A plea for concrete universals.
PALABRAS CLAVE: creacion, repetibilidad, obras musicales, obras literarias, metafisica
SUMMARY: This paper is concerned with the metaphysics of created repeatable objects, such as musical works and literary fictions. In section 2 we lay out what we take to be intuitive and plausible desiderata for any theory of created repeatable objects. In sections 3 and 4 we proceed with an extended disjunctive syllogism. Created repeatable objects are either concrete universals, concrete particulars, abstract universals, or abstract particulars. We show how accounts that take them to be either one of the latter three fail egregiously. Therefore, we must take them to be concrete universals. In section 5 we offer a brief account of the metaphysical nature of concrete universals and then show how concrete universals can account for the desiderata while avoiding the objections presented against alternative theories.
KEY WORDS: creation, repeatability, musical works, literary fictions, metaphysics
Why concrete universals? When thinking about things in general, a pair of metaphysical distinctions comes immediately to mind: concrete versus abstract and particular versus universal. Each notion may be difficult to analyze, but the categories are intuitive enough to work with. For example, abstract objects are typically understood to be non-spatiotemporal entities that are, thus, causally isolated and necessarily existing. (1) On the other hand, concrete objects are contingent entities and enter into causal relations. Universals can have instances, whereas particulars cannot. Unlike universals, particulars exist in a specific location and at a specific time (or set of locations and set of times) without repetition.
Putting these two sets of distinctions together, we get the following space of possible kinds of objects: (i) concrete universals, (ii) concrete particulars, (iii) abstract universals, and (iv) abstract particulars. Examples of some of these are obvious enough. Nominalists opt for concrete particulars in their account of properties, whereas Platonic realists opt for abstract universals. Abstract object theorists such as Parsons (1980) take abstract particulars seriously and provide sophisticated theories about them, whereas some might hold that there are only concrete particulars and everything else supervenes on them. But among this space of views, concrete universals are not taken seriously. (2) We think they should be.
By taking a closer look at the existence of created repeatable objects such as musical works, we argue that a satisfactory account of what kind of objects they are must treat them as concrete universals. In section 2 we lay out what we take to be intuitive and plausible desiderata for any theory of created repeatable objects. In sections 3 and 4 proceed with an extended disjunctive syllogism. Created repeatable objects are either concrete universals, concrete particulars, abstract universals, or abstract particulars. We show how accounts that take them to be either one of the latter three fail egregiously. Therefore, we must take them to be concrete universals. This establishes our plea for the acceptance of concrete universals. In section 5 we show how concrete universals can account for the desiderata while avoiding the objections presented against alternative theories. Finally, in section 6 we offer a brief account of the metaphysical nature of concrete universals. As such, the acceptance of concrete universals has substantial benefits. By accounting for created repeatable objects concrete universals do not only explain the nature of musical works and literary fictions, they also account for photographs, car models, computer models, drugs, scientific creations, and all sorts of created reproducible objects that are part of our ordinary life. (3)
A brief note on terminology is in order. We use "objects" to refer to either particulars or universals. When we specifically want to talk about either particulars or universals, we will use the appropriate qualification or names to signal our intention. "Properties" refers to any object that can have instances. Since we need a term to talk about properties that does not presuppose an ontological thesis about the nature of properties, this term is meant to leave open whether properties are reducible to particulars or are irreducible ontological entities. On the other hand, "universals" refers to irreducible properties, if there are any at all. When we say that concrete universals are objects we do not mean to say they are particular entities. We intend our uses of these terms to broadly cohere with general usage in the philosophical literature, while recognizing that this is a difficult task to achieve.
This terminological clarification should illuminate our claim that created repeatable objects, such as musical works, are concrete universals. In what follows, we provide an extended argument intended to support the acceptance of concrete universals as part of our ontology, leaving it for a later occasion to discuss the deeper metaphysical nature of this kind of object.
2. Created Repeatable Objects
What is it that Beethoven created when he composed his Sonata No. 29? We believe that whatever Beethoven created should play the following roles. First, it should be capable of being created voluntarily. What Beethoven created came into existence in 1818; it did not exist prior to this time. It follows from this that Beethoven is responsible for creating it. Put another way, Sonata No. 29 depends for its existence on Beethoven. Put the other way around, if the Sonata exists independently, in the relevant sense, of Beethoven, then he cannot be said to have created it. One way in which there can be independent existence is that of preexistence. For example, had Beethoven's Sonata No. 29 preexisted Beethoven, it would be false to say that he created it. Thus, dependence turns out to be a necessary condition for creation. (4) Second, it is repeatable. Beethoven's Sonata No. 29 can be performed and written down. Whether written down or performed on different occasions, it is one and the same object, namely, Beethoven's Sonata No. 29 that is written or performed in each of these cases. Thus, there are two important ideas here. First, to say that Beethoven's Sonata is repeatable is to say that it is the very same object that is repeated every time--in other words, it is not to say that there can be several numerically different objects that are similar to it--. Second, the musical work does not depend on any one medium for its existence. It can be repeated in multiple modalities. We take these roles to be plausible desiderata for any metaphysical account of the kind of object Beethoven created when he composed his Sonata No. 29. Thus, we have two substantial desiderata for the account we are looking for:
Creation: the object must not have existed prior to its creation, thus, its existence depends upon its creator's voluntary decision to create it.
Repeatability: the very same object may be instantiated on several occasions and in different modalities.
A satisfactory account must explain what kind of objects are repeatable objects, such as musical and literary works, so that they can be "brought into existence by means of the creative activity of an author or a composer" (Deutsch 1991, p. 209).
Now, it is difficult to get clear on what these desiderata demand without prejudging the case on behalf of some or other account. This is so because distinct accounts of created repeatable objects will have different ways of understanding the desiderata. Abstract object theories, whether about particulars or about universals, tend to have problems with our first desiderata. Thus, as we will see, they end up offering their own understanding of what it is for an object to be capable of being voluntarily created. Theories that appeal to concrete particulars also have trouble, but this time with the second desiderata. Hence, they will end up offering their own view of what it is for a particular to be repeated. In what follows, we will consider how these theories interpret creation and repeatability, and argue that the resulting theories are unacceptable.
3. Musical Works and Stories as Abstract Objects
Like musical works, literary works of fiction (fictions) are also taken to place the same desiderata upon a proper account of them: they are both creatable and repeatable. Several philosophers have proposed what are known as "abstract object" theories of musical works and fictions (most prominently Parsons (1980) and Deutsch (1991)). In this section we will focus on Deutsch's (1991) account, as we consider it to be the best available abstract object account, and because most (if not all) other abstract object theories conceive of the relevant abstract object as a Platonic, eternal, causally isolated object. In this section we show why theories of this sort fail. Although these accounts primarily deal with abstract particulars, we go on to show that any abstract object account, whether about particulars or universals, fails because of general features of abstractness.
3.1. The Account
On Deutsch's view, it is "clearly and literally true" that "stories, fictitious characters, and musical works are created". He also claims "stories, fictitious characters, and musical works are, in the final analysis, purely abstract objects." All the "abstract object" theorist must do to solve her problems is to deny that "creating a thing entails bringing it into being or causing it to exist" (Deutsch 1991, p. 210). The heart of Deutsch's account consists, thus, of understanding "creation" in a way that does not presuppose that a created object must not exist prior to its creation. His argument has two stages: on the one hand, he offers an account of creation in terms of stipulation; on the other hand he motivates this account by showing how well the resulting notion contrasts from that of discovery. We believe this account fails for several reasons. First, it comes at an extraordinary ontological cost: the acceptance of a plenitude of abstract nonexistent objects. Second, even if we accept such costs, it requires a mistaken notion of creation and, third, it does not account for the multi-modal repeatability of musical works. To see why this is the case let us consider Deutsch's account with more detail.
Deutsch 1991 begins by endorsing a basic version of Parsons' (1980) principles of object abstraction and object identity: (5)
Object abstraction: for any given set of properties there is an object having such properties (p. 210). (6)
Object identity: objects are the same if and only if they have the same properties (ibid.).
It follows from these principles that there is a plenitude of such objects. For example, no matter what set of musical properties you pick, there is an object that has such properties. All such objects are part of what there is, even though they do not all exist. On this view, reality is made up of everything that there is and there are two major kinds of things: the existent and the non-existent ones. It also follows from these principles that there is no point in time at which these non-existent objects were not part of what there is. These objects are and always were, so to speak, already there. Furthermore, given that they are nonexistents, these objects are also not spatiotemporally located and, thus, are causally isolated from any existent object and, hence, from any author or composer.
Abstract objects (AO) have, then, the following properties:
Eternal: there is no point in time at which an AO was not part of what there is.
Isolated: all AOs are causally isolated. (7)
It is one such object that, according to the "abstract object" theorist, Beethoven referred to when he composed his Sonata No. 29.
3.2. Developing the Abstract Object Theory
3.2.1. Creation Becomes Linguistic
This naturally prompts the question: how can any AO be created? Deutsch replies with an account of "creation" in terms of "stipulation" as follows:
[W]hen an author creates a character and the story in which the character figures, the author makes various stipulations that serve to describe the character and tell the story. [...] These are stipulations in the sense that if an author indicates (in the course of creating the story) that a character has a certain property, then it is true (in that story) that it has that property. Since it is up to--and open to--an author to stipulate that a character have whatever properties he or she may wish it to have, we credit the author with having created something, (p. 218)
This way of putting things suggests that there is something "creation-like" in this act of stipulation. Consider for example the case of Sherlock Holmes. Let us grant that the object Conan Doyle created is an AO. Suppose, then, that A[O.sub.1] is the relevant abstract object that Conan Doyle ends up describing with his Sherlock Holmes stories. Deutsch's account of creation in terms of stipulation would suggest, then, that it is up to the author to determine which properties A[O.sub.1] has and, second, that it is in virtue of the act of stipulation that, say, "Sherlock Holmes is an opium addict" is true of A[O.sub.1], But we know that these suggestions are false given that, like any other AO, A[O.sub.1] is eternal and isolated. So it cannot be that A[O.sub.1] has any property in virtue of anything that is up to the author. Thus, as we will see, this is not the right way to interpret Deutsch. The proposal is indeed somewhat tricky. It appears to be, at first blush, about musical works and fictions, yet it turns out to be about descriptions of them.
