## 1. What is Computer Simulation?


No single definition of computer simulation is appropriate. In the
first place, the term is used in both a narrow and a broad sense. In
the second place, one might want to understand the term from more than
one point of view. 


### 1.1 A Narrow definition




In its narrowest sense, a computer simulation is a program that is
run on a computer and that uses step-by-step methods to explore
the approximate behavior of a mathematical model. Usually this is
a model of a real-world system (although the system in question might
be an imaginary or hypothetical one). Such a computer program is
a *computer simulation model*. One run of the
program on the computer is a computer simulation of the system. The
algorithm takes as its input a specification of the system's
state (the value of all of its variables) at some time t. 
It then calculates the system's state at time t+1. 
From the values characterizing that second state, it then calculates
the system's state at time t+2, and so on. When
run on a computer, the algorithm thus produces a numerical picture of
the evolution of the system's state, as it is conceptualized in
the model. 




This sequence of values for the model variables can be saved as a
large collection of "data" and is often viewed on a
computer screen using methods of visualization. Often, but
certainly not always, the methods of visualization are designed to
*mimic* the output of some scientific instrument--so that the
simulation appears to be measuring a system of interest.




Sometimes the step-by-step methods of computer simulation are used
because the model of interest contains continuous (differential)
equations (which specify continuous rates of change in time) that
cannot be solved analytically--either in principle or perhaps only in
practice. This underwrites the spirit of the following
definition given by Paul Humphreys: "any computer-implemented method
for exploring the properties of mathematical models where analytic
methods are not available" (1991, 500). But even as a narrow
definition, this one should be read carefully, and not be taken to
suggest that simulations are only used when there are analytically
unsolvable equations in the model. Computer simulations are often
used either because the original model itself contains discrete
equations--which can be directly implemented in an algorithm suitable
for simulation--or because the original model consists of something
better described as *rules of evolution* than as
*equations*.




In the former case, when equations are being
"discretized" (the turning of equations that describe
continuous rates of change into discrete equations), it should be
emphasized that, although it is common to speak of simulations
"solving" those equations, a discretization can at best
only find something which approximates the solution of continuous
equations, to some desired degree of accuracy. Finally,
when speaking of "a computer simulation" in the narrowest
sense, we should be speaking of a particular implementation of the
algorithm on a particular digital computer, written in a particular
language, using a particular compiler, etc. There are cases in
which different results can be obtained as a result of variations in
any of these particulars.


### 1.2 A Broad Definition




More broadly, we can think of computer simulation as a comprehensive
method for studying systems. In this broader sense of the term, it
refers to an entire process. This process includes choosing
a model; finding a way of implementing that model in a form that can be
run on a computer; calculating the output of the algorithm; and
visualizing and studying the resultant data. The method includes
this entire process--used to make inferences about the target
system that one tries to model--as well as the procedures used to
sanction those inferences. This is more or less the definition of
computer simulation *studies* in Winsberg 2003 (111).
"Successful simulation studies do more than compute numbers. They
make use of a variety of techniques to draw inferences from these
numbers. Simulations make creative use of calculational
techniques that can only be motivated extra-mathematically and
extra-theoretically. As such, unlike simple computations that can be
carried out on a computer, the results of simulations are not
automatically reliable. Much effort and expertise goes into deciding
which simulation results are reliable and which are not." 
When philosophers of science write about computer simulation, and make
claims about what epistemological or methodological properties
"computer simulations" have, they usually mean the term to
be understood in this broad sense of a computer simulation
study. 


### 1.3 An Alternative point of view




Both of the above definitions take computer simulation to be
fundamentally about using a computer to solve, or to approximately
solve, the mathematical equations of a model that is meant to represent
some system--either real or hypothetical. Another approach
is to try to define "simulation" independently of the
notion of computer simulation, and then to define "computer
simulation" compositionally: as a simulation that is carried out
by a programmed digital computer. On this approach, a simulation is any
system that is believed, or hoped, to have dynamical behavior that is
similar enough to some other system such that the former can be studied
to learn about the latter. 




For example, if we study some object because we believe it is
sufficiently dynamically similar to a basin of fluid for us to learn
about basins of fluid by studying the it, then it provides a
simulation of basins of fluid. This is in line with the definition of
simulation we find in Hartmann: it is something that "imitates
one process by another process. In this definition the term
'process' refers solely to some object or system whose
state changes in time" (1996, 83). Hughes (1999) objected that
Hartmann's definition ruled out simulations that imitate a system's
structure rather than its dynamics. Humphreys revised his definition
of simulation to accord with the remarks of Hartmann and Hughes as
follows:



> 
> 
> System S provides a core simulation of an object or process B just
> in case S is a concrete computational device that produces, via a
> temporal process, solutions to a computational model ... that
> correctly represents B, either dynamically or statically. If in
> addition the computational model used by S correctly represents the
> structure of the real system R, then S provides a core simulation of
> system R with respect to B. (2004, p. 110)




(Note that Humphreys is here defining computer simulation, not
simulation generally, but he is doing it in the spirit of defining a
compositional term.) It should be noted that Humphreys' definitions
make simulation out to be a success term, and that seems
unfortunate. A better definition would be one that, like the one in
the last section, included a word like "believed" or
"hoped" to address this issue.




