Do Computer Simulations Include Digital Artifacts?

Introduction

As in many other research fields, in cosmology it is now common to run computer simulations. One of these simulations, the Hubble Volume Project, is described as follows:

The results of the simulations are visualized and show structures that look like clusters of galaxies, filaments, and voids.

But do the particles within the simulation exist? And what about the clusters of galaxies and filaments formed in the simulations? Are they objects that we have to accept in our ontology? More specifically, are they digital artifacts?

This is the research question of the present paper. The question has recently been touched upon in discussions of David Chalmers’s virtual realism. Chalmers (2017; 2022) holds that we encounter real objects when we use headsets to plunge into virtual reality. Suppose, for instance, that I play “Horizon Call of the Mountain” using a suitable headset. According to Chalmers, the boat on which I find myself sitting, the mountains I see, and the robot animals I encounter in the game are real objects. In a comment, Beisbart (2019) argues that Chalmers’s virtual realism, if it is true of objects from virtual reality environments, also holds of objects in all kinds of computer simulations. Beisbart thinks that this is an implausible consequence of virtual realism and amounts to a reductio of the latter, but Chalmers (2019) replies that he is prepared to bite the bullet and accept this consequence. There are thus good reasons to analyze in more detail whether objects in computer simulations can be said to exist.

To do this, I will proceed as follows. In Sect. 2, I will briefly characterize computer simulations by drawing on recent work from the philosophy of science. In Sect. 3, I will motivate and explain realism about simulated objects, e.g. the particles from cosmological simulations. Realists should be able to specify to which objects a simulation gives rise. In Sect. 4, I investigate how realists may meet this challenge. I try to specify on their behalf which objects exist in a simulation. However, these attempts will run into problems, and I will ultimately argue that we are well-advised not to admit simulated objects in our ontology. I will draw my conclusions in Sect. 5.

Before I start, a few remarks are useful. First, in what follows, the term “simulations” refers to computer simulations unless otherwise noted. I will thus neglect, in particular, so-called analog simulations (e.g., Trenholme 1994). I will focus on what I call “simulated objects” such as the particles and clusters from cosmological simulations. Here, the term “simulated objects” is not supposed to carry the assumption that they are real objects; rather, it is a convenient façon de parler. The term may be defined as “objects as they appear to figure in computer simulations.” It thus functions similarly to terms like “alleged object” and “assumed object”. Alleged objects are not objects that happen to have the property of being alleged. Rather, talk about them is suppositional. To stress that some objects do exist, I will sometimes call them “real objects”, but the adjective “real” is not meant to assign them a status that goes beyond their being. All objects are real objects; simulated and assumed objects may not be.

Second, as I will explain in Sect. 3, my paper concentrates on the question of whether simulated objects are real objects. This is an important part of the question of whether they are digital artifacts, simply because artifacts are (real) objects. The artifactual character of the objects will not be important for my argument.

Third and finally, this paper is not a contribution to the debate about the simulation argument (Bostrom 2003; see, e.g., Beisbart 2014 for a response). This argument tries to show that we likely live in a computer simulation, given certain assumptions cited by Bostrom. If we do live in a computer simulation, according to the argument, this is because the computer hardware on which simulations of human brains are running is associated with conscious experiences of the kind humans have. In this paper, I’m not concerned with conscious experiences that may accompany the execution of specific simulation codes that try to trace human brains, but rather with objects that may exist within all kinds of simulations.

Computer simulations

To answer the main question of this paper, it is first useful to clarify what computer simulations are and what kinds of simulations exist. To do this, I can draw on the extensive literature on simulations from the philosophy of science (see e.g. Winsberg 2010).

In the introduction, I have already mentioned an example from cosmology. A different computer simulation project from cosmology is the Illustris project. On their website, the researchers explain the rationale of their simulations as follows:

Here, the researchers motivate their simulations by referring to the difficulties of solving a mathematical model of the main components of matter in the universe. The model consists of differential equations that express laws of physics and assume continuous time. To allow a digital computer to provide approximate and partial solutions to the equations, scientists discretize the latter.

There are also computer simulations not aimed at approximating the solutions to differential equations. For instance, Oswald et al. (2024) have used a so-called agent-based model to simulate early political reactions to the COVID-19 pandemic. The general idea is that the countries’ policies are a matter of policy diffusion. In more detail, each country, or its government, is taken to be an agent, and at each time, a country checks those 18 countries that are most similar to it. If more than a certain fraction of these countries have decided to impose a lockdown, the country under consideration follows suit. The simulation was tuned to available data and could make predictions on how many countries would adopt a lockdown at a specific time.

