What follows is a paper by a reader, posted with his permission, together with some comments of mine. I will make my comments as time permits and not all in one session. Others are invited to add their comments in the ComBox.
On the Individuation of Tropes
Introduction
Trope theorists see their view as a happy middle ground between nominalism and universalism. It is not too hot or too cold; it’s just right. It does not scandalously posit entities that are said to be simultaneously in multiple places, like universalism. And, at least at first blush, it does not seem to be plagued by an appeal to a primitive notion of resemblance, like some prominent versions of nominalism.
BV: 'Universalism' is used in more than one way in ontology alone. So I would like to see a definition of this term right at the outset of the paper. I take it that universalism as here intended is the doctrine that there are universals. But what exactly are universals? Here too a definition would be helpful. And please note that a commitment to universals does not bring with it a commitment to entities that are wholly present in multiple places. For example, van Inwagen thinks of properties as universals but, eschewing as he does constituent ontology, does not view them as present in the things that have them.
One distinction that needs to be made is that between transcendent and immanent universals. A transcendent (immanent) universal is one that can (cannot) exist unexemplified. A second needed distinction is between universals that enter into the structure of the things that have them and those that don't. Call the first constituent universals; call the second nonconstituent universals. The two distinction-pairs cut perpendicular to each other yielding four combinatorially possible views according to which properties are: (a) transcendent non-constituent universals (Peter van Inwagen, e.g., if we leave aside haecceities); (b) immanent non-constituent universals (e.g., R. Grossmann); (c) immanent constituent universals (e.g., G. Bergmann, D. Armstrong); (d) transcendent constituent universals.
As for nominalism, we need to distinguish between extreme nominalism according to which there are no properties at all, and moderate nominalism according to which there are properties, but they are as particular as the things that have them. Trope theorists are moderate nominalists.
My use of the word ‘trope’ is meant to be consistent with its use by prominent trope theorists, such as D.C. Williams and Keith Campbell. Tropes are commonly called ‘abstract particulars’. Like universals, they are supposed to explain how two distinct entities can resemble each other. Tropes exactly resemble when they confer a property or properties that are qualitatively identical, but not numerically identical, on their bearers. Unlike universals, tropes are not multiply instantiated; they can only be present at one place at one time. A trope is wholly present in only the individual that instantiates it.
BV: You ought to begin by telling us what a trope is before telling us what they can be used to explain. And you should also point out that you are using 'abstract' in the old way, not the way most analytic philosophers today use the term, following Quine's lead. You speak of an individual instantiating a trope. But this makes no sense if ordinary concrete individuals, a tomato, say, are bundles of tropes. Instantiation is an asymmetrical tie; but bundled tropes are compresent, and compresence is symmetrical. Or perhaps you are thinking of tropes as inhering in a substratum along the lines of C. B. Martin. Whether you are operating with a bundle theory or a substratum theory needs to be clarified. If you are thinking of tropes as like the individual accidents of a substance, then I would speak of inherence rather than instantiation.
It is also quite unclear how tropes could explain how two distinct entities could resemble each other. Suppose you have two tomatoes of the same shade of red. Each has its own redness trope. How could the existence of two redness tropes explain the resemblance of the two tomatoes? That would be explained if one and the same universal were exemplified by both.
It is also unclear what it could mean for a trope to confer a property. Tropes are properties: they are properties construed as particulars.
My concern is with the individuation of tropes. How do we distinguish one trope from another? One way we might individuate tropes is in reference to the individuals that have them.1 We might also individuate them spatiotemporally.2 A third way to individuate tropes is to say that two tropes are distinct if and only if they are primitively quantitatively distinct.3 There may be other sensible ways to individuate tropes, but these ways are the most discussed. In what follows, I examine these three ways of individuating tropes and argue that they all suffer from problems that are variations of, or are closely related to, the problem of piling. If I am right, this does not refute trope theory, but I think it should make trope theorists blush. It would be evidence against the theory.
