There is unity and distinctiveness in the world. Regarding distinctiveness, notice that things—particulars—have characters. Things in the world are charactered objects. Socrates is wise, snub-nosed, and the teacher of Plato, for example. Regarding unity, consider that there are natural classes of things: red things, human things, sweet things, round things, and the like. Two key questions are these: First, do we need to postulate characters in addition to charactered objects, properties in addition to particulars? Second, how do we explain the similarities among charactered objects? Do we need to postulate shareable properties—universals—or just particular properties that exactly resemble? Questions about the existence and nature of properties are traditionally associated with the age-old debate over the problem of universals.
Willard V. O. Quine put the problem of universals as follows: “Now let us turn to the ontological problem of universals. . . . Speaking of attributes, he [McX] says: ‘There are red houses, red roses, red sunsets; this much is prephilosophical common sense in which we must all agree. These houses, roses, and sunsets, then, have something in common; and this which they have in common is all I mean by the attribute of redness.’”1 Quine’s imaginary interlocutor McX thinks there are two facts about the world that are just obvious: (1) there are attributes and (2) similar things share one and the same attribute. McX here is representing the position of the metaphysical realist, the believer in universals, where a universal is understood as a shareable property that can be possessed by distinct particulars, individual things, at once. Those who deny the existence of universals are called nominalists. Some nominalists—trope theorists—think there are properties but deny they are shareable: all properties are particularized properties. Other nominalists go further, denying the existence of properties themselves, believing in charactered objects but not in characteristics. In this chapter we shall explore the debate over the existence and nature of properties. We begin with the question of whether properties exist at all.
Do Properties Exist?
Those who think properties exist are called property realists. Those who deny that properties exist are called extreme nominalists. There are two kinds of extreme nominalism: ostrich nominalism, characterized by denial that resemblance facts need to be explained or grounded in any way, and reductive nominalism, which purports there is a general explanation for resemblance.2
The ostrich nominalist thinks that only charactered objects exist. The ostrich nominalists don’t deny that charactered objects are similar in various ways; rather, they deny that this poses any real problem. This is why the realist David Armstrong dubbed them “ostrich nominalists.”3 They stick their heads in the sand when it comes to the problem of explaining resemblance. True sentences of the form “a and b are both F” are analyzed as “a is F and b is F.” As long as these qualitative facts can be accounted for in nominalistically friendly ways, so too can the conjunction of these qualitative facts and the various similarities among charactered objects. So, for example, the fact that grass and gummy bears are green is explained in terms of the fact that there is green grass and there are green gummy bears. No ontological commitment to properties, let alone shareable properties, is needed. There are only charactered objects: green things, sweet things, round things, human things, tree things, dog things, and so on. Period. As Michael Devitt puts it, “We have nothing to say about what makes a [to be] F, it just is F; that is a basic and inexplicable fact about the universe.”4 Or as Quine responds to McX, “That the houses and roses and sunsets are all of them red may be taken as ultimate and irreducible.”5
In reply to the ostrich nominalist, some have argued that resemblance facts cannot be magically waved away by a mere sleight of hand.6 The idea is that “a and b are both F” is not explanatorily equivalent with “a is F and b is F” but rather with “a is F and b is F and the F’s of a and b resemble each other.” If so, then resemblance facts remain among the inventory of the world in need of an explanation or ontological ground. It is open to the ostrich to reply, as Quine does above, that resemblance facts, if they are genuine facts at all, are brute too. This is a fair move, but it comes with a cost. Typically it is thought that the more economical a theory, either in terms of its number of undefined predicates (ideological economy) or in terms of the number of entities the theory postulates (ontological economy), the better. For the ostrich, however, the amount of primitive or unexplained facts is quite high, and thus ostrich nominalism will be less ideologically parsimonious, and hence worse off, than other theories in terms of ideological economy (such as property realism) that don’t require as many primitive facts.