What, then, is a computer simulation in general? Stephan Hartmann gave a very influential answer to this question: “a simulation imitates one process by another process … If the simulation is run on a computer, it is called a computer simulation (Hartmann 1996: §2.2).” Paul Humphreys has characterized computer simulations as follows:

We can summarize the essential points from these characterizations of (computer) simulations as follows. A computational device, viz. a digital computer, undergoes a process. This process can be regarded as imitating another process because the computer yields information about the dynamic behavior of some system, e.g. our cosmic neighborhood. The computer does so by providing a series of state descriptions. The state descriptions state that certain variables, e.g. the positions and velocities of particles, take specific values. The computer obtains these values by solving equations from a model. The state descriptions can often be visualized; the series of state descriptions can then be shown as an animation. (For Humphreys, a computer simulation may be restricted to a single instance of time, but this is not a common view and not important for what follows.)

This characterization of computer simulations is concentrated on one single run of a suitable computer program. Sometimes, the term “simulation” does not refer to such a single simulation run but rather to a general method (which contrasts with e.g. experimentation), or to a larger unit of research in which the computer is not just run but also set up with certain initial values and in which the results are observed (Parker 2009: 488; Frigg & Reiss 2009: 596 are willing to include even more activities in a computer simulation study). Still, for an ontological analysis, it is most convenient to focus on one single run of a simulation program.

This very run of a simulation program is a process that can be described in various ways using different vocabularies (e.g. Barberousse et al. 2009). For instance, the process can be described as a purely physical process in which processors and other physical parts of the computer hardware interact following the relevant laws of nature. It can also be described as a computational process in which the computer does various calculations, e.g. adds numbers. Further, the process can be described using the model the equations of which are evaluated. For instance, cosmologists can describe their simulations by saying that certain particles interact via gravitational forces and move in this and that way.

Note that computer simulations can differ from each other in various ways. One important distinction is between simulations that refer to a real-world target system, e.g. the atmosphere of the Earth, and those that do not. Simulations of the latter sort are only supposed to trace the behavior of a fictive or merely imagined model to explore its consequences. It may be objected that we cannot talk about simulations if there is no real-world target, but this objection is not convincing. The reason is that even simulations referring to a real-world target first and foremost evaluate equations from a model of the target, where the model may represent the target system more or less faithfully. Accordingly, there is a huge class of computer calculations that evaluate equations from models and that resemble each other in this respect. It is appropriate to call them all computer simulations. The fact that some models evaluated with the computer are intended to represent a real-world target system does not make a difference to the computer calculations.

Other distinctions can be used to typify simulations, e.g. the distinction between deterministic and Monte Carlo simulations, but these distinctions do not matter for this paper.

Are simulated objects digital artifacts?

Let us now start with the ontological analysis of computer simulations with a special focus on digital artifacts. This section aims to clarify how computer simulations may give rise to digital artifacts.

What is most characteristic of all computer simulations is that they trace the behavior of a model system. Accordingly, as mentioned above, the run of a computer simulation can be described in terms of the processes in the model it is supposed to trace.

Assume thus that a simulation scientist tells us: “In my computer simulation, one billion particles interact with each other due to gravitation. At the very beginning, in an early period of the universe, the particles are almost homogeneously distributed in space, but as time passes, they form clusters of galaxies and filaments.”

What the scientist tells us may be true or false. It is false, for instance, if the scientist gets the number of particles in the simulation wrong. Now with expressions like “one billion particles” or “clusters”, the scientist seems to refer to objects that help make the sentences true, if they are true. If the scientist is correct in what they say, then, it seems, there are one billion particles that form clusters.

If there are such particles and clusters, they are excellent candidates for digital artifacts. An artifact is often defined “as an object that has been intentionally made or produced for a certain purpose (Hilpinen 2011, abstract).” The particles in the computer simulation and the clusters they form would be objects, and it seems that they are made by scientists; at least, they result from human activities, and humans pursue certain purposes when they create simulations with these and these particles; for instance, they want to know what a certain model implies for the universe. The particles also seem to be digital artifacts because a digital computer is decisive for their existence. Indeed, objects created by 3D printers based on computer programs seem less like digital artifacts. Their blueprint has gone through a digital computer, but the printing is something that is not merely due to a computer. By contrast, particles from simulations seem to be created using the digital computer only.