In most philosophical discussions of computer simulation, the more
useful concept is the one defined in 1.2. The exception is when it is
explicitly the goal of the discussion to understand computer
simulation as an example of simulation more generally (see section
5). Examples of simulations that are not computer simulations include
the famous physical model of the San Francisco Bay (Huggins &
Schultz 1973). This is a working hydraulic scale model of the San
Francisco Bay and Sacramento-San Joaquin River Delta System built in
the 1950s by the Army Corps of engineers to study possible engineering
interventions in the Bay. Another nice example, which is discussed
extensively in (Dardashti et al., 2015, 2019) is the use of acoustic
"dumb holes" made out of Bose-Einstein condensates to
study the behavior of Black Holes. Physicist Bill Unruh noted that in
certain fluids, something akin to a black hole would arise if there
were regions of the fluid that were moving so fast that waves would
have to move faster than the speed of sound (something they cannot do)
in order to escape from them (Unruh 1981). Such regions would in
effect have sonic event horizons. Unruh called such a physical setup a
"dumb hole" ("dumb" as in "mute")
and proposed that it could be studied in order to learn things we do
not know about black holes. For some time, this proposal was viewed as
nothing more than a clever idea, but physicists have recently come to
realize that, using Bose-Einstein condensates, they can actually build
and study dumb holes in the laboratory. It is clear why we should
think of such a setup as a simulation: the dumb hole simulates the
black hole. Instead of finding a computer program to simulate the
black holes, physicists find a fluid dynamical setup for which they
believe they have a good model and for which that model has
fundamental mathematical similarities to the model of the systems of
interest. They observe the behavior of the fluid setup in the
laboratory in order to make inferences about the black holes. The
point, then, of the definitions of simulation in this section is to
try to understand in what sense computer simulation and these sorts of
activities are species of the same genus. We might then be in a better
situation to understand why a simulation in the sense of 1.3 which
happens to be run on a computer overlaps with a simulation in the
sense of 1.2. We will come back to this in section 5.




Barberousse et al. (2009), however, have been critical of this
analogy. They point out that computer simulations do not
work the way Unruh's simulation works. It is not the case that the
computer as a material object and the target system follow the same
differential equations. A good reference about
simulations that are not computer simulations is Trenholme 1994.


## 2. Types of Computer Simulations


Two types of computer simulation are often
distinguished: *equation-based simulations*
and *agent-based* (or
*individual-based*) *simulations*. Computer
Simulations of both types are used for three different general sorts of
purposes: prediction (both pointwise and global/qualitative),
understanding, and exploratory or heuristic purposes.


### 2.1 Equation-based Simulations




Equation-based simulations are most commonly used in the physical
sciences and other sciences where there is governing theory that can
guide the construction of mathematical models based on differential
equations. I use the term "equation based" here
to refer to simulations based on the kinds of global equations we
associate with physical theories--as opposed to "rules of
evolution" (which are discussed in the next section.) Equation
based simulations can either be particle-based, where there are n many
discrete bodies and a set of differential equations governing their
interaction, or they can be field-based, where there is a set of
equations governing the time evolution of a continuous medium or
field. An example of the former is a simulation of galaxy
formation, in which the gravitational interaction between a finite
collection of discrete bodies is discretized in time and space. 
An example of the latter is the simulation of a fluid, such as a
meteorological system like a severe storm. Here the system is
treated as a continuous medium--a fluid--and a field representing its
distribution of the relevant variables in space is discretized in space
and then updated in discrete intervals of time.


### 2.2 Agent-based simulations




Agent-based simulations are most common in the social and behavioral
sciences, though we also find them in such disciplines as artificial
life, epidemiology, ecology, and any discipline in which the networked
interaction of many individuals is being studied. 
Agent-based simulations are similar to particle-based simulations in
that they represent the behavior of n-many discrete individuals. 
But unlike equation-particle-based simulations, there are no global
differential equations that govern the motions of the
individuals. Rather, in agent-based simulations, the behavior of
the individuals is dictated by their own local rules




To give one example: a famous and groundbreaking agent-based
simulation was Thomas Schelling's (1971) model of
"segregation." The agents in his simulation
were individuals who "lived" on a chessboard. 
The individuals were divided into two groups in the society (e.g. two
different races, boys and girls, smokers and non-smokers, etc.) 
Each square on the board represented a house, with at most one person
per house. An individual is happy if he/she has a certain percent
of neighbors of his/her own group. Happy agents stay where they are,
unhappy agents move to free locations. Schelling found that the board
quickly evolved into a strongly segregated location pattern if the
agents' "happiness rules" were specified so that
segregation was heavily favored. Surprisingly, however, he also found
that initially integrated boards tipped into full segregation even if
the agents' happiness rules expressed only a mild preference for having
neighbors of their own type.


