A New Puzzle About Aristotelian Accidents

I present a new puzzle that concerns Aristotle’s accidents. This puzzle arises when applying a basic requirement of accidentality to the variety of cases Aristotle provides. In short, Aristotle seems to offer, now the thought that a is accidental to b, and now that b is accidental to a; but if accidentality is asymmetric, as it seems to be, then a’s being accidental to b implies that b is not accidental to a. One might offer a schooled Aristotelian solution, allowing that while a is in a sense accidental to b, b is accidental to a in a quite different sense. But, as I will argue, this solution does not work, for there are cases in which a and b are accidental to each other in the same sense. Ultimately, the solution to the new puzzle relies not on distinguishing between senses of ‘accident,’ but rather on unearthing a new feature of accidentality: accidentality is contextual, in a sense to be defined in the paper.

The thought that some properties are more metaphysically significant to their bearers than others is traceable back to Aristotle. His concept of what belongs 'in itself' -that is, what belongs essentially or intrinsically -plays an important role in his ontology. 1 So too does the corresponding notion of belonging 'incidentally' -that is, what belongs accidentally, what is an accident -for as Aristotle held, what belongs intrinsically cannot alone fully capture the grain of what there is; to fill in the details, accidents are required. To be sure, the metaphysical significance of essential properties explains the fact that philosophers today focus on them rather than accidental properties, and why scholarly work on Aristotle's ontology focuses on what belongs intrinsically rather than what belongs accidentally. But Aristotle himself did not isolate the two branches of this distinction in that way. For one, he attributed to some accidental properties the same modal profile enjoyed by intrinsic properties; for another, he held that some things that belong intrinsically are also accidental properties. So what Aristotle says about what belongs intrinsically is intertwined with his account of accidents.
This paper focuses on that account. In particular, I argue that there is an unappreciated puzzle therein, one that has implications for both what it takes to belong accidentally and what it takes to belong intrinsically. That seeming inconsistencies would manifest in Aristotle's discussion of accidents is, of course, hardly surprising: that some accidents have the same modal profile as intrinsic properties and that some accidents also belong intrinsically are notoriously difficult to explain. 2 For Aristotle sometimes seems to hold that some accidents are necessary features, just as intrinsic properties are (Top. 102b4-7); at other times, he seems to say that accidents are merely contingent features, that accidents are only what both can belong and can fail to belong to something (Met. 1025a30-34). Another puzzle arises when Aristotle seems to say now that being an accidental feature is incompatible with being an intrinsic one (APo. 73a34-b5), now that there are such things as intrinsic accidents (τὰ� καθ' αὑ� τὰ� συμβεβηκότα) (APo. 75b1). Typically, these issues are resolved by distinguishing among senses of 'accident'; indeed, Aristotle admits that the word is polysemous in Metaphysics 5.30 [1025a14-34], and scholars put this admission to good use in resolving just these problems. 3 The result is a framework in which only some accidents belong contingently, with others belonging necessarily; and in which only some accidents belong intrinsically, with others failing to do so.
A puzzle of a similar sort manifests when considering what is accidental to what in physical contexts, cases of accidentality that arise in causal interactions. And just as explaining the older puzzles sheds light on accidentality in Aristotle, resolving the new puzzle does as well. The previous puzzles concern accidentality having some feature or other -is accidentality compatible with necessity, is it compatible with intrinsicality? -and in this regard, the new puzzle is no different: given the cases we will see below, how can accidentality be asymmetric? For that it is asymmetric is widely appreciated. 4 But we will see that Aristotle seems to offer, now the thought that a is an 1 I use 'intrinsic' as a translation of καθ' αὑ� τὸ� throughout, though others prefer 'essential.' One reason in favor of 'intrinsic' is Aristotle's use of τὰ� καθ' αὑ� τὰ� συμβεβηκότα in Posterior Analytics and elsewhere. Rendering καθ' αὑ� τὸ� with 'essential' would translate τὰ� καθ' αὑ� τὰ� συμβεβηκότα as 'the essential accidents.' If one takes 'essential' and 'accidental' to be incompatible predicates, this translation makes a mess of Aristotle's thought. But we can avoid this issue by rendering of καθ' αὑ� τὸ� with 'intrinsic,' which is a perfectly acceptable translation of καθ' αὑ� τὸ� ; and 'intrinsic accidents' does not have the ring of contradiction.

4
On this asymmetry, Lewis writes that 'it [that is, the relation 'x is an accident of y'] is irreflexive but asymmetric […]' (Lewis 1991: 105). Additionally, Studtmann says that 'All other entities bear some sort of asymmetric ontological relation to primary substances. For example, all accidents inhere in primary substances while primary substances do not inhere in anything (Cat. 1a20-1b8)' (Studtmann 2012: 71). See also Corkum, who says generally that 'the asymmetry between substances and non-substances is well recognized ' (2008: 70n6). For all that, care must be taken in assessing claims of asymmetry, since oftentimes the relation scholars are analyzing is dependence, which may be a relation distinct from accidentality. For instance, Wedin explains that 'The asymmetry between substance and accident rests on the fundamental fact that the world contains two kinds of individuals that stand in a relation of one-way ontological dependence' (Wedin 2000: 86). So for Wedin, ontological dependence is asymmetric, and accidents are ontologically dependent on substances; but there is no explicit avowal of the asymmetry of accidentality. (Cohen (2009: 198) and Loux (2008: 47n66) are additional such examples.) It is, of course, a brisk inference from (i) accidents are just items accidental to what they are dependent on and (ii) dependence being asymmetric to (iii) accidentality being asymmetric. To be sure, accidentality is just that relation in virtue of which we call the items mentioned in (i) 'accidents.' So I take it that Cohen et al. agree that accidentality is asymmetric. Huismann Metaphysics DOI: 10.5334/met.68 accident of b -or, equivalently, that a is accidental to b -now that b is accidental to a, and it is not immediately obvious how to square these. Here, one might take the same approach that resolved the other puzzles, reading Aristotle as holding that, while a is an accident of b, b is an accident of a in a quite different sense. But this brings us to the crucial difference between the new puzzle and the old ones: as I will argue, this solution does not work, for there are cases in which a and b are accidental to each other in the same sense. Ultimately, the solution to the new puzzle relies not on distinguishing between senses of 'accident,' but rather on unearthing a new feature of accidentality: accidentality is contextual, in a sense to be defined below.