1. Piling
Piling, first characterized by Armstrong (1978), is captured in a question asked by Peter Simons: “What is to stop several tropes of the same kind, e.g. rednesses, from being compresent in one bundle?”4 Simons speaks of a bundle here because trope theorists typically say that objects are bundles of tropes—and by objects I mean normal, everyday things like tables and chairs. They are sometimes called concrete particulars. So chairs, for instance, are collectively constituted by bundles of compresent tropes. A paradigm case of piling is when there are two or more exactly resembling tropes occupying the exact same place. Piling of exactly resembling tropes also occurs when the overlap is non-exact. Whether the overlap is exact or not does not matter, because in either case, it is undesirable.
To see why it is undesirable, imagine a red rose. According to trope theorists, it has a unique redness trope. Why couldn’t it have two or more? There seems to be no reason. But if there is no reason, then we have an empty possibility of the rose, or any object, being made up of piles of redness tropes. The possibility is empty because most of these tropes seemingly contribute nothing. They are not needed to give the object a property, since there is another exactly similar trope already there in the exact same spot. This objection depends on the plausible Eleatic Principle according to which we should only posit entities that have a causal effect on the world.
Eleatic Principle: Entities that have no effect on the spatio-temporal world ought not be postulated.5
When we have a pile of tropes, most of the tropes in the pile do not bring about a causal effect. Since trope theory allows this empty possibility, it should be rejected.
Perhaps trope theorists need not fear all kinds of piling, however. Both Jonathan Schaffer and Douglas Ehring discuss two kinds of piles—stacks and pyramids. A stack of tropes is a pile of exactly resembling tropes whose multiplicity is hidden in the sense that the extra tropes are not doing any work. Consider a red rose. Suppose that the rose has five redness tropes overlapping, four of which make no causal difference. These redness tropes constitute a paradigm stack.
A pyramid of tropes is a pile of exactly resembling tropes whose multiplicity is discernible in the sense that all of the exactly resembling tropes are contributing to a property possessed by an object. Ehring uses an example with two point-sized particles, a and b, with exactly resembling massiveness tropes. b has only one of these tropes, while a has several.6 Thus, a is discernibly more massive than b. We say that a’s massiveness tropes constitute a pyramid.
Stacks have tropes that have no effect on their possessors, so a theory that allows for the possibility of stacks does so in violation of the Eleatic Principle.7 In pyramids, however, the exactly resembling tropes are making a discernible, causal difference. So, at least initially, it seems more embarrassing for a theory of individuation if it allows for the possibility of stacking, than if it allows for the possibility of pyramids.
However, there is something else undesirable about pyramids. Qualitatively identical objects could have a different number of mass tropes. Suppose a can of tennis balls contains three balls, each with a mass of exactly two ounces. The first ball might have a two-ounce trope, the second might have two one-ounce tropes, and the third might have four half-ounce tropes. The possibility of pyramiding adds complexity to explanation, and it seems that there is no need to add this complexity. The mass of tennis balls (or any object) could be explained by one mass trope if pyramiding is not allowed. An explanation of the mass of (say) two ounce tennis balls that ascribes to the tennis balls one mass trope is more simple and uniform than an explanation according to which there is no limit on the number of mass tropes that a tennis ball of a given total mass might have, and this number might not be the same as the number of mass tropes that other balls of the same total mass might have.
So, whether a theory of individuation allows for stacks or pyramids, I think there is a cost. Allowing stacks amounts to a violation of the Eleatic Principle, while allowing pyramids adds complexity, perhaps needlessly, and makes explanation less straightforward. With this in mind, I begin an investigation of the three ways of individuating tropes that I mentioned above with an eye to whether they can avoid the uncomely results of piling.
2. Object Individuation
The first way of individuating tropes fits nicely with the way that trope theorists often talk. It is normal for trope theorists to say that the shape of this box, or the color of my shirt, are tropes. When they talk this way, it sounds like they are using the tropes’ objects in order to individuate the tropes. So, a natural way to individuate tropes would be with reference to their objects.