### 2.3 Multiscale Simulations




In section 2.1 we discussed equation-based models that are based on
particle methods and those that are based on field methods. 
But some simulation models are hybrids of different kinds of modeling
methods. Multiscale simulation models, in particular,
couple together modeling elements from different scales of
description. A good example of this would be a model that
simulates the dynamics of bulk matter by treating the material as a
field undergoing stress and strain at a relatively coarse level of
description, but which zooms into particular regions of the material
where important small scale effects are taking place, and models those
smaller regions with relatively more fine-grained modeling methods.
Such methods might rely on molecular dynamics, or quantum mechanics, or
both--each of which is a more fine-grained description of matter
than is offered by treating the material as a field. Multiscale
simulation methods can be further broken down into serial multiscale
and parallel multiscale methods. The more traditional
method is serial multi-scale modeling. The idea here is to
choose a region, simulate it at the lower level of description,
summarize the results into a set of parameters digestible by the higher
level model, and pass them up to into the part of the algorithm
calculating at the higher level.




Serial multiscale methods are not effective when the different scales
are strongly coupled together. When the different scales interact
strongly to produce the observed behavior, what is required is an
approach that simulates each region simultaneously. This is called
parallel multiscale modeling. Parallel multiscale modeling is the
foundation of a nearly ubiquitous simulation method: so called
"sub-grid" modeling. Sub-grid modeling refers to the
representation of important small-scale physical processes that occur
at length-scales that cannot be adequately resolved on the grid size
of a particular simulation. (Remember that many simulations discretize
continuous equations, so they have a relatively arbitrary finite
"grid size.") In the study of turbulence in fluids, for
example, a common practical strategy for calculation is to account for
the missing small-scale *vortices* (or *eddies*) that
fall inside the grid cells. This is done by adding to the large-scale
motion an *eddy viscosity* that characterizes the transport and
dissipation of energy in the smaller-scale flow--or any such
feature that occurs at too small a scale to be captured by the
grid.




In climate science and kindred disciplines, sub-grid modeling is
called "parameterization." This, again, refers to the
method of replacing processes--ones that are too small-scale or
complex to be physically represented in the model-- by a more
simple mathematical description. This is as opposed to other
processes--e.g., large-scale flow of the atmosphere--that are
calculated at the grid level in accordance with the basic theory. It is
called "parameterization" because various non-physical
*parameters* are needed to drive the highly approximative
algorithms that compute the sub-grid values. Examples of
parameterization in climate simulations include the descent rate of
raindrops, the rate of atmospheric radiative transfer, and the rate of
cloud formation. For example, the average cloudiness over a 100
km2 grid box is not cleanly related to the average humidity
over the box. Nonetheless, as the average humidity increases, average
cloudiness will also increase--hence there could be a parameter linking
average cloudiness to average humidity inside a grid box. Even
though modern-day parameterizations of cloud formation are more
sophisticated than this, the basic idea is well illustrated by the
example. The use of
sub-grid modeling methods in simulation has important consequences for
understanding the structure of the epistemology of
simulation. This will be discussed in greater detail in
section 4.




Sub-grid modelling methods can be contrasted with another kind of
parallel multiscale model where the sub-grid algorithms are more
theoretically principled, but are motivated by a theory at a different
level of description. In the example of the simulation of bulk matter
mentioned above, for example, the algorithm driving the smaller level
of description is not built by the seat-of-the-pants. The algorithm
driving the smaller level is actually more theoretically principled
than the higher level in the sense that the physics is more
fundamental: quantum mechanics or molecular dynamics vs. continuum
mechanics. These kinds of multiscale models, in other words, cobble
together the resources of theories at different levels of
description. So they provide for interesting examples that
provoke our thinking about intertheoretic relationships, and that
challenge the widely-held view that an inconsistent set of laws can
have no models. 


### 2.4 Monte Carlo Simulations




In the scientific literature, there is another large class of
computer simulations called Monte Carlo (MC) Simulations. MC
simulations are computer algorithms that use randomness to calculate
the properties of a mathematical model and where the randomness of the
algorithm is not a feature of the target model. A nice
example is the use of a random algorithm to calculate the value
of p. If you draw a unit square on a piece of
paper and inscribe a circle in it, and then randomly drop a collection
of objects inside the square, the proportion of objects that land in
the circle would be roughly equal to p/4. A
computer simulation that simulated a procedure like that would be
called a MC simulation for calculating p. 




Many philosophers of science have deviated from ordinary scientific
language here and have shied away from thinking of MC simulations as
genuine simulations. Grune-Yanoff and Weirich (2010) offer the
following reasoning: "The Monte Carlo approach does not have a
mimetic purpose: It imitates the deterministic system not in order to
serve as a surrogate that is investigated in its stead but only in
order to offer an alternative computation of the deterministic
system's properties" (p.30). This shows that MC
simulations do not fit any of the above definitions aptly. On the
other hand, the divide between philosophers and ordinary language can
perhaps be squared by noting that MC simulations simulate an imaginary
process that might be used for calculating something relevant to
studying some other process. Suppose I am modeling a planetary orbit
and for my calculation I need to know the value of p. If I do the
MC simulation mentioned in the last paragraph, I am simulating the
process of randomly dropping objects into a square, but what I am
modeling is a planetary orbit. This is the sense in which MC
simulations *are* simulations, but they are *not*
simulations *of* the systems they are being used to study.
However, as Beisbart and Norton (2012) point
out, some MC simulations (viz. those that use MC techniques to solve
stochastic dynamical equations referring to a physical system) are in
fact simulations of the systems they study. 