Suppose that it could be established that ostrich nominalism is explanatorily on par with its property realist competitors. Would this establish the rational preferability of ostrich nominalism, since it postulates fewer entities than theories that rely on properties? Perhaps, surprisingly, it could be argued that ostrich nominalism is ontologically less parsimonious than realism, and this too provides reason to think the view false.7 Philosophers distinguish between qualitative and quantitative economy. A theory’s qualitative economy is measured in terms of the number of kinds of fundamental things the theory posits, whereas a theory’s quantitative economy is measured in terms of the number of fundamental things posited. For the property realist, depending on the specifics, there are a handful of fundamental kinds of things. For example, according to the metaphysical realist (to be discussed below), the sentence “Socrates is wise” ontologically commits the speaker to the particular (Socrates), to the universal (wisdom), and to the exemplification relation (tying Socrates and wisdom together): three kinds of fundamental things (particulars, universals, and the exemplification relation). However, the ostrich nominalist is committed to as many fundamental kinds of things as there are charactered objects that are similar along various dimensions. Assuming there are more similarities in the world than three, it follows that ostrich nominalism is costlier in terms of qualitative economy than realism. Since, as it is argued, qualitative economy is more important than quantitative economy, ostrich nominalism is costlier ontologically than realist theories.
Reductive nominalists deny the existence of properties by offering a reductive analysis of sentences that seem to be about properties, identifying predicates (e.g., “is red”) with nominalistically friendly objects such as words, concepts, classes, or particulars. The main versions of reductive nominalism include predicate nominalism, concept nominalism, mereological nominalism, class nominalism, and resemblance nominalism.
Predicate nominalism and concept nominalism are similar enough to be considered together. According to predicate nominalism, “a is F” is further analyzed as “a falls under the predicate F”; for concept nominalism, “a is F” is further analyzed as “a falls under the concept F.” A notoriously difficult problem for the predicate and concept nominalist is that if there were no speakers or thinkers, there would be no charactered objects in the world. But a sunset, for example, undoubtedly would still be red even if there were no human speakers or thinkers to enjoy it. Even if there are human speakers and thinkers, however, it seems possible that there are charactered objects such as undiscovered scientific properties for which no predicates or concepts exist now (and perhaps never will exist).8 A further problem is that predicates and concepts seem to be types and not merely tokens. The predicate “is red” applies to both the ball and the fire truck. But then predicate (and concept) nominalism substitutes one kind of universal (a property) for another kind of universal (semantic or conceptual).9 If it is argued that there are only token predicates or concepts, then it must be held, implausibly, that if our language/thoughts were just a bit different, a red truck would not have been red or an electron would not have been negatively charged.10
Another extreme nominalism is mereological nominalism, according to which “a is F” is further analyzed as “a is a part of the aggregate F thing.” Something is red by virtue of being a part of the aggregate of red things. This aggregate of red things is a particular thing, but it is a rather odd particular thing: a scattered object located everywhere and only where there is something red. A problem with mereological nominalism is that it seems to get the explanatory relationship backward.11 It is natural to think that something is a part of an aggregate of red things because it is red, not that something is red by virtue of being a part of an aggregate of red things. Moreover, mereological nominalism requires the acceptance of a counterintuitive view called mereological universalism, the idea that any mereological aggregate of parts is an object, no matter how scattered and disparate the parts.12
Two related but better views are class nominalism, according to which “a is F” is analyzed as “a is a member of the class of F things,” and resemblance nominalism, according to which “a is F” is analyzed as “a is a member of a class of resembling F things.” For class nominalism, properties are classes of things. So, for example, the property of being red is just the class of red things, the property of being round is just the class of round things, and the property of being sweet is just the class of sweet things. For an apple to exemplify redness is just for the apple to be a member of the class of red things. Regarding resemblance facts, two red things resemble just in case they are both members of the same class, the class of red things (which is the property of being red).
Two serious problems for class nominalism are the Companionship Problem and the Naturalness Problem.13 The Companionship Problem is this: some pairs of properties are coextensive such that every time one property is possessed by a charactered object, so too is the other. For example, the class of things with a heart is coextensive with the class of things with a kidney, the class of featherless bipeds is coextensive with the class of things having a sense of humor, and the class of triangular things is coextensive with the class of trilateral things. What this means, according to class nominalism, is that the property of being a heart is identical with the property of being a kidney, and so on for each coextensive property. This is because properties are identified with classes, and classes are identical if they have the same members. But then class nominalism postulates an identity where there isn’t one: the property of being a heart is not the same as the property of being a kidney.
The class nominalist can respond to the Companionship Problem by construing properties as classes of actual and possible objects.14 It certainly seems possible that there are creatures with hearts but not kidneys. If so, then the property being a heart is not coextensive with the property being a kidney since there are possible worlds, and thus possible creatures, and classes of actual and possible objects, with hearts but not kidneys. This response is problematic, however, even if we set aside that contentious issue of taking possible worlds and possible creatures as equally real with each other and with the actual world, for there are coextensive properties that are necessarily coextensive and thus range over all possible worlds (including the actual world) such as the properties being triangular and being trilateral.