If we consider the particles from simulations to be real, we take a realist stance toward the kind of talk exemplified above. For our purposes, we can say that realists about a certain discourse agree with the following statements: The discourse is supposed to describe a certain part of reality, a certain domain of things; this part of reality exists largely independently of what we intend and believe to be the case about it; and we can acquire some knowledge about it. In this paper, we are interested in realism regarding talk that describes computer simulations in terms of particles, agents, etc. The corresponding part of reality would thus consist of the objects that seem to figure in computer simulations. In the terminology defined in the introduction, the central realist thesis is, therefore, that simulated objects exist, i.e., are real objects, independent of our intentions and beliefs about them. (Recall that simulated objects were defined merely as objects that appear to exist in computer simulations; they need not exist). In what follows, “realism” refers to this variety of realism, if not specified otherwise.

It may be argued that we must define objecthood and existence to make sense of realism. Admittedly, there is some leeway regarding the question of what exactly objects and existence are. One possible strategy is to embrace digital realism, according to which simulated objects are, or are constituted by, realizations of data structures in the hardware (Chalmers 2017). However, I do not want to assume digital realism, and rather try a more general argument. Despite this, I can make sense of realism regarding simulated objects as follows.

Consider simulated boats, mountains, and robot animals as they appear in “Horizon Call of the Mountain”. They seem to have certain properties, e.g. to be located in certain regions of space, to produce certain appearances, and to allow for certain interactions with the users. In most cases, we have a pretty good grasp of the simulated objects and the properties they seem to have because both are supposed to be counterparts of, or similar to, types of objects and properties that we know from ordinary reality. Accordingly, we have some ideas of what the objects and what their existence would be like. Thus, we can meaningfully ask whether they exist and have the properties that are assigned to them independently of our corresponding intentions and beliefs. As will become clear below, the crucial issue for my arguments will be mind-independence. I thus do not need more specific assumptions about objecthood or existence. This is an advantage because such assumptions would likely be controversial.

Chalmers (2017; 2022) is a realist regarding talk about objects that we experience in virtual reality environments, e.g. the boat, the mountains, and the robot animals that players encounter in “Horizon Call of the Mountain” (see Chalmers 2017: 312 for his notion of virtual reality environment). Chalmers calls the objects “virtual objects” and thinks that they instantiate certain properties and are involved in real events (Chalmers 2017: 310). He further thinks that virtual objects are digital objects. At a first approximation, digital objects are physical realizations of data structures in the hardware of a computer (Chalmers 2017: 317). see Declos 2024 for useful clarifications regarding virtual realism).

Since virtual reality environments are based on computer simulations, realism about simulated objects from computer simulations implies realism about objects that appear in virtual reality. The converse is not true, however. One may be a realist about virtual reality environments without being a realist about all computer simulations because virtual reality environments have features not shared by all computer simulations. In a virtual reality environment, we can perceive objects and interact with them, which is impossible for many simulations because the outputs are not visualized. Accordingly, the realism considered in this paper applies to more computer simulations than does Chalmers’s realism. That said, for metaphysical purposes, it does not seem attractive to draw a line between computer simulations that are connected to VR headsets and those that are not. The reason is that the “generation” of the objects is the same. If there is a VR headset, there are better opportunities to perceive the objects, but realists typically allow for the possibility that some objects may not be perceived.

Problems with simulated objects

Is it plausible to think that simulated objects exist? In what follows, I will try to develop a realist position. Ultimately, this attempt will fail, and it is for this reason that I think that realism about computer simulations is not a tenable position.

To be realists about simulations, we have to explain precisely what objects a simulation contains. That is, what objects are in a specific simulation? The answer has to be in the vicinity of the following claim:

Which variables are traced by a computer simulation is best determined by checking the computer program as written in a programming language such as C++. For an ontological analysis of a computer simulation, we would thus have to consider all variables in the program and find out to which objects they refer. This reference is determined by the interpretation that working scientists give to the simulation. This is as it should be because we would not talk of a computer simulation if the calculations were not interpreted in terms of a model.

The notion of a property used in C must not be too broad. To see this, take any object O from a simulation and form the mereological sum of it and either another arbitrary particle from the simulation or even an arbitrary object that is not traced by the simulation. If we take the position of O to be a property of the mereological sum because it is a property of a part of the new object, we are committed to accepting arbitrary pairs of objects from simulations, or even pairs of simulated objects and other objects, as real objects, and this seems weird. To undercut this move, we have to say that not every property of a part of an object is a property of this very object. I will not discuss further what exactly the appropriate notion of property is at this point. It is well known in philosophy that we sometimes must distinguish genuine properties from “mere Cambridge properties” (Francescotti 1999). In what follows, I will interpret the properties from C in such a way that avoids the problem.