Object Individuation (OI): For all tropes a and b such that a exactly resembles b, a=b iff a belongs to the same object as b does.8
I know of no trope theorists who defend OI, probably because it faces very difficult problems. For example, both Schaffer and Ehring argue that there is a problem of circularity.9 According to OI, tropes are individuated by referencing the objects to which the tropes belong. But, if we adopt the standard view that objects are bundles of tropes, then objects are nothing but a collection of mutually compresent tropes. So, the individuation of the object at least partially depends on the prior individuation of the tropes.10 This is circular though, since tropes are individuated by appealing to the objects to which they belong, and these objects are themselves individuated by the tropes. This is a serious problem for OI so long as it is coupled with a bundle theory of property bearers (and most trope theorists are bundle theorists).11
We have seen that OI has a circularity problem when coupled with bundle theory, but we have not yet assessed whether it avoids the problem of piling. Let’s consider the red rose again. Does OI eliminate the possibility of two (or more) exactly resembling redness tropes being compresent in the red rose (stacks)? Does OI eliminate the possibility of pyramids? Initially, it seems as though it handles both. Consider two exactly resembling redness tropes a and b. We can infer from OI that a≠b if and only if a belongs to an object that is distinct from the object b belongs to. This means that there could not be two or more exactly resembling tropes residing in the same object, for there is only one way for tropes to be distinct. They must belong to different objects.
However, OI allows for other kinds of closely related strangeness. Consider the rose once again. Exactly resembling tropes are identical if and only if they belong to the same object, and they are not identical if and only if they belong to distinct objects. Up to this point, I have been using ‘object’ to describe everyday things like tables and chairs, and that is consistent with how trope theorists use the word. Under this usage, a rose counts as an object. According to OI, the red rose of our example only needs one redness trope to bear the property of redness on the whole rose. This is because OI does not allow two exactly resembling tropes to reside in the same object.
But notice what happens when I pull a petal off of the red nose. Either I have split the one redness trope, or I have created a new trope! Either way, this is a surprising result. Intuitively, when I pulled the petal off of the rose I did not make anything red that was not already red. I can keep pulling off petals, resulting in a large increase in either trope creations or trope divisions. I call this the problem of splitting.
Here are four options that I think are available for trope theorists in response to the problem of splitting. They could say that I am creating tropes each time I pull off a petal. This is possible, but it goes counter with the intuition that I just mentioned.
A second option is to say that I divide the redness trope of the rose when I pull off the petal. So, after I pull off the petal, there is a partial trope making red what is left of the rose, and there is a partial trope making red my petal. I think this option is worse. Partial tropes cannot confer properties on objects. If they could, it would seem that being a whole trope is not relevant to the ability to confer properties on their objects, but this is one of the primary roles for which trope theorists posited tropes in the first place. Tropes would not do anything more than what their parts are fully capable of doing on their own. Furthermore, many trope theorists think that tropes are simple12, and if they are right, then tropes cannot divide into parts. But if tropes cannot divide into parts, there cannot be a part making what is left of the rose red and another part making the petal red unless trope theorists allowed the trope to be wholly located at multiple places simultaneously. At that point, the trope is not much different from a universal and universals are anathema to trope theorists.13 If trope theorists were to adopt this option, they would have to give up on the simplicity of tropes and say that partial tropes are tropes.
A third option is to deny that the rose had only one redness trope. Trope theorists could say that there is a redness trope for each non-overlapping minimal red part of the rose. This option has significant ramifications. First, it seems to force trope theorists to give up the normal view of objects—that they are tables and chairs and roses. To see why, consider a different object. The box below represents a 2’x2’ white expanse; it could be a piece of paper or sheet metal—whatever white expanse you like best. Call the expanse, ‘A.’ A is made white by the whiteness trope, T. Consider just the left half of A. I will call it ‘B.’ A seems like a perfectly normal object. Recall that there cannot be two or more exactly resembling tropes residing in the same object, if OI is true. I say that B is also a distinct object. It is the left half of A object. If there cannot be two or more exactly resembling tropes in the same object, then it looks like T has double duty. It must be the whiteness trope for both A and B. B cannot have its own distinct whiteness trope, since B is a part of A and B’s having its own whiteness trope would mean that A had two whiteness tropes.
