’s metaphysics by arguing that (i) relations of focal meaning entail the logical (definitional) priority of the prior items over the dependent items standing in such relations; (ii) the changeless and separate substance is not logically prior to the other types of substances distinguished by Aristotle; and, therefore, (iii) the changeless and separate substance is not focally prior to (the focal meaning of) substance.


I
A long-standing problem in Aristotelian scholarship concerns the question of how to reconcile the apparently conflicting characterizations of metaphysics provided by Aristotle in Met Γ 1 and Met E 1. In the former, he characterises metaphysics as a science devoted to the study of 'being qua being' (to on hê(i) on) (1003a21), one of whose distinctive feature is that, unlike special sciences, it investigates all beings insofar as they are. In Met E 1, however, Aristotle identifies metaphysics -now referred to as 'first philosophy' (1026a24) -with theology (theologiké epistéme), a science which does not deal with all beings, but rather singles out a particular kind of object as its subject of investigation, namely the 'changeless and separate' substance -the unmoved mover of Met Λ (henceforth S 1 ).
Aristotle was not unaware of the tension. After having identified first philosophy with theology in Met E 1, he explicitly contends that given this identification, 'one might indeed raise the question whether first philosophy is universal or deals with one genus, i.e. some one kind of being' 1 (1026a24-5; emphasis added). 2 Nor was he doubtful, however, about how the tension could be resolved: 9 FOCAL DEPENDENCE, LOGICAL PRIORITY AND THE UNITY OF ARISTOTLE'S METAPHYSICS [T]he science of this [sc. the unmovable substance] must be prior and must be first philosophy, and universal in this way, because it is first (kathólou… hóti próte). And it will belong to this [sc. theology] to consider being qua being '. (1026a30-31) However brief, this passage suggests at least one thing, namely that the clue to solve the tension between Aristotle's characterizations of metaphysics lies in the concept of priority: it is in virtue of its being 'first' (próte) 3 -as he tersely points out -that first philosophy, even if it is concerned with one particular being, can nonetheless coincide with the universal science of being qua being.
In a justly famous article, Günther Patzig (1979) took this suggestion seriously and claimed to find a way to reconcile Aristotle's conflicting accounts of metaphysics in the priority relations holding between being, substance and S 1 . The main insight governing his position is captured by the following argument: (P1) Substance is the primary/focal meaning 4 of being.
(P2) S 1 is the primary/focal meaning of substance.
Hence, (C1) S 1 is the primary/focal meaning of being. Now, (P3) theology is the science of S 1 . Therefore, given (C1), it follows that (C2) theology is the science of being in general. divine substance itself. As Wedin (2009, p. 139) rightly points out, the mere fact that Aristotle saw a problem in his twofold account of the metaphysical science and, even more -as we shall immediately see -, that he explicitly offered a solution to this problem precludes the plausibility of this strategy. As many commentators have noted (see e.g., Wedin, 2009, p. 126;Shields, 2012, p. 374), the qua-locution featuring in Aristotle's characterisation of metaphysics as a science which 'studies being qua being' (theôrei tò òn hê(i) òn) does not qualify the first occurrence of 'being' (as Merlan's reading implies), but the verb 'theorein': 'that-it-is' is the particular perspective through which metaphysics studies 'that-which-is'. For a criticism of Merlan's position, see also Vigo (2007, pp. 145-6), to whom I am indebted in this footnote.
Thus, Aristotle's accounts of metaphysics in Met Γ and E, despite their prima facie inconsistency, would in fact turn out to be two descriptions of the same unitary science; or so Patzig and his followers think.
The aim of this paper is to assess the viability of this kind of approach to the problem of the unity of metaphysics in Aristotle. While the issue has been subject to much debate among Aristotle scholars, here I shall focus on (P2), the premise that S 1 is the primary/focal meaning of substance. To this effect, I shall adopt the following strategy. Patzig-type interpretations combine two main ideas: that substance -as (P1) states -is the primary/focal meaning of being, and that S 1 -as (P2) claims -is the primary/focal meaning of substance. Besides the term 'substance', (P1) and (P2) have one further element in common: both claim for their terms -'substance-being' in (P1) and 'S 1 -substance' in (P2)to stand in the same kind of relation, namely that of 'focal priority' (or 'focal dependence', if seen the other way around). Ultimately, this seems to be the crucial claim on which Patzig-type strategies rest, for they intend to reconcile Aristotle's twofold characterization of metaphysics precisely by extending the focal priority model from the level of 'substance-being' to the level of 'S 1substance'. This suggests that a good test for assessing the viability of (P2) is to analyse, first, the conditions for there to be a relation of the focal priority type between the pair 'substance-being', and then ask whether these conditions can be satisfied in the case of the type of relation connecting the 'S 1 -substance' pair. I shall call this test the Replicability Test.