## 3. Purposes of Simulation




There are three general categories of purposes to which computer
simulations can be put. Simulations can be used for
heuristic purposes, for the purpose of predicting data that we do not
have, and for generating understanding of data that we do already
have.




Under the category of heuristic models, simulations can be further
subdivided into those used to communicate knowledge to others, and
those used to represent information to ourselves. When Watson and Crick
played with tin plates and wire, they were doing the latter at first,
and the former when they showed the results to others. When the army
corps built the model of the San Francisco Bay to convince the voting
population that a particular intervention was dangerous, they were
using it for this kind of heuristic purpose. Computer simulations can
be used for both of these kinds of purposes--to explore features of
possible representational structures; or to communicate knowledge to
others. For example: computer simulations of natural processes, such as
bacterial reproduction, tectonic shifting, chemical reactions, and
evolution have all been used in classroom settings to help students
visualize hidden structure in phenomena and processes that are
impractical, impossible, or costly to illustrate in a "wet"
laboratory setting.




Another broad class of purposes to which computer simulations can be
put is in telling us about how we should expect some system in the
real world to behave under a particular set of circumstances. Loosely
speaking: computer simulation can be used for prediction. We can use
models to predict the future, or to retrodict the past; we can use
them to make precise predictions or loose and general ones. With
regard to the relative precision of the predictions we make with
simulations, we can be slightly more fine-grained in our
taxonomy. There are a) Point predictions: Where will the planet Mars
be on October 21st, 2300? b) "Qualitative" or global or
systemic predictions: Is the orbit of this planet stable? What scaling
law emerges in these kinds of systems? What is the fractal dimension
of the attractor for systems of this kind? and c) Range predictions:
It is 66% likely that the global mean surface temperature will
increase by between 2-5 degrees C by the year 2100; it is
"highly likely" that sea level will rise by at least two
feet; it is "implausible" that the thermohaline will shut
down in the next 50 years.




Finally, simulations can be used to understand systems and their
behavior. If we already have data telling us how some system
behaves, we can use computer simulation to answer questions about how
these events could possibly have occurred; or about how those events
actually did occur.




When thinking about the topic of the next section, the epistemology
of computer simulations, we should also keep in mind that the
procedures needed to sanction the results of simulations will often
depend, in large part, on which of the above kind of purpose or
purposes the simulation will be put to.


## 4. The Epistemology of Computer Simulations




As computer simulation methods have gained importance in more and
more disciplines, the issue of their trustworthiness for generating new
knowledge has grown, especially when simulations are expected to be
counted as epistemic peers with experiments and traditional analytic
theoretical methods. The relevant question is always whether or not the
results of a particular computer simulation are accurate enough for
their intended purpose. If a simulation is being used to
*forecast* weather, does it predict the variables we are
interested in to a degree of accuracy that is sufficient to meet the
needs of its consumers? If a simulation of the atmosphere above a
Midwestern plain is being used to *understand* the structure of
a severe thunderstorm, do we have confidence that the structures in the
flow--the ones that will play an explanatory role in our account of why
the storm sometimes splits in two, or why it sometimes forms
tornados--are being depicted accurately enough to support our
confidence in the explanation? If a simulation is being used in
engineering and design, are the predictions made by the simulation
reliable enough to sanction a particular choice of design parameters,
or to sanction our belief that a particular design of airplane wing
will function? Assuming that the answer to these questions is sometimes
"yes", i.e. that these kinds of inferences are at least
sometimes justified, the central philosophical question is: what
justifies them? More generally, how can the claim that a simulation is
good enough for its intended purpose be evaluated? These are the
central questions of the epistemology of computer simulation
(EOCS).




Given that confirmation theory is one of the traditional
topics in philosophy of science, it might seem obvious that the
latter would have the resources to begin to approach these questions.
Winsberg (1999), however, argued that when it comes to topics related
to the credentialing of knowledge claims, philosophy of science has
traditionally concerned itself with the justification of theories, not
their application. Most simulation, on the other hand, to the extent
that it makes use of the theory, tends to make use of the
well-established theory. EOCS, in other words, is rarely about testing
the basic theories that may go into the simulation, and most often
about establishing the credibility of the hypotheses that are, in part,
the result of applications of those theories.


### 4.1 Novel features of EOCS




Winsberg (2001) argued that, unlike the epistemological issues that
take center stage in traditional confirmation theory, an adequate EOCS
must meet three conditions. In particular it must take account of
the fact that the knowledge produced by computer simulations is the
result of inferences that are *downward*, *motley*, and
*autonomous*.



