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 be 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

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 be 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 be 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 α₁-α _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 α₁-α_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 α₁-α _n . Another possibility is permanent overlap: M shares all its parts with some fusion of its atoms α₁-α _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 1^st, 2011 in a private residence in New York City where a virtuoso is playing piano and another performance of it on January 2^nd, 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.

5.1.1. Instantiation

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 nonspatiotemporal 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.

5.1.4. Abundance

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.