On the Coherence of Aristotelian Universals

On the Coherence of Aristotelian Universals: A Reply to Costa and Alvarado (forthcoming, Synthese; please cite the published version) The current interest in the notions of ontological dependence and metaphysical grounding is usually associated with a renewal of interest in Aristotelian metaphysics. Curiously, some authors have recently argued that the Aristotelian view of universals, according to which universals depend for their existence on their exemplifiers, is incoherent from a grounding perspective. In this paper I argue that such criticism is misleading. I shall examine their arguments and clarify the supposed incoherence. 1. Aristotelian Universals and Grounding According to immanent realism, universals depend for their existence on their exemplifiers. Thus, the fact that a universal exists is grounded in the fact that it is exemplified by some particular object. For instance, redness exists because—among other things—this apple is red. This is sometimes called the ‘Aristotelian view of universals’ and is held by some realists (see e.g. D. M. Armstrong 1978 and J. Lowe 2006).1 The recent interest in the notions of ontological dependence and metaphysical grounding has opened a new perspective for evaluating this view. I think this is a welcome development, for, like many others (Correia 2005, Bennett 2011, Koslicki 2013, Azzouni 2012, Cameron 2014), I believe that an adequate understanding of Aristotelian metaphysics requires these notions. In fact, the growing interest in such notions is usually associated with a renewal of interest in Aristotelian metaphysics (see paradigmatically Fine 1994 and Schaffer 2009). Curiously, some authors have recently argued that the Aristotelian view of universals, according to which universals depend for their existence on their exemplifiers, is incoherent from a grounding perspective. This is the case of Costa (2019) and Alvarado (2019 and 2020), whose arguments will be criticized in this paper. For the contemporary debate on the Aristotelian view, see the essays by Loux, Van Inwagen, Lowe and Galluzzo in Galluzzo and Loux 2015. 1 1 In section 2, I examine Costa’s argument, and in section 3, I investigate Alvarado’s argument. 2. Costa’s Argument against Aristotelian Universals In a recent paper, Costa (2019) argued that the Aristotelian conception of universals, when it is property spelled out in terms of grounding, is open to objection. His objection is based on a set of five assumptions: (i) The Aristotelian view. If a universal U exists, then U exists is grounded in Something exemplifies U. (ii) The relata first principle. R(x, y, ...) is grounded in x exists, y exists, ... (iii) The instances first principle. Instances ground existential quantifications: Something is F is grounded in F(a) (iv) The transitivity of grounding. If φ is grounded in ψ, and ψ is grounded in ω, then φ is grounded in ω. (v) The irreflexivity of grounding. It is not the case that φ is grounded in itself. While (i) expresses the core of the Aristotelian view of universals, (ii) to (v) express, according to Costa, ‘other common metaphysical principles about exemplification and grounding’. The argument runs as follows. Take a particular instance of (i), as (I will use square brackets for marking facts): (1) [redness exists] is grounded in [something exemplifies redness] Since the fact (2) [this apple exemplifies redness] does obtain, based on the instances first principle we get that 2 (3) [something exemplifies redness] is grounded in [this apple exemplifies redness] Finally, based on the relata first principle, we get (4) [this apple exemplifies redness] is grounded in [redness exists], from which we may derive by transitivity of grounding (twice to -1, -3 and -4) (5) [redness exists] is grounded in [redness exists], which contradicts the irreflexivity of grounding. Indeed, Costa is right: the fact that [redness exists] cannot be grounded in itself. Costa rejects some alternatives that Aristotelians could choose in trying to meet this criticism. I will spare the reader the details and focus directly on what is, in my view, the main problem of his argument, viz. the relata first principle. Costa considers this principle to be a ‘common metaphysical principle about exemplification and grounding’. If this principle were true, for any relation R, the fact that R holds among some terms x, y, … is grounded in the facts that x exists, that y exists, … In Costa’s words: ‘No x and y could ever be related in any way if they did not exist in the first place. And here the phrase “in the first place” must express a sort of ontological priority’. Costa discusses some