Consider the first suggestion: i.e., it is up to the author that A[O.sub.1] has such and such properties. Now, it follows from the principle of object abstraction that no matter which properties those are, there will be an AO having such properties. And it follows from the principle of object identity that such an AO just is A[O.sub.1]. So it is in virtue of there being a plenitude of AOs that A[O.sub.1] has such and such properties. If we add to this that A[O.sub.1] is eternal, it turns out that it is in no sense up to the author that A[O.sub.1] has such and such properties. That object has those properties eternally.
The same goes if you put the idea in terms of true sentences, as the second suggestion presents the case: i.e., that it is in virtue of Conan Doyle's act of stipulation that "Sherlock Holmes is an opium addict" is true of A[O.sub.1]. Of course, it is true that if Conan Doyle stipulates Sherlock Holmes is an F, then it is true that Sherlock Holmes is an F. But this conditional, namely, "if Conan Doyle stipulates Sherlock Holmes is an F, then it is true that Sherlock Holmes is an F," is vacuously true. (8) Whichever AO Conan Doyle ends up identifying it will be eternal and isolated. This, together with the principle of object identity entails that the relevant AO will necessarily have the properties it does. So the consequent "it is true that Sherlock Holmes is an F" will be necessarily true, no matter which AO "Sherlock Holmes" is used to refer to. So it is not in virtue of Conan Doyle's act of stipulation that "Sherlock Holmes is an opium addict" is true of A[O.sub.1]. Deutsch himself seems to grant this point when he says that the stipulations in question "are invariably correct, whatever their content, [...] in virtue of there being a plenitude of characters" (p. 219).
Thus, it cannot be that, on Deutsch's view what Conan Doyle created was A[O.sub.1], or any AO for that matter. So, what is it that, on this view, gets to be created?
What was really up to Conan Doyle was the act of selecting A[O.sub.1]. In Deutsch's words, it is up to the author to determine "which properties entered into the description, and open to [her] to choose any such properties whatsoever" (p. 219). Alternatively, what is up to an author or composer is the fact that she used this or that description in her stipulation. So, for example, it was up to Conan Doyle to stipulate that Sherlock Holmes is an opium addict, since he could have also stipulated
that Sherlock Holmes is a morphine addict. Of course, it was not up to Conan Doyle to stipulate that A[O.sub.1] is a morphine addict. For, as we know, there is nothing Conan Doyle could have done to change any single property of A[O.sub.1]. Yet he could have determined whether he wanted to refer to A[O.sub.1] or to a different AO by determining whether to use this or that description in his Sherlock Holmes stories. Thus, on this view, what is created is a way of identifying AOs.
At this point one wonders where the creative element lies. Deutsch claims the following about the descriptive act of stipulation: firstly, "which (fictitious) character is being described is fixed attributively by the description itself and not by referential devices that function independently of the content of the description; and secondly, whatever the content of the description, there is an object that satisfies it" (p. 220). It should be, then, that any one or both of these two features accounts for the creative part of the act of stipulation.
We have already talked about the second feature (which is true in virtue of there being a plenitude of objects) and why it fails to explain why Conan Doyle's act of writing down the Sherlock Holmes stories counts as an act of creation. So we are left with the first feature. Could it be that we grant Conan Doyle the merit of having created Sherlock Holmes in virtue of the fact that to determine which object is the referent of "Sherlock Holmes" one must understand the descriptions used by Conan Doyle? Suppose we grant Deutsch the claim that there is no description-independent means of referring to the same non-existent object that Conan Doyle stipulates to be the referent of "Sherlock Holmes". Is that enough to claim that Conan Doyle created Sherlock Holmes? It seems more like what Conan Doyle created were the descriptive means to identify Sherlock Holmes.
Stipulating the means by which one is to refer to an object -even if they are the only possible means--is not in any sense the same as creating (or even stipulating) that object. So if we grant that creation is the act of stipulating a way of referring to an object we are interested in, yet not an act of creating that object then, strictly speaking, Conan Doyle did not create Sherlock Holmes. Similarly, Beethoven did not create his Sonata No. 29--what we listen to when we listen to Beethoven's Sonata No. 29--but a means to refer to it by using musical notation. (9)
Abstract object theories of musical works have a prima facie problem with creation. If the musical work is an abstract, non-spatiotemporal and so causally isolated object, it is hard to see how it can be created. If we accept Deutsch's proposal according to which creation is an act of stipulating the means to refer to abstract objects, then it is no longer hard to see how there is creation involved in the way we humans relate to musical works. On this view, we do have an account of creation that makes it possible to achieve. It is just not the kind of thing that we need. As you may recall, we wanted it to be that it is "clearly and literally true" that "stories, fictitious characters, and musical works are created" (Deutsch 1991, p. 210). But, as a result we get that it is not stories, fictitious characters and musical works that are created, but descriptive means to refer to them.
So we get to see two of the outstanding features of the abstract object theory of the creation of repeatable objects: first, it requires us to accept a wildly unrestricted Meinongian ontology of nonexistent objects; second, it involves a change of topic when it comes to creation. When Beethoven "composed" his Sonata No. 29 there was something he created, it was not the musical work, but something close: the means to refer to it with musical notation. We think these two features are enough to reject the abstract object theory. It is not giving us what we want (i.e., an account of the creation of musical works) but something else (i.e., an account of the creation of means to refer to them) and it comes at a very high ontological cost. Frege (1892) famously argues against linguistic accounts of informativeness for reducing scientific discoveries to linguistic discoveries of coreference. In a similar vein, we argue against abstract object theories of creation for reducing artistic creation to the linguistic creation of descriptions in some or other language.
In what follows we will offer some independent reasons to think that the account of creation in terms of stipulation is itself mistaken.
3.2.2. Stipulation Is Not Creation
Stipulation overgenerates creation. Following Deutsch's account, there will simply be much more creation than we can plausibly accept. On this view, an author's fundamental creative power "derives from an author's immunity from error" (1991, p. 220). For once we assume that there is a plenitude of objects, no matter which descriptions we stipulate as true of an object there will be an object that responds to them. We think there are several stipulations that satisfy this requirement, even those that we would not take to be creations.
Consider the case of Sherlock Pounds. Johnny is a fan of the Sherlock Holmes stories. He has read them all several times. So he is bored and decides to write down his own version of the Sherlock Pounds stories. He takes pretty much everything from Conan Doyle's work but adds a little twist: Sherlock Pounds weighs ten more pounds than Sherlock Holmes. Given the plenitude of objects, it follows both that Johnny is immune to error, and that there is an object that has such properties. Given the principle of object identity, it follows that Sherlock Pounds and Sherlock Holmes are two different objects. Strictly speaking, Johnny has stipulated a new descriptive means to identify a different object. It follows, on the "stipulation" account of creation, that Johnny has created something new. This, however, seems like the wrong result. Johnny has merely managed to copy Conan Doyle. By merely stipulating that Sherlock Pounds is to have ten more pounds than Sherlock Holmes he has not managed to create anything.
Other more ordinary cases may suffice to illustrate our point. As a matter of fact there are several retellings of Superman's story where Superman has several different properties. One of them, perhaps the most well known one, tells us what happens when Clark Kent is raised in the U.S. But there is an alternative version, Red Son (Millar 2003), which works under the premise that Clark Kent is raised in the Soviet Union. There are important differences between both stories. For example, in Red Son Superman fights for the common good and the common worker, whereas the American Superman fights for truth, justice and the American way. Yet, in spite of all these differences, competent speakers take both versions to be about one and the same object, namely, Superman. Furthermore, it is well known that Jerry Siegel created Superman in 1932. Yet, if we were to accept the claim that creation is the act of stipulating the means to refer to an abstract object, it seems there should be several different homonymous fictional characters named "Superman", each one with its own creator. That seems like an unwelcome consequence.
There is also a problem with one of Deutsch's motivating assumptions. Creation is sometimes understood in contrast with discovery. This contrast is useful insofar as nothing that is created can be discovered prior to its creation. Deutsch 1991 motivates his account of creation by underscoring the fact that his view offers an adequate contrast against discovery. Since abstract objects are causally isolated and discovery requires causal connection, the former cannot be discovered, but can be "created".
However, we think the contrast between creation and discovery can be misleading. It is true that nothing that is created can be discovered prior to its creation, but it does not follow that what cannot be discovered is ipso facto something created at some point in time. The dichotomy is not exclusive. There may very well be things that cannot be either created or discovered. Consider the still unsolved Goldbach's conjecture (i.e., that every even integer greater than 2 can be expressed as the sum of two primes). Suppose both that it is true and that it cannot be proved to be true. Then it is something that cannot be discovered. Yet, it is still not something that can he created. Thus, the sole fact that Deutsch's account offers a notion that contrasts with discovery does not guarantee that such notion is in fact that of creation. Indeed, the overgeneration problem strongly suggests that it is not.
So far we have shown why Deutsch's account of creation in terms of stipulation, together with his acceptance of the principle of object abstraction and his proposal that the created objects be nonexistent abstract objects, fails to give a satisfactory account of the creation of repeatable objects, such as Conan Doyle's Sherlock Holmes stories or Beethoven's Sonata No. 29. We presented two reasons to support this claim. On the one hand, the theory involves a very costly topic change: what gets created is no longer the musical work but the descriptive means to refer to it, yet we must accept a plenitude of nonexistent abstract objects. On the other hand, if we accept that creation is the act of stipulating a descriptive means to refer to an abstract object, creation overgenerates. (10)
3.3. Abstract Objects Fail
Overall, "abstract object" theories according to which created objects, such as Beethoven's Sonata No. 29, are abstract non-existent objects, do not offer satisfactory accounts. A satisfactory account must be able to satisfy the following intuitive desiderata:
Creation: the object must not have existed prior to its creation, thus, its existence depends upon its creator's voluntary decision to create it.
Repeatability: the object may be instantiated on several occasions and in different modalities.
We have argued that abstract object theories that take the relevant objects to be platonic in the sense of Deutsch 1991 fail to satisfy the first desideratum. On their view, the only salient objects that satisfy creation--e.g., Deutsch's stipulation--are not the objects we talk about when we consider, say, Beethoven's Sonata No. 29. We have presented two reasons to reject such theories based on their account of this notion.