The plan of the paper follows the above sketch of the new puzzle. I begin by going through a number of examples in which one thing is said to be accidental to another, focusing especially on causal examples that involve accidentality ( §1). I then turn to the evidence that accidentality is asymmetric, namely a passage from Metaphysics 4.4 ( §2). Finally, I conclude by presenting the new puzzle and considering two candidates for solving it ( §3). I argue that distinguishing among senses of 'accidental' fails to solve the new puzzle, but attributing to Aristotle the idea that accidentality is contextual does solve it. With this solution in hand, we will have a better understanding both what belongs accidentally to some bearer and what belongs intrinsically to some bearer.

§1: A VARIETY OF CASES
It is safe to say that Aristotle uses 'accidental' (κατὰ� συμβ β βηκὸ� ς) and 'accident' (συμβεβηκὸ� ς) to denote something relational. 5 Accidents are always accidents of something, whatever modal profile they might have or explanatory work they might do (or fail to do). Perhaps the bestknown example of accidents in this regard are qualities, quantities, and generally whatever fall into categories outside the category of substance: such items are accidental to substances. 6 The quality pale, say, is accidental to Socrates, just as 6' tall is accidental to Callias. 7 Now, it will turn out that more items than those from non-substance categories are accidents of something, so it will be helpful, at this point, to introduce some fresh terminology. I will call items that fall under non-substance categories -that is, items that are qualities, quantities, relatives, and so onattributes. Put as such, Aristotle's best-known examples of accidentality are attributes that are accidental to substances. One need only reflect on the ease with which we refer to attributes simply as 'accidents' to see this.
To be sure, attributes are examples of accidents of something. But we must take care not to conclude that, for Aristotle, only attributes are accidents of something. He says nothing to preclude 'is an accident of something' from holding of a substance, and in fact gives us an example of this sort in Metaphysics 5.2. He there develops a number of causal distinctions, and in the course of doing so gives the following example of an accidental cause of some effect and that effect's correlative intrinsic cause: See, e.g., Ackrill (1963), 147-148;Lewis (1985), 59; Loux (2012), 375;Studtmann (2012), 71;Wedin (2000), 38-66. 7 There is some debate as to whether Aristotle holds items such as pale and 6' tall to be universals or particulars; see Frede (1987). I do not take a stance on this issue in the main text. Huismann Metaphysics DOI: 10.5334/met.68 b; or by being an intrinsic cause of what b is an accident of. 8 Now, the case Aristotle describes in [T1] is one in which something is an accidental cause in the first way: Polyclitus is an accidental cause of a statue produced by a sculptor because Polyclitus is accidental to the sculptor. Just as the quality pale is an accident of Socrates when he's pale, so too is Polyclitus an accident of an intrinsic cause, the sculptor -indeed, Aristotle holds that it's because Polyclitus is an accident of the sculptor that Polyclitus is an accidental cause. Now, Polyclitus is a substance, and no substance is a quality, quantity, or any other attribute. 9 And generally, when a is an accident of b, a need not be a attribute.
In addition to [T1], we find Aristotle committed to 'is an accident of something' holding of another non-attribute in Metaphysics. The opening chapter of Metaphysics 7 describes the relationship between a substance and an accidental unity as one where the latter is an accident of the former. But before examining that passage, I need to say a word about accidental unities. Throughout, I write as if, for Aristotle, accidental unities are different compounds than substances, as if accidental unities comprise substances and attributes. 10 There is, however, disagreement over this, with some attributing to Aristotle the thought that accidental unities are identical to substances. 11 Those who take this view likely would prefer to explain what is an accident of what in a manner different from my exposition. Still, I do not intend to engage in this debate here. My aim in this paper is to show that accidentality has a philosophically significant feature, and as I argue below, this consequence follows whether or not accidental unities are identical to substances.
As the opening of Metaphysics 7.1 illustrates, accidental unities are accidents of something, giving us further reason to think that, when a is an accident of b, a need not be an attribute: [T2] Other things are said to be by being either quantities of what is in this way [i.e. by being quantities of substances], or qualities, or affections, or something else of this sort. That is why one might indeed be puzzled as to whether walking and recovering and sitting do signify each of these things as beings, and similarly for any other thing of this sort; for none of them either is of a nature to be in its own right, or is capable of being separated from substance. If anything, it is the walking one and the seated one and the recovering one that is. These things are clearly more real, because there is some definite thing that underlies them (τὸ� ὑ� ποκείμενον) -namely the substance and the particular -which is apparent in such a predication; for one cannot speak of the good one or the seated one apart from this. Evidently, then, it is on account of this, i.e. substance, that each of those is also; and therefore what primarily is -not is something but is without qualification -will be substance. Admittedly, [T2] does not explicitly invoke the relationship of accidentality. Still, we can see that the passage's reference to a 'the thing that underlies them' (τὸ� ὑ� ποκείμενον) commits Aristotle to an accidental unity being accidental to its underlying substance when we consider the following. The walking thing, the sitting thing, and the healthy one are, in this context, accidental unities, substances taken together with certain qualities. They are not themselves qualities, for they are more real than the qualities of walking, sitting, and recovering. And neither are they substances, for substances underlie the walking thing, the sitting thing, and the one being healthy. In this case, a substance's underlying the walking one entails that the latter is an accident of the former, a sense Aristotle gives to 'underlying' elsewhere in Metaphysics 7: Now, about two of these we have already spoken, namely, about the essence and the underlying subject, and said that it underlies in two ways, either by being a this something (as the animal underlies its attributes) or as the matter underlies the actuality. (Metaphysics 7.13 [1038b3-6]; trans. Reeve.) 8 This is the standard model that interpreters rely on in explaining accidental causation; see, e.g., Allen (2015, 76-77), Freeland (1991), and Judson (1991, 78-79).