issues concerning this principle. He recalls correctly that some metaphysicians (see Bennett 2011, Cameron 2014) have recognized that there are some relations, so-called ‘superinternal relations’, whereby the existence of one relatum is a full ground for the existence of the other relatum and of the relational fact. Unfortunately, Costa does not go far enough in his analysis and does not recognize another special kind of relation, which I call a ‘creating relation’. These are relations such that holding them (i.e. the relational facts themselves) grounds the existence of one relatum. For these relations the relata first principle fails. Wittgenstein said once that a ‘main cause of philosophical disease is the onesided diet: one nourishes one’s thinking with only one kind of example’ (PI § 593). I think the relata first principle is a very good example of this one-sided diet. Indeed, it 3 sounds at first glance very reasonable that, whenever a relation R holds between x and y, x and y must, first of all, exist in some way. Although the relata first principle is valid for a large number of (probably most) relations, ‘creating relations’ are a clear counter-example to this principle. Take just three examples: [Mary generated (gave birth to) Peter] (Mary is Peter’s mother), [John built the table], and [Wittgenstein wrote the Tractatus]. According to the principle subscribed to by Costa, Mary only stands in the generating relation to Peter because ‘in the first place’ Mary and Peter existed, John stands in the building relation to the table because ‘in the first place’ John and the table existed and, finally, Wittgenstein stands in the writing relation to the Tractatus because, ‘in the first place’, he and his first book existed. This is clearly false. The existence of Peter is grounded in the fact that his mother generated him, the existence of the table is grounded in the fact that John, the joiner, built it, and the existence of the Tractatus is grounded in the fact that Wittgenstein, ‘in the first place’, wrote it. In all these cases, the relation is not grounded in the relata. Rather, the relation, or the relational fact, grounds the existence of one relatum. This is certainly the kind of relation Aristotelians have in mind when they claim that universals exist only if—and ‘in virtue of’ the fact that—they are exemplified. Exemplification facts ground the existence of universals, and do not presuppose their existence ‘in the first place’.2 It is worth mentioning that Costa (footnote 2) correctly distinguishes the relata first principle from the principle that relations are existence entailing: if aRb, then both a and b exist. Both principles agree that, given a relational fact, all relata have to exist. But the first principle is stronger than the latter insofar as it also establishes an order of priority between the relation and its relata. In any case, creating relations are counterexamples to the first, but not to the latter principle, for creating relations are relations between existing relata: Peter, the table and the Tractatus do exist, even if they are grounded entities. To avoid misunderstandings, let me stress one point: A creation relation is not a superinternal relation. When R in aRb is superinternal, b and R are both grounded in a. When R in aRb is a creation relation, b is grounded in ‘its being in the R relation to a’. Neither the Tractatus nor the writing relation are grounded in Wittgenstein. Rather, the (existence of the) Tractatus is grounded in the fact that Wittgenstein wrote it. Similarly, as regards Aristotelianism, it is not the case that both the facts of exemplification and the universals included in such facts are grounded in objects. Universals alone are grounded in facts of exemplification. If a is contingently F, then neither does a ground F, nor does a ground the exemplification fact (that a is F). Instead, the fact that a is (contingently) F grounds the fact that F exists. Thanks to an anonymous referee for comments on this point. 