> 
> *Downward*. EOCS must reflect the fact that in a large
> number of cases, accepted scientific theories are the starting point
> for the construction of computer simulation models and play an
> important role in the justification of inferences from simulation
> results to conclusions about real-world target systems. The
> word "downward" was meant to signal the fact that, unlike
> most scientific inferences that have traditionally interested
> philosophers, which move *up* from observation instances to
> theories, here we have inferences that are drawn (in part) from
> high theory, *down* to particular features of phenomena.
> 
> 
> 
> *Motley*. EOCS must take into account that simulation results
> nevertheless typically depend not just on theory but on many other
> model ingredients and resources as well, including parameterizations
> (discussed above), numerical solution methods, mathematical tricks,
> approximations and idealizations, outright fictions, ad hoc
> assumptions, function libraries, compilers and computer hardware, and
> perhaps most importantly, the blood, sweat, and tears of much trial and
> error.
> 
> 
> 
> *Autonomous*. EOCS must take into account the autonomy
> of the knowledge produced by simulation in the sense that the knowledge
> produced by simulation cannot be sanctioned entirely by comparison with
> observation. Simulations are usually employed to study phenomena where
> data are sparse. In these circumstances, simulations are meant to
> replace experiments and observations as sources of data about the world
> because the relevant experiments or observations are out of reach,
> for principled, practical, or ethical reasons.
> 
> 
> 




Parker (2013) has made the point that the usefulness of
these conditions is somewhat compromised by the fact that it is overly
focused on simulation in the physical sciences, and other disciplines
where simulation is theory-driven and equation-based. This seems
correct. In the social and behavioral sciences, and other
disciplines where agent-based simulation (see 2.2) are more the
norm, and where models are built in the absence of established and
quantitative theories, EOCS probably ought to be characterized in other
terms.




For instance, some social scientists who use agent-based simulation
pursue a methodology in which social phenomena (for example an
observed pattern like segregation) are explained, or accounted for, by
generating similar looking phenomena in their simulations (Epstein and
Axtell 1996; Epstein 1999). But this raises its own sorts of
epistemological questions. What exactly has been accomplished, what
kind of knowledge has been acquired, when an observed social
phenomenon is more or less reproduced by an agent-based simulation?
Does this count as an explanation of the phenomenon? A possible
explanation? (see e.g., Grune-Yanoff 2007). Giuseppe Primiero
(2019) argues that there is a whole domain of "artificial
sciences" built around agent-based and multi-agent system based
simulations, and that it requires its own epistemology--one where
validation cannot be defined by comparison with an existing real-world
system, but must be defined vis a vis an *intended* system.




It is also fair to say, as Parker does (2013), that the
conditions outlined above pay insufficient attention to the various and
differing purposes for which simulations are used (as discussed in
2.4). If we are using a simulation to make detailed
quantitative predictions about the future behavior of a target system,
the epistemology of such inferences might require more stringent
standards than those that are involved when the inferences being made
are about the general, qualitative behavior of a whole class of
systems. Indeed, it is also fair to say that much more work could
be done in classifying the kinds of purposes to which computer
simulations are put and the constraints those purposes place on the
structure of their epistemology.




Frigg and Reiss (2009) argued that none of these three conditions
are new to computer simulation. They argued that ordinary
'paper and pencil' modeling incorporate these
features. Indeed, they argued that computer simulation could not
possibly raise new epistemological issues because the epistemological
issues could be cleanly divided into the question of the
appropriateness of the model underlying the simulation, which is an
issue that is identical to the epistemological issues that arise in
ordinary modeling, and the question of the correctness of the solution
to the model equations delivered by the simulation, which is a
mathematical question, and not one related to the epistemology of
science. On the first point, Winsberg (2009b) replied that
it was the simultaneous confluence of all three features that was new
to simulation. We will return to the second point in section
4.3


### 4.2 EOCS and the epistemology of experiment




Some of the work on the EOCS has developed analogies between
computer simulation in order to draw on recent work in the epistemology
of experiment, particularly the work of Allan Franklin;
see the entry on 
 experiments in physics.




In his work on the epistemology of experiment, Franklin (1986,
1989) identified a number of strategies that experimenters use to
increase rational confidence in their results. Weissart (1997) 
and Parker (2008a) argued for various forms of analogy between these
strategies and a number of strategies available to simulationists to
sanction their results. The most detailed analysis of these
relationships is to be found in Parker 2008a, where she also uses
these analogies to highlight weaknesses in current approaches to
simulation model evaluation.




Winsberg (2003) also makes use of Ian Hacking's (1983, 1988,
1992) work on the philosophy of experiment. One of Hacking's
central insights about experiment is captured in his slogan that
experiments have a life of their own' (1992: 306). Hacking
intended to convey two things with this slogan. The first was a
reaction against the unstable picture of science that comes, for
example, from Kuhn. Hacking (1992) suggests that experimental results
can remain stable even in the face of dramatic changes in the other
parts of sciences. The second, related, point he intended to
convey was that 'experiments are organic, develop, change, and
yet retain a certain long-term development which makes us talk about
repeating and replicating experiments' (1992: 307). Some of the
techniques that simulationists use to construct their models get
credentialed in much the same way that Hacking says that instruments
and experimental procedures and methods do; the credentials develop
over an extended period of time and become deeply tradition-bound. In
Hacking's language, the techniques and sets of assumptions that
simulationists use become 'self-vindicating'. Perhaps a
better expression would be that they carry their own credentials. This
provides a response to the problem posed in 4.1, of understanding how
simulation could have a viable epistemology despite the motley and
autonomous nature of its inferences.