9
On the referent of a proper name being a substance, see Metaphysics 5.6 [1015b20-23]. When a substance underlies, say, the sitting thing, either this relation is the same relation as that between an animal and its attributes -its various qualities, quantities, and so on -or it is the same relation as that between matter and the actuality (Reeve, 2016: 438). Presumably 'the actuality' is here to be understood as actual form that, having combined with the matter, yields a compound substance. I.e., the latter possibility is one where matter underlies a form; e.g., Socrates' flesh and bones underlies Socrates' human soul. But this is not the relation between an accidental unity and the substance that partly comprises it. For if it were, the walking thing would be related to the substance underlying it as Socrates' soul is related to his flesh and bones; but Socrates' soul and his flesh and bones comprise a substance, unlike the walking thing and its underlying substance. Thus the relation between the sitting thing and the substance that underlies it is the kind of relation that obtains between an animal and its attributes. Which is to say, the sitting thing is an accident of some substance. Here is another example, then, of a being an accident of b and a not being an attribute; rather, a is an accidental unity. We must not get into the habit of thinking that a's being an accident of b entails that a is a attribute -hence my reluctance simply to call attributes 'accidents.'

ITEMS THAT ACCIDENTS ARE ACCIDENTS OF
Nor does a's being an accident of b entail that b is a substance. In [T1], Polyclitus is an accident of the sculptor. Now, to those who include accidental unities in Aristotle's ontology, the sculptor is in all likelihood an accidental unity comprising a human being and the art of sculpting. Indeed, that experts generally are accidental unities seems clear enough from Aristotle's scattered remarks on the topic. One of his preferred examples of an expert is a house-builder, and he is explicit that the art of house-building, and arts in general, are specific kinds of qualities, namely states. 12 Because states are a kind of quality, there are no states that exist separate from some substance; the nature of the relationship between humans and the art of house-building being one of possession in Metaphysics 9.8 [1050a10-12]. For there to be arts at all, there must be humans that possess them, and this entails the existence of an accidental unity in which a human is conjoined to the art. Generally, then, experts are accidental unities.
When Aristotle says, in [T1], that Polyclitus is an accident of the sculptor, this is therefore a case of a substance being an accident of an accidental unity. There are additional examples in Aristotle's corpus of something being an accident of an accidental unity. For instance, he describes a case where a house-builder is an accident of a doctor as follows: [T3] And it is an accident that the house-builder heals someone, because a doctor naturally makes it, not a house-builder, but the house-builder was an accident of a doctor; and a confectioner, aiming to give pleasure, might produce health in somebody, but not according to the art of confectionary -and so, it was an accident, we say, and in a way he produces [health], but not simply (Metaphysics 6.2 [1026b37-1027a5]; trans. Kirwan, modified.) Aristotle again uses an example of efficient causation to illustrate accidental causation, since doctors naturally (πέφυκε) efficiently cause health. Now, the house-builder and the doctor are both experts -both have a characteristic art, the art of medicine for doctors, the art of house-building for housebuilders -and in this example it seems that the same human being possesses both of those arts. The house-builder and the doctor are, then, accidental unities of one and the same human being and the corresponding arts. And so, when Aristotle relates the house-builder and the doctor using a variant of 'is accidental' (συμβαίνω), he takes one accidental unity to be an accident of another.
In addition to accidental unities being accidental to each other, it seems that some attributes are accidents of accidental unities: [T4] That which is may be so called either accidentally or in its own right: accidentally, as for instance we assert someone just to be cultured, and a man cultured, and someone cultured a man; in much the same way as we say that someone cultured Huismann Metaphysics DOI: 10.5334/met.68 builds, because cultured is accidental to a housebuilder or a housebuilder to someone cultured (for 'that this is this' signifies 'this is accidental to this'). (Metaphysics 5.7 [1017a7-13]; trans. Kirwan.) Here, we are told the quality cultured is an accident of a house-builder, and so, we have another case of something being an accident of an accidental unity. So not only are some items accidental to substances, some items are also accidental to accidental unities.
The texts examined in this section, and specifically these lines from Metaphysics 5.7, invite the following sort of concern. Aristotle holds that some predications, while true, are not metaphysically perspicuous and are not parts of any demonstration; he dubs such predications accidental predications in Posterior Analytics 1.22. 13 His example there concerns a substance (a log) and a quality (pale), the latter of which is accidental to the former. In this case, both 'the log is pale' and 'the pale one (β β β β β β β β ) is a log' are true. However, Aristotle has it that the grammatical structure of the latter conceals that the pallor in question is accidental to the log; the grammatical structure of the former does no such thing. And so, 'the pale one is a log' is true, but its truth condition is not the log's being accidental to the quality pale, rather it is the quality pale's being accidental to the log. Generally, the grammatical subjects of accidental predications do not denote substances, so one might look for instance to 1017a10 in [T4], and wonder if the truth conditions for 'the cultured one builds' require a nuanced approach, in the way that the truth conditions of 'the pale one is a log' do. But even if 'the cultured one builds' is an accidental predication in virtue of its grammatical subject denoting a non-substance, there is no difficulty in understanding the truth conditions for what we find at 1017a10, because Aristotle gives those conditions at 1017a11: 'the cultured one builds' is true because the quality cultured is accidental to a house-builder. And even though the texts I am relying on often have a grammatical subject that denotes a non-substance, so too are their truth conditions clearly laid out. So even if accidental predication abounds in these passages, Aristotle's use of 'is accidental' (συμβαίνω) in them precisifies what, exactly, is accidental to what. In the next section, I explain why Aristotle denies that attributes are accidental to other attributes. As for the other possible combinations, I leave them aside because I do not know of examples that clearly fall into these categories. But even in leaving them aside, there is a certain variety evinced by the cases in the table, which jointly show that there are more lines of accidentality than might be thought at first glance. Just as attributes are accidental to substances, so too are accidental unities, and even substances themselves, identified as accidents of something. So there are more entities that are accidents than just attributes, and when we appreciate this fact, the identification of a substance as an accident of something in [T1], or of one accidental unity being an accident of another in [T3], is not peculiar at all. Rather, these texts fit into an account of the accidental that is as fine-grained as Aristotle holds the world itself to be.