A
B
So, T belongs to both A and B. I will show that T belonging to A and B leads to a contradiction. Remember that, according to OI, a=b if and only if a and b belong to the same object. Since T belongs to the same object, A, T=T. Now note the other half of OI: a≠b if and only if a belongs to an object that is distinct from the object to which b belongs. Since T belongs to distinct objects A and B, T≠T! This is a very grave problem for OI.
If you think that OI is the best account of individuation, and you think that the third response is the best response to the problem of splitting, then you will have to deny that A or B or both are objects. This is to reject the normal view of objects. Suppose you deny B the status of object-hood. In this case, T would not belong to B, so we do not get the result T≠T. That is good, but there needs to be justification for denying B the status of object-hood, other than a bad result followed from saying that B is an object, since it is intuitive to think that B is an object.
Perhaps a better reason for denying B the status of object-hood is that, in one sense, it does not seem like a distinct thing. After all, it is a part of A. In response, I say that we can point to the left half of A, we can talk about it, we could mark it off on the white expanse, we could even cut A in two and then we would see B quite clearly. All these facts indicate that B is a distinct object. So, I do not think that B should be denied the status of object-hood for this reason.
One could deny A the status of object-hood, but this seems even less intuitive than denying object-hood to B. Why would B be an object and A not? I can think of no good reason.14
The only option that remains is to deny the status of object-hood to both A and B, and this also is a rejection of the normal view of objects. Unlike the other two options, however, I think there might be good reasons for thinking that A and B are not objects. This is because denying object-hood to A and B is compatible with mereological nihilism—the view according to which composite entities do not exist.1516 Ted Sider (2013) offers arguments in favor of nihilism as do Cian Dorr and Gideon Rosen (2002). Taking up these arguments would take us afield, but they might give someone good reason for denying object-hood to A and B.
Even if arguments for nihilism give us some compelling reasons to accept the position, I do not think trope theorists should be happy with the situation. What I have shown is that the trope theorist who accepts OI and denies object-hood to A and B to avoid the paradox is committed to an answer to the Special Composition Question that most consider radical. I take it that trope theorists developed their theory with the intention that it be noncommittal regarding an answer to the Special Composition Question. If, in attempting to avoid the problem of splitting they commit themselves to an answer to the Special Composition Question, this would be undesirable.
Finally, there is a fourth option.17 Perhaps the rose has one redness trope all over it, and also each non-overlapping minimal red part has its own redness trope. The one redness trope that is “all over it” would make the whole rose red, but would not make each part red.
This option strikes me as incoherent. How could something make a whole rose red and fail to make a part red? If there is one trope making the whole rose red, then it must be making this petal and this petal red. So, I respond to the fourth option by insisting that an all-over trope would make each part red. And, if the all-over trope makes each part red, there is no reason to posit the existence of redness tropes for the non-overlapping minimal red parts.
Let’s take stock. We have been considering whether OI adequately handles the problem of piling. At first it seemed as though it did since, according to OI, there cannot be two or more exactly resembling tropes that belong to the same object. This seems to eliminate the possibility of both stacks and pyramids. I then argued that there is another closely related problem for OI—the problem of splitting. I considered four responses to the problem of splitting and found them unsatisfying. I think these four responses exhaust the options for defending OI. You can say that I create a new trope each time I pull a petal off of the rose, which is counterintuitive. You can say that the original redness trope divides, but then you would have to accept that tropes are not simple and that partial tropes can play the role of bearing properties to objects. You could say that the rose has many redness tropes, but this would be to deny that the rose is an object, since, according to OI, there cannot be two or more exactly resembling tropes in the same object. If a rose is an object, then there is a violation of OI, since it would contain many redness tropes, according to the third response. Thus, object-hood must be denied to things like roses. Lastly, you could say that the rose has one over-all redness trope and each non-overlapping minimal part also has its own redness trope. But, this view mistakenly asserts that the all-over redness trope does not make red each non-overlapping minimal red part. I suspect that most trope theorists would not like the results of OI.