The Naturalness Problem gains traction by noting that class nominalism is an abundant theory of properties. Since properties are just classes of objects, then for any unique class there is a unique property. So consider the class of objects constituted by my left eye, the White House, Alpha Centauri, and my copy of Plato’s Republic. Call this class Jumble and the corresponding property jumble. Next, consider the class of humans and the corresponding property being human. Since according to class nominalism no class is metaphysically more fundamental than any other class, it follows that there is no explanation for why the class of humans is pretheoretically natural whereas the class Jumble is nonnatural. The problem of explaining why reality seems to be easily categorized in terms of natural classes of charactered objects is called the Naturalness Problem.
Resemblance nominalism presents a solution to the Naturalness Problem by offering a way to distinguish between natural and nonnatural classes. Resemblance nominalism privileges natural classes (such as the class of humans) in terms of the notion of resemblance. Resemblance is metaphysically fundamental: it does not need to be explained; it does the explaining. The character of objects is grounded in the metaphysically fundamental resemblance relation between objects in the resemblance class. The similarity between objects is grounded in the fact that they are members of the same resemblance class. As Gonzalo Rodriguez-Pereyra explains it, red things do not resemble one another because they are red; rather, red things are red because they resemble one another; something is red because it resembles other red things.15
Resemblance nominalism is not without problems, however. Some problems that plague class nominalism, such as the Companionship Problem, plague resemblance nominalism too. The same proffered solution of appealing to both actual and possible object classes helps only with properties that are contingently coextensive and requires a commitment to a highly controversial theory of possible worlds. Yet there are other problems unique to resemblance nominalism that appear devastating. One such problem is called the Imperfect Community Problem.16 Consider a class of three objects, called Mishmash, of the following kinds: a blue round thing, a metal round thing, and a blue metal thing. Since each of these objects resembles every other to a certain degree (all sharing either color or shape or material), Mishmash is a resemblance class. Yet Mishmash does not have any significant degree of naturalness since the only candidate property that all and only the members of Mishmash share is a “cooked” property, the property mishmash (or alternatively, the nonnatural disjunctive property being the same color or shape or material). So, there are resemblance classes that can’t serve as natural properties, and the Naturalness Problem surfaces again. The most plausible solution to this problem is to abandon resemblance nominalism in favor of trope nominalism and to admit that there are, after all, properties (even if they are not shareable).
Are Properties Shareable?
According to trope nominalism, properties are unshareable tropes. A red ball, for example, is red by virtue of a red trope and round by virtue of a round trope. Thickly charactered objects have multiple tropes, then; each individual trope grounds one dimension of character within a fully characterized object. Similarity among red things or sweet things or round things is grounded in the various degrees of resemblance relations that obtain between the classes of red tropes, sweet tropes, and round tropes, respectively. Since resemblance classes are constituted by tropes—particularized properties—instead of thickly charactered objects, trope nominalism avoids the worries raised by the Companionship and Naturalness Problems. Coextensive tropes belong to different resemblance classes, unproblematically referring to different properties, and the color, shape, and material tropes from Jumble form resemblance classes that do pick out natural properties.
Additionally, trope nominalism is thought to be superior to metaphysical realism because tropes are thought to be perfectly respectable objects, whereas universals are not. Tropes, for example, are wholly located where and only where the objects that have them are, can stand in causal relations, and are the objects of perception. Universals, however, misbehave—either being multiply located at nonoverlapping places at once (according to immanent realism) or being multiply instantiated without being located at all (according to Platonic realism). What is hopefully obvious by now is that the fundamental divide between trope theories and realist theories of properties has to do with the issue of shareability. According to the trope theorist, properties are not shareable, whereas according to the metaphysical realist, some properties are shareable.17 A shareable property is a universal: a multiply instantiable property that can be had by distinct particulars at once.
Unfortunately for trope nominalism, there is an ambiguity in how tropes are understood that undermines its viability.18 The issue has to do with how tropes ground the character of the thickly charactered objects that have them. Tropes, according to the philosopher Robert Garcia, come in two varieties. Modular tropes are self-exemplifying tropes; modifier tropes are non-self-exemplifying tropes.19 Thus, according to modular trope theory, a red ball is red by virtue of its red trope and round by virtue of its round trope, and the tropes are themselves red and round, respectively. According to modifier trope theory, a red ball is red by virtue of its red trope and round by virtue of its round trope, and the tropes themselves are neither red nor round, respectively. Modifier tropes, like realist universals, confer character on objects without themselves being the character they confer.