§2: UNCOVERING ASYMMETRY
The examples of accidents in causal situations that Aristotle offers reveal that there is more to accidentality than attributes being accidental to substances. However, you might reasonably offer 13 The account of accidental predication offered in the main text follows Barnes'; see Barnes (1993, 176). the following worry at this point. Even if you agree that the correct set of possible relata for the relation denoted by 'is an accident of' is that of substances, attributes, and accidental unities, some of the cases above seem to stand in direct opposition to better-known facts about accidentality. First and foremost in this regard is that Aristotle takes 'is an accident of' to denote an asymmetric relation, and above, the asymmetry seemed to be fixed by the type of entity at stake. Substances are ontologically prior to attributes, so when Socrates and the quality pale are accidental to each other, the latter is accidental to the former and the former is not accidental to the latter. But it's difficult to see how this line of thought would run in [T3], where the house-builder is accidental to the doctor, because the entities are of the same type: the doctor and the house-builder are both accidental unities, so neither is ontologically prior to the other, and the type of entity at stake does not, in this case, fix what is accidental to what. It's also hard to see how [T1] and [T2] fit together: if, according to considerations of type, accidental unities are accidents of substances and accidentality is asymmetric, then substances should not be accidents of accidental unities; or, if substances are accidents of accidental unities, and accidentality is asymmetric, then accidental unities should not be accidents of substances. So one might think that, on the basis of [T2], because the sculptor is an accidental unity and Polyclitus is a substance, the former is accidental to the latter. But if accidentality is asymmetric, then Polyclitus is not accidental to the sculptor, in direct opposition to what Aristotle says in [T1].
Addressing these issues is the business of this section. To do so, I turn to the evidence for accidentality being asymmetric. The principal reason for attributing this idea to Aristotle is an argument from Metaphysics 4.4. To be sure, the conclusion of that argument is not that accidentality is asymmetric. Rather, his argument there crucially presupposes the thought that accidentality is asymmetric, for it would be obviously invalid without it. And so, it is reasonable to read the argument as containing a commitment to the asymmetry of accidentality.
The broader context of the argument is as follows. Aristotle considers an opponent who claims that whenever something holds of something else, the former is an accident of the latter. This position undermines Aristotle's claim that some features hold intrinsically, and so it is no surprise that Aristotle offers a reductio of the opponent's position: Aristotle says that, if everything that holds of something is an accident of that something, it follows an accident will be accidental to an accident. But this cannot be the case: [T5] Not even more than two combine; for the accidental is not accidental to the accidental, unless because both are accidental to the same thing -I mean for instance that pale may be cultured and the latter pale because both are accidents of a man. But Socrates is not cultured in that way, that both are accidental to some other thing.
[…] Nor indeed will there be any other thing accidental to pale, e.g. cultured, for there is no more reason (οὑ� θέν μᾶλλον) that the latter is an accident of the former than the former of the latter. (Metaphysics 4.4 [1007b1-13]; trans. Kirwan, modified.) The accidental is not accidental to the accidental, and what this means in our terminology is that no attribute is accidental to an attribute. Of course, two attributes, pale and cultured say, might be accidents of the same substance, and Aristotle even seems to say that cultured is accidental to pale when he adds to his original restriction the rider 'unless because both are accidental to the same thing.' What exactly this rider means, and what exactly the sense of [T5] is, is difficult. Kirwan, for instance, takes the rider to amount to a concession on Aristotle's part that one attribute can be accidental to another, an allowance that 'mutual coincidence of a and b is possible' (Kirwan, 1993: 218). But the rider cannot mean that, when the two attributes mentioned in [T5] are accidental to Socrates, cultured is accidental to pale: Aristotle denies this very state of affairs at the end of [T5], saying that nothing, not even cultured, is accidental to pale. We therefore cannot understand the rider as a concession that cultured is accidental to pale, without saddling him with inconsistency. And to be sure, Aristotle explains the rider by saying, not that pale is accidental to cultured when the two qualities are accidental to the same human, but simply that pale is cultured; and he concludes [T5] by saying that nothing, not even cultured, is accidental to pale. It is for these reasons, then, that I disagree with Kirwan's reading, and resist interpretations according to which this passage supports accidentality's being symmetric, for Aristotle. Rather, the key to understanding the rider lies in the example Aristotle uses to explain it: in the first sentence of [T5], Aristotle holds that, when the two attributes are accidental to Socrates, the accidental predication 'pale is cultured' is true. Now, the truth of that sentence does not entail that one attribute is accidental to another -after all, the sentence contains no form of 'is accidental' (συμβαίνω) -but we might suspect it does have this entailment because of its grammatical structure. For when Socrates is pale and cultured, 'pale is cultured' and 'Socrates is cultured' are both true and have the same predicate term. But, as Aristotle emphasizes, cultured is only accidental to Socrates, not to pale. In short, the rider 'unless because both are accidental to the same thing' explains the truth conditions for the accidental predication 'pale is cultured;' it does not allow that cultured is accidental to pale. The reason that one cannot be accidental to the other, the reason that 'is an accident of' denotes an asymmetric relation, comes in the final sentence of this passage.
