Edelhoff in her contribution to the Cambridge Elements series provides an analysis of ontological priority (‘priority in substance’, ‘priority in nature’) in Aristotle’s Categories. In her interpretation Aristotle uses two independent sufficient conditions for ontological priority that are disjunctively necessary: (A) necessary asymmetrical existential dependence (necessarily, if X exists, then Y exists, but not vice versa) and (B) necessary symmetrical existential dependence with the prior item being the cause of the posterior item.
The book consists of five chapters, of which the concluding Chapter 5 takes stock of the results, highlighting the advantages and acknowledging the remaining problems. In the Introduction (Chapter 1), Edelhoff clearly and succinctly settles the context and the methodology for her study. First, she connects Aristotelian ontology to contemporary metaphysics using a clear taxonomy for the structure of reality (flat, sorted and ordered structures). According to this, Aristotle conceives of reality as an ordered structure with entities falling under different categories and having different ontological status. Different ontological status is rooted in ontological priority. This can mean that (i) an entity’s existence depends on another entity’s existence, or (ii) the essence of the former depends on the essence of the latter. Edelhoff argues for a more context-sensitive understanding of priority that takes the type of relata into account (e.g., whether they are objects or properties). As statements of priority in Aristotle involve the use of the verb einai (or semantically related verbs), she understands einai in the passages to mean ‘existence’, ‘essence’, or ‘truth’ according to what fits best with the relata and the context. This is her explicit methodological principle: to reconstruct each statement about ontological priority with the most fitting reading of einai (and this is pursued consistently throughout, somewhat meticulously).
Also, Edelhoff connects Aristotle to the Academic tradition. She demonstrates that Aristotle attributed a notion of ontological priority to Plato and that other Academics like Xenocrates also participated in the debate, where, it is argued, ontological priority is understood as asymmetrical existential dependence. An existential reading seems to be straightforward in most passages discussed. Yet, in the most central one, EE 1217b10–14, the only reason put forward for the existential reading is that for Plato the Forms are nothing but themselves, so that ‘the predicative reading of the antecedent seems forced (“if the form of the Good were not good…”)’. It can be argued that the existential reading is the most plausible one here, but this conclusion about it seems too quick, especially in light of the prevalence of self-predication of Forms in Plato (‘the Good Itself is good’) and the scholarly debates over the meaning of it. The neglect of this issue highlights the strange fact that Edelhoff does not indicate any reference to Plato or interpreters of Plato for claims about his metaphysics. Even if this is beyond the scope of a book in this series, it would have been useful to indicate some sources, especially for the less specialized reader.
In Chapter 2, Edelhoff investigates passages from Categories 12 and 13. She demonstrates convincingly that Aristotle provided here the twofold criteria for priority in nature: (A) and (B). She proceeds from arguing that in Categories 13, 15a4–7 Aristotle claims that a genus is ontologically prior to its species insofar as there is an asymmetric necessary existential dependency between instances of a genus and instances of the species. That is, necessarily, if an instance of a species exists, an instance of the relevant genus exists, but not vice versa. Edelhoff appeals to grammar convincingly in arguing against alternative readings of the passage (readings of einai predicatively and existentially for universals), as well as to another case of priority in nature—of one to two (Categories 12, 14a29–35)—where it is clear that the predicative reading cannot be intended (that would imply that if something is two, it must also be one).
Yet, Edelhoff seems to overlook the context of Categories 13, 15a4–7, which is to clarify what simultaneity in nature means. Instead, she considers another context of similar statements in the Prior Analytics, where einai has been read predicatively. In particular, she does not explain how several species of one genus (like bird and fish of animal) can be called simultaneous in nature (cf. 14b32–15a4), and how can this case be accommodated into her interpretation overall. This case of simultaneity possibly does not alter the case for Edelhoff’s reading (the priority of genus over species at 15a4–7 is arguably contrasted with the simultaneity between half and double at 14b27–32, despite the placing of the passages). But then her claim to give ‘the first systematic analysis of Aristotle’s discussion of ontological priority in Categories 12 and 13’ (17) is somewhat too bold.
In Chapter 3, Edelhoff analyses ontological simultaneity and priority of relatives in Categories 7. Based on 7b15–22, for simultaneity in nature she identifies (A*) symmetrical existential dependence as a necessary condition (although it is erroneously called a ‘sufficient condition’ twice, cf. pages 36–37); and (C*) simultaneity in time as an indicator for simultaneity in nature. Additionally, she imports another necessary condition for simultaneity in nature from Categories13, 14b27–32, namely that (B*) neither item is the cause of the other.