3. Spatiotemporal Individuation
The aim now is to determine whether spatiotemporal individuation rules out the possibility of piling. Spatiotemporal individuation attempts to individuate tropes with reference to the location of the trope. It is slightly more popular than OI (Jonathan Schaffer supports it (2001)), but it is not widely accepted. Maurin formulates it in the following way:
Spatiotemporal Individuation (SI): For all tropes a and b such that a exactly resembles b, a=b iff a is at zero distance from b, and a≠b iff a is at non-zero distance from b.18
There is ambiguity in SI due to the fact that it says nothing about how a trope gives the property it instantiates to its object. Consider again the white expanse, A. According to SI, does A have one whiteness trope, or many? SI leaves both possibilities open. It could be that A has a whiteness trope, T, located at a specific spatiotemporal point within A. In this case, T would somehow project it’s whiteness to the rest of A, making it entirely white. A second possibility is that T might be spread out across the entirety of A. A third possibility is that A has whiteness tropes at every specific spatiotemporal point within A. So, each unique trope would make its specific location white, and no other location. A fourth option is that A has multiple whiteness tropes, and each trope has its own region within A that it makes white.19 SI allows for all four possibilities.
Of the three options, I think the third fares the best with respect to the problems we have been considering. The first two options allows for the problem of splitting again. For if there is only one trope that makes the entirety of A white and I cut A in two, I am either creating a new whiteness trope with my cutting act, or part of T makes the right half of A white, and another part of T makes the left half white. We have already discussed why each possibility is undesirable in section 2.
The fourth option seems the worst. If tropes can make whole regions white, as the fourth option suggests, then why can’t they make whole objects white? Or, if they cannot make whole objects white, then why think they can make a region white? I can think of no good answer to either question. To make matters worse, this option is also subject to the problem of splitting. We could split regions of A in half, in which case we would be either creating new tropes or splitting the old ones.
The third option only suffers from the mildly unintuitive result that A is made up of many whiteness tropes. If you are like me, you probably would not have suspected, prior to thinking about trope individuation, that there might be as many whiteness tropes in A as there are spatiotemporal points, but it does seem possible. Better still is the fact that the problem of splitting does not arise on this option. This is because spatiotemporal points cannot be divided. For the remainder of this section, I will assume that the best way to construe SI is as option three—that is, an object has as many exactly resembling tropes of a certain property (call it P) as it has spatiotemporal locations within it that have P. For example, a perfectly cut slab of marble is smooth because each spatiotemporal point on the surface of the marble possesses its own smoothness trope. The smoothness of each point on the surface explains the smoothness of the whole slab.
Regardless of how advocates of SI choose to resolve the ambiguity, I think Schaffer correctly points out that SI flattens piles.20 The only way for tropes to be distinct is to either not exactly resemble, or be at distant locations (Distance(x,y)>0). The piled tropes do not meet these conditions, since they exactly resemble and are at the same location, so SI effectively eliminates the phenomena of piling, which, initially at least, looks good for SI. In particular, it is good that SI eliminates the empty possibility of stacks. I noted before that when there is a stack of tropes, most of the tropes exactly resembling tropes make no empirical difference (unlike in pyramids).
SI also eliminates the possibility pyramids, and we might think this is good if my argument is correct that permissiveness about pyramiding brings complications in explanation. However, Ehring argues that a theory of individuation should allow pyramiding. He thinks that pyramiding explains the phenomenon of “purely intensive differences,” and that there is no acceptable alternative explanation for the phenomenon. I will now consider purely intensive differences, examining whether Ehring is right that a theory of individuation should allow pyramiding.