2 4 Of course, one may try to reject the existence of creating relations and refuse to accept my examples. One may, for instance, defend a Platonism about book-types and claim that a book is a specific abstract (atemporal) sequence of propositions. So, Wittgenstein did not strictly bring the Tractatus into existence, but merely ‘discovered’ it. Now, this seems to me a quite radical and implausible form of Platonism. Further, a similar strategy for the table and Peter is completely extravagant, in particular in the case of generation. The mereological universalist may claim that the table is identical to the mereological sum of all particles and so the table existed before these particles were table-wise-arranged. So, she may insist that the table was not ‘created’ by the joiner. But the claim that Mary only stands in the generating relation to Peter because ‘in the first place’ Peter existed is highly extravagant and I cannot see anyone seriously defending it. One may reject my examples for considering them cases of causation and not of grounding.3 The relation between grounding and causation is quite complex and cannot be developed here. For some metaphysicians, ‘grounding is a way of causing’ (see Wilson 2018), for Bolzano causation always corresponds to true grounding claims (see Correia and Schnieder 2012: 9) However, according to the standard view, there are important differences between causation and grounding.4 Anyway, although some causation is certainly involved in my three examples (e.g. the joiner’s mind causes some movements of his hands that cause some deformation of the pieces of wood, etc.), they seem to be cases of grounding. Firstly, the relata of my examples are facts (which are typical relata of grounding links) and not concrete entities or events (as in causal connections). According to my second example, for instance, it is the fact (rather than the event) that Wittgenstein wrote the Tractatus that grounds (rather than causes) the fact (rather than the event) that this book exists. This is not to deny that there may be corresponding concrete events which may have causal connections (if this true, this case of causation corresponds to a grounding claim, as Bolzano suggested). Secondly, grounding is usually considered a kind of metaphysical explanation which emerges from, and is grounded on, the natures of the relata (see Fine 2012, Rosen 2010), although it is a controversial matter, what does ground a grounding link such as ‘A grounds B’: the nature of A, of B, or of both? In any case, in my examples, both 3 4 Thanks to an anonymous referee for making this point. For a detailed discussion of the differences, see Bernstein (2017). 5 options are plausible. Plausibly, the existence of the book lies in the nature of the fact that Wittgenstein wrote the Tractatus. More than a simply modal coincidence, this is a hyperintensional correlation: In any possible world in which Wittgenstein wrote the Tractatus, this book exists (under the assumption that books may exist at all), and, more important, it exists because it was written by Wittgenstein (or by someone else)5, and not the other way round. Further, it lies in the nature of the fact that this book exists (under the same assumption), that it was written by Wittgenstein (or by someone else). For, arguably, an unwritten book does not exist. Finally, while grounding is usually supposed to be a necessary connection between its relata (‘A grounds B’ entails ‘A necessitates B’),6 causation is indeterministic (‘A causes B’ does not entail ‘A necessitates B’, but rather ‘A makes it to some degree probable that B’).7 In my examples, the creation fact necessitates, rather than makes to some degree probable, the existential fact, even if the grounded entity existed only at the very instant of its creation: If Wittgenstein wrote the Tractatus, the book cannot fail to exist (otherwise, Wittgenstein could not really have written it), if John built the table, the table cannot fail to exist (otherwise, John could not really have built the table), etc. Perhaps one may still remain unconvinced by my three examples and claim, for instance sticking to mereological nihilism, that tables, organisms and books do not ‘really’ exist. One may argue that the existential facts of my examples and the corresponding grounding connections do not really obtain. In order to face this, I may appeal to the possibility of God creating a particle—a mereological atom—ex nihilo. Even a mereological nihilist may plausibly accept that this scenario is metaphysically coherent and that, in this example, this particle exists because it was created by God (and, perhaps additionally, because it has no parts). All these examples are supposed to support the plausibility of the notion of a creating relation, i.e., a relation in which one relatum is a ‘creator’ and the other the I do not consider the origin essentialism of books plausible, i.e. I believe that in any possible world in which someone writes this book (i.e. the same sequence of sentences), the Tractatus does exist. Anyway, my example does not depend on this controversial point. 6 For this default view, according to which grounding is a kind of necessary relation see Audi (2012b); Dasgupta (2014); deRosset (2010); Rosen (2010); Trogdon (2013). For an exception to this view, see Skiles (2014). It may be noticed that neither Costa nor Alvarado reject the view that grounding is a form of necessitation. 