Some bugs in the simulation program raise additional interesting issues about C. These bugs affect the objects in the simulations. Of course, many bugs are not of this kind. For instance, due to a typo in the code, the forces with which particles interact in the simulations may not be the forces that scientists are interested in. This bug does not have an impact on the objects that are in the simulation. We can say that the objects in the simulations are those that the scientists believe are in the simulation, but that the scientists are mistaken about the interactions operative in the simulations. Contrast this with cases in which a bug affects the essential properties of particles. Suppose, for instance, that negative electric charge is an essential property of electrons and that a simulation is supposed to trace the motion of electrons. Due to a bug, however, the particles have been assigned positive charges. What, then, are the objects in a simulation, according to C: electrons, or positively charged particles that have the properties of electrons (i.e., positrons)? I guess the most attractive answer on behalf of realists is that neither is the case. Realists are well advised to avoid assignments of natural kinds to objects in the simulations, and to say that the objects are simply particles with certain determinable properties (e.g. a counterpart to charge, call it simulated charge); the values of the related variables are just those that the simulation assigns to them. That the simulation is about electrons can then be reconstructed as saying that electrons are the target of the simulation model.

C is meant to be a sufficient condition on objects in computer simulations, but it is not necessary. The reason is that, in many simulations, objects arise at a higher level. For instance, regarding a cosmological simulation, scientists want to say that clusters of galaxies and filaments form. Ultimately, such objects are constituted by other objects in the simulations. However, in the computer program, there are no variables that directly trace the values of determinable properties of the emerging objects (unless we work with an exceedingly broad notion of property).

To allow for such objects, we must introduce additional principles that specify which higher-level objects exist in simulations. There is an analogous task for physical objects, the question being under which conditions a bunch of physical objects form a new object. Since there are standard answers to this question (see, e.g., van Inwagen 1990), they can be transferred to computer simulations. I will thus not discuss this issue any longer but rather concentrate on problems with C.

C only gives rise to specific objects if there is a unique correct mapping from the variables to the objects. There have to be facts of the matter regarding the question of which variable belongs to which object. However, this condition is not always fulfilled.

Consider, for instance, N-body simulations used in fluid dynamics or cosmology (see Klypin & Shandarin 1983 for pioneering work). At first sight, the simulations contain particles the positions of which are traced in the simulation. However, the simulations are ultimately an attempt to discretize continuous field equations. These equations (e.g., the Navier Stokes equations) connect several fields, e.g., the mass density and velocity fields. The equations thus describe a continuous fluid and assume a very different ontology from a particle ontology. Now, there are different stories of how to get from the fluid and the related fields to the variables used in the simulation. One story is that the phase-space density is traced using particles (e.g. Dolag et al. 2008: 231). This leads to a particle ontology. Alternatively, one can say that the positions evaluated by the simulation are those of so-called Lagrangian fluid elements. These are tiny parts of the continuous fluid, comoving with the fluid (see e.g., Bertschinger & Jain 1994 for an explanation). A slightly different story is that the positions trace so-called integral curves. These are mathematical constructions that can be associated with the solutions to differential equations (see e.g., Berger & Gostiaux 2012: 33 for a definition). For the scientific work with the simulations, how the positions are interpreted does not make much of a difference. Working scientists are most interested in the density field, which can be constructed under either interpretation.¹

The problem, then, is that the same simulation can be given different interpretations in terms of objects. This is an underdetermination problem: the simulations as such (the program and the outputs) underdetermine the choice of the ontology. It seems odd to read several different ontologies into the simulations and claim that e.g., particles and fluid elements exist. Nor are there clear reasons to prefer one or the other ontology. (An underdetermination problem is also a challenge for scientific realism. See, e.g., Tulodziecki 2017 for an overview).

This is not the only underdetermination problem that realists face regarding simulated objects. It is well known that the same equation (or the same set of equations) can describe very different systems. For instance, the equation $\frac{d^2}{d{t}^{2 }}x= \hspace{0.17em}-k x$ for the harmonic oscillator can be used to describe the motion of a pendulum, the motion of one end of a string, the distance between two atoms in a molecule, etc., depending on what exactly “x” is meant to refer to. Suppose now that a computer simulation is used to solve this equation. What objects are associated with the computer simulation (e.g., a pendulum, a string, etc.)? The calculations in the computer hardware are exactly the same for these cases. If there is no reason to choose one particular interpretation, we are facing an underdetermination problem.