In rendering that sentence 'there is no more reason that the latter is accidental to the former than the former to the latter,' I identify it as an indifference premiss, a premiss of the form 'there is no more reason for p than for q'. An argument containing such a premiss is a specific type of Principle of Sufficient Reason argument, namely an indifference argument. 14 Usually, though not always, indifference premisses are expressed by coordinating two terms, 'no' (οὐ ) and 'more' (μᾶ λλον). 15 Given his expression 'no more than' (οὑ� θέν μᾶλλον) in the final sentence of [T5], we see that this passage is an instance of Aristotle using this kind of reasoning. And taking him to do so makes good sense of the overall argument, for Aristotle's reliance on indifference arguments shows fairly clearly what he thinks follows from an indifference premiss: according to him, if there is no more reason for p than for q, then either both p and q or neither p nor q. 16 If we read the argument of [T5] as an indifference argument, then the sense of the passage becomes simpler to grasp. There is no more reason for pale to be an accident of cultured than for cultured to be an accident of pale. So either each is an accident of the other, or neither is an accident of the other. Now, Aristotle clearly concludes that neither is an accident of the other, so he must presuppose that each being accidental to the other cannot be the case. Without that crucial presupposition, the argument in [T5] is invalid. And so, pale is not an accident of cultured, nor is the latter an accident of the former. Finally, the argument is supposed to support the more general claim that the accidental is not accidental to the accidental, so it must be that this example is suitably arbitrary and that the facts of this particular case generalize: if there is no more reason for a to be accidental to b than for b to be accidental to a, then neither is accidental to the other. 17 Now, the presupposition that is required for Aristotle's argument to go through is the denial of pale and cultured both being accidental to the other; it is a matter of course to show that this is equivalent to the thought that if one is accidental to the other, then latter is not accidental to the former. And this is just asymmetry. Of course, this presupposition coheres with the indifference argument in [T5]: in cases where something is accidental to something else, it follows that there will be some reason that a is accidental to b instead of b being accidental to a. If there were no reason for b's not being an accident of a, then the indifference argument of [T5] would block a's being an accident of b in the first place. But again, this is just asymmetry: when something is accidental to something else, there's a reason the latter is not also accidental to the former.

ACCIDENTALITY OR ACCIDENTAL SAMENESS?
The argument of [T5] contains, then, Aristotle's commitment to the asymmetry of accidentality, and we can see exactly why he needs this claim: without it, his argument that the accidental 14 On indifference reasoning both generally and in ancient philosophy, Makin (1993)  17 Given that we have seen, in §1, cases in which one accidental unity is accidental to another, it must be that, in such cases, there is a reason for one to be accidental to the other while the latter is not accidental to the former. (It is for this reason that I understand 'the accidental is not accidental to the accidental' in [T5] as the thought that attributes are not accidental to attributes.) I discuss this more in §3, but for now I will simply say that the reason an accidental unity is accidental to another, but not the converse, is causal in nature. Huismann Metaphysics DOI: 10.5334/met.68 is not accidental to the accidental does not go through. But at this point, I need to consider an alternative possibility for the relation that the entities in [T1] -[T4] stand in. I am arguing that those entities are accidental to one another, but it is possible that they stand in an altogether different relation: it is possible that they are merely accidentally the same (ταὑ� τὰ� κατὰ� συμβεβηκός). Aristotle describes accidental sameness in Metaphysics 5.9 [1017b27-30], and the relation is typically understood to be a symmetric relation between substances and accidental unities. 18 (Items that are accidentally the same are sometimes called 'accidental sames.') In many of our examples, the entities involved stand in relations of accidentality and accidental sameness, and so, we need to keep in mind the fact that the items Aristotle mentions in the passages above stand in both an asymmetric relation and a symmetric one. Of course, the fact that accidental sameness is symmetric is perfectly compatible with accidentality's being asymmetric. A mundane example of relations exhibiting the same logical features might help, for instance, fatherhood and being a biological relative: Aristotle is the father of Nicomachus and is a biological relative of Nicomachus; and, of course, being a biological relative is a symmetric relation. And these two facts do nothing to undermine the asymmetry of Aristotle's being the father of Nicomachus, just as the fact that the items mentioned previously are accidental sames does not undermine the fact that one is asymmetrically accidental to another. Still, if the most that could be said of the passages considered below is that the items Aristotle speaks of are accidental sames, then there would be no puzzling violation of asymmetry. It will be good, then, to reconsider the passages discussed in the previous section, to confirm that they are cases where the asymmetry requirement latent in [T5] holds good, and not merely cases where two things are accidentally the same and therefore need not stand in an asymmetric relation.
Let me start by saying that Aristotle's expression 'things accidentally the same' (ταὑ� τὰ� κατὰ� συμβεβηκός) does not appear in any of the texts considered in §1; nor does his word for same things (ταὑ� τὰ� ) appear on its own. Nor still does accidental sameness hold between entities in all of our examples: accidental sames are typically thought to be pairs consisting in exactly one substance and exactly one accidental unity; Lewis, who provides the standard account of accidental sameness, has it that 'x is accidentally the same as y if and only if (i) exactly one of x and y is a substance and exactly one is an accidental compound' (1991: 103) But neither [T3] nor [T4] fit this condition. This absence is not decisive, of course, but I take it to suggest that Aristotle is, more likely than not, bringing forward cases in which one thing is accidental to another, and not merely cases where two things are accidentally the same.
This suspicion is confirmed when we consider the end of the argument of [T5]. Aristotle says there that one attribute cannot be accidental to another, where Aristotle marks out this relation with the verb 'is accidental' (συμβέβηκεν). That is, he marks out the relation with the construction he uses in [T1], where he uses the verb 'is accidental' (συμβέβηκε) to describe the relation between the sculptor and Polyclitus. Because both constructions are perfect tense forms of the same verb (συμβαίνω), I take it that they mark out the same relation. But this is hardly a surprise, given that Aristotle's concern in [T1] is elucidation of a case of accidental causation, a phenomenon that, according to the standard model, manifests when something is accidental to an intrinsic cause; the intrinsic cause in the particular case is the sculptor, the accidental cause Polyclitus, so Aristotle there takes Polyclitus to be accidental to the sculptor.