7 For this difference, see Bernstein (2017) section 2.1. See also Schaffer (2016): ‘(…) indeterministic grounding seems impossible. Grounding seems to imply supervenience: fix the grounds and one fixes the grounded’. 5 6 ‘creature’. We may wonder if there are even relations such that both relata are ‘creatures’, i.e., grounded in the relation. I cannot find any plausible example of such double-creating-relations, but it seems like wise advice not to reject this possibility without good reasons. Anyway, the argument of this paper does not depend on it. It is enough to recognize that some relations ‘create’ one relatum. Exemplification is, in the Aristotelian view, such a creating relation. Thus, the fact that this apple exemplifies redness is not grounded in the existence of redness. The apple ‘creates’ redness by exemplifying it. Thereby, -4 is false, and no inconsistency follows. 3. Alvarado’s Argument against Aristotelian Universals Alvarado (2019, 2020) diagnosed three inconsistencies in the Aristotelian view (the first inconsistency is presented in both his 2020 book and his 2019 article, the other two only in his 2019). In this section, I shall argue that all three are mistaken. The first inconsistency (2020:194-197) derives from the conjunction of the two following assumptions: (a) [redness exists] is grounded in [a instantiates redness]8 (b) [a instantiates redness] depends on [redness exists] According to (a), the instantiation of universals is grounding-prior to their existence, while according to (b) their existence is dependence-prior to their instantiation. There is a minor issue with this supposed incoherence: (a) is a claim about grounding, while (b) is a claim about dependence. Grounding and dependence are correlate notions, but it is far from obvious that one may expect, without further arguments, that both yield the same fundamentality profile. This is ‘far from obvious’, among other things, because they are relations with (at least: typically) different ranges of application: grounding applies only to facts, ontological dependence to any kinds of entities.9 Alvarado himself recognizes that ‘there may be cases in which there is While Costa (2019) used ‘exemplification’, Alvarado (2020) prefers the term ‘instantiation’ for the relation between the universal and the particular substance. I assume both are synonymous and follow each author in his terminology. 9 Although some metaphysicians (Shaffer (2009), Jago (2016)) claim that grounding is a relation which holds between any kinds of entities, including facts, objects, properties, etc., most of them—Rosen (2010), Fine (2012), Audi (2012a), (2012b), Raven (2012), Cameron (2016) among others—take facts 8 7 grounding-priority without there being dependence-priority or vice versa’ (2020: §4 and 197). But he explicitly denies that A may be grounding-prior to B, while B is dependence-prior to A—‘that is impossible’ (2020: 197). And this is exactly what happens with (a) and (b), according to him. This inconsistency has a similar source as Costa’s argument: the assumption that, since instantiation is a relation which depends on the existence of relata, these relata, in particular universal redness, must ‘in the first place’ exist. Now, there is a subtle but important difference between Costa and Alvarado. While Costa makes a claim about grounding (any exemplification is partly grounded in a universal), Alvarado makes a claim about ontological dependence (the instantiation of universal U depends upon the prior existence of U). But why does Alvarado assume (b)? In his (2019: 12) he simply says that ‘it is evident that the instantiation of a universal by a thin particular is essentially the instantiation of that universal by that particular. The fact of instantiation is ontologically dependent on that universal’. Since Alvarado (see 2020:10 and 2019: 5) rejects the simple modal existential account of dependence and assumes a constitutive essential account (‘x depends on y when y is included in the essence of x’), his reason for assuming (b) is that the universal is an essential constituent of the fact of its instantiation: ‘It is obvious that the instantiation of a universal is not such without the universal of which it is an instantiation’ (Alvarado 2020:196). Indeed, necessarily, if a instantiates redness, redness exists and is an essential part of the fact of instantiation. But the fact that redness is an essential constituent of the instantiation fact does not imply that this fact ontologically depends on the prior existence of redness—in particular not in the