A realist may answer that underdetermination does not arise because the intention of the working scientist determines the correct interpretation of the simulation in terms of objects. For instance, if the working scientist intends to, and takes themselves to, trace the motion of a pendulum, then the simulation ought to be interpreted in terms of a pendulum. This solution may, at first sight, seem unsatisfactory because it lets the answer to the underdetermination problem depend on the intention of a person. This, in turn, may seem to violate the independence condition implicit in realism. However, the independence condition is not violated in a way that compromises realism. The reason is that the correct interpretation depends on the creator or user of the simulation but not on anyone who has beliefs about the simulation. For anyone different from the creator or user of the simulation, there are mind-independent facts to the effect that the simulation is associated with these or these objects. That the creator or user determines what the objects are is no problem because humans can create objects that depend on them. True, realists would have to admit that facts about the simulations supervene on facts about scientists, but this is not a decisive objection against realism.

Still, it is dubious whether the realist reply to the challenge is always viable. For instance, the working scientist may not have a determinate idea of how they think about the positions in the N-body simulations; after all, for practical purposes, the answer does not make any difference. Further, we can construct cases where two scientists decide to run a simulation together but interpret the results differently. It is even possible that a mathematician and a physicist do this, where the mathematician interprets the results without reference to any physical system (but as solutions to certain equations), while the physicist interprets them in terms of physical objects (e.g., a pendulum). Conversely, it is possible to “illustrate” a purely mathematical calculation in terms of a physical story. For instance, every Monte Carlo integration (an integration using random numbers) can be illustrated by saying that someone randomly throws objects into a region of space. A scientist may occasionally, but not always, use this illustration to explain their program. Are we then to say that there are objects associated with the simulation or not?

Realists may also want to avoid the underdetermination problems by identifying the objects with material objects in the real world. This is what Chalmers does with his digital realism: virtual objects are digital objects, i.e., physically realized data structures. Still, this solution has its own problems and cannot solve all underdetermination problems (Beisbart 2019: 327). The reason is that the identification of simulated objects with certain material objects does not help answer the question of which kinds of simulated objects we are concerned with. Are we talking about a set of point particles or fluid elements, for instance? A main attraction of virtual realism is that it allows us to take talk about simulated cells, cats, etc. at face value, but the problem is that the underlying computer calculations are too poor to determine what the objects really are.

Realists may also try to escape underdetermination by pointing to the target system of those simulations that have a determinate real-world target. They might hope that the target helps fix the simulated objects’ identity. But this trick does not work. The reason is that many computer simulations are based on highly simplified and abstract models. Accordingly, many characteristics of the target system and its parts are not represented in the simulation. Consider, for instance, a simple random walk model of Brownian motion (see, e.g., Lawler & Limic 2010 for examples). In this model, a particle randomly jumps between neighboring sites of a lattice, and there is no need to assign the particle a mass, an extension, or a shape. The question for realism regarding simulations is whether the particles do have these properties. Several answers are possible, but they all have problems, so it is plausible to say that the choice is underdetermined. Many realists will tend to give an affirmative answer because the targeted particles (colloids, etc., that undergo Brownian motion) have mass, extension, and shape. But the question then is which mass, extension, and shape the particles have. One cannot always answer this question by pointing to a real-world target system because the model may be applied to several Brownian particles with different masses, extensions, and shapes. Alternatively, a realist may deny that the particles in the simulation have mass, extension, and shape, but this answer is not very plausible because the particles would then be very different from particles that we know; in particular from particles that are targeted with the model. Finally, the realist may answer the question by saying that it is objectively indeterminate whether the particles have mass, extension, and shape or what their mass, extension, and shape are, but the question then is why we should be committed to a domain of reality in which many questions do not have answers.

Admittedly, there are domains of things that we do not know well, and we often acknowledge that many of our questions do not (yet) have answers. Accordingly, it may be suggested that the underdetermination is merely an epistemic problem, but no reason to deny a domain of things. Although this move may be viable in some debates about varieties of realism, I do not think it is attractive for virtual realists. The reason is that it is unclear what kind of facts may provide the answers we are missing. Relatedly, there is no good explanation for why we do not know what the real simulated objects are like. It is not the case, for instance, that our senses or our inferential capacities are too poor to learn related facts.