One might yet resist this reading along the following lines. , to show that it is more plausible that the relations he speaks of in these passages are instances of accidentality; rather than his word order suggesting that we supply a missing 'same' (ταὑ� τὸ� ) and understanding the relations merely as instances of accidental sameness.
The asymmetry requirement in [T5] applies, then, to the relation between the sculptor and Polyclitus as it is outlined in [T1]: in that passage, Polyclitus is accidental to the sculptor. To be sure, the two are, additionally, accidentally the same, and Polyclitus' being accidentally the same as the sculptor is perfectly compatible with the sculptor's being accidentally the same as Polyclitus. But even though the two stand in a symmetric relation, they also stand in an asymmetric one, just as Aristotle and Nicomachus stand in a symmetric relation (denoted by 'is a biological relative of') and an asymmetric one (denoted by 'is a father of'). Aristotle similarly holds, in [T4], that the quality cultured is accidental both to a house-builder and to a man, and he does so using forms of 'is accidental' in the perfect tense (συμβέβηκε and συμβεβηκέναι). It must be that the same relation is at stake in both [T4] and [T5]. The asymmetry requirement of [T5] therefore applies to both of these cases: the quality cultured is accidental to a house-builder and the house-builder is not accidental to cultured; and cultured is accidental to a man, and the man is not accidental to cultured. Again, these entities are also accidentally the same, but the fact that accidental sameness is symmetrical is perfectly compatible with the asymmetry of accidentality.
Finally, in [T3], Aristotle takes the builder to be accidental to a doctor, using the verb 'is accidental' (συνέβη) to mark out the relation between the two. This construction differs from what we find in [T5]: where the requirement that no attribute be accidental to another is expressed in perfect tense forms of 'is accidental' (συμβαίνω) the relation between the builder and doctor is expressed with an aorist form. One might reasonably wonder if the fact that the construction he uses an aorist form in [T3] indicates a relation different from that of accidentality. However, accidental sameness does not manifest between two accidental unities; and what is more, Aristotle's use of aorist forms of 'is accidental' elsewhere suggests that these too mark out when one thing is accidental to another. Recall,, he says that accidental causation is ubiquitous, that an effect has many accidental causes, and the way he expresses this is relevant for our purposes. Again, according to the standard model, all of the accidents that belong to a are accidental causes of whatever a intrinsically causes. Now, a given effect has many accidental causes, and Aristotle says that this fact is explained by the fact that many things may be related to something, presumably the intrinsic cause of the effect in question. The relation between them is marked out by συμβαίη, an aorist construction form of συμβαίνω. But this must mean that the many things are accidental to the intrinsic cause of the effect in question, for it is only in this way that the effect will have many accidental causes. It follows, then, that in each case considered in the previous section, one item is asymmetrically accidental to another. §3: THE NEW PUZZLE The cases described in §1 should satisfy the asymmetry requirement outlined in §2, and it will be good to start working out how they might do so. Start with an example of an attribute being accidental to a substance, pale being an accident of Socrates. If pale is an accident of Socrates, there must be a reason why Socrates is not an accident of pale. In this particular case, the reason is ontological: Socrates is ontologically prior to pale, and this prevents Socrates from being an accident Huismann Metaphysics DOI: 10.5334/met.68 of pale. But this explanation also holds for similar cases: generally, substances are ontologically prior to attributes, and this prevents substances from being accidents of attributes. And so, both in the specific case of pale being an accident of Socrates, and generally in the case of attributes being accidents of substances, there is an asymmetry between what is accidental to what.

Similar reasons explain examples
where an attribute is accidental to an accidental unity and an accidental unity is accidental to a substance. One instance of the former is outlined in the Metaphysics 5.7 passage above, where cultured is accidental to the house-builder. If this is the case, then there should be a reason that the house-builder is not accidental to cultured. The reason, just as in the case of Socrates and pale, has to do with ontological priority. In [T2], Aristotle says that the seated one is 'more real' than seated, by which he likely means the seated one is ontologically prior to seated. 19 And we should expect this result, for the seated one is an accidental unity comprising a human substance and a quality. Which is to say, part of the seated one is a substance, whereas no part of seated is a substance. There is a reason, then, that cultured is accidental to the house-builder though the house-builder is not accidental to that quality: the house-builder is ontologically prior to cultured. Similarly, if the seated one is accidental to Socrates, the reason that Socrates is not accidental to the seated one is that Socrates is ontologically prior to the seated one. In short, attributes being accidental to substances, attributes being accidental to accidental unities, and accidental unities being accidental to substances easily satisfy the asymmetry requirement: in these cases, a is an accident of b and the reasons that b is not an accident of a are readily available.
The other examples of accidentality require a different approach. One example of a substance's being accidental to an accidental unity that we saw above is Polyclitus' being an accident of the sculptor. Now, Polyclitus is ontologically prior to the sculptor, and if we simply apply reasoning based on ontological priority to this instance of case, the sculptor would be an accident of Polyclitus and Polyclitus would not be an accident of the sculptor. But this result is in direct opposition to what Aristotle says in [T1], where he tells us that Polyclitus is an accident of the sculptor. But nothing forces us to deploy ontological priority to understand [T1] -indeed, it better had not, for if we use ontological priority to explain [T1] we get the direction of the relation backwards, since Aristotle says there that Polyclitus is accidental to the sculptor. In fact the context of the passage suggests an altogether different concept for explaining why Polyclitus is an accident of the sculptor and not the other way around: recall, [T1] tells us that the sculptor is an intrinsic efficient cause of statues, but Polyclitus is not. What I propose here is that, just as a being accidental to b relative to ontological priority prevents b being accidental to a relative to that same priority, so too does a being accidental to b relative to intrinsic causation prevents b being accidental to a relative to such causation. And so, the fact that Polyclitus is accidental to the sculptor relative to intrinsic efficient causation prevents the sculptor -an accidental unity -from being an accident of Polyclitus relative to such causation. So the reason that the sculptor is not an accident of Polyclitus relies not on ontological priority, but on intrinsic efficient causation.