case instantiation is a creating relation. The creation fact [a creates b] essentially entails b, but this fact does not depend on the prior existence of b. Creation relations constitute a good reason for rejecting the constitutive essential account of dependence.10 Instantiation is a creating relation: the universal comes into existence by being instantiated. The second alleged inconsistency derives from the conjunction of the two following assumptions: (c) [a exists] is grounded in [a instantiates redness] (propositions or similar) as the only adequate relata of grounding links. For a recent discussion about the relation between grounding and dependence, see among others Schnieder (2017) and Rydéhn (2018). 10 For more reasons to reject the constitutive essential account of dependence, see Koslicki 2013: 55-7. 8 (d) [a instantiates redness] depends on [a exists] According to (c), facts of instantiation are more fundamental than the existence of particulars, while (d) states the opposite. In my view, the problem here lies in assumption (c). Let’s start by noticing that Alvarado rejects the modal existential definition of grounding and defends a constitutive-sufficient definition: ‘if x is constitutively sufficient for y, x grounds y’ (2019: 4). What ‘constitutively sufficient” exactly means is left unexplained. Alvarado considered (c) an assumption of Aristotelianism because, according to him, this theory requires that thin particulars instantiate at least one universal. If Socrates exists, he must instantiate a color. He must not be white, or red, but he must have a color. Now, since ‘instantiations are constitutively sufficient for the thin particulars’, facts of instantiation ground the existence of particulars.11 Contra Alvarado, (c) is not an assumption of Aristotelianism. Although the fact that a instantiates a universal is sufficient to the fact that a exists (plausibly because relations are existence entailing), the first fact does not ground the latter fact. Not every sufficiency is a kind of grounding, just like not every necessitation is a kind of grounding. The existence of the singleton Socrates is sufficient for—but does not ground—the existence of Socrates. From the Aristotelian point of view, the fact that Socrates is white may be constitutively sufficient for—but does not ground—the existence of Socrates, just like as fact that Wittgenstein wrote the Tractatus is sufficient for—but does not ground—the fact that Wittgenstein exists. Finally, the third supposed inconsistency derives from the conjunction of the two following assumptions: (e) [a exists] is partly grounded in [redness exists] (f) [redness exists] is partly grounded in [a exists] Alvarado (2019: 13) writes: ‘Aristotelianism requires that thin particulars instantiate at least one universal. This requirement can be understood as a ‘generic’ dependence of thin particulars on instantiations, but it is also a case in which instantiations are ‘constitutively sufficient’ for the thin particular –or particulars– involved in the fact.’ 11 9 The assumption (e) is given by the transitivity of the grounding relation applied to (c) and (b), and (f) by the transitivity of the fundamentality relation applied to (a) and (d). We may firstly note that Alvarado is making connections here by transitivity grounding and dependence relations, which is not obviously valid (if A is grounded in B, and B depends on C, can we conclude that A is partly grounded in C?). Anyway, the main problem with the third incoherence is, as we already argued, that (b) and (c) are both false. Therefore, (e) is false and no incoherence follows. For Aristotelians, no fact grounds (or even ‘helps ground’) the existence of a particular substance. 4. Conclusion In this paper, I have argued that Costa’s (2019) and Alvarado’s (2020) accusation of incoherence against the Aristotelian view of universals is ungrounded. In their criticisms, both authors employ a fairly welcome approach: they try to characterize the Aristotelian view in terms of grounding and ontological dependence. But both failed to recognize the fundamental principle of the priority of the particular substance over any other category in Aristotelianism. Any assumption which contradicts this principle must be considered non-Aristotelian. Costa failed because he did not recognize the existence of creating relations, i.e. relations which ground the existence of one of its relata. For Aristotelians, universals come into existence by being instantiated. Alvarado failed because he did not fully recognize that not any relation of necessitation or sufficiency is a case of grounding. 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