Here is the example of a purely intensive difference used by Ehring. Consider two partless point particles, a and b. a is twice as massive as b. Pyramiding offers the following explanation of how the two point particles could differ in mass as they do: a might have two 1-unit massiveness tropes, while b might have only one.21
Schaffer offers a non-pyramiding explanation of this case of purely intensive differences, which Ehring finds unsatisfying. Schaffer’s explanation is based on inexact resemblances, rather than piles. He says, “Here is my point-particle with mass x, and there is my point-particle with mass y (x≠y). The trope theorist should explain this in terms of each bundle of compresent tropes at their respective points having a particular massiveness that inexactly resembles the other.”22
Ehring’s response is to argue that SI must complicate its theory of predication to account for a new kind of phenomena that he describes, called “imperfect trope piling,” which SI does not exclude.23 Imperfect trope piles are piles of tropes that do not exactly resemble each other with respect to a certain kind of property, for instance, mass. Here is Ehring’s example: a 6g object made up of a 1g mass trope, a 2g mass trope, and a 3g mass trope.24 SI does not rule out the possibility of imperfect trope piles because SI is specifically about exactly resembling tropes, and 1g mass tropes, 2g mass tropes, and 3g mass tropes do not exactly resemble. He then argues that, because SI does not exclude the phenomena of imperfect trope piling, it ought not exclude the possibility of normal trope pyramiding.25
This is an odd response for Ehring to make to Schaffer, given that Schaffer was trying to show that SI is able to explain the phenomenon of purely intensive differences. Rather than address whether Schaffer’s response accomplishes this, Ehring changes the subject. He does, however, admit that, “If Schaffer is right, the advocate of spatio-temporal individuation gets the right result in excluding “empty” trope stacking, while still providing an alternative, non-pyramidal understanding of purely intensive differences, a phenomenon which the Primitivist fails to explain adequately.”26
It seems to me that Schaffer is right; however, the advocate of SI should respond to this new challenge of imperfect trope piling. It is arbitrary of SI to allow imperfect piling while disallowing plain piling. One idea that advocates of SI might take is to complicate SI in order to disallow imperfect piles so that bundles of tropes only have one unique trope with respect to a certain kind of property. There is a concern with this approach though. One must give an account of what a kind of property is.
In summary of this section, I argued that there was an ambiguity in SI. There are three ways to resolve this ambiguity. I suggested that the most promising resolution is to think of tropes as bearing their properties to specific spatiotemporal points. Next, I agreed with Schaffer that SI flattens both stacks and pyramids, and that SI is capable of handling cases of purely intensive differences, despite what Ehring says. However, SI theorists need to complicate there theory in order to handle cases of imperfect piling, and this will require an account of what a kind of property is.
4. Primitive Individuation
The most popular theory of trope individuation is Primitive Individuation.27
Primitive Individuation (PI): For all tropes a and b, a=b iff a=b, and a≠b iff a≠b.28
PI does not offer an analysis or a reduction of trope individuation.
PI clearly allows the possibility of piling, which again, should cause the trope theorist to blush. In the stacking cases, advocates of this view must give up the Eleatic Principle. It is not so obviously bad to allow pyramiding, as our discussion has already indicated. In cases of pyramiding, the Eleatic Principle is not violated. Moreover, pyramiding is a candidate explanation for cases of intensive differences (if there are any such cases).
The fact that PI allows stacking might cause some to wonder why many trope theorists prefer PI to SI. Most of them have reasons independent of the problem of piling. Ehring offers four such reasons. His first reason is that he thinks that stationary enduring tropes are possible, but that SI does not allow their possibility. Stationary enduring tropes, as the name implies, are tropes that remain in a single location and endure through time. Here is Ehring’s argument against SI: “If there could be such tropes then even if there is a temporal distance between tropes t and t’—but say, no spatial distance between them—that is not sufficient for the nonidentity of t and t’.”29 Assume t and t’ are tropes occupying the same spatial location, but at different times. Noting their temporal difference is not sufficient for establishing that they are different tropes, since it is possible that t and t’ could be one and the same trope, occupying that spatial location the whole time.
Ehring’s argument is based on a mistaken interpretation of SI. It is a useful mistake, however, because it is rooted in a lack of clarity in the formulation of SI. Here is an improved version of SI:
Spatiotemporal Individuation* (SI*): For all tropes a and b such that a exactly resembles b, a=b iff a is at zero distance from b at time t, and a≠b iff a is at a nonzero distance from b at time t.