Again, if ontological priority is all we think is available to Aristotle for explaining asymmetry, examples of one accidental unity being accidental to another are not obviously asymmetric. The doctor is not ontologically prior to the house-builder, nor is the house-builder prior to the doctor, so if the house-builder is accidental to the doctor, why would the doctor fail to be accidental to the house-builder? Again, we can explain the asymmetry between the two causally: as Aristotle says in [T3], it is characteristic of the doctor, and not the house-builder, to heal. That is, the doctor is an intrinsic efficient cause of health and the house-builder is not; and just as being an intrinsic efficient cause of statues prevents the sculptor from being an accident of Polyclitus, so too does being an intrinsic efficient cause of health prevent the doctor from being an accident of the housebuilder.
Taken individually, each of the cases listed at the end of §1 seems to abide by the constraint laid out in §2, namely that when a is an accident of b, there is a reason that b is not an accident of a. Huismann Metaphysics DOI: 10.5334/met.68 However, a moment's thought reveals that this first pass account leads to a puzzle. Polyclitus is as much of a human substance as Socrates is, while the sculptor is an accidental unity and therefore not a substance. So while reflection on the asymmetry requirement might help to explain the case of Polyclitus' being an accident of the sculptor in isolation, the following question still remains: is Polyclitus an accident of the sculptor, or is the sculptor an accident of Polyclitus? There is a causal reason to think that Polyclitus is an accident of the sculptor, and an ontological reason to think that the sculptor is an accident of Polyclitus. But it cannot be that both are accidents of each other, for that state of affairs is ruled out by the asymmetry of accidentality. So which is it?

FALSE STARTS
The puzzle of explaining how Aristotle's examples of accidents jointly satisfy the asymmetry requirement is what I am calling the new puzzle about Aristotelian accidents. And in a way, the new puzzle is more difficult to solve than the older puzzles, for it is not susceptible to the general strategy that resolves the older ones so well. That strategy consists in distinguishing between senses of 'is an accident of.' Applying this strategy to the new puzzle would consist, then, in giving a schooled Aristotelian answer to the question 'is Polyclitus accidental to the sculptor, or the sculptor to Polyclitus?' along the following lines: in a physical sense, Polyclitus is an accident of the sculptor, and in another, metaphysical sense, the sculptor is an accident of Polyclitus; but because these senses differ, there is no threat to the asymmetry of a single sense of 'is an accident of.' Such a distinction would cohere with Aristotle's numerous detections of ambiguity in philosophical terms of art, including his claim that 'accident' is polysemous in Metaphysics 5.30. Moreover, the fact that this expression has different senses has been used to resolve other puzzles of accidentality, suggesting that distinguishing among senses of the term should be the default candidate for resolving the new puzzle.
To be sure, none of what I have said above is incompatible with such a distinction. It might be that the results of the previous sections evince another sense of 'accident,' a sense pertaining to physics more so than metaphysics. But even if the expression enjoys these senses, this fact does not explain adequately all of the cases we have seen so far. For consider the case outlined in [T3], the house-builder who is accidental to the doctor. One might want to say that the sense in which the house-builder is an accident of the doctor is the physical sense. After all, the house-builder is not ontologically prior to the doctor, nor is the doctor ontologically prior to the house-builder, so one could not be an accident of the other in the metaphysical sense; rather, the reason for one being accidental to the other is causal. In particular, the doctor intrinsically efficiently causes health, whereas the house-builder does not, which explains why the house-builder is accidental to the doctor but the doctor is not accidental to the house-builder. But it is not as if the house-builder fails to intrinsically efficiently cause anything, for the house-builder intrinsically efficiently causes houses. In the case of the doctor and the house-builder, then, the doctor intrinsically efficiently causes something the house-builder fails to cause thusly; but the house-builder too intrinsically efficiently causes something the doctor fails to cause thusly. But they cannot both be accidents of each other, due to accidentality being asymmetric. And so, the question remains as to whether the house-builder is an accident (in the physical sense) of the doctor, or the doctor is an accident (in the physical sense) of the house-builder. (in the physical sense) of the sculptor, and the sculptor is an accident (in the physical sense) of Polyclitus. But we cannot have it both ways.
In cases like these, settling whether a is an accident of b or b is an accident of a depends on more than just the type of entity a and b are and the kind of accidentality at stake. For even if we specify that these entities are accidental unities, and that one is an accident of the other in the physical sense, the fact that both the doctor and the house-builder are intrinsically efficiently causal of something or other leads to running afoul of the asymmetry of accidentality. Nor can we divide 'is an accident (physically) of' into still further senses, taking Polyclitus to be an accident (physically) of the sculptor in one sense, and the sculptor to be an accident (physically) of Polyclitus in another sense. At least, we cannot do so for the same reason we distinguished among senses of 'is an accident of.' For at least in the case of the latter, 'is an accident of' applied to different types of entity -Polyclitus is a substance, the sculptor an accidental unity -and our initial response consisted in the following: when an accidental unity is accidental to a substance, the type of accidentality is ontological; and if a substance is accidental to an accidental unity, the type is physical. But while this justifies, in part, taking 'is an accident of' to be polysemous, it does not further support taking 'is an accident (physically) of' to have multiple senses. For either the conditions on the entities at stake are the same as those just outlined, in which case 'is an accident of (physically)' has the same sense as 'is an accident of'; or the conditions on the entities are not the same as those just outlined, in which case the initial distinction between being an accident (physically) and being an accident (metaphysically) is undermined.