While each version of trope theory has advantages over the other, Garcia importantly points out that they are both unstable. Modular trope theory threatens to collapse into ostrich nominalism, and modifier trope theory threatens to collapse into metaphysical realism.20 Either way, the viability of trope theory is called into question, or so the argument goes.
Modular tropes are singly charactered properties. Thus, according to modular trope theory, a red trope is red and only red. However, some thin particulars plausibly just don’t stay thin. Red things, it seems, must also be shaped things, and shaped things must be extended things.21 Thus it seems that our red modular trope is not singly charactered after all. It is multiply charactered. It is red, shaped, and extended. The modular theorist must either deny very plausible “Thickening Principles”22 or allow for multiply charactered tropes that ground the character of fully characterized objects. If the modular theorist goes for the second option (allowing for multiply charactered tropes), then the view threatens to collapse into ostrich nominalism. The reason why, as Garcia notes, is that both the modular theorist and the ostrich nominalist now agree that no analysis of multiply charactered objects is necessary.23 The character of multiply charactered objects is a primitive fact. It is in this sense that modular trope theory is said to be unstable.
Regarding modifier trope theory, we may ask, What guarantees the unshareability of modifier tropes? Recall that modifier tropes are non-self-exemplifying; they have no intrinsic character of their own beyond purely formal characteristics such as being self-identical, being a particular, being a trope, and the like. A typical answer offered by trope theorists is that the distinctness of a trope is grounded by its location.24 In other words, tropes are individuated by their location, being wholly located wherever the object that has them is located. A trope is a respectable, perfectly behaving particular had by only one thickly charactered object and individuated by being wholly located at the same place as the thickly charactered object of which it is a part. The problem is that being located is incompatible with a plausible Thickening Principle such that “spatially located objects have a definite size and shape.”25 Again, the trope theorist, on modifier trope theory, is faced with a dilemma, needing either to give up an extremely plausible thickening principle or to admit that location does not individuate tropes (and thus does not guarantee unshareability).
Going for the second option has its own costs. If it is maintained that being unshareable is part of the formal character of modifier tropes, modifier trope theory threatens to collapse into realism for at least two reasons. First, tropes are no longer respectable. Since modifier tropes lack an intrinsic nature—round tropes are not themselves round, for example—it seems that they lack shape, size, mass, and so on. But then modifier tropes are not, after all, the immediate objects of sense perception or the sorts of entities that play a direct causal role. Worse, as Garcia argues, it is difficult to see how modifier tropes can be located in space and time.26 After all, they lack a definite size and shape. Thus it seems that modifier tropes are nonspatiotemporal, and for this reason they are no longer respectable. Second, modifier tropes ground the character of a located object without being wholly located where that object is located.27 Modifier tropes seem to behave more and more like universals (at least according to Platonic realism), and in this sense modifier trope theory threatens to collapse into realism.
In the end, however, even if these worries about misbehaving can be set aside, in stipulating primitively distinct modifier tropes, modifier trope theory is quantitatively less parsimonious than metaphysical realism.28 Where realism postulates a distinct universal, redness, had by the class of red things, modifier trope nominalism postulates a distinct property redness1–rednessn for each red thing, and so on for every distinct characteristic had by thickly charactered objects. Moreover, with respect to resemblance facts, trope nominalism (of either variety) is explanatorily inferior to realism. Realism explains why the F’s of a and b resemble (a shared universal), whereas nominalism must settle for primitive resemblances among classes of tropes. For at least these reasons, many philosophers are attracted to realism, the view that there are universals.
Are Universals Transcendent?