The deeper reason for the underdetermination problems is that computer simulations can be described at different levels, and the highest level, where the simulation is described using representations, is not completely fixed by the underlying computational layer. The same computations may be used for different purposes, and various objects can be read into them. Further, although the purposes or intentions of users can, in principle, help to determine the simulated objects, they often do not suffice to fix objects uniquely.

So far, I have constructed underdetermination arguments against realism about simulated objects. Even if some of them can be disputed, I think the situation is problematic for realism overall. Still, my discussion suggests another argument against realism about simulated objects. All kinds of programs are run on computers. It is straightforward to interpret them in terms of calculations either at the level of the machine code that works on numbers in binary representation or at the level of the programming language, in which integers and reals are added. With a sufficiently broad notion of computation, this point of view can be extended to simulations that work with string-valued variables. Some calculations run on computers are computer simulations. But qua computations, they do not at all differ from other calculations run on computers. It thus seems odd to assign real objects to some computations and not to others. We have a unified ontology of the working of computers if we consider them to run calculations. This unified ontology is given up if some computer simulations are assigned additional digital artifacts. We would have to assume the artifacts if this was necessary to explain certain features of the simulations. But this is not the case. To explain the calculations as such, we do not have to refer to simulated objects. Further, if some calculations have an unequivocal interpretation in terms of a model, we can say that the calculations evaluate the model equations and add this to our description of the simulations.

Account for talk about simulated objects

My argument that realism has undeniable disadvantages may still be objected to. Realists regarding simulated objects take talk about computer simulations at face value (this point is noted by e.g. Godfrey-Smith 2009), and they have a simple explanation of how we can say correct or incorrect things about simulations and VR: expressions like “the boat” refer to entities that exist and have properties independently of us. So, if we deny virtual realism, how can we account for the correctness and falsity of statements that describe simulations in terms of simulated objects? For instance, why is it correct to say that galaxy clusters form in certain cosmological simulations?

I propose to answer this question by saying that scientists talk about a fictional model that is evaluated using computer simulations. There are two broad ways to make sense of such talk about fictional models: either we adopt a kind of fictionalism and think of talk about fiction as K. Walton (1990) does, or we postulate objects as constituents of fictional models. In what follows, I argue that both ways are not attractive to realists regarding simulated objects. While the first strategy does without any objects, the other is not attractive either because it postulates objects that we must acknowledge independently of computer simulations.

Turn first to the first strategy, viz. to understand talk about fiction (here: talk about a fictional model evaluated by a computer simulation) as proposed by Walton (1990) (see McDonnell & Wildman 2019 for an application to virtual reality). Very roughly, the idea is that certain statements about computer simulations are “true in a game of make-believe” (Walton 1990: 35). A statement is true in a game of make-believe if the rules of the game entail that participants can, or should, pretend that the statements are true.² Accordingly, talk about the fiction is correct not by virtue of certain objects, but rather because people are required to behave as if certain objects existed, following the rules of the game. For the fictional models underlying computer simulations, the rules of the game (here: the rules of the practice of engaging with a particular model) articulate a certain interpretation of a computer simulation; for instance, people are supposed to understand the outputs as descriptions of a certain model system. The rules function similarly as they do for fictional novels.

This is not the place to discuss this proposal in more detail. For our purposes, it is crucial that the proposal can explain why certain statements about fictional models and related computer simulations are correct while others are false. Another point is noteworthy, too. This account of talk about fiction does not imply that either a statement or its negation is correct of a simulation. There can be gaps in the correctness in fiction because the rules of the game require participants neither to pretend that the statement was true, nor to pretend that its negation was true. Gaps in the correctness of fiction are welcome for our purposes because they can explain why the choice of an ontology for a simulation is sometimes underdetermined. Note also that such a fictionalist view of models underlying simulations can deal with bugs. If, due to a bug, a computer simulation doesn’t trace what should be pretended according to the model the working scientists have in mind (the original model, for short), then it still traces what should be pretended under a different model. When people talk about what happens in the computer simulation, they talk about this different model, even if they think they are talking about the original model. If the computer simulation gets essential properties of objects from the original model wrong, then people who do not know this will be wrong about the objects they take to be in the simulations. For instance, they may say that there are electrons in the simulation, but this is wrong because the model that is actually evaluated using the simulations does not contain electrons. This is as it should be because people who do not know about the bug are mistaken about the simulation.

In sum, if we claim that statements about simulations are statements about a fictional model and understand this model in the terms proposed by Walton, we do not need any simulated objects in our ontology to make sense of related talk. Under this account, simulated objects are superfluous. Given that the postulation of simulated objects led to problems, it seems better to do without them.