Drawing inspiration from another philosopher of experiment (Mayo
1996), Parker (2008b) suggests a remedy to some of the shortcomings in
current approaches to simulation model evaluation. In this work,
Parker suggests that Mayo's error-statistical approach for
understanding the traditional experiment--which makes use of the
notion of a "severe test"--could shed light on the
epistemology of simulation. The central question of the epistemology
of simulation from an error-statistical perspective becomes,
'What warrants our taking a computer simulation to be a severe
test of some hypothesis about the natural world? That is, what
warrants our concluding that the simulation would be unlikely to give
the results that it in fact gave, if the hypothesis of interest were
false (2008b, 380)? Parker believes that too much of what passes for
simulation model evaluation lacks rigor and structure because it:



> 
> 
> consists in little more than side-by-side comparisons of simulation
> output and observational data, with little or no explicit argumentation
> concerning what, if anything, these comparisons indicate about the
> capacity of the model to provide evidence for specific scientific
> hypotheses of interest. (2008b, 381)




Drawing explicitly upon Mayo's (1996) work, she argues that
what the epistemology of simulation ought to be doing, instead, is
offering some account of the 'canonical errors' that can
arise, as well as strategies for probing for their presence.


### 4.3 Verification and Validation




Practitioners of simulation, particularly in engineering contexts,
in weapons testing, and in climate science, tend to conceptualize
the EOCS in terms of *verification and validation*. 
*Verification* is said to be the process of determining whether
the output of the simulation approximates the true solutions to the
differential equations of the original model. *Validation*, on
the other hand, is said to be the process of determining whether the
chosen model is a good enough representation of the real-world system
for the purpose of the simulation. The literature on verification and
validation from engineers and scientists is enormous and it is
beginning to receive some attention from philosophers.




Verification can be divided into solution verification and code
verification. The former verifies that the output of the *intended
algorithm* approximates the true solutions to the differential
equations of the original model. The latter verifies that the
code, as written, carries out the intended algorithm. Code
verification has been mostly ignored by philosophers of science;
probably because it has been seen as more of a problem in computer
science than in empirical science--perhaps a mistake. Part of solution
verification consists in comparing computed output with analytic
solutions (so called "benchmark solutions"). 
Though this method can of course help to make case for the results of a
computer simulation, it is *by itself inadequate*, since
simulations are often used precisely because analytic solution is
unavailable for regions of solution space that are of interest. Other
indirect techniques are available: the most important of which is
probably checking to see whether and at what rate computed output
converges to a stable solution as the time and spatial resolution of
the discretization grid gets finer.




The principal strategy of validation involves comparing model output
with observable data. Again, of course, this strategy is
limited in most cases, where simulations are being run because
observable data are sparse. But complex strategies can be
employed, including comparing the output of subsystems of a simulation
to relevant experiments (Parker, 2013; Oberkampf and Roy
2010).




The concepts of verification and validation has drawn some criticism
from philosophers. Oreskes et al. 1994, a very widely-cited article,
was mostly critical of the terminology, arguing that
"validity," in particular, is a property that only applies
to logical arguments, and that hence the term, when applied to models,
might lead to overconfidence.




Winsberg (2010, 2018, p.155) has argued that the conceptual division
between verification and validation can be misleading, if it is taken
to suggest that there is one set of methods which can, by itself, show
that we have solved the equations right, and that there is another set
of methods, which can, by itself, show that we've got the right
equations. He also argued that it is misleading to think that the
epistemology of simulation is cleanly divided into an empirical part
(verification) and a mathematical (and computer science) part
(validation.) But this misleading idea often follows discussion of
verification and validation. We find this both in the work of
practitioners and philosophers.




Here is the standard line from a practitioner, Roy:
"Verification deals with mathematics and addresses the
correctness of the numerical solution to a given model. Validation, on
the other hand, deals with physics and addresses the appropriateness
of the model in reproducing experimental data. Verification can be
thought of as solving the chosen equations correctly, while validation
is choosing the correct equations in the first place" (Roy
2005).




Some philosophers have put this distinction to work in arguments
about the philosophical novelty of simulation. We first
raised this issue in section 4.1, where Frigg and Reiss argued that
simulation could have no epistemologically novel features, since it
contained two distinct components: a component that is identical
to the epistemology of ordinary modeling, and a component that is
entirely mathematical. "We should distinguish two
different notions of reliability here, answering two different
questions. First, are the solutions that the computer provides close
enough to the actual (but unavailable) solutions to be
useful?...this is a purely mathematical question and falls within
the class of problems we have just mentioned. So, there is nothing new
here from a philosophical point of view and the question is indeed one
of number crunching. Second, do the computational models that are the
basis of the simulations represent the target system correctly? That
is, are the simulation results externally valid? This is a serious
question, but one that is independent of the first problem, and
one that equally arises in connection with models that do not involve
intractable mathematics and ordinary experiments" (Frigg
and Reiss 2009).