The main divide among versions of metaphysical realism is over the nature of universals: Are universals spatiotemporal? As already noted, the immanent realist thinks universals are wholly located at distinct places at once.29 Universals are concrete shareable properties located in space and time. The Platonic realist, however, thinks universals are multiply instantiated without being located at a place.30 According to the Platonic realist, universals are abstract objects that either (1) are nonspatially “in” concrete particulars as metaphysical parts (according to the constituent ontologist) or (2) are possessed by concrete particulars via a sui generis exemplification relation without being metaphysical parts of the objects that have them (according to the relational ontologist).31
The debate over immanent and Platonic versions of realism depends on what one thinks regarding what Reinhardt Grossmann calls the “axiom of localization.” The axiom of localization is the principle such that “no entity whatsoever can exist at different places at once or at interrupted time intervals.”32 The immanent realist rejects the axiom of localization whereas the Platonic realist accepts it. The Platonic realist argues that if the axiom of localization is rejected, then absurdities follow. The immanent realist, in response, argues that the conjunction of the axiom of localization with realism leads to the abandonment of naturalism, and it is better to reject the axiom of localization than to abandon naturalism. In other words, immanent realism is consistent with naturalism, and Platonic realism is not; if one wants to be a naturalist and a realist, then the only viable option is to endorse immanent realism.
Consider two yellow balls, b1 held in my right hand and b2 held in my left.33 According to realism, each individual ball exemplifies the shared universal yellowness or being yellow. On immanent realism, yellowness is wholly located where b1 is located (in my right hand) and where b2 is located (in my left hand). But it is absurd for one and the same thing to be located at two distinct places at once, or so it seems. It gets worse, however. As I move my hands toward each other and then away, yellowness moves both toward itself and then away from itself. This picture, argues the Platonic realist, is absurd and implausible and provides reasons in favor of Platonic realism.
On the Platonic realist picture, the yellowness exemplified by each ball is not spatially located where the ball is: it is either nonspatially “in” the ball as a metaphysical part or nonspatially tied to the ball relationally via exemplification. Either way, the absurdities of rejecting the axiom of localization are avoided. In reply, the immanent realist retorts that ordinary objects, in the hands of Platonic realists, become queer or spooky.34 How is it, they wonder, that the ordinary objects of everyday experience, firmly located in space and time, have properties that are nonspatial? Either way, something must be given up, says the immanent realist: either the axiom of localization or commonsense notions about how ordinary concrete objects have properties.
By maintaining a commitment to naturalism, the immanent realist thinks the gains outweigh any cost associated with rejecting the axiom of localization. The Platonic realist thinks, alternatively, that the costs in rejecting the axiom of localization are too high and the charge of queerness is not particularly troublesome. This is especially so if one is not wed to naturalism in general, or physicalism in particular, since it seems that mental properties (thoughts, beliefs, desires) can be nonspatially in the minds that have them, and thus the concept of being nonspatially “in” something is not entirely implausible.
Conclusion
In this chapter we’ve considered three questions that provided structure to our philosophical investigation of the characteristics of charactered objects: Do properties exist? Are properties shareable? Are universals transcendent? It is easy to wonder after reading a chapter like this why it all matters. What is the “real world” pay-off? We sympathize. We also think the debate over the existence and nature of universals is of utmost importance, as are many debates in philosophy, even if not initially obvious. To tip our hands a bit, we think universals do important work and that some version of realism is not only rationally preferable in its own right but usefully employed in other areas of philosophy (e.g., appeal to universals in the philosophy of language can help secure objective meaning) and theology (e.g., in helping us understand how the incarnate Christ can share a nature with humans). Undoubtedly the debate over the existence and nature of universals will continue.35 It is, in many ways, the central issue in the age-old quarrel between the gods and giants over the nature of reality.
1. Willard V. O. Quine, “On What There Is,” in From a Logical Point of View (Cambridge, MA: Harvard University Press, 1953), 9–10.
2. Robert C. Koons and Timothy H. Pickavance, Metaphysics: The Fundamentals (Malden, MA: Wiley Blackwell, 2015), 85–86.
3. David Armstrong, Universals and Scientific Realism, vol. 1, Nominalism and Realism (Cambridge: Cambridge University Press, 1978), 16; and Armstrong, “Against ‘Ostrich’ Nominalism: A Reply to Michael Devitt,” Pacific Philosophical Quarterly 61 (1980): 440–49.
4. Michael Devitt, “‘Ostrich Nominalism’ or ‘Mirage Realism’?,” Pacific Philosophical Quarterly 61 (1980): 436.
5. Quine, “On What There Is,” 10.
6. See, e.g., Paul M. Gould, “The Problem of Universals, Realism, and God,” Metaphysica 13, no. 2 (2012): 183–94.
7. The argument summarized in this paragraph is from Bryan Pickel and Nicholas Mantegani, “A Quinean Critique of Ostrich Nominalism,” Philosophers’ Imprint 12, no. 6 (2012): 1–21.