As mentioned above, there is a second way to make sense of talk about fictional models. The idea is to postulate suitable objects; call them fictional objects. In novels, some of these objects are characters such as Prospero in Shakespeare’s “The Tempest”. These are likely abstract objects, but in what follows their precise nature does not matter if only they can have properties and stand in relation to each other, which makes correct talk about them possible.

I do not think that this proposal to postulate objects for fictional models is attractive (see Godfrey-Smith 2009). After all, it introduces objects that are agreed not to exist in an important sense. Further, there is the threat that the underdetermination problem mentioned before arises again. This is because we have to account for the fact that it can be undetermined what kinds of objects are in a simulation and what properties they have. One way of accounting for this is to say that the models themselves leave open what the objects are and what properties they have. But, as before, why postulate fictional objects when it is largely open what they are and what properties they have? An alternative is to claim that models are fully determinate. However, this only pushes the problem back because it is now unclear which model underpins the computer simulation. For instance, in one model, there are particles with such and such masses; in another model, there are fluid elements with such and such properties, and so on. To account for the fact that some simulations do not have an unequivocal interpretation in terms of objects and their properties, we have to say that the simulation is meant to evaluate several determinate models. This is not attractive because we sometimes need several classes of objects to make sense of a simulation; several ontologically distinct models are associated with the same simulation.

Even if we bracket this theoretical dilemma, there is another problem. As noted in Section 2, some computer simulations are based on independent prior models. These models are fictional, i.e., they are constructed in thought, and they existed before they were implemented in the simulations. We can say true or false things about such models, so we need to explain how this is possible. That is, we have to give an account of the objects that seem to be part of such a model, e.g. the particles bearing spin in the Ising model of magnetism. The position currently under investigation provides such an account by postulating suitable objects. But this creates the following problem. To make sense of the prior fictional model on which the simulation is based, we need fictional objects independently of the computer simulation. Now, if a fictional model is successfully evaluated using a computer simulation, we can say that the computer obtains (possibly approximate and partial) solutions to the model. But this doesn’t cut any ice, ontologically speaking. The computer simulation just delivers descriptions of objects that we must admit anyway following the position currently under investigation. Therefore, we need no special ontology for computer simulations. But this seemed to be the main idea behind virtual realism.

This argument is not directed against every attempt to account for computer simulations in terms of objects. In fact, under the proposal presently under discussion, computer simulations are accounted for using objects, viz., the objects we need to make sense of fictional models. However, the argument decouples the objects from the fact that computer simulations are carried out. This fact has no ontological import. We need an account of how we can say correct and false things about fictional models anyway, but we need no special account of computer simulations.

Admittedly, my present argument needs development. First, in the literature from the philosophy of science, it is common wisdom that many computer simulations based on a prior model do not simply evaluate this model. For instance, models that use differential equations have to be discretized; the computer introduces round-off errors, which lead to deviations from the true model behavior, and so on (Winsberg 1999). That is why some authors distinguish between the conceptual model and the computerized model (Schlesinger 1979). The latter can be considered a model of its own, viz., the model that is evaluated by the computer simulation. In many cases, it inherits the ontology of the conceptual model but uses slightly modified equations to evaluate the values of the relevant variables. In any case, we can use the computerized model to make sense of the objects in computer simulations: talk about the simulations is talk about the computerized model. The resulting proposal is very natural. We need some strategy to make sense of the conceptual model, anyway, and we extend this strategy to make sense of the computer simulation by referring to the computerized model. Appeal to the computerized model is also crucial when we want to explain how people can say correct or false things about simulations that contain bugs. If, in such a case, people use the output of computer simulations to make claims such as, “In the simulation, this and this particle is in a particular region at time t,” then they talk about the computerized model, and what they are saying is true, but possibly false of the conceptual model. If bugs affect the ontology of the model, then some claims to the effect that objects from the conceptual model exist in the simulation will be wrong. This is again as it should be.

Second, some simulations are not based on prior models. However, each simulation is interpreted in some way, and this allows us to read a model into each simulation. Although the creation of the model may be causally intertwined with the computer simulation, we can, in principle, formulate the model independently of the simulation. In practice, this will be very difficult if the simulation is very complex; still, it is, in principle, possible.³

Overall, then, if we account for fictional models by postulating fictional objects, it seems appropriate to use these kinds of objects to make sense of simulations, too. This is the most economical solution and can help avoid additional ontological commitments. Consequently, the fact that simulations are run on computer hardware does not matter for ontological questions. Simulations do not create objects. If they refer to objects, the latter are not digital artifacts that are mainly constructed by the computer. This finishes the discussion of the second ontological account of fictional models.