But verification and validation are not, strictly speaking, so cleanly
separable. That is because most methods of validation, by themselves,
are much too weak to establish the validity of a simulation. And most
model equations chosen for simulation are not in any straightforward
sense "the right equations"; they are not the model
equations we would choose in an ideal world. We have good reason to
think, in other words, that there are model equations out there that
enjoy better empirical support, in the abstract. The equations we
choose often reflect a compromise between what we think best describes
the phenomena and computational tractability. So the equations that
are chosen are rarely well "validated" on their own. If we
want to understand why simulation results are taken to be credible, we
have to look at the epistemology of simulation as an integrated whole,
not as cleanly divided into verification and validation--each of
which, on its own, would look inadequate to the task.




So one point is that verification and validation are not
independently-successful and separable activities. But the other point
is that there are not two independent entities onto which these
activities can be directed: a model chosen to discretized, and a method
for discretizing it. Once one recognizes that the equations to be
"solved" are sometimes chosen *so as* to cancel out
discretization errors, etc. (Lenhard 2007 has a very nice example of
this involving the Arakawa operator), this later distinction gets harder
to maintain. So success is achieved in simulation with a kind of
back-and-forth, trial-and-error, piecemeal adjustment between model and
method of calculation. And when this is the case, it is hard even to
know what it means to say that a simulation is separately verified and
validated.




No one has argued that V&V isn't a useful distinction, but
rather that scientists shouldn't overinflate a pragmatically
useful distinction into a clean methodological dictate that
misrepresents the messiness of their own practice. Collaterally, Frigg
and Reiss's argument for the absence of epistemological novelty
in simulation fails for just this reason. It is not "a purely
mathematical question" whether the solutions that the computer
provides close enough to the actual (but unavailable) solutions to be
useful. At least not in this respect: it is not a question that can be
answered, as a pragmatic matter, entirely using mathematical
methods. And hence it is an empirical/epistemological issue that does
not arise in ordinary modeling.


### 4.4 EOCS and Epistemic Entitlement




A major strand of ordinary (outside of the philosophy of science)
epistemology is to emphasize the degree to which it is a condition for
the possibility of knowledge that we rely on our senses and the
testimony of other people in a way that we cannot ourselves justify.
 According to Tyler Burge (1993,1998), belief in the results of
these two processes are warranted but not justified. Rather,
according to Burge, we are *entitled* to these beliefs. 
"[w]e are entitled to rely, other things equal, on perception,
memory, deductive and inductive reasoning, and on...the word of
others" (1993, p. 458). Beliefs in which a believer is
entitled are those that are unsupported by evidence available to the
believer, but which the believer is nevertheless warranted in
believing.




Some work in EOCS has developed analogies between computer
simulation and the kinds of knowledge producing practices Burge
associates with *entitlement*. (See especially Barberousse
and Vorms, 2014, and Beisbart, 2017.) This is, in some ways, a
natural outgrowth of Burge's arguments that we view computer
assisted proofs in this way (1998). Computer simulations
are extremely complex, often the result of the epistemic labor of a
diverse set of scientists and other experts, and perhaps most
importantly, epistemically opaque (Humphreys, 2004). Because of
these features, Beisbart argues that it is reasonable to treat computer
simulations in the same way that we treat our senses and the testimony
of others: simply as things that can be trusted on the assumption
that everything is working smoothly. (Beisbart,
2017). 




Symons and Alvarado (2019) argue that there is a fundamental problem
with this approach to EOCS and it has to do with a feature of
computer-aided proof that was crucial to Burge's original
account: that of a being a 'transparent conveyor'.
"It is very important to note, for example, that Burge's
account of content preservation and transparent conveying requires
that the recipient already has reason not to doubt the source"
(p. 13). But Symons and Alvarado point to many of the properties of
computer simulations (drawing from Winsberg 2010 and Ruphy 2015) in
virtue of which they fail to have these properties. Lenhard and
Kuster 2019 is also relevant here, as they argue that there are
many features of computer simulation that make them difficult to
reproduce and that therefore undermine some of the stability that
would be required for them to be transparent conveyors. For these
reasons and others having to do with many of the features discussed in
4.2 and 4.3, Symons and Alvarado argue that it is implausible that we
should view computer simulation as a basic epistemic practice on a par
with sense perception, memory, testimony, or the like.


### 4.5 Pragmatic Approaches to EOCS




Another approach to EOCS is to ground it in the practical aspects of
the craft of modeling and simulation. According to this view, in
other words, the best account we can give of the reasons we have for
believing the results of computer simulation studies is to have trust
in the practical skills and craft of the modelers that use them. 
A good example of this kind of account is (Hubig and Kaminski,
2017). The epistemological goal of this kind of work is to
identify the locus of our trust in simulations in practical aspects of
the *craft of* modeling and simulation, rather than in any
features of the models themselves. (Resch et al, 2017) argue that
a good part of the reason we should trust simulations is not because of
the simulations themselves, but because of the interpretive artistry of
those who employ their art and skill to interpret simulation
outputs. Symons and Alvarado (2019) are also critical of this
approach, arguing that "Part of the task of the epistemology of
computer simulation is to explain the difference between the
contemporary scientist's position in relation to epistemically
opaque computer simulations.." (p.7) and the believers in a
mechanical oracle's relation to their oracles. Pragmatic
and epistemic considerations, according to Symons and Alvarado,
co-exist, and they are not possible competitors for the correct
explanation of our trust in simulations--the epistemic reasons are
ultimate what explain and ground the pragmatic ones. 