Another way out of the puzzle is to deny that accidentality is asymmetric. If a's being accidental to b is compatible with b's being accidental to a, then no inconsistency arises from the cases outlined in §1. Such a solution would require an alternate reading of [T5] of course, one according to which the text shows, at most, that accidentality is non-symmetric. To be sure, one might reasonably think that this is all [T5] shows. Normally R is symmetric just in case (if Rxy then Ryx). 21 And so, if no attribute is accidental to another attribute, there is a substitution instance that satisfies both of these conditions, due to the falsehood of the antecedent of the right-hand side. 22 Nevertheless, the trivial satisfaction of these conditions due to false antecedents presents problems of its own: if the fact that ~Rab and ~Rba, in conjunction with the typical conditions on symmetry and asymmetry, jointly entail that R is non-symmetric, then many relations we take to be symmetric are non-symmetric, and so are many relations we take to be asymmetric. To take only two examples: fatherhood is asymmetric, identity is symmetric. Moreover, we typically do not take the facts that no sister is another sister's father, that Jo is not identical to Robert, and that Robert is not identical to Jo to threaten the symmetry and asymmetry of those relations. Ultimately, I take what Aristotle is committed to by [T5] -namely, that whenever a is accidental b, there is a reason b is not accidental to a -to be more concrete than trivially satisfying symmetry conditions. So I continue to characterize his view as one according to which accidentality is asymmetric, even if there are post-Aristotelian logical reasons to fashion it as non-symmetric.

THE RIGHT WAY OUT: CONTEXTUAL ACCIDENTS
The way through is not to divide 'is an accident (physically) of' into still further senses, nor to deny that accidentality is asymmetric, but to take into account that, in addition to the type of entity a and b are and the kind of accidentality at stake, a's being an accident of b depends on conditions that a and b are constituents of. It is not merely that the house-builder is an accident of the doctor, perhaps even in the physical sense; rather, the house-builder is an accident of the doctor 21 See, e.g., Dorr (2004).
22 Additionally, one might find general support for this proposal in Aristotle's syllogistic: he appreciates that particular affirmative statements are logically equivalent to their converses, that if some As are Bs then some Bs are As. That is, we find a symmetry in statements that concern the cases from §1: if some humans are white, then some white things are humans. Still, this does not by itself show that accidentality is not asymmetric, since as we have seen, Aristotle allows for the possibility of true but metaphysically imperspicuous statements. Despite the equivalence of some humans being white and some white things being humans, only the latter is an accidental predication. So we should not infer anything about the metaphysics of accidents from that equivalence. Huismann Metaphysics DOI: 10.5334/met.68 that certain accidents might be contextual in the way I argue for, they are not entertained for long. Ferejohn, for instance, suggests that accidentality is contextual, saying, of Aristotle's discussion of snubness in Metaphysics 7.4, that 'snubness is what Aristotle calls a 'per se affection': an attribute which cannot be defined without somehow bringing in its proper subject (in this case, nose).
[…] To a modern reader, this might just be seen as a tip-off that 'snub' can only be defined contextually […]' (Ferejohn, 1994: 296;original emphasis). However, Ferejohn takes Aristotle to 'draw a different moral' from this observation, and does not attribute contextualism to him. Wright similarly takes virtue to be contextual, and connects this account to Aristotle's doctrine of the mean (2010). But the case that Wright examines is one where Aristotle describes variation between different sets of entities, not variation within the same set of entities; e.g., Aristotle's holding that F is good for a and F is bad for b, not Aristotle's holding that F is good for a and also bad for a (where such attributions require contextualizing).
Rather, the contextualism I am attributing to Aristotle likely fits best with what Sullivan calls explanation-relative accidents. For Sullivan, a property is accidental to its bearer relative to an explanatory framework: accidents are properties that do not feature all explanations of some type or other; but those same properties might feature in explanations of another type, and relative to that explanatory framework, those very same properties are essential, not accidental. 24 Similarly, Aristotle holds that, sometimes, when a is an accident of b in C, b is an accident of a in another context. Indeed, in some of the cases above, when a is an accident of b in some context, that relation does not disappear when the context is changed. Rather, the direction of the relation changes: when there is a line of accidentality that runs from a to b in an ontological context, there is still such a line in a causal context, though the line runs from b to a. For example, with respect to ontological priority, Polyclitus is not an accident of the sculptor, the sculptor is instead an accident of Polyclitus; but with respect to the sculptor's intrinsic causal activity, Polyclitus is an accident of the sculptor. Moreover, an accidental unity will never be ontologically prior to a substance, so any instances akin to the one outlined in [T1], where a substance is accidental to an accidental unity, must obtain in causal contexts. But every accidental unity is underlied by some substance, and therefore is, in an ontological context, an accident of some substance. So whenever a substance is an accident of an accidental unity in a causal context, that very accidental unity is an accident of that very substance in an ontological context.
However, there is a point of disanalogy between Aristotle's contextualism and explanationrelative accidents. For Sullivan, a property's belonging to a bearer does not vary with variation of explanatory framework. But for Aristotle, it's possible that in some contexts it's true that a is an accident of b, and in other contexts it's false that a is an accident of b. E.g., for cases akin to what is outlined in [T4], where one accidental unity is accidental to another, it must be that a is an accident of b in a causal context. With respect to intrinsically efficiently causing health, the house-builder is an accident of the doctor; with respect to intrinsically efficiently causing a house, the doctor is an accident of the house-builder; and so on. But there's no difference in ontological priority between the doctor and the house-builder, for both are accidental unities. So with respect to ontological priority, it's false that one is an accident of the other. Sometimes, then, when a is an accident of b in C, there's another context in which neither a is an accident of b, nor b is an accident of a.