When we understand SI as SI*, stationary enduring tropes do not serve as counterexamples. They are permitted in SI*. Ehring’s understandable mistake was to think that the distance in the definition was partly a temporal distance.30
Ehring makes a similar mistake in his second counterexample to SI. He says, “…there are moving enduring tropes, but that is not consistent with the Spatio-Temporal Principle according to which not sharing a location is sufficient for non-identity.”31 It is true that not sharing a location is sufficient for non-identity, but relative to a time t. Using SI*, we see that moving enduring tropes are possible.
Ehring’s third and fourth reasons are closely related. He believes that time travel is possible, and that SI does not permit time travel. He also believes that extended simple tropes are possible.32 These are tropes that are multiply located, much like a universal.
Ehring is wrong on both counts. 33 An extended simple trope cannot be any distance from itself. It is exactly where it is! This might come as a surprise to some people, even to Schaffer, who favors SI partly because he thinks it eliminates multiplied located entities. That Ehring thinks SI does not allow for extended simple tropes seems to be why he thinks SI does not allow for the possibility of time travel; he says, “A time-traveling enduring trope that meets itself would be wholly present at two locations at the same time, which is incompatible with the Spatio-Temporal Principle of trope individuation.”34 Ehring is right that a time-traveling trope would be wholly present at two locations at the same time. Even still, it will be at zero distance from itself.
5. Conclusion
There are three views concerning the necessary and sufficient conditions for tropes a and b being identical. Each of these views struggles either to satisfactorily resolve the problem of piling, or resolve closely related problems to piling. We just saw that that the most popular theory of trope individuation, PI, clearly allows piling, meaning that advocates of this view must give up the plausible Eleatic Principle. Furthermore, the most recent arguments for favoring PI over SI offered by Ehring are not very compelling. Two of them, the possibility of stationary enduring tropes and the possibility of moving enduring tropes, were criticisms rooted in a mistaken interpretation of SI. Ehring’s mistakes gave me the opportunity to provide a clearer formulation of SI. The other two reasons, the possibility of time travel and the possibility of multiply located tropes, are possibilities that are compatible with SI.
Concerning piling, SI faired the best. It denied the possibility of all piling. This seems especially good for stacking, but Ehring argues that this is the wrong result because of the possibility of purely intensive differences. It seems to me that Schaffer’s explanation of how SI can explain the phenomenon of intensive differences is right and that Ehring’s response fails to show otherwise. However, Ehring correctly points out that there is arbitrariness in SI’s allowance of imperfect trope piles and disallowance of pyramids. Advocates of SI should clear up this arbitrariness by disallowing imperfect trope piles. To do this adequately, they need to give an account of what a kind of property is. I think this is a challenging task. A second challenge to proponents of SI is to specify how a trope bears a property (or properties) to its object.
Regarding OI, it seems that no one currently holds this view for good reason. Although it appears equipped to handle the problem of piling, it does so by opening itself up to the problem of splitting, and there is no satisfactory way to resolve this problem.
So, each of the three ways to individuate tropes is lacking in some substantial way. As I suggest in the introduction, the problems I identify here do not amount to a refutation of trope theory. But, as these sorts of problems pile up (pun intended), it is easy to lose belief in tropes. Trope theorists owe us a better account of individuation.
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Ehring, Douglas (2011). Tropes: Properties, Objects, and Mental Causation. Oxford: Oxford University Press.
Maurin, Anna-Sofia. “Tropes.” The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), ed. by Edward N. Zalta. URL=<http://plato.stanford.edu/archives/spr2014/entries/ tropes/>.
Schaffer, Jonathan (2001). “The Individuation of Tropes.” Australasian Journal of Philosophy 79, No. 2: 247-257.
________ (2013). “Against Parthood.” In Oxford Studies in Metaphysics volume 8, ed. by Karen Bennett and Dean Zimmerman. Oxford: Oxford University Press.