Some reflection on the second desideratum gives us a third reason to reject such theories: even if we somehow accept the high ontological cost, the overgeneration and the topic change, the resulting theory is still not an account of musical works for the latter are taken to be not only created but also repeatable. Beethoven's Sonata No. 29 can be performed and listened to. Whatever set of musical notation Beethoven stipulated in his act of creation, it is not something that can be repeated thusly, for musical notation is not something that can be performed or listened to. Of course, Deutsch can claim that what can be repeated is (perhaps an instance of) the abstract object that is referred to, but that is not what was created. Briefly put, on this view what is creatable (a descriptive means) is not repeatable and what is repeatable is not creatable. It is, thus, important to keep in mind that what we are looking for is an account of created and repeatable objects. So, we think there are enough reasons to exclude abstract, non-existent objects as candidates for "created repeatable objects."
Although we primarily focused on abstract object theories where the relevant object was treated as a particular, many of our arguments still apply if we consider abstract object theories where the relevant object is treated as a universal. It might seem that such an account of Beethoven's Sonata No. 29 would fare better than a particularist account, since repeatability can easily be accounted for if the object posited is one that can have instances, such as a universal. We heartily agree. But as long as the universal is treated as an abstract object, it will still suffer from being eternal and isolated. Given these features of abstract objects, whether particulars or universals, creation will remain unaccounted for. For these reasons and those presented throughout this section, we argue that abstract object theories of repeatable objects should be rejected.
4. Against Concrete Particulars
4.1. Setting out the Particularist View in General
Particularist views begin with the assumption that what Beethoven created when he created his Sonata No. 29 is something wholly concrete and particular. As such, it shares in all the intuitive features of other concrete particulars: it exists across a set of locations in space and time and for some interval of time. The explanatory burden on particularist views is to meet the desiderata laid out in section 2 by only appealing to concrete objects.
We argue that this cannot be done. We will set out different ways one could provide a particularist view and argue that in each case the desiderata in question cannot be satisfactorily met. Whatever it is that Beethoven created, it is clear to us that it cannot be a wholly concrete particular.
4.2. Against Particularist Views (11)
4.2.1. Against Error Theoretic Particularist Views
According to the error theoretic particularist view, the object created by Beethoven when he created the Sonata No. 29 is a concrete particular. As a concrete object, it shares in all the virtues of other concrete objects, most notably for us are the following: it exists across some set of locations and during some interval of time and it can enter into causal relations with other concrete objects.
These features allow the error theoretic particularist view to account for one of the desiderata at issue: creation. The error theoretic view does not posit anything special about Beethoven's creative act. His act of creation is similar to other, perhaps more familiar acts of creation such as making a cake and building a house. In these cases, it is clear that the object created does not exist before the act of creation. Once created, the thing created came into existence as a result of the act of creation and thereby depends, in a causally relevant sense of "depends", for its existence on the person doing the creating. Since Beethoven's creation of the Sonata No. 29 is just an act of creation of some concrete object, it will also be the case that the Sonata No. 29 did not exist before Beethoven's creative act and, as a result, that its existence is dependent on Beethoven.
The specifically error theoretic part of this view is the denial of repeatability. Paradigm cases of concrete objects are not repeatable. Take for example the Golden Gate Bridge. If we set out to recreate it, we might be able to come up with a stunning replica. If the technology is advanced enough, we could make our replica match the original bridge in San Francisco in all its nuances. But despite all this, our new bridge would not be the Golden Gate Bridge. It would be a replica of it, perhaps a perfect one, but it would not be the Golden Gate Bridge. As a concrete particular, it exists across some set of locations and for some interval of time, but it cannot be repeated. (12)
The error theoretic view is committed to a similar response regarding Beethoven's Sonata No. 29. As Beethoven's creation, it came into existence at some interval of time. But it cannot be repeated on other occasions. Scores of Beethoven's Sonata No. 29, performances of it, and recordings of it are not, in general, repetitions of the thing Beethoven created. When we set out to play Beethoven's Sonata No. 29, we are replicating it, creating a representation of it, but we are not playing the Sonata No. 29 itself--at least not anymore than we are creating the Golden Gate Bridge when we set out to make another bridge just like it--. Since Beethoven's Sonata No. 29 cannot be repeated in this sense, it is clear that it cannot exist across different modalities (scores, performances, recordings).
Without providing any additional resources, the error theoretic view is committed to the incorrectness of judgments of performances, recordings, and scores of Beethoven's Sonata No. 29. When a suitably trained musician performs something that seems like it is Beethoven's Sonata No. 29, it is not actually Beethoven's Sonata but only a copy or representation of it. If we were to say that she played Beethoven's Sonata No. 29 beautifully, we would be speaking falsely, just as we would be speaking falsely if we said we created Michelangelo's David when we only made a copy of it. This commitment to incorrectness provides the error part of the error theoretic particularist view.
This view is unacceptable on at least two counts. First, any error theory should be considered our last resort. The cost to theory building and testing by positing widespread error among intuitive judgments is too high. Second, this view reduces the philosophical difference between musical works such as Beethoven's Sonata No. 29 and typically concrete particular objects such as statues. Take, for example, Michelangelo's David. There does seem to be a significant difference between the sonata and the statue, as evidenced by our intuitive judgments about these kinds of objects as well as our practices surrounding them. The difference seems to consist in the fact that one has instances or repetitions, whereas the other does not. Given the resources of the error theoretic particularist view, it will not be possible to capture this difference. And apart from claiming that our judgments about this purported difference are incorrect, it does not seem to us that erasing it is acceptable. If we can have a theory that accounts for the intuitive judgments above mentioned, then that theory is preferable.
4.2.2. Against Revisionary Particularist Views
The problem with the error theoretic view is its commitment to error theory. A plausible alternative is to retain the commitment to Beethoven's Sonata No. 29 being a concrete particular, but provide a strategy of reinterpretation of our statements about performances, scores, and recordings of what Beethoven created. On this revisionary view, error is eschewed in favor of correct judgments and truthful statements, just not the ones we unreflectively thought we were making.
Let's begin with musical recordings, since they are most amenable to this strategy. Let our target expression be "recording of Beethoven's Sonata No. 29." In similar "of' contexts, such as "drawing of a horse" and "painting of Michelangelo's David," there is no presumption that the drawing reproduces an actual horse or the painting reproduces the statue itself. The drawings and the paintings produce representations of the objects they are about, not the objects themselves. Similarly, according to this view, when we say we have heard a recording of Beethoven's Sonata No. 29, we need not be interpreted as saying that the recording produced the sonata itself, but rather a representation of it.
This strategy likens recordings to paintings and drawings. However, it seems that recordings of musical pieces are more like taking photographs. The difference between paintings and photographs is important. Unlike the former, the latter are intentional representations. They represent by being directed towards something distinct from themselves: that which they represent. Drawings need not represent in this way. A drawing of a unicorn, for example is a representation of it, but there is nothing that it is directed towards. In the case of photographs, it is not possible to take a picture of some object if that object does not exist at the time the photograph was taken. The photograph itself does not reproduce the object. In this sense it is an intentional representation of the object. If recordings of Beethoven's Sonata No. 29 are more like photographs, then the recording will be a representation of the sonata that needed to exist in order to be recorded in the first place. When we say we are listening to a recording of Beethoven's Sonata No. 29, on this alternative interpretation, we are indeed listening to the thing Beethoven created with the proviso that the thing we are listening to is a representation that required the sonata to be played in order to be recorded. For these reasons, we are led to think that the recording of the sonata is an intentional representation, just like a photograph of a given object.
But the analogy with photographs fails when we recall that our target object is supposed to be repeatable. The object represented by a photograph, its intentional content, is not repeatable. So it must be that when we talk about recordings we are really talking about something more similar to paintings and drawings (non-intentional representations) than photographs. But we already had good reasons to think this analogy fails as well: the sonata itself is not its recording but what this latter thing represents. Given that our discourse about recordings of music is either interpreted as discourse about drawings or discourse about photographs, it is an open question what the correct interpretation is regarding discourse about recordings. And moving from one interpretation to the other in order to meet the desiderata seems ad hoc. So far, the revisionary strategy does not seem to be working.
The inadequacy of the theory becomes clearer when we consider performances. When a trained musician plays Beethoven's Sonata No. 29, we typically use expressions such as "played Beethoven's Sonata No. 29" or "performed Beethoven's Sonata No. 29." When we use expressions such as these in a sentence, it seems as if we are talking directly about the sonata itself and the fact that it was performed. The revisionary strategy would either claim: that when we talk about performances we are actually talking about performances of representations of the musical work in question or that musical works are nothing other than the recordings. If it makes the first claim, it would appear to he changing topics, for discourse about performing a musical work and discourse about performing representations of a musical work are about different topics altogether. If, on the other hand, it makes the second claim, it would leave the question open as to what a recording of Beethoven's Sonata is a recording of, which is the question it should answer to begin with.
The revisionary strategy attempts to deflate repeatability by suggesting that the seeming features of repeatability and existence across diverse mediums are merely representations of the object created by Beethoven when he created his Sonata No. 29. This is a step above denying these desiderata, given their intuitive plausibility, but it is not plausible given the general failures of the revisionary strategy. Furthermore, as a consequence of this deflationary tactic, it will still be the case that Beethoven's Sonata No. 29 will be treated as the same kind of object as Michelangelo's David. As argued in the previous section, this seems like a significant philosophical cost. The distinction between Beethoven's Sonata No. 29 and Michelangelo's David ought to be preserved in one's account of the kind of objects created by Beethoven.
4.2.3. Against Nominalist Particularist Views
The next particularist view about repeatable objects we will consider takes Beethoven's Sonata No. 29 (and repeatable objects in general) to be something like a property (i.e., an object suitable to have instances). This property of being Beethoven's Sonata No. 29 is instantiated by concrete particulars such as performances (concrete particular events) or scores (concrete particular objects). However, since we are considering views that take repeatable objects to be concrete particulars (not universals), it is necessary to give a nominalist account of properties.