The core of my argument runs as follows. First, in Section II, I analyse (P1). I argue that the focal-priority type of relation at the level 'substance-being' entails for substance to enjoy not only ontological priority but also logical priority over the non-substantial categories of being. 5 With the analysis of focal priority at hand, Section III applies the Replicability Test to (P2): for (P2) to be true (i.e., for S 1 to be the primary or focal meaning of substance), S 1 must satisfy the strong condition of being logically prior to the other types of substance, and not only, as some commentators have believed, ontologically prior to them. I evaluate one line of argument for the view that S 1 does meet the requirement of logical primacy. I argue, however, that it is unpersuasive. A final section concludes the article by summarizing its main theses and by contrasting them with a different approach to the issue of the relationship between theology and the general science of being.
One additional remark is in order before moving on. As I mentioned, the unity of Aristotle's metaphysics is an old topic, one which has exercised philosophers for centuries. 6 Moreover, Patzig's article was written forty years ago, 7 and several scholars have commented on it since then (whether for or against). 8 If so, why to address these issues again? The answer is simple: the view I will question in this article continues to be with us. Thus, in a recent monograph devoted to the concept of priority in Aristotle's metaphysics, Michail Peramatzis (2011) has argued that, for Aristotle, there is a parallel (an exact one-one correspondence) between the definitional (i.e. logical or conceptual) order and the ontological order: 'Schematically speaking, my interpretation introduces the idea of an ontological hierarchy every level of which corresponds to a parallel level of a coordinate definitional or conceptual hierarchy' (Peramatzis, 2011, p. 2). This implies that, for every item x and for every item y, if x is ontological prior to y, then x is logically prior to y. And this in turn implies that S 1 -the primary substance -is logically prior to the other types of substance (for S 1 is of course ontologically prior to the other types of substance). That is precisely the view I aim to refute.

II
Met Γ 2 opens by observing that 'being' is spoken of in several ways, but that this does not turn 'being' into an instance of unqualified ambiguity or homonymy, in which the graphical and phonetic identity of the terms is purely accidental and no semantic connection can be found between them. Although 'being' is predicated in various ways, they are in fact connected with one another insofar as they 'make reference to' or 'point towards' (pros) 'one thing' (hen) (1003a33-4), namely substance (ousía) (1003b5-10). Owen (1979) famously explained this doctrine by contending that 'being' has a 'focal meaning', which is the sense in which substances are said to be -in contrast with the non-substantial categories of being, which are always said to be in a derivative sense or 'in relation to' the substantial way of being.
This idea plays an important role in Aristotle's metaphysical enterprise. Two points are important for the purposes of my argument in this section.
(1) First, Aristotle's account of 'being' as a case of pros hen homonymy allows him to solve a pressing problem concerning the possibility of a science of being. Briefly, the problem is this. In APo A 28, Aristotle states that every science has a subject genus (87a37). The genus is that which the science is about and constitutes a condition of its unity. But something which is said in many ways is not a genus, for a genus is predicated univocally (this is in fact the reason it can bestow unity on the science which takes it as its subject). Hence, given that, for Aristotle, being is not a genus, 9 it seems that there can be no science of being. By introducing the pros hen homonymy apparatus, however, Aristotle is able to weaken the condition for scientific unity stated in APo, and to argue that not only those things which have 'one common genus' can pertain to one science, but also those which 'are related to one common nature ' (1003b12-14), as is the case of being in relation to substance. The following formula captures Aristotle's idea:

Possibility Statement 1:
There is a science S such that S studies x ∧ y ↔ (i) x ∧ y fall under one common genus ∨ (ii) x ∧ y are said 'in relation to' one common nature. 10 (2) Secondly, from the identification of substance as the primary instance of being, Aristotle is able to draw a conclusion that significantly affects the way in which the theory of being must be understood and that constitutes one of the most relevant upshots of (P1): the science of being is essentially a theory of substance. This does not mean that the study of being entails the study of being-substantial as one of its programmatic parts. More strongly, it means that the study of being coincides with a theory of substance. As Aristotle famously put it: 'the question which, both now and of old, has always been raised, and 13

always been the subject of doubt, viz. what being is (tí tò ón) is just the question what is substance (tís he ousía)' (1028b4). 11
Having established these two points, we can now turn to the main issue of this section: what means for substance -as (P1) affirms -to be focally prior to being? In other words, how exactly should we interpret the content of the expression 'being related to' (pros) so that substance, in being so related to the non-substantial categories of being, can be said to be focally prior to them? What is at stake here are the conditions that must be satisfied for focal priority to obtain. In the remainder of this section, I will first state my interpretation of Aristotle's position on this matter. Then I will try to justify it.