## 5. Simulation and Experiment




Working scientists sometimes describe simulation studies in
experimental terms. The connection between simulation and
experiment probably goes back as far as von Neumann, who, when
advocating very early on for the use of computers in physics, noted
that many difficult experiments had to be conducted merely to determine
facts that ought, in principle, to be derivable from theory. Once
von Neumann's vision became a reality, and some of these
experiments began to be replaced by simulations, it became somewhat
natural to view them as versions of experiment. A
representative passage can be found in a popular book on
simulation:



> 
> 
> A simulation that accurately mimics a complex phenomenon contains a
> wealth of information about that phenomenon. Variables such as
> temperature, pressure, humidity, and wind velocity are evaluated at
> thousands of points by the supercomputer as it simulates the
> development of a storm, for example. Such data, which far exceed
> anything that could be gained from launching a fleet of weather
> balloons, reveals intimate details of what is going on in the storm
> cloud. (Kaufmann and Smarr 1993, 4)




The idea of "in silico" experiments becomes even more
plausible when a simulation study is designed to learn what happens to
a system as a result of various possible interventions: What would
happen to the global climate if *x* amount of carbon were added
to the atmosphere? What will happen to this airplane wing if it is
subjected to such-and-such strain? How would traffic patterns change
if an onramp is added at this location?




Philosophers, consequently, have begun to consider in what sense, if
any, computer simulations are like experiments and in what sense they
differ. A related issue is the question of when a process that
fundamentally involves computer simulation can counts as measurement
(Parker, 2017) A number of views have emerged in the literature
centered around defending and criticizing two theses:



> 
> *The identity thesis*. Computer simulation studies are
> literally instances of experiments.
> 
> 
> *The epistemological dependence thesis*. The identity
> thesis would (if it were true) be a good reason (weak version), or the
> best reason (stronger version), or the only reason (strongest version;
> it is a necessary condition) to believe that simulations can provide
> warrants for belief in the hypotheses that they support. A
> consequence of the strongest version is that only if the identity
> thesis is true is there reason to believe that simulations can confer
> warrant for believing in hypotheses.
> 
> 
> 




The central idea behind the epistemological dependence thesis is
that experiments are the canonical entities that play a central role in
warranting our belief in scientific hypotheses, and that therefore the
degree to which we ought to think that simulations can also play a role
in warranting such beliefs depends on the extent to which they can be
identified as a kind of experiment.




One can find philosophers arguing for the identity thesis as early as
Humphreys 1995 and Hughes 1999. And there is at least implicit support
for (the stronger) version of the epistemological dependence thesis in
Hughes. The earliest explicit argument in favor of the epistemological
dependence thesis, however, is in Norton and Suppe 2001. According to
Norton and Suppe, simulations can warrant belief precisely because
they literally are experiments. They have a detailed story to tell
about in what sense they are experiments, and how this is all supposed
to work. According to Norton and Suppe, a valid simulation is one in
which certain formal relations (what they call
'realization') hold between a base model, the modeled
physical system itself, and the computer running the algorithm. When
the proper conditions are met, 'a simulation can be used as an
instrument for probing or detecting real world phenomena. Empirical
data about real phenomena are produced under conditions of
experimental control' (p. 73).




One problem with this story is that the formal conditions that they
set out are much too strict. It is unlikely that there are very many
real examples of computer simulations that meet their strict standards.
Simulation is almost always a far more idealizing and approximating
enterprise. So, if simulations are experiments, it is probably
not in the way that Norton and Suppe imagined.




More generally, the identity thesis has drawn fire from other
quarters.




Gilbert and Troitzsch argued that "[t]he major difference is
that while in an experiment, one is controlling the actual object of
interest (for example, in a chemistry experiment, the chemicals under
investigation), in a simulation one is experimenting with a model
rather than the phenomenon itself." (Gilbert and Troitzsch 1999,
13). But this doesn't seem right. Many (Guala 2002, 2008, Morgan 2003,
Parker 2009a, Winsberg 2009a) have pointed to problems with the
claim. If Gilbert and Troitzsch mean that simulationists manipulate
models in the sense of abstract objects, then the claim is difficult
to understand--how do we manipulate an abstract entity? If, on
the other hand, they simply mean to point to the fact that the
physical object that simulationists manipulate--a digital
computer--is not the actual object of interest, then it is not
clear why this differs from ordinary experiments. 




It is false that real experiments always manipulate exactly their
targets of interest. In fact, in both real experiments and
simulations, there is a complex relationship between what is
manipulated