Nominalism is a view about the kinds of things there are in general. According to Rodriguez-Pereyra (2014), there are two broad versions of nominalism: that which rejects the existence of universals and that which rejects the existence of abstract objects. This gives us three different kinds of nominalist objects: abstract particular, concrete particulars, and concrete universals. We have already seen why abstract objects will not do, so we will not consider the nominalism that claims the relevant objects are abstract particulars (e.g., Quine 1964; 1981). And since our own view is that musical works are concrete universals, we will also not consider the nominalism that does not reject universals (e.g., Armstrong 1978; 1997). Thus, the only sensible alternative left is the nominalism that claims there are concrete particulars and everything is reducible to them.
That said, the goal of the nominalist is to offer an account of the entities that are allegedly universal, properties and relations, by appealing only to particular objects. The most plausible way to be a nominalist about properties and relations requires objective resemblance. According to this view it is not that different particulars resemble each other because they share a property but, rather, that they share a property simply because they resemble each other. For example, it is not that two white spheres resemble each other because they are white, but rather they are white because they resemble each other. Something is white because it resembles white things. (13)
To account for similarity among distinct objects, resemblance nominalism theory must appeal to resemblance conditions between the relevant particulars things. On Rodriguez-Pereyra's (2002) view these conditions come in terms of degrees of resemblance: for two white spheres to be white they must resemble each other, there must be a degree of resemblance d such that no two white things resemble each other to a degree less than d. (14) Similarly, two Sonata No. 29 performances can be similar with respect to the sonata played if they resemble each other no less than that determined by those things that happen to be Beethoven's Sonata No. 29.
Since nominalism is meant to provide an account of properties and relations that reduces them to particulars in a way that avoids reifying resemblance, it is important to treat the degree of resemblance among particulars to be an intrinsic element of the particular objects. The resemblance explaining why two white spheres are white does not require three objects: the two spheres and the resemblance between them. The only entities involved are those resembling each other to a certain degree, the two white spheres. As should be clear from this explanation, the crucial component of any nominalist theory of properties is the resemblance relation. (15)
Before showing that this view cannot be sustained, it is important to see its potential benefits. As part of the general family of views that takes Beethoven's Sonata No. 29 to he a concrete object, the nominalist is committed to Beethoven's creation being a concrete object. This should allow the nominalist to account for creation without much trouble. Although the work itself is treated as a property, on the nominalist account properties are just concrete particulars and things share in a property insofar as they resemble each other. So Beethoven's creation of Sonata No. 29 is of that sonata because it resembles later instances of that sonata and it is creatable because, like any other concrete particular, the relevant object is not causally isolated from its creator.
Similarly, we should expect that accounting for the multi-modal repeatability should be no problem since this view is designed to treat Beethoven's Sonata No. 29 as a repeatable object, specifically as an object that has instances (where this is to be understood nominalistically). This sonata can occur across different modes as long as each instance resembles other instances. On this view, accounting for multi-modal repeatability with regards to Beethoven's Sonata No. 29 should be no more difficult than accounting for the repeatability of whiteness and the fact that vastly different objects across different modes can be white.
We contend that the nominalist strategy cannot account for all the desiderata. For the only criterion the nominalist has for determining whether something counts as a repetition (or instance) of Beethoven's Sonata No. 29 is that of resemblance. This criterion of repeatability may be adequate for some cases, for example, that of natural kinds. Perhaps resemblance is a good criterion for determining whether some particular object counts as an instance of water. But the criterion for repeatability varies from case to case, especially if we are considering objects that can be repeated (or have instances) in multiple modalities, unlike some (or most?) natural kinds. For the latter kind of objects, resemblance may very well be a poor guide to repeatability or instancehood.
To see that the nominalist cannot account for Beethoven's Sonata's repeatability, we need to consider a hypothetical case due to Walton (1988a). Suppose that on Mars scores of music specify very different sorts of properties from those that our scores specify. Whereas our scores specify in detail what pitches a performer is to play and for what durations, Martian scores give detailed instructions concerning dynamics, tempos, articulations, and nuances of accents and timbre. A Martian performer is free to play any pitches they like when playing from a particular score as long as they adhere to other instructions. Different performances of a Martian score will sound vastly different with respect to the pitches played, but will resemble each other in terms of dynamics, tempos, articulations, and nuances and accents, just like different performances of a Beethoven score, for instance, will sound vastly different with respect to dynamics and tempos, but will resemble each other with respect to pitches and durations of pitches.
Now imagine that a Martian composer named "Ludwig van Marthoven" wrote a sonata called "Sonata No. 29" and that the dynamics, tempos, articulations, and nuances and accents called for in this score happen to be precisely those that characterize a certain performance p of Beethoven's Sonata No. 29 by a performer in New York. Imagine further that a certain performance p* of Marthoven's Sonata No. 29 has, by coincidence, the same notes as does Beethoven's Sonata No. 29. Suppose that, in these and all other respects, the two performances p and p* are acoustically indistinguishable. In more technical terms, both performances resemble each other to a degree d that is no less than the degree to which they both resemble to instances of Beethoven's Sonata No. 29.
Walton's judgment, and our own for that matter, is that p is of Beethoven's work only and p* is of Marthoven's work only. An important reason as to why there is a difference between these performances is that the latter is causally related to Marthoven and not to Beethoven, while the former is causally related to Beethoven and not to Marthoven. Yet, both performances are physically (i.e., acoustically) identical. So we have two different concrete events p and p* that are acoustically indistinguishable yet of different works. In other words, p has the property of being Beethoven's Sonata No. 29 while p* has the property of being Marthoven's Sonata No. 29 despite their acoustic indistinguishability.
According to the nominalist theory of properties under consideration, two objects share the same property such as being Beethoven's Sonata No. 29 when they resemble each other to a degree no less than that to which other instances of the sonata resemble each other qua Beethoven's Sonata No. 29. But look at p and p*. These two performances resemble each other to a degree no less than such degree since, by assumption, they are acoustically indistinguishable. Furthermore, given that they are acoustically indistinguishable, they resemble each other with respect to the kind of sonata played. Surely, if p and p* resemble each other in this way, they must share the property of being of the same work, whether it is Beethoven's or Marthoven's sonata. But p and p* differ on the property of which work they are a performance of. Hence, the property being Beethoven's Sonata No. 29 is not determined by the resemblance between p and p* or the degree to which they resemble each other.
It cannot be claimed that p is a performance of Beethoven's Sonata because it resembles other Beethoven sonatas to a relevant degree since p* also resembles other Beethoven pieces to the same degree and it is not a Beethoven piece. Similarly, it cannot be claimed that p* is a performance of Marthoven's Sonata because it resembles other Marthoven sonatas since p also resembles other Marthoven sonatas and it is not a Marthoven sonata. Whether a performance is of a particular work cannot be determined simply by its resemblance to other performances of that work. But on the nominalist strategy, a performance is of Beethoven's Sonata No. 29 because it resembles other performances of Beethoven's Sonata No. 29. Hence, the nominalist strategy cannot give a resemblance account of what Beethoven's work is and so cannot account for repeatability. (16) It is important to note that this result stands no matter how strict or relaxed is the nominalist's notion of resemblance (see Goodman 1976). Unless it resorts to types, resemblance among particulars will not be enough to distinguish performances of Beethoven's symphony from those of Marthoven's. There is nothing in the single performance to carve out distinct things to resemble distinct objects.
These remarks will naturally prompt a host of questions. Why can't the nominalist simply add more to her theory? Why can't she, for example, add the intentions of the performers as part of what needs to be resembled? We believe there is a straightforward answer here: because the very goal of the nominalist is to make use of only concrete particular objects and, hence, to do so without appealing to properties and relations. That is why she appeals to an unanalyzable and irreducible resemblance. Appealing to the intentions of the performers --which are not so obviously concrete particulars--(17) would require the use of properties or relations (e.g., being the musical work that the performer intended to perform) that would get rid of the unanalyzable and irreducible resemblance.
Interestingly enough, this problem parallels that of overgeneration for abstract object theories. The latter have a prima facie difficulty when it comes to accounting for creation, so theorists opt for relaxing the problematic notion of creation, resulting in a criterion that is too easy to satisfy. Concrete object theories seem to have no problems accounting for creation, but they do appear to have difficulties with repeatability. And, just as abstract object theorists do, concrete particular theorists opt for relaxing the problematic notion of repeatability, resulting in a criterion that is too easy to meet.
Now, just like other particularists, the nominalist faces problems when accounting for the difference between repeatable and nonrepeatable works of art. Beethoven's Sonata No. 29 is significantly different than Michelangelo's David insofar as there is and can be only one David whereas there are numerous instances (or repetitions) of the Sonata No. 29. Objective resemblance is the only criterion for instancehood (or repetition) available to the nominalist. This gives place to another dimension in which this account overgenerates. For if all there is to repeatability is an irreducible resemblance relation, then all sufficiently resembling copies of Michelangelo's David are really instances of it. Thus, the nominalist is committed to claiming that paintings and sculptures may have repetitions or instances. It asks us to revise the apparently established view that (at least some) sculptures are not repeatable objects. The nominalist cannot explain why there is a difference between musical works and sculptures when it comes to repeatability.
The problem just posed for the nominalist arises because the nominalist offers a narrow criterion of instancehood: objective resemblance. Such a narrow criterion might be good for certain kinds of objects or properties (like the natural ones), but it fails with others. It does especially in cases where the object (or property) in question can have instances in different modalities (as happens with musical works).
4.2.4. Against Persistence Particularist Views
Another version of particularism looks more closely at the metaphysics of objects and persistence. Assuming musical works are concrete entities that persist, it might be possible to capture both creation and repeatability without commitment to error theory and with minimal revisions of our everyday statements about performances, scores, and recordings. The key to working out this family of views requires a closer look at the metaphysics of persistence. (18)
Let M stand for some musical work. Let [[alpha].sub.1] - [[alpha].sub.n] be the musical atoms of M. Musical atoms manifest their works. Assuming that performances of Beethoven's Sonata No. 29 are musical atoms of Beethoven's work, then we say that the performances manifest Beethoven's sonata. (19) So far, this terminology is meant to be neutral between different accounts of manifestation. Persistence particularist views provide a specific account of manifestation. They take both M and [[alpha].sub.1] - [[alpha].sub.n] to be concrete entities and proceed to account for the relationship of manifestation in terms of persistence. (20)
Looking more closely at persistence, there are two questions to answer: one concerning occupation and another concerning constitution. First, we consider how musical works occupy the regions occupied by their atoms. On one view, musical atoms are temporal parts of the musical works they manifest and musical works are fusions of their musical atoms. (21) Call this view Musical Perdurantism. On a second view, musical works are wholly located in each region occupied by their musical atoms but, contrary to musical perdurantism, musical works are not fusions of their musical atoms. Call his view Musical Endurantism.