8. If God exists, this objection can be averted because there is always a divine mind that thinks and speaks. While this is an option for theists, many extreme nominalists are motivated by a commitment to naturalism and would not be able to avail themselves of this move. For a nice defense of theistic conceptualism, see Greg Welty, “Theistic Conceptual Realism,” in Beyond the Control of God? Six Views on the Problem of God and Abstract Objects, ed. Paul M. Gould (New York: Bloomsbury, 2014), chap. 3. For more on extreme nominalism and naturalism, see J. P. Moreland, “Naturalism and the Ontological Status of Properties,” in Naturalism: A Critical Analysis, ed. William Lane Craig and J. P. Moreland (New York: Routledge, 2000), chap. 4.
9. D. M. Armstrong, Universals: An Opinionated Introduction (Boulder, CO: Westview, 1989), 10–11.
10. Robert K. Garcia, “Platonism and the Haunted Universe,” in Loving God with Your Mind: Essays in Honor of J. P. Moreland, ed. Paul M. Gould and Richard Brian Davis (Chicago: Moody, 2014), 39.
11. Francesco Berto and Mateo Plebani, Ontology and Metaontology: A Contemporary Guide (New York: Bloomsbury, 2015), 224.
12. Berto and Plebani, Ontology and Metaontology, 224.
13. The Companionship Problem was coined by Nelson Goodman: see The Structure of Appearance (Cambridge, MA: Harvard University Press, 1951), 160–61. The Naturalness Problem is developed in David Manley, “Properties and Resemblance Classes,” Nous 36, no. 1 (2002): 75–96.
14. This is what David Lewis does in On the Plurality of Worlds (Oxford: Blackwell, 1986), 50–69.
15. Gonzalo Rodriguez-Pereyra, “Nominalism in Metaphysics,” in The Stanford Encyclopedia of Philosophy, ed. Edward N. Zalta, last modified April 1, 2015, §4.1, http://plato.stanford.edu/entries/nominalism-metaphysics.
16. Raised and developed by Goodman, Structure of Appearance, 162–64.
17. The metaphysical realist need not think that all properties are shareable, however. Some properties, such as the property being identical with Socrates, are only instantiated by one substance if at all.
18. See Robert K. Garcia, “Two Ways to Particularize a Property,” Journal of the American Philosophical Association 1, no. 4 (2015): 635–52.
19. Garcia, “Two Ways to Particularize a Property,” 637.
20. Garcia, “Two Ways to Particularize a Property,” 645–49.
21. See Koons and Pickavance, Metaphysics, 99.
22. Koons and Pickavance, Metaphysics, 99. They borrow the term from Robert Garcia.
23. Garcia, “Two Ways to Particularize a Property,” 649.
24. Koons and Pickavance, Metaphysics, 107.
25. Koons and Pickavance, Metaphysics, 108.
26. Garcia, “Two Ways to Particularize a Property,” 646.
27. Garcia, “Two Ways to Particularize a Property,” 646.
28. Koons and Pickavance, Metaphysics, 108.
29. A prominent defender of immanent realism is David Armstrong; see, e.g., Armstrong, Universals.
30. A prominent defender of Platonic realism is J. P. Moreland; see, e.g., Moreland, Universals (Montreal: McGill-Queen’s University Press, 2001).
31. For a nice canvassing of the issues and options for realist versions of constituent and relational ontologies, see Koons and Pickavance, Metaphysics, 104–25, as well as the discussion in chap. 9 below.
32. Reinhardt Grossmann, The Existence of the World: An Introduction to Ontology (New York: Routledge, 1992), 13.
33. This example is from Garcia, “Platonism and the Haunted Universe,” 46.
34. For more on the queerness worry, see Paul M. Gould and Stan Wallace, “On What There Is: Theism, Platonism, and Explanation,” in Gould and Davis, Loving God with Your Mind, 26–27.
35. The debate over the problem of universals becomes even more complicated when God is added to the picture. For an introduction to the issue of God and the problem of universals, see Paul M. Gould, ed., Beyond the Control of God? Six Views on the Problem of God and Abstract Objects (New York: Bloomsbury, 2014); Gould, “The Problem of Universals, Realism, and God”; and Brian Leftow, “God and the Problem of Universals,” Oxford Studies in Metaphysics, ed. Dean Zimmerman (Oxford: Clarendon, 2006), 2:325–56.