All in all, it seems attractive to claim that computer simulations deliver descriptions of the behavior of fictional models. We can make sense of talk about simulated objects using these models. Talk about such models can either be accounted for using Waltonian fictionalism, or the proposal that fictional models are constituted of fictional objects. Under both accounts, it is not true that computer simulations as such give rise to real simulated objects. Either there are no objects at all, or the objects exist largely independent of the simulations.

Conclusions

In the Hubble Volume Project, scientists used one billion particles to simulate structure formation in the Universe. At least, this is what scientists say. The particles used in the simulation would seem to be perfect candidates for digital artifacts. After all, they seem sustained by the computations of digital computers, and we do not even need 3D printers to obtain them. However, they are only perfect candidates if they exist. In this paper, I have argued that we should not grant them existence. Realists who do that can make some progress in explaining what objects a simulation gives rise to. However, they ultimately run into underdetermination problems that make their position doubtful. In a nutshell, the calculations done by the computer plus the context, particularly the intentions of scientists, often underdetermine the choice of the objects. I have suggested that a fictionalist account à la Walton is preferable to explain how statements about simulations can be true or false.

Let me finish this paper with three clarifications. First, in this paper, I have concentrated on objects. The question was whether we must assume objects to explain ordinary talk about simulations. It may be objected that the search for objects is too narrow-minded and that we have to be open to other kinds of ontologies, e.g. ontologies that take events or processes to be basic. But my argument can be generalized to such ontologies. There is a leap from the computational events and processes running in the computer to events and processes that realists want to read into the simulations, e.g. transitions between energy levels or revolutions. This leap can be used to construct underdetermination problems. The crucial issue is not the sort of ontology but rather the fact that suitable ontologies introduce a kind of determinacy that is inappropriate in view of simulations. I have also argued that we need not expand our ontology to be able to talk about our simulations. So why expand our ontology and add a realm of things about which many questions are open if this is not necessary?

There are admittedly some ontologies that allow for indeterminate objects, and it has also been proposed that the world might be indeterminate (see, e.g., Smith & Rosen 2004). However, such ontologies are developed for different purposes, e.g., for quantum mechanics (see, e.g., Pipa 2024). Postulating an indeterminate domain of things is not attractive if everything we want to say is possible without assuming such a domain. Other possible objects that are rather poor in properties are arbitrary objects (Fine 1985: 15–21). Still, if we refer to them in mathematical proofs, it may be necessary to assume such objects. However, in this paper, I have argued that we do not need to refer to simulated objects to make sense of the simulations.

Second, the project of this paper is closely related to that of a paper by Peter Godfrey-Smith (2009). Godfrey-Smith notes that it is very natural to describe many models as involving fictional objects, i.e., objects that are merely imagined. But he then argues that it seems inappropriate to add such objects to our ontology. As Godfrey-Smith puts it, “we might reasonably start resisting at the point where the explanation [of the working of models] treats the model system [the merely imagined system] as a shadowy additional graspable thing” (2009: 108). One reason for the resistance is that many models are used in the sciences to learn about the physical world. If philosophers want to understand how this works, it is unattractive to postulate new objects that are not part of the physical world, for it is unclear how we can obtain knowledge about them. In this paper, I have also disputed the need to account for certain alleged objects in terms of ontology. However, I have concentrated on simulated objects, which are associated with computer simulations, which is not the case with objects merely imagined by humans. The fact that we have simulated data about simulated objects and can even visualize them may seem to make them “more real” than mere imaginations of the human mind. Also, our argumentative strategies differ. Godfrey-Smith’s argument focuses on how we can access the alleged objects, while I have stressed an underdetermination problem. Godfrey-Smith discusses several solutions to the problem he raises, including fictionalism à la Walton. In this paper, I have also appealed to this position.

Third and finally, I have not addressed all ontological questions that arise in the context of computer simulations. For instance, many computer simulations are based on differential equations, and one may ask what objects we are committed to when using such equations. These questions are independent of the questions addressed in this paper. The reason is that mathematical objects are independent of whether the equations are evaluated using a computer. Questions of this kind have to be left for another opportunity; answering them does not contribute to the ontological study of digital artifacts.

Competing Interests

The author has no competing interests to declare.