As I see it, Aristotle's position as to the conditions of focal priority (FP) can be expressed in the form of the following biconditional statement: FP: An item x is prior in the focal sense ↔ (i) x is ontologically prior to the non-focal items which are said 'in relation to' x ∧ (ii) x is logically prior to the non-focal items which are said 'in relation to' x.
Taken together, (i) and (ii) form the definiens of the focal sense of priority. Taken separately, they are its necessary conditions. For reasons of space, I will leave condition (i) aside and focus on condition (ii) alone, which is precisely the point -as we will see in section II -that will prove to be problematic for Patzig-type accounts of the relationship between theology and ontology.
There are a number of places in which Aristotle explains the concept of logical priority (tô(i) logô(i) prôtos). In all these places, its basic sense is the same: 'the primary [in the logical sense] is that of which the definition is contained in the definition of all' (EE 1235a20-21). 12 We can formulate this idea as follows: (LP) A term T is prior in the logical sense ↔ T's definition (formula, account, lógos) is contained in the definitions (lógoi) of those terms which are said in 'relation to' T, and not vice versa.
Logical priority is therefore conceived of as definition-inclusion or formula-containment. Primary in this sense, for instance, are the right angle over the acute angle -for an account of the latter can only be given in terms of the former (Met M 8, 1084b10-14; Met Z 10, 1034b30-33) -and letters over syllables -because the definition of syllable includes that of letter (Met Z 10 1034b28-29). And logical primacy is ascribed to substance over the other categories too. For 'in the formula of each term the formula of its substance must be present' (Met Z 1, 1028a35-b1; see also Z 13, 1038b23-29). Now, that logical priority is entailed by focal priority seems to be already suggested by the particular terms in which Owen paraphrases Aristotle's doctrine that being is a case of pros hen homonymy, terms which I have already introduced but for which no justification has been given so far. In fact, by rephrasing Aristotle's idea in terms of 'focal meaning', Owen infuses, as Ferejohn (1980, p. 118) points out, an intentional character to the pros hen homonymy model, which places the model at an explicitly semantic level and, therefore, seems to accommodate the idea of definitional inclusion described above: substance, in Owen's view, is the primary sense of being in terms of which the non-substantial senses of being must be defined. Thus, Owen explains that a term is primary in the focal sense insofar as 'its definition reappears as a component' in the definitions of those terms referring to it: 'all the senses of on', therefore, 'must be defined in terms of ousía' (Owen, 1979, p. 17).