Apparently, (B*) is indeed a necessary condition for simultaneity in nature for Aristotle. However, in the context of Categories 7 this condition does not seem to be relevant. Aristotle’s point there is not to analyse simultaneity, but to analyse some examples (knowledge and perception) where instead of simultaneity between the relatives there is a priority relation. It is not the case that (C*) knowables or perceptibles exist simultaneously with (respectively) knowledge or perception of them. Rather, knowables and perceptibles exist prior in time to knowledge and perception. Again, it is not the case that (A*) a given knowable or perceptible implies the existence of knowledge or perception of it. Rather, it is possible that an object of knowledge or perception exists (as such) without knowledge or perception existing. Even though Aristotle could have appealed to the thesis that the perceptible is the cause of perception—so that (B*) is not fulfilled for the perceptible and perception—he does not do so. Thus, it seems not surprising that the condition of causality is not mentioned in Categories 7 (pace 41).
Again, Edelhoff argues that condition (C*) is not meant to be a strong one. However, she misses that (C*), simultaneity in time, follows from (A*), symmetrical existential dependence. If necessary existence of X implies existence of Y, and vice versa, it is necessary that X and Y can exist only at the same time, because at any moment, if either exists, the other exists too, by necessity. So temporal simultaneity is a necessary condition for symmetrical existential dependence, and hence for simultaneity in nature (this is hinted at in note 95, although curiously disconnected from simultaneity in time). Obviously, it will not be a sufficient condition (shown also by Edelhoff), as Aristotle himself seems to allow cases (7b23–25) when an ontologically prior item (a knowable) exists simultaneously in time with its posterior item (knowledge). Curiously, Edelhoff takes these cases to imply that it is not a necessary condition either (42).
In Chapter 4, Edelhoff analyses the primacy of primary substance over secondary substance and other categories. She argues (Chapter 4.7) that this is not an asymmetric ontological priority, but is due to the ultimate subjecthood of primary substances (individuals). In particular, she argues (Chapter 4.2–4.5) that the famous statement at 2b3–6 that without primary substances nothing else would be is a consequence of the subjecthood of primary substances, and it should not be added to this that primary substance can be without the other categories or secondary substances, as many interpreters add. This is fairly clear, as Socrates (a primary substance) could not be without being also a human (secondary substance) or having certain colour (quality, another category). Edelhoff argues for this convincingly with sophisticated and illuminating philosophical and textual arguments. An important point here (Chapter 4.6) is that the existential dependence of secondary substances on primary substances is still interesting and relevant in context of Academic debates, where universals (Platonic Forms) are said to exist independently of particulars. Aristotle’s move then is to be understood as polemic with Platonic metaphysics.
Edelhoff restricts the scope of her study reasonably (considering the limitation of the series) in two ways. She focuses on the Categories and imports as few ideas from other works of Aristotle as possible (especially the Metaphysics, to which she only turns in Chapter 5 as subject for further study). Again, she cites secondary literature on Aristotle’s metaphysics mainly from the mid-20th century. At some points, however, restrictions are less reasonable. Let me note two cases. As mentioned earlier, Edelhoff appeals to the philosophical context of the Academy without citing Plato or Plato scholarship (which is most pressing for self-predication). Again, she positions her interpretation for the primacy of primary substances in terms of subjecthood as somewhat exclusive (citing only one similar interpretation). Yet, although she refers at one point to Simplicius’ Commentary on the Categories (note 100), she does not mention Simplicius’ interpretation of the primacy of primary substances that seems to be the same as hers (Simplicius, In Cat. 86.23–34). Generally, it could have been worthwhile to consider interpretations of the analysed concepts and texts from the long commentary tradition on Aristotle’s Categories, both for possible interpretations and for the philosophical context of Aristotle’s views.
The topic of this book, ontological priority, is a lively one both in contemporary metaphysics and in Aristotle scholarship. Edelhoff’s clear and thorough analysis contributes to the latter with valuable insights in a way that can be interesting to the former debate as well. The format of the series too is appropriate. Within the limited scope of 70 pages the text manages to be a fairly original interpretation of Aristotle’s Categories for the expert, while mostly due to its clarity also accessible for non-specialists or students.
 In this approach she invokes classic studies on the verb ‘to be’ in Ancient Greek, cf. Charles H. Kahn, ‘The Greek Verb “To Be” and the Concept of Being’, Foundations of Language 2 (1966): 245–65 and Lesley Brown, ‘The Verb “to Be” in Greek Philosophy’, in Language, ed. Stephen Everson (ed.), Language (Cambridge University Press, 1994), 212–36.