Simons, Peter (1994). “Particulars in Particular Clothing: Three Trope Theories of Substance.” Philosophy and Phenomenological Research 54: 553-575.
van Inwagen, Peter (1990). Material Beings. Ithaca, NY: Cornell University Press.
1. Anna-Sofia Maurin, “Tropes”, The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/spr2014/entries/tropes/>.
2. Ibid.
3. Jonathan Schaffer, “The Individuation of Tropes,” Australasian Journal of Philosophy, 79 (June, 2001), 248.
4. Peter Simons, “Particulars in Particular Clothing: Three Tropes Theories of Substance,” Philosophy and Phenomenological Research 54 (September 1994), 558.
5. This formulation of the Eleatic Principle is based on the following David Armstrong statement: “It is then argued that we have no good reason to postulate anything which has no effect on the spatio-temporal world” (Universals and Scientific Realism, Vol. 2, p. 5). Here, I construe a causal effect in a broad enough way to ensure that it includes entities for abstract explanations, such as mathematical explanations. These sorts of entities can have a causal effect on the world.
6. Douglas Ehring, Tropes: Properties, Objects, and Mental Causation, Oxford University Press: Oxford (2011), 87.
7. One could object that stacks result in instances of causal overdetermination rather than violations of the Eleatic Principle. According to this objection, the extra tropes in a stack are indeed contributing an effect, but this effect is overdetermined. Allowing overdetermination is a possibility for trope theorists, but doing so allows for the possibility that two seemingly identical tennis balls have differing numbers of yellow tropes. This is counterintuitive and complicates (perhaps needlessly) our explanations for why objects resemble each other.
8. Maurin, “Tropes,” The Stanford Encyclopedia of Philosophy.
9. Schaffer’s argument occurs on p. 249 of (2001) and Ehring’s argument occurs on p. 77 of (2011).
10. Anna-Sofia Maurin. “Tropes.”
11. Maurin says, “Most trope theorists (but not all) believe that there is nothing but tropes.”
12. According to Maurin’s SEP entry, some critics of trope theory argue that to say that a trope is a kind of property is to make a trope into an entity with a complex structure. She says, “More or less all trope proponents disagree.”
13. A notable exception is Ehring, who thinks that that multiply located tropes, which are present at more than one location, are possible (2011, 78).
14. Earl Conee notes that real objects could be the minimal simple parts of apparently larger “objects.” That is true and Ted Sider holds a view like this (which I mention in the next paragraph), but B is not a minimal simple part of A.
15. Theodore Sider, “Against Parthood,” in Oxford Studies in Metaphysics volume 8, edited by Karen Bennett and Dean Zimmerman (Oxford: Oxford University Press, 2013), 237.
16. According to Sider, this should be softened a little. He thinks a more refined nihilism allows for sets. This refinement matters little to me here. I will continue to use ‘nihilism’ in the harder sense that I defined above.
17. Thanks to Earl Conee for pointing out this option.
18. Maurin, “Tropes,” The Stanford Encyclopedia of Philosophy.
19. It might be that each of these tropes make their region white by either projection or by being spread out across the entirety of their respective regions.
20. Schaffer, “The Individuations of Tropes,” 251.
21. Ehring, Tropes: Properties, Objects, and Mental Causation, 87-88.
22. Schaffer, “The Individuation of Tropes,” 254.
23. Ehring, Tropes: Properties, Objects, and Mental Causation, 89-90.
24. Ibid., 89.
25. Ibid., 90-91.
26. Ibid., 88.
27. Keith Campbell endorses Primitive individuation in (1990, p. 69), as does Ehring (2011, p. 76).
28. Maurin, “Tropes,” The Stanford Encyclopedia of Philosophy.
29. Ehring, Tropes: Properties, Objects, and Mental Causation, 77.
30. For more on why SI* is what Schaffer intended, see his comments on time travel (2001, 249).
31. Ibid., 77-78.
32. Ibid., 78.
33. Thanks, again, to Earl Conee for helping me to see these points.
34. Ibid.
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