But while Owen's semantic interpretation of focal priority can of course be viewed as a plausible one, it is not immediately obvious that it must be correct. One could argue, for example, as Ferejohn (1980, pp. 118 ff.) himself does, that Aristotle's way of theorising about language and reality is not usually concerned with such items as meanings and senses, and that his ontology, instead, usually moves within the limits of a domain comprising nothing but pieces of language (word and phrases) and extra-linguistic entities that stand for, or are denoted by, them. Or, more simply, one could argue that the expression 'pros' ('make reference to', 'point towards' or 'be in relation to') connecting the 'substance-being' pair is neutral enough to involve only a relation of ontological or 'natural' priority (some sort of causal dependence, for instance) between items standing at two different levels, but nothing of the sort of the intrinsic, conceptual dependence demanded by the idea of logical primacy. The fact that Aristotle, as I pointed out earlier, explicitly says that substance is logically prior to the non-substantial categories of being does not help here, for it is not immediately obvious whether it is precisely this sense of being prior the one which is relevant for grounding a connection of focal reference. 13 So why must logical priority be included in FP? In addressing this question, little progress can be made by concentrating on the pros hen model in isolation. Rather, attention must be drawn to what Aristotle does with it. And it is here that the two points established at the beginning of this section enter into play. The pros hen model, we saw, enables Aristotle (1) to offer an alternative to the subject-genus condition for the unity of science advocated in APo, and (2) to give an account of the science of being in terms of a science of substance. Now, if we concede these points, it follows that the primacy which substance enjoys (and which allows to ground a relation of the focal type) must be such that, in having this priority, substance must be capable of fixing (though not in genere) the domain of inquiry of metaphysics. Further, it follows that the particular way in which substance fixes this domain must be such that it permits to reduce the general theory of being to a theory of substance. But it is hard to understand how this could be so if the focal priority of substance over the nonsubstantial categories were of an ontological sort only. By this I do not mean to suggest -as Owen sometimes does -14 that ontological priority is irrelevant in this connection. However, it seems clear to me that the mere fact that different items are ontologically related (through connections of ontological inherence, for instance) does not suffice for grounding the kind of strong unity that focal priority is supposed to ground. What is needed is a principle of unity that can serve as a genuine alternative to the model of unity in genus (which implies relations of conceptual inclusion), and, more strongly, that can make possible for the science of being to be concerned with one item in its domain (sc. the focally primary item: substance), without putting the other items (sc. the focally dependent items: the non-substantial categories of being) outside this domain. Only a conceptual, definitional dependence of the non-substantial categories upon substance can guarantee this possibility. 15 Hence, logical priority is a necessary component of focal priority. 13 Nor does it help, and for the same reason, the thesis that substance is prior in every sense of priority (i.e. ontologically, logically, in the order of knowledge, and temporally), for this does not specify which of these senses is actually relevant for focal priority to arise. For the thesis that substance is prior in every sense of priority, see Met Z 1, 1028a33-b3. 14 See Owen (1979, p. 19). 15 Owen's reading of pros hen homonymy in Met Λ as focal meaning is based on similar considerations. He writes: "The claim of Met IV that 'being' is an expression with focal meaning is a claim that statements about non-substances can be reduce to -translated into -statements about substances." But this is only possible if Besides this systematic line of argument, there is also textual evidence for the view I am defending. To my mind, particularly explicit is a passage in which Aristotle rephrases what I called earlier Possibility Statement 1. In Met Λ 2, 1004a24-25, he writes: [A] term belongs to different sciences not if it has different senses, but if its definitions (i) neither are identical (ii) nor can they be referred to one central meaning.
In positive terms, the point can be put as follows: Possibility Statement 2: There is a science S such that the terms x ∧ y belong to it ↔ (i) the definitions of x ∧ y are identical ∨ (ii) the definitions of x ∧ y can be 'referred to (pros) one central meaning.' Condition (i) corresponds here to those items which in Possibility Statement 1 were said to 'fall under one common genus' (i.e., synonymous or univocal terms). Condition (ii), on the other hand, refers to those items (such as 'being') which were said to be spoken of 'in relation to (pros) one common nature'. Unlike Possibility Statement 1, however, this formulation of the conditions for the possibility of science does not leave unspecified the nature of the prosrelation in (ii): the focally prior item is a semantic focus, a central meaning which, having definitional primacy over the items which point towards it, can gather them together so that they can fall under the scope of one unitary science.

III
Hitherto I have argued that logical priority is a necessary component of focal priority. With this thesis in place, we are now in a position to apply the Replicability Test to Patzig-type strategies -and particularly to (P2) of their argument, the premise that S 1 (the primary substance) is focally prior to the other types of substance. Given the results of the foregoing discussion, the the non-substantial categories are, as he puts it, 'logical shadows of substance ' (1979, p. 25). This, as Owen (1979, p. 25) remarks, is enough evidence for rejecting those interpretations which read Aristotle's pros hen theory in Met Λ as a doctrine of 'analogy of being' (in the Aristotelian sense): focal meaning amounts to a relation of definitional inclusion and internal connection of meaning, whereas (Aristotelian) analogy consists in arranging certain terms in a scheme of proportion. challenge for these strategies is this: they must show that the focal item within the domain of substance -S 1 -is both (i) ontologically and (ii) logically prior to the non-focal items within this domain. 16 As in the previous section, condition (i) will be assumed. In fact, that S 1 is ontologically prior to the other types of substance (at least in the causal sense of ontological priority) 17 is uncontroversial: it is well established in Aristotle's texts 18 and sufficiently agreed upon in the literature. 19 The same cannot be said of condition (ii), however. True, most interpreters agree that a relation of focal priority within the intra-substantial domain must entail (as I have argued in relation to the 'substance-being' pair) the logical priority of S 1 over the other types of substance. 20 Patzig himself agrees with this, for he explicitly recognizes that 'the concept of an ousía other than the ousía of the prime mover logically presupposes the concept of the first mover ' (1979, p. 42). However, it is by no means obvious how exactly the move from ontological priority to logical primacy can actually be done. 21 In this section I will discuss one line of argument which has been advanced in favour of S 1 's logical priority. If this line of reasoning succeeds, then Patzig-types strategies would prove to pass the Replicability Test. Yet I will argue it has some problems.