Second, we consider how musical works are constituted by some fusion of their musical atoms. One possibility is identity: M is identical to some fusion of its atoms ay-an. Another possibility is permanent overlap: M shares all its parts with some fusion of its atoms [[alpha].sub.1] - [[alpha].sub.n]. This produces four different views: Musical Perdurantism with Identity, Musical Perdurantism with Permanent Overlap, Musical Endurantism with Identity, and Musical Endurantism with Permanent Overlap. (22)
Before arguing against these views, it is important to see how they relate to creation and repeatability. Since persistence particular views take musical works and their atoms to be concrete entities, it should be no problem to account for creation. With regard to repeatability, musical works are repeatable because they persist. Beethoven's Sonata No. 29 can be played on one occasion and yet again on another occasion insofar as the musical work is a persistent entity. The relationship between each performance or score and the musical work will depend on the account of persistence on offer, but the general story will be that musical works repeat through persistence. As we will argue, these attempts to account for creation and repeatability are deeply problematic.
It is important to point out a metaphysically significant difference between musical works and ordinary concrete objects like chairs and people when it comes to persistence conditions. A chair or a person persists insofar as they are extended in time. It might be that the chair or person persists by perduring or by enduring, but in the typical case the chair or person will not be gappy. The chair's existence or the person's existence at each moment is causally contiguous with its existence at nearby future and past moments. Even if we entertain far-fetched hypothetical scenarios where the person is taken back in time to meet an earlier version of herself or the chair is transported from one spot to another via some futuristic teleportation machine, there is a clear sense in which the person or the chair is causally connected with its past and future states at each moment. Let us sum this up by saying that persistence conditions for ordinary concrete objects are non-gappy.
The persistence conditions for musical works must be gappy, assuming we are accounting for repeatability in terms of persistence. On this assumption, a performance of Beethoven's Sonata No. 29 on January 1st, 2011 in a private residence in New York City where a virtuoso is playing piano and another performance of it on January 2nd, 2012 in a bar in Berlin where a completely unrelated person takes to the piano to play the only musical work she knows are both parts of Beethoven's work as it persists through time. Unlike the chair or person, where each moment of its existence is contiguous with its next moment of existence, musical works persist through causally unrelated moments of manifestation, such as the two unrelated moments just mentioned. Although this is a strange feature for a purported concrete entity to have, it is not damming enough in itself. But it does pose serious issues for creation when the persistence views with identity are considered.
One supposed benefit of persistence particularist views is that by treating musical works as concrete entities then creation can be explained. But this benefit is incompatible with accounting for repeatability in terms of perdurance with identity or endurance with identity. On the identity views, musical works are identified with some fusion of their atoms. So Beethoven's Sonata No. 29 is identical to some fused object that includes performances that are non-causally contiguous in space and time with each other. This poses a difficulty for accounting for Beethoven's role in creating his Sonata No. 29. Although Beethoven played a role in coming up with the sonata, on the identity views of persistence the sonata is not those performances or scores that Beethoven had a causal role in creating. The sonata is a highly scattered object that includes performances and scores that exist well beyond Beethoven's death and so well beyond Beethoven's creative and causal reach. On the identity view, the most we can say is that Beethoven created a small part of the Sonata No. 29 but not the Sonata No. 29 itself, thereby undermining one significant motivation for this family of particularist views.
What about perdurance or endurance with permanent overlap? Consider perdurance with permanent overlap. There is still a conflict with creation because the view posits too many objects. For Beethoven's Sonata No. 29, there is the musical work itself, the musical atoms that are temporal parts of the musical work, and the fusion of all the temporal parts. But what did Beethoven create? He could not have created the fusion of temporal parts. That object goes well beyond Beethoven's creative and causal reach. He could not have created the musical work itself. That object is understood to have temporal parts that exist after Beethoven's death. At most, Beethoven could have created a small part of the Sonata No. 29 but not the Sonata No. 29 itself. Lastly, whether he created the musical atoms that make up Sonata No. 29 is irrelevant to whether he created the musical work itself. So perdurance with permanent overlap posits three different types of objects, none of which seem to help with accounting for creation.
Endurance with permanent overlap fares the best in terms of accounting for creation. On this view, the object Beethoven created is wholly present in each region occupied by its musical atoms. So the musical work itself is clearly within Beethoven's creative and causal reach. The problem with this view is that it accounts for creation at the cost of complicating ontology with a sui generis type of concrete object. Remember that ordinary concrete objects are causally contiguous. Even if a chair or person is transmitted through space and time via some hypothetical teleportation machine, there will be a causally contiguous sequence connecting the person or chair through their travels. Assuming repeatability is persistence and assuming that musical works persist in a gappy way, then musical works will not be causally contiguous in this way. There will be performances that are causally unrelated to one another. What could explain this behavior of musical works? Assuming they are concrete particulars as endurance with permanent overlap does, then the explanation would have to come from features of its concreteness or its particularity and none of these options look promising. So although a view such as endurance with permanent overlap fares better than the rest of the persistence particular views in terms of handling creation, it does so at the cost of unnecessarily complicating ontology with objects that behave in unexplainable ways.
There is also another objection against using persistence to account for repeatability. Persistence is neither sufficient nor necessary for repeatability. Clint Eastwood persists through time, but he is not repeatable. His empty chair persists through time, but it is not repeatable. So persistence is not sufficient for repeatability. Neither is persistence necessary for repeatability. Consider an abstract universal. Since it is a universal, it will repeat insofar as it will be wholly present in its instantiations. Since it is abstract, it will be a-temporal and non-concrete. But since it is a-temporal and non-concrete, it does not persist. So repeatability cannot be accounted for in terms of persistence.
The most plausible persistence particularist view is endurantism with permanent overlap. But it faces two serious objections: it posits sui generis a-typical concrete objects without any possibility for explaining their behavior and it attempts to account for repeatability using persistence. A more plausible view would take the best of endurantism with permanent overlap but leave out the problematic parts. This would be a view that treats musical works as creatable entities that are wholly present in the areas occupied by their musical atoms. It would also be a view that can account for repeatability by connecting it with the musical work's ability to be wholly present in the areas occupied by its musical atoms. But this is just the view we are advocating in this paper: musical works are concrete universals.
4.3. Concrete Particulars Fail
Particularist theories according to which created repeatable objects, such as Beethoven's Sonata No. 29, are concrete particulars, do not offer satisfactory accounts. A satisfactory account must be able to satisfy the following intuitive desiderata:
Creation: the object must not have existed prior to its creation, thus, its existence depends upon its creator's voluntary decision to create it.
Repeatability: the object may be instantiated on several occasions and in different modalities.
We argued that particularist theories cannot account for repeatability. We saw additional problems with nominalist theories and persistence particularist views. Each of these theories leaves something unaccounted for, something that is philosophically significant when it comes to giving a satisfactory story of what Beethoven created when he composed the Sonata No. 29, why this object is repeatable, and how it differs from other artistic creations such as Michelangelo's David. For these reasons, we argue that particularist theories of repeatable objects should be rejected.
5. From Repeatable Objects to Creatable Concrete Universals
Beethoven's Sonata No. 29 is a repeatable object that was created by Beethoven and played during his lifetime. Since then it has been played, written down, and recorded numerous times. These facts are obvious. The desiderata we formed on the basis of these facts (creation and repeatability) are meant to place obvious and plausible constraints on any metaphysical account of the kind of object that Beethoven created. So it may come as some surprise that upon closer inspection we arrive at the existence of concrete universals from the existence of created repeatable objects such as musical works.
This is no surprise to us. As we argued, any abstract object theory, where "object" is referring to either particulars or properties, cannot properly account for creation in virtue of general features of abstractness. Furthermore, abstract object theories that take creation to involve stipulation overgenerate created objects, as well as misdiagnose linguistic stipulation for artistic creation. On the other hand, any concrete particularist theory will not be able to account for repeatability in virtue of general features of particulars. The particularist view that comes closest to doing so (i.e., endurantism with permanent overlap) unnecessarily complicates physical ontological while falsely assuming that persistence can account for repeatability. The only option left: concrete universals. Because Beethoven's Sonata No. 29 is a universal, it can have instances across various modalities, irom performances to written scores. Because it is concrete, it is creatable. This solution seems far from surprising. Rather, it is an elegant way of accounting for the metaphysics of created repeatable objects. (23)
In the following sections we will provide a brief account of concrete universals as well as show how concrete universals avoid the problems presented to the alternative accounts we have rejected. (24)
5.1. The Metaphysics of Concrete Universals
Even though a fully detailed account of concrete universals is beyond the scope of this paper, we do want to present some brief remarks to substantiate our proposal. So far, what we have said may give place to several worries: Are they different from Armstrong's in re universals? How is a concrete universal instantiated? Is it spatiotemporally located? Is it an object or a property? Are concrete universals abundant? Are they complex? Do they account for common features? Can they be created more than once? Do they exist independently of their instances? We will answer these and further questions in what follows.
According to Lewis (1983) and Armstrong (1978):
A universal is supposed to be wholly present wherever it is instantiated. It is a constituent part (though not a spatiotemporal part) of each particular that has it. A property, by contrast, is spread around. The property of being a donkey is partly present wherever there is a donkey, in this or any other world. (Lewis 1983, p. 10)
On our view, concrete universals are not spread around. They are wholly present wherever they are instantiated. They are a constituent part but not a spatiotemporal part of the objects that instantiate them. So in this response, our concrete universals are like Armstrong's universals.
Thus, universals unify reality in a peculiar way. It is not that their instances are merely members of a certain class. "They literally have something in common. They are not entirely distinct. They overlap" (Lewis 1983, p. 11). All performances of Beethoven's Sonata No. 29 overlap, they all have the universal in common as a constituent non-spatiotemporal part.