In order to argue for the view that the intra-substantial domain is organised according to relations of logical dependence, a first point that must be shown is that, as in the case of 'being', there are different senses in which 'substance' itself is said, and that these senses are focally dependent on one which is primary; put differently, a second level of homonymy of 'being' must be introduced: just as 'being' is said in many senses but all of them in relation to 'substance', so 'substance' must be spoken of in many senses, all of which are interrelated by 16 A further condition is that the different types of substances cannot be reducible to one common genus. For if substance is a genus to which all kinds of substances can be reduced, then substance would be predicated univocally, which would in turn eliminate the possibility of proper homonymy, whether accidental or nonaccidental, within the intra-substantial domain. This might seem controversial, for substance is a category and categories are usually conceived of as genera of being (cf. e.g Phys 189a14, 189b23-24; DA 412a6). For the sake of Patzig's argument, however -and following Berti (1975, p. 56-9) -I will assume that a case can be made for the view that substance is not a genus. This is borne out by Met X 2 1053b22-24, where Aristotle says that 'the one cannot be a genus, for the same reasons that being and substance cannot be genera' (translation in Berti 1975, p reference to one prior sense of 'being-substantial'. Now, for this to be so, it is not enough to say that the substances distinguished by Aristotle are different kinds or types of beings. Human beings, horses and chestnuts, for example, are different types of beings. Yet this does not amount to a proper distinction between the senses in which they are said to be: all of them are in the sense in which matter-form compounds are 22 and therefore take the predicate 'being substantial' univocally. So, type-distinctions are not the relevant point here. What is needed, rather, is that the different types of substances distinguished by Aristotle be different ways of being substance.
Such a reading has been defended by Frede. 23 His view can be divided into three main steps: Step 1: The first step consists in saying that, as I have just explained, the different types of substances are substances in different senses, one of which is the focal sense of being substance (1987, p. 85).
Step 2: The second step, based on Aristotle's position in Met Z (see 1029a5-7, 1041b7-9), identifies the focal sense of substance with the notion of 'form'. The form is that in virtue of which things are said to be 'something this' or 'determinate' (tóde ti) and 'separate' (choristón) (= 'existing in itself', as opposed to 'existing in other') (1037a29-30). Since, according to Met Z 3 (1029a27-28), 'individuality' and 'separability' are the fundamental criteria of substantiality, it follows that that in virtue of which things are 'separate and determinate', i.e., the form, is the primary meaning of substance, the sense which focally unifies the other ways in which 'substance' is predicated (1987, p. 89).
Step 3: Finally, the third step consists in saying that the object(s) of theology, particularly S 1 , enjoys the way of being that Step (2) claims to be the most proper way of being substance: unlike the other substances, S 1 is 'pure actuality, and thus form, and thus substance, and thus being in a paradigmatic way' (1987, p. 90; my emphasis). 24 22 See Frede (1987, p. 87). 23 See esp. Frede (1987). See also Frede (2000) and (2000a). 24 Frede formulates this in the plural ('separate substances…are pure actualities'). This does not affect my argument, since Frede explicitly says that he is primarily thinking in the unmoved mover of Met Λ: 'separate substances, in particular the unmoved mover, are pure actualities, etc.' Now, according to Frede, Steps 1-3 allow us to conclude that S 1 , insofar as it is 'pure form', is 'the focal way or sense of being in terms of which all other beings have to be explained ' (1987, p. 87). As the phrase 'in terms of which' suggests, the dependence of substances (and thereby of being in general) on S 1 would not only be ontological, but also logical or conceptual: S 1 is logically presupposed for the explanation of the way in which the other substances are substances (Frede, 1987, p. 88;cf. Wedin, 2009, p. 140). If so, since the conditions for focal dependence -including logical priority -are met at the level 'S 1 -substance', (P2) of the Patzig-type argument for the unity of metaphysics passes the Replicability Test.
Or does it?
The entire burden of Frede's argument rests on a transition from the premise that the form is the focal meaning of substance to the conclusion that S 1 is the focal meaning of substance and hence notionally required for explaining the concept of substance. The linking premise that would allow us to make this transition is that the form, as instantiated by S 1 , enjoys some sort of especial status, a status which is given by the fact that S 1 is 'pure' form: unlike the other substances, S 1 lacks all matter and potentiality, is pure actuality and thus nothing but form. We can put Frede's reasoning as follows: (P1) Form is the focal meaning of substance (=Step 2) (P2) S 1 is pure form, the form par excellence (=Step 3) (C) S 1 is the focal meaning of substance I have nothing to say against (P1) of this reasoning, evidence for which can be found in the doctrine of Met Z summarized in Step 2. Yet (P2), I think, does not allow passing from (P1) to (C). In particular, what I want to suggest is that for the transition from (P1) to (C) to be justified, one must show that pure form, i.e., form as it is instantiated by S 1 , is focally prior to the formal way of being itself. That is, what is needed for the conclusion to follow is a third level of homonymy of being: substance, first, is the primary meaning of, or focally prior to, being; the form, furthermore, is the primary meaning of, or focally prior to, substance; and the form, thirdly, as it is exhibited in S 1 -as pure form -is the primary meaning of, or focally prior to, form itself. Yet to say, as Frede's (P2) states, that the form, as instantiated by S 1 , is pure form, a form separated from all material principle, does not suffice for this purpose.

Why?
The point can be appreciated by drawing a contrast between S 1 and matterform compounds, the kind of 'separate and perishable' substance which occupies the sublunary region in Aristotle's cosmological scheme. S 1 , we have seen, is pure form. Sublunary substances, by contrast, are composites that 'have' an enmattered form. But the contrast between these two types of substances is not based on different senses in which the formal principle itself is predicated. For the form of a matter-form compound substance does not differ qua form from the form as exhibited in S 1 . Matter-form compounds do in fact differ from the simple, immaterial substance. But, as Wedin (2009, p. 141) rightly points out, it seems hard to understand why one should think of the form of a form-matter compound as having a different way of being from a pure form just because the compound itself differs from the simple, immaterial substance. Rather, the difference between them lies in that compounds have forms, while S 1 is a form; 25 or in that the former are material beings with an indwelling form, while S 1 is itself a form. It does not lie, however, in the formal way of being itself. As far as form as such is concerned, the form as exhibited in S 1 is just as form as the form of matter-form compounds. Hence, pure form is not the focal sense of form. Therefore, S 1 is not the focal sense of substance.
That the form in which S 1 consists does not differ qua form from the form of a sensible substance can be appreciated by reconsidering the reason Aristotle claims that the form is the primary sense in which 'substance' is predicated. As seen in Step 2, what leads Aristotle to consider form as the primary sense of substance in Met Z is that the form is the cause for which a thing is what it is, i.e. a 'determinate and separate' entity, which constitutes (according to Met Z ) the fundamental criterion of substantiality. 26 Now, if the form in which S 1 consists were different from the form of the composite qua form, then one would expect S 1 to be 'separate' in a higher degree than the matter-form composite. However, 25 That S 1 is a form is Frede's claim. It is, however, a controversial claim, which many interpreters have rejected (See Wedin 2009, p. 141 for discussion). In fact, Aristotle never says that the divine substance is a form, neither in those texts dealing explicitly with the existence and nature of the divine substance/prime mover (Met Λ 6-10 and Phys. VIII 5-6) nor elsewhere. On the other hand, however, there are some reasons to think that, as Frede believes, S 1 is a form for Aristotle. For example, in Met Λ 6 Aristotle says that a substance of the kind of the divine substance must be not only eternal, but also lack matter (1071b20-22), which suggests it should be pure form. In any case, we need not resolve this issue here. For if it could be demonstrated that, for Aristotle, S 1 is not a form, then Frede's view would be flawed from the outset. For the sake of his argument, therefore, I will assume that S 1 is a form for Aristotle. 26 As is well known, this is not the only criterion of substantiality that Aristotle distinguishes. See especially Cat.

FOCAL DEPENDENCE, LOGICAL PRIORITY AND THE UNITY OF ARISTOTLE'S METAPHYSICS
in Met E 1 (1026a13-16) 'separation' is said to belong to the same extent to both types of substance. 27 This last argument might seem too specific, so let me reinforce my main claim by looking at it from a more general angle. Frede, recall, contends that S 1 is the focal meaning of form (and hence the focal meaning of substance, and hence the focal meaning of being in general) because S 1 is pure form. Yet I wonder whether 'purity' is relevant here. For purity indicates a degree. And differences of degree do not amount to differences in sense or way of being. 28 Consider something which exemplifies the colour purple in its purest expression -call it 'primordial purple'. Now think of a shade of purple. Would we say that primordial purple and the shade of purple have different ways of being? No, because they are both qualities, and quality is one way in which being is spoken of. Whatever falls under the category of quality is predicated as just that: quality. A distinction of degree is not, then, a distinction of sense, but rather cuts across one sense in which being is predicated -the category of quality, in the present argument. 29 So, it is false that pure form, because it is pure, is the focal meaning of form.
To be clear, the arguments I have been developing do not aim to invalidate (P1) of Frede's argument: form is the focal meaning of substance and, as such, it enjoys logical primacy. However, that which is prior (both in an ontological and logical sense) is the form of the compound with respect to the compound itself, not S 1 in relation to the compound. As the formal cause of the compound substance, the form is ontologically prior to it; and, insofar as it is included in the compound's definition, the form is logically prior to it as well. But S 1 is neither the formal cause of a concrete composite, nor it is included in its definition. The same point can be made, as Berti (1975, p. 63) remarks, if we shift the focus from the concept of form to the concept of actuality. Compound substances differ from S 1 in that the latter is pure actuality, while compounds contain matter and hence potentiality. And actuality, Aristotle says, is logically (and ontologically) prior to potentiality (see e.g., Met Θ 8, 1049b11-17). However, this does not mean that S 1 , which is the pure actuality, is conceptually included in the account of compounds: what is logically (and ontologically) 27 As noted by Berti (1975, p. 68, n. 44). That the form in hylomorphic compounds and in separate substances has the same meaning or sense is also supported by the opening lines of Met Z 17, where Aristotle states that the study of the (nature of) sensible substances may help us have 'a clear view of that substance which exists apart of sensible substances' (1041a6-9). I am grateful to an anonymous referee for drawing my attention to this passage. 28 Beyond Aristotelian scholarship, this thesis has been defended by McDaniel (2009) and(2013). 29 The argument can of course be extended to other categories, for quality is not the only category that admits degrees.
prior to potentiality is the actuality of that which is in potentiality, not the actuality of S 1 . 30

Concluding remarks
Patzig-types strategies aim to unify ontology and theology by organizing S 1 and the other types of substance in accordance with relations of focal dependence, which implies the logical priority of S 1 . I have argued that while such a relation obtains at the horizontal, inter-categorical level of 'substance/ non-substantial categories of being', it cannot be extended to the vertical, intrasubstantial level of 'S 1 /other types of substances'. For even if the form can be considered as the primary sense in which 'substance' is predicated, it does not follow from this that S 1 , qua pure form and pure actuality, is the focal sense of form, that in terms of which all other substances (and thereby being in general) must be accounted for. Since logical priority cannot be ascribed to S 1 , Patzigtype strategies fail the Replicability Test.
But if this is so, how are we to understand the relationship between ontology and theology? A full treatment of this question would of course require extended exposition, well beyond what is feasible in the present context. However, I should like in closing to briefly sketch the outline of an approach to the problem of the unity of Aristotle's metaphysics which is different from and, I want to suggest, more promising than the Patzig-type strategy we have been discussing. At the same time, this will allow me to underscore and further clarify, by way of contrast, some of the main ingredients of that strategy.
As we have seen, Patzig-type accounts attempt to explain the relationship between theology and ontology by relating the different types of substances in accordance with a model of conceptual or definitional inclusion. What this model claims to be prior is prior in the logical, definitional sense of priority. Thus, S 1 would be notionally included in the concepts of 'sensible and perishable' and 'sensible and non-perishable' substance. The main methodological upshot of 30 In a more recent paper, Berti (2001) has strongly criticised Patzig-type interpretations on more general grounds.
According to him, the thesis that S 1 enjoys logical priority over the other types of substance introduces the idea of 'exemplaristic and paradigmatic' causation, an idea which gets Aristotle's metaphysics too close to Platonism (2001, pp. 202-4). For the way in which a logically or definitionally prior item unifies a derivative multiplicity is precisely the way in which Platonic Forms unify the particular instances falling under them, that is, by being 'common to', and appearing in, the definitions of these instances, which in turn fall short of purely and unqualifiedly instantiating the Forms to which they relate (in this connection, recall that, as some interpreters believe, Platonic Forms can be seen as the end-point at which Socrates' search for definitions -i.e. for proper answers to questions of the form 'what is X' -arrives. See Sedley (2013, p. 114)). To use Plato's words, a Form is a 'one-thing that holds of all' (Meno,73cd) or 'what is the same over all' (ibi. 75a) and that is 'present' in all (Phd, 100d).
this model is that, in keeping with Aristotle's tenet that 'science deals chiefly with that which is primarily' (Met 1003b16), it would allow us to reduce a multiplicity to the primary meaning which is included in that multiplicity as its semantic nucleus, and which logically unifies it. On the Patzig-type view, S 1 is not an external term of reference but something 'in terms of which' any substance other than S 1 must be accounted for: the changeless and separate substance features in the definition or account of finite beings. Now, if this is so, to offer an account of S 1 is all that is needed in order to offer an account of substance (and, via substance, of being in general): in studying S 1 , one also studies substance in general and thereby being in general. Frede expressly endorses this idea when he writes that 'a study of the way of being of separate substances outside theology would, to a large extent, just reduplicate the study of the theologian' (1987, p. 92). One this view, therefore, the primary, proper object of metaphysics is the divine substance. Like this line of thought, the interpretation advanced by many Latin commentators of Aristotle 31 acknowledged the pivotal place that the divine substance occupies within the context of metaphysical inquiry. Yet, unlike Patzig-types accounts, the approach favoured by them conceived of S 1 as the external explanatory principle in which the program of an inquiry into being as being finds its final consummation. On this view, S 1 is not that way of being on which the metaphysician must primarily focus and whose understanding would enable him to understand the other, dependent ways of being. Rather, this approach puts things the other way around. The proper object of metaphysics is being qua being. And, in keeping with Aristotle's tenet that metaphysics is a kind of wisdom dealing with 'first principles and causes' (Met 982b8-9), it turns out that, in studying being as being, it 'ascends' towards S 1 as the ultimate cause of being: S 1 is the ad quem term towards which metaphysics points; it is not that 'from' and 'through' which it explains everything else. 32 But it is not only in relation to the order of inquiry that this interpretation differs from Patzig-type strategies. Another, perhaps more fundamental difference concerns the kind of knowledge of S 1 that each of these conceptions 31 See next note for references. 32 See e.g., Aquinas, In Met Ar Comm, Proemium, where he claims that although metaphysics does investigate the divine substance, it does not investigate it 'as its subject (ut subjectum)': its proper subject is 'only being in general (ens commune)'. The reason for this, he points out, is that the 'subject of a science is the genus (genus) whose causes and attributes' one seeks, not 'the causes themselves (ipsae causae)' of the genus (Note that 'genus' here must not be taken in the strict logical sense: thinks metaphysics can yield. For Patzig-type interpretations, and especially in Frede's view, metaphysics focuses on the 'way of being' or nature of S 1 . For Aristotle's Latin commentators, by contrast, the knowledge of the nature of the divine substance -i.e., of its attributes and specific way of being -does not formally pertain to the metaphysical enterprise. As part of metaphysics, 'natural theology' does of course make reference to the divine substance. Yet, as these commentators see things, this reference is not to S 1 's nature and specific way of being. Rather, the divine substance is taken into consideration only under a particular respect: insofar as it is a cause. 33 The primary task of the metaphysician is to account for beings from the perspective of their being beings. In accordance with the strictures of Aristotle's conception of scientific knowledge, this entails searching for those causes which pertain to being considered as being. And this in turn requires, in the end, a reference to S 1 as the ultimate cause on which everything else depends. But no knowledge of the intimate essence of the divine substance is formally implied by this reference: what is known of S 1 is the (more modest) fact that it-is-a-cause. 34 The identification of the divine substance as a cause makes possible to know scientifically those beings which depend on the cause, yet not (primarily) the nature of that which is cause.