5.1.2. Identity and Distinction
Universals are fully present in their instances. This means that the universal Sonata No. 29 instantiated in the score is identical with the one instantiated by the performance. This does not mean, obviously, that this score and that performance are identical. That is false. Concrete universals are properties in the sense that they can have instances and, hence, are not particular objects. What is identical between the score and the performance is the universal they instantiate, not the particular substances that instantiate them.
Thus, it is also not the case that, on our view, there are at least two objects wherever there is the score of Beethoven's Sonata No. 29. What we claim is that there is one concrete particular object, the score, and one concrete universal, Beethoven's Sonata No. 29. Since concrete universals are in re, they share the same space-time location.
5.1.3. Location and Copresence
It is intuitively true that objects cannot occur repeatedly, but such intuitions are concerned with particular objects, not with universals. This or that specific performance of Beethoven's Sonata cannot occur repeatedly, nor can it be multilocated. But that is no problem for the universal Sonata No. 29. It occurs repeatedly in this and that performance and it is located both here and there, wherever there is an instance of it. (25)
Suppose that "two entities are copresent if both are wholly present at one position in space and time" (Lewis 1983, p. 11). For the reasons above, copresence is not transitive among universals. Suppose this performance (the particular object) is copresent with the universal Sonata No. 29 and that that other performance is also copresent with the same universal. Yet this performance and that other are not copresent with each other.
Unlike Armstrong's and Lewis' view, on our view concrete universals are abundant. Universals may very well be needed to ground the objective resemblances and the causal powers of things. But, as we have argued, there is reason to believe in more universals, particularly concrete ones. There is one for every created repeatable object in reality.
Yet, even though they are abundant, we still think they observe Armstrong's guiding principle that "the world's universals should comprise a minimal basis for characterizing the world completely" (Lewis 1983, p. 12). Throughout the debate we've been assuming that created repeatable entities are part of what the world has in offer. We have argued that concrete universals are needed to account for such entities. Yet created repeatable entities abound.
5.1.5. Structural Resemblance and Linguistic Universals
It seems natural to think that created repeatable objects have structural complexity that allows structural resemblance among different created repeatable objects. Such structural resemblance is what accounts for the multi-modality of musical works, for example. Musical scores and performances resemble each other structurally, but not qualitatively. Thus we must face Lewis' (1986) famous critique of structural universals. In defense of our view we will make two points: first, we will recall that Lewis' critique is directed against the use of structural universals to account for the natural properties (i.e., against Armstrong's project (1978)); and, second, we will show how musical works can be linguistic structural universals in Lewis' sense.
Lewis (1986) considers six different theoretical jobs that structural universals are meant to do when it comes to serving as natural properties: (i) account for our use of predicates and complex predicates of natural classes (p. 27); (ii) account for resemblance in general (p. 28); (iii) serving as ersatz possible worlds (p. 28); (iv) provide resources for an anti-Humean theory of the laws of nature (p. 29); (v) account for resemblance among universals (p. 30); and (vi) to account for the possibility that there are no simples and that the universe is infinitely complex (p. 30). Lewis then goes on considering four different versions of structural universals--linguistic, pictorial, variants of pictorial, and magical--and rejects them, each for distinct reasons that amount to a common failure: there is no coherent way of spelling out the parthood relation of structural universals and still manage to do the jobs (i)-(vi).
This should be enough to clarify the first point of this section. Lewis (1986) is worried about the use of structural universals for purposes (i.e., jobs (i) to (vi)) distinct from ours. So, even if structural universals fail to achieve the goals considered by Lewis (1986), it remains to be seen if they can achieve a different one, namely, accounting for created repeatable objects, such as musical and literary works. We believe they can and, furthermore, that the linguistic conception is adequate for this purpose, this is our second point.
Let us recall the desiderata that linguistic structural universals should satisfy when it comes to serving as musical works and other created repeatable objects: (a) they should be created; (b) they should be repeatable; (c) they should account for the structural nature of the created repeatable object; and (d) they should provide the resources to account for the resemblance among musical works or literary fictions. It is important to note that these desiderata do not include any of the jobs considered by Lewis (1986)--except, perhaps, for (v) when considered as an account of resemblance among musical and literary works, which is desideratum (d)--most importantly, our theory need not get job (vi) done (i.e., accounting for the possibility of infinite complexity). To see that linguistic structural universals can successfully satisfy desiderata (a) to (d) consider Lewis' own account of them.
On the linguistic conception, a structural universal is a set-theoretic construction out of simple universals, in just the way that a (parsed) linguistic expression can be taken as a set-theoretic construction out of its words. [ ... ] think of the structural universal as being a complex predicate in a language in which [...] simple universals are some of the words; they comprise the nonlogical vocabulary. We also need [ ... ] the usual connectives, quantifiers, and variables --and we need mereological predicates of identity, inclusion, and overlap--. [...] The words of the language are interpreted by stipulation [...]. Complex expressions, including those that we take as the structural universals, are interpreted in a derivative way. Recursive rules are stipulated whereby the interpretation of a parsed expression depends on the interpretations of its immediate constituents under the parsing, and in one step or several we get down to the stipulated interpretations of the words from which that expression is built up. Thus we specify, in particular, what it is for something to satisfy a complex predicate in the language [1986, p. 31].
Linguistic structural universals are set-theoretic constructions out of simples. Take the simples to be musical notes or even simple phrases of a natural language. These constructions and their interpretation are stipulated and can be created, hence satisfying (a). They will be repeatable, since they are universals, thus satisfying (b). The set-theoretic structure of the universal can be used to account for the structure of the musical or literary work, thus satisfying (c). And the resemblance between different set-theoretic constructions will account for the resemblance among different musical works or literary fictions, thus satisfying (d).
Lewis himself has no serious problems with linguistic structural universals, since they provide a very clear account of the parthood relations of a structural universal. These relations are determined by stipulation during the construction of the set-theoretic object.
It is an easy matter to believe in structural universals, so understood. The hard thing would be not to believe in them. Once we have the simples, we need only believe in set-theoretic constructions out of things we believe in. There is no extra ontic commitment, apart from the commitment to sets that most of us accept as unavoidable. (Lewis 1986, P-32)
Lewis (1986) rejects because they cannot account for the possibility that the world is infinitely complex--job (vi) in Lewis' laundry list--. Linguistic structural universals assume that there are simples. We cannot use them to account for infinite complexity, but we can use them for a different purpose. As Lewis says, "if we put aside worries about infinite complexity, the structural universals of the linguistic conception might be some use" [ibid., p. 32]. This is precisely what we intend them to do. It is safe to assume that musical and literary works are not infinitely complex objects and, hence, that the needed simples (i.e., musical notes and simple expressions of natural language) exist. Thus, "we are content to limit ourselves to possibilities that are fully given by arrangements of [this] stock of actually existing simples" [ibid., p. 33]. All the possibilities that are given by set-theoretic arrangements of musical notes and simple expressions of natural languages are enough to account for created repeatable objects such as musical and literary works.
5.1.6. Existential Dependence on First Instance
We have claimed that even though a particular performance of Marthoven's Sonata may resemble a particular performance of Beethoven's in all relevant aspects, they are still performances of different musical works. What happens in the opposite case? What if, say, Schumann decides to compose a piano sonata that, unbeknownst to him, Beethoven had already composed. The performances are similar. The score is identical. What follows? Has Schumann created something new? Is there another universal associated with Schumann's work?
On our view, for a concrete universal to be created it must not exist prior to its creation. It follows that they cannot be created twice at different times. In this sense, concrete universals that are musical works ontologically depend on their first instance. (26) Although they only have one first instance at a world, they may have different first instances at other worlds. In this sense, their existential dependence upon their first instance is non-rigid.
This provides another difference between Armstrong's and our concrete universals. Armstrong's universals ontologically depend on some instance at a world, but not necessarily the first instance let alone any particular instance at a world. So the difference comes out modally. Concrete universals that are musical works depend on their first instances, which may vary from world to world but will always be the first instance of the work in question at that world. Armstrong's universals, on the other hand, depend on some instances at a world without the further constraint that any particular instance is the first instance of that universal at that world.
We may go back to Schumann's case now. What should we say about Schumann's Sonata that was already created by Beethoven a few decades earlier? We do not say they are the same universal that was created twice or that Schumann created a distinct universal. What we do say is that this is another Paderewski case. Like Kripke's Paderewski (1979), it is one and the same entity yet one may fail to believe so because of one's presuppositions and prior beliefs.
Peter does not believe that Paderewski is Paderewski even though they are one and the same. This is because Peter thinks the former is a pianist, the latter a politician, and that politicians are not pianists. Similarly, Peter may not believe that Schumann's Sonata is Beethoven's Sonata even though they are one and the same. This may be so because Peter thinks Schumann composed the former, Beethoven the latter, and that Schumann would have never composed what Beethoven did. It is one and the same Sonata we are talking about, yet we can see good reasons why people may fail to believe so.
5.2. Musical Works As Concrete Universals
We will now show how concrete universals account for the desiderata while avoiding the problems presented in sections 3 and 4.
First, they are concrete. Thus, they are spatiotemporally located and, hence, causally related to other concrete objects. Now, just like other concrete things in this world, some are creatable (e.g., chairs, and tables) others are not (e.g., the cosmos). (27) Just what the difference is between the class of creatable universals and the class of non-creatable ones is something we will leave for later. For now suffice it to say that the non-creatable ones are, to put it somehow, eternal. There is no problem with the creation desideratum so long as we take musical works to be among the creatable class of concrete universals. Beethoven created his Sonata No. 29, because he was able to causally relate to it and because it did not pre-exist Beethoven's voluntary decision to create it.
Second, they are not particular but universal objects. Hence, they may have instances. The universal is not any of its parts. Thus they are not analyzable in terms of parts. They are fully present wherever they are. So they are repeatable. Since their repeatability does not depend on the objective resemblance among their different repetitions, at least some may be repeated in different modalities. Beethoven's Sonata No. 29 is repeatable in different modalities because it is a universal.
Now, we objected to abstract object theories that their account requires a notion of creation that overgenerates (e.g., the case of Sherlock Pounds and the different versions of Superman). Can we avoid this problem by taking musical works and literary fictions to be concrete universals? We also objected to concrete particular theories that their accounts use one of various notions of repeatability that either overgenerates (e.g., Marthoven's case) or fails to account for repeatability (e.g., when persistence is the relevant notion) as well as erases an important distinction between repeatable and nonrepeatable works of art (e.g, between musical works and sculptures). Can we also solve these problems by taking the relevant works to be concrete universals?
The important lessons from all these cases are, first, that the relevant set of properties that determine whether something counts as a new or distinct work of fiction (or musical work) are intrinsic as opposed to accidental; and, second, that which among them are relevant may differ from case to case of different fictions (or musical works). Whatever they are, the relevant intrinsic properties of a musical work need not be the same as those of a super hero. Thus, a proper account should be such that the nature of the object is independent of whatever accidental or intrinsic (but irrelevant) properties the object turns out to have in the relevant case. This independence is not achieved if the identity of the relevant object is determined by any set of properties stipulated in a context, for this will include accidental properties (as with the abstract object theory); nor is it achieved if the identity of the relevant object is determined by intrinsic yet irrelevant properties, such as objective resemblance with a contextually given set of objects (as with the nominalist account).
It is also important to see why the abstract object theorist, as well as the nominalist, cannot really do otherwise. The abstract object theorist, for example, cannot exclude accidental properties as part of the set of properties that determines the relevant abstract object because that would be inconsistent with the principles of object abstraction (i.e., one of them being that any set of properties determines an abstract object) that substantiate the account and which make sense of at least a weak notion of creation in terms of stipulation (see section 3.1). Without these restrictions, the abstract object theory would be completely lacking an account of how musical works can be created.
Likewise for the nominalist: she has no way to exclude irrelevant intrinsic properties by focusing, say, on the property of being an instance of the relevant musical work because that would require more resources than the ones available to her, i.e., objective resemblance of intrinsic properties and only that. The nominalist, by definition, cannot appeal to properties, relations and what have you.
However, if the identity of the created repeatable object is determined to be an instance of the relevant universal, we have enough flexibility with respect to all accidental properties the object may have, as well as with most intrinsic properties except, of course, for the property of being an instance of the relevant universal. Thus, our account achieves the desired independence. To illustrate this, let us show how our theory takes care of each one of the cases mentioned.
To avoid the Sherlock Pounds problem all we need to do is accept the claim that by merely stipulating the descriptive means to refer to an object we are not thereby creating anything. Since, on this view, creation is not a matter of stipulating a means for referring to an object, we can easily accept such claims and reject "Sherlock Pounds" cases as involving no creation whatsoever. Our theory acknowledges that the difference between creating a new piece of literary fiction and merely copying one by adding a few different features may be a matter of degree. Determining where exactly the divide is may prove to be a difficult matter, but one that we need not solve here. The burden of our theory is to make the correct predictions in the clear cases, not to issue judgment on the controversial ones. And it seems quite clear that by merely adding that Sherlock Holmes is to weigh ten more pounds and copying everything else from Conan Doyle's work is not a way of creating fiction.
Something similar may be said with respect to the different versions of Superman. Changing a few of Superman's properties is not enough to create a new fictional character (even changing its upbringing and ideals does not seem to he enough). Yet, changing his most salient set of properties that make him a super hero, so that Superman is now, say, a fat, alcoholic, sixty year old man with no goals, no hopes in life or superpowers is perhaps enough to say that we are now talking of a different fictional character with a homonymous name to that of the super hero.
If you recall, a particular performance of Marthoven's Sonata No. 29 was problematic because it objectively resembles a given performance of Beethoven's Sonata No. 29 and, according to nominalist accounts, objective resemblance is enough for property identity. Thus, on the nominalist view, both performances should count as instances of the same musical work. Yet, they are not. This problem is easily avoided on our view since it does not take repeatability to be a matter of objective resemblance. The intuition that performances of Marthoven's Sonata are instances (or repetitions) of a distinct property (or universal) than performances of Beethoven's Sonata seems to be based on the fact that both performances are unrelated to the relevant musical work. This case is no more difficult to account for than that of concrete objects instantiating various distinct properties. On our view it is possible, for example, to distinguish the whiteness from the roundness of a white sphere, and this can be done independently of there being other resembling spheres or white things. Similarly, we can distinguish the objective (e.g., acoustic) features of a performance from the musical work it instantiates, independently of whether and how such a performance objectively resembles other performances. This is simply a consequence of the fact that objective resemblance does not determine whether or not a given performance is an instance of the relevant concrete universal that a musical work is supposed to be.
Finally, given that to exhibit objective resemblance is not enough to count as a repetition (or instance) of a concrete universal, to claim that some sculptures (e.g., Michelangelo's David) may be copied in the form of different concrete sculptures that resemble it objectively does not amount to claiming that they may be repeated or that they may have several distinct instances. So, our view is not committed to the claim that, like musical works, sculptures and paintings are repeatable (or may have instances). The difference here may be a matter of genre. If so, then we don't see why we could not accept it.
Aside from its ability to avoid crucial objections, our account has one further advantage: it is the only one that can offer a straightforward account of a rather peculiar feature of the phenomena of created repeatable objects, i.e., that they can be fully present in multiple locations. Consider musical works and their performances and repetitions in different modalities. Beethoven's Sonata No. 29 is fully present wherever it is performed: e.g., what someone in Berlin's Volksbuhne is listening to is exactly the same as what someone else is listening to while sitting on her couch in downtown Tokyo, provided they are both listening to performances of Beethoven's Sonata No. 29. The same applies, mutatis mutandis, to literary fictions. Consider Cervantes' Don Quixote. What someone in Madrid is reading is exactly the same as what someone else in New York City is reading, provided they are both reading Cervantes' Don Quixote. Furthermore, common sense seems to have no problems accepting this feature of musical works and literary fictions.
So common sense dictates that fictions and musical works can be multi-located. Historically speaking, concrete universals have had little or no popularity among philosophers precisely because their concreteness and universality seem to be at odds with one another: they are fully present wherever they are and (since they are spatiotemporally located) they are wherever their instances are. Thus, accepting the existence of concrete universals is tantamount to accepting the existence of a kind of concrete object that can be fully present in different locations of space at the same time. It seems then that common sense dictates that there are concrete universals. Hence, more than a costly revision of common sense opinion about what there is, our claim that musical works and literary fictions are concrete universals delivers a straightforward vindication of it, one that no other account appears to have on offer.
This is probably a proper place to clarify our view. We are not claiming that all properties should be taken to be concrete universals. Nor are we claiming that all works of art should be considered to be so. We are merely claiming that the best account of creatable repeatable objects, such as musical works and literary fictions, requires us to accept the existence of concrete universals. Maybe we still have to accept the existence of abstract objects (or even abstract universals) in order to explain other recalcitrant phenomena. If so, then so be it. Also, as we already said, we are not claiming that all concrete universals are creatable. Maybe there are phenomena that require us to accept the existence of non-creatable concrete universals. If so, then so be it. Our plea is merely for the acceptance of the following claim: that among the concrete things some of them are universals; that among the latter, some are creatable; and that some of these ere atable concrete universals are musical works like Beethoven's Sonata No. 29.
6. Final Remarks
We ordinarily think there are created repeatable objects. Musical works, literary fictions, photographs, and car models are examples of them. We have argued, convincingly we hope, that it is not possible to account for such entities if we limit our ontology to that of abstract universals and concrete particulars. We need concrete universals. Yet, it has been objected that the existence of such entities is counterintuitive. We contend that there is little substance behind this objection.
It is common to accept that reality is made up of either abstract (isolated in space and time) or concrete entities, on the one hand, and either particular or universal ones, on the other. We happily accept that there may be abstract universals. And we seem to have no qualms accepting concrete particulars either. Why should we worry about concrete universals? One reason may be the assumption that concreteness goes with particularity and universality with abstractness. But those that believe there are abstract particulars reject this assumption (see Parsons 1980 and Salmon 1998). Why not accept there are concrete universals too?
One of the odd features associated with concrete universals seems to be its spatial and temporal relation. Copresence is not transitive for them and they may be located at different places at the same time. But once we realize that copresence is a feature of particularity (and not concreteness) and that repeatability is a feature of universality, concrete universals do not appear to be eerie entities any more.
What is surprising to us is that debates about metaphysical categories such as universals, particulars, concreteness, and abstractness have not fully considered the existence and nature of concrete universals. For our part, we argued that there are fully concrete and universal entities in the form of musical works. We now take it as incumbent upon ourselves to provide an extended metaphysical theory of these kinds of objects, a theory that must wait for another occasion. We also take it as incumbent upon metaphysicians to move beyond the typical and obvious examples we use to illustrate our metaphysical concepts. Looking closely at the complexities of aesthetic objects such as musical works tests our metaphysical intuitions about what kinds of objects there are. Unless we keep looking closely at all the things before us, both unusual and ordinary, we risk falling out of touch with the very world we are theorizing about. (28)
Instituto de Investigaciones Filosoficas
Universidad Nacional Autonoma de Mexico
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Received: November 2, 2013; revised: August 25, 2014; accepted: December 11, 2014.
(1) Even though this seems to be the most widely accepted view of abstract objects, it is not without troubles (see Rosen 2012). There seem to be several different ways of drawing the abstract/concrete object distinction. Some even seem to think that abstract objects may be concrete (see ibid.) as they consider them to be the result of a process of abstraction from concrete particulars. Settling this debate is irrelevant for the debate concerning created repeatable objects, and it is definitely outside the scope of this paper. It will be enough, for our purposes, to settle on the abovementioned (widely accepted) distinction and simply assume that by "abstract" we mean "non-spatiotemporal".
(2) In fact, most people seem to think that universals must be abstract objects (see Rodriguez-Pereyra 2014) since, it is argued, they would otherwise have to be multi-located spatiotemporal objects (i.e., concrete objects that can be fully present in distinct locations). More on this in section 5.
(3) Benacerraf (1973) argued that mathematics presents a substantial challenge for philosophers, for what is necessary for mathematical truth appears to make it unknowable. The best (or perhaps most common) way to account for the necessity of mathematical truths is to take mathematical objects to be abstract. This naturally prompts the question: how is it that concrete human beings can learn anything about them? It is tempting, then, to take mathematical truths to be about concrete objects. That would help us explain how mathematical knowledge is possible. Yet, when we think about concrete objects we usually think of the realm of concrete particulars that are what they are only contingently so. We seem to need concrete entities to account for knowability, and universal entities to account for necessity. Perhaps concrete universals may be of help here.
(4) This condition will play a central role in our discussion of abstract object theories in section 3. Abstract objects preexist any human being and, in that sense, human beings cannot create them. For more on the relation of dependence, both ontological and existential, see section 5.1.6 for further details.
(5) Parsons 1980 theory of nonexistent objects is much more complex, it includes distinctions between nuclear and non-nuclear properties, for example. Fine (1984) argues for a more refined view. None of these further distinctions will be relevant for our discussion here.
(6) Indeed, "any" set of properties is acceptable (even inconsistent ones). This is so because the theory is meant to explain, among other things, the use of language to talk about fiction, and there's nothing precluding fiction from having some or other (or many) contradiction(s) (see, for example, J.L. Borges" short story "The book of sand").
(7) It is important to note that although these features apply to the particular theory of abstract objects endorsed by Deutsch, they also apply to abstractness in general. Abstract particulars and abstract properties are typically taken to be eternal and isolated in virtue of their being abstract.
(8) That is to say, the proposition expressed by the conditional statement is vacuously true, but the sentence itself is not. This goes to show that, on this view, what we come to know or create is some kind of metalinguistic object.
(9) Depending on how one goes on individuating linguistic entities, one could also make the case that what Conan Doyle created is not what competent speakers understand when reading the Sherlock Holmes Stories, for that is something that can and has been translated into different languages, yet the stipulations made by Conan Doyle (his act of creation) are certainly in English and not any other language (by stipulating this or that English description to refer to Sherlock Holmes he did not thereby stipulate this or that German description to refer to the same object).
(10) In a recent paper (2006), Bruno has offered a different version of the abstract object theory of musical works. His main concern is the relation between a performance of a musical work and the musical work itself. His goal is to show that such relation is not that of instantiation but, rather, that of representation. The performance represents the musical work. Bruno considers several reasons to defend this thesis: (i) discourse: we often talk as if performances were intentional objects, they are performances "of' something; (ii) properties: performances differ from musical works in ways that force us to distinguish between both, a performance may be stirring or delicate, while the musical work is not; and (iii) existence: it is possible for a musical work to exist without ever being performed. Bruno does not consider the problem of creation and it is not clear whether he is worried about the repeatability of musical works. Whatever the merits of this account of the work-performance relation within the abstract object view, it is not to be considered an alternative account for our purposes. For, presumably, when Beethoven first composed Sonata No. 29, he was not representing it. If he was, then he did not create it perhaps because, on this view, it does not seem to be the sort of object that can be created.
(11) With the exception of Persistence Particularist Views, we have developed the positions presented throughout this section in order to complete our argument. As far as we know, these views, with respect to fictions or musical works, cannot be found in the literature.
(12) We need to make clear that the Golden Gate Bridge cannot be repeated in the sense that I could use elements wholly different from those that constitute it and create it again. It is surely possible that the Bridge might be destroyed, but someone finds a way to gather all the components that constituted it when it was created and then rearrange those components so we get the bridge again. This would not be repeatability in the sense important to us. Of course, finding a more precise way of making these intuitions clear will be difficult. Although we do not need to do this for our paper, it would be worth the exercise trying.
(13) There are other forms of nominalism that we will not be considering in this paper partly because others such as Armstrong (1978) and Rodriguez-Pereyra (2002; 2014) rule them out as plausible nominalist alternatives and because they raise more questions and problems than they do answers. For example, consider Ostrich Nominalism. One way of understanding this view (that explains the references to head-ducking ostriches) is to simply take a is F (John's performance is Beethoven's Sonata No. 29) at face value; there simply is no deeper metaphysical fact to this predication. However, this view would explode ontology with a myriad of unrelated facts (or propositions, depending on the view) that intuitively seem to be related in deep ways. And of course the Ostrich Nominalist could simply take a and b are F (John's performance and Sally's performance are both Beethoven's Sonata No. 29) at face value as well, but the absurdity of this view, especially in the face of plausible alternative metaphysical explanation, becomes all the more apparent.
(14) See Rodriguez-Pereyra 2002, pp. 156-198 for more details.
(15) For the most part we are following Armstrong (1978) and Rodriguez-Pereyra (2002 and 2014) in our account of nominalism. We only consider resemblance varieties of nominalism because other varieties such as predicate or concept nominalism require recourse to type or property level concepts that are not nominalistically reducible. This is why we also treat the resemblance relation as an intrinsic feature of the particulars that populate the ontology of the resemblance theorist's account of properties. Lastly, we appeal to resemblance nominalism because it seems to be less problematic than trope theory, by insisting that resemblance not be itself reified (it avoids the resemblance regress problem, for example). Nothing much hangs on our use of resemblance nominalism, since our arguments are specifically against the resemblance part and will affect any resemblance theory about properties.
(16) One option for the nominalist is to complicate her account by introducing paradigms. On this account, two objects o and o* share the same property of being white if they resemble each other with respect to whiteness and if they resemble paradigm cases of white things. Armstrong 1978 presents strong arguments against paradigm resemblance nominalism about properties. Furthermore, we contend that our argument against irreducible resemblance accounting for the distinction in properties between p and p* applies to paradigm resemblance nominalism as well.
(17) Intentions are used in philosophy in order to account for a subject's ability to have mental states directed towards certain contents. As such, intentions can be shared among subjects. This precludes them from being particulars. In this sense, intentions are more like properties or general objects.
(18) What we call "Persistence Particularist Views" is what Chris Tillman calls "Musical Materialism" (2011). We have decided to change the name of this family of views from the literature on this topic so that their relationship to the broader range of particularist views we discuss in this paper is made clear.
(19) In the following discussion, we will assume that scores and performances are manifestations of musical works. It is important to note that nothing hinges on this assumption. Our primary interest here is in the manifestation relation independent of which entities count as manifesting works.
(20) This terminology is due to Tillman (2011). In this section, we will closely follow Tillman's presentation and reject two views of persistence particularism he lays out: Musical Perdurantism and Musical Endurantism. We will not consider whether musical works are spanners. This is partly because our arguments against musical perdurantism and musical endurantism will also count against taking musical works to be spanners. It is also because it is simply implausible that musical works are spanners. For more on spanning, see Tillman 2011, pp. 15-20 and references therein, especially McDaniel 2007, p. 134.
(21) Following Tillman (2011), we will simplify the discussion by only talking about temporal parts. The discussion can be recast more generally in terms of spatiotemporal parts thereby allowing us to talk about musical atoms across time and across space at a particular time. The more general discussion is not necessary for our purposes here.
(22) Tillman (2011) only considers musical perdurantism with identity and musical endurantism with permanent overlap, which he calls musical perdurantism and musical endurantism respectively. Our arguments apply to all four views so we consider them all here for the sake of completeness.
(23) A referee carefully pointed out the following seeming incompatibility. We use the fact that musical works can have instances across various modalities (written scores, audible performances, etc.) to argue against resemblance nominalist theories. However, if the instances do not resemble one another across modalities, then we lose some of the motivation to appeal to universals in our account of musical works. The reason this is a seeming incompatibility is that there are different ways objects can resemble one another, some of which help our case and not the nominalist's case. Musical works structurally resemble one another when they have instances across modalities. These instances across modalities need not qualitatively resemble one another. If the nominalist wants to account for structural resemblance, she will need to appeal to structures, which will be type level entities that are barred from the nominalist's ontology. So we retain our motivation for concrete universals since musical works do resemble (structurally) one another across modalities, just not in a way that helps the resemblance nominalist. We thank an anonymous referee for this journal for pointing out this issue and encouraging us to clarify our position.
(24) Anthony Ralls argues for the conclusion that some works of art are creatable universals. He states that the "work of art is a created universal, concretely embodied through the intentional activity of people, for people's enjoyment; and the artist makes its archetype" (1972, p. 18). However, Ralls's claim is unclear because, as we point out earlier in this essay, an object can be either an abstract or a concrete universal. If the work of art is abstract, then it is not creatable. Going on to say that it is concretely embodied only speaks to the universal's instantiation conditions and does not address its ability to be created. We argue that some works of art are concrete universals, which entails their ability to be created. It is only by accepting the existence of concrete universals that we can explain the unique features and challenges that some works of art introduce.
(25) This seems to justify assertions such as "The Sonata No. 29 is on the second floor, third door on the left". But this is, at first glance, an odd assertion to make. As such, this seems to be evidence against our view. We think this assertion seems odd only because it lacks contextual information. The same goes for other more "normal" assertions, such as "The hundred dollar bill is on the table to your left". What makes an assertion odd or normal is, at least partly, its relevance. Thus, consider a music festival where several different musical works are being interpreted at the same time in different concert halls. It then makes sense to ask "Where is the Sonata No. 29?" To which it makes sense to answer "The Sonata No. 29 is on the second floor, third door on the left".
(26) We specify "that are musical works" because we do not want to exclude the possibility of there being concrete universals that do not have such dependence. Further discussion on other topics may show that concrete universals are useful to solve several other problems aside from that of created repeatable entities (e.g., musical works) some of which will ontologically depend on their instances but not particularly on their first instance. For more on ontological dependence, see Lowe 2009.
(27) We are not claiming that the cosmos (the idea of a universe) is metaphysically necessary. But it does strike us as intuitive to claim that it is not possible to think of our world without it including the cosmos.
(28) The authors would like to thank two anonymous referees for their helpful comments. Thanks are also owed to Gonzalo Rodriguez-Pereyra, Jose Tomas Alvarado, Luis Robledo, Axel Barcelo, Ekain Garmendia, and Lenny Clapp. This work was presented at different venues, including the II ALFAn Congress in Buenos Aires, and the Springs Philosophy Discussion Group.
Eduardo Garcia-Ramirez. The research for this paper was supported by PAPIITIA400112 and CONACYT CCB-2011--166502 research projects. The paper was completed as a visiting scholar at the UBA, Buenos Aires, Argentina. Thanks are owed to CONACYT (Of. 233188) and DGAPA (UNAM), PASPA program.
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|Author:||Garcia-Ramirez, Eduardo; Mayerhofer, Ivan|
|Date:||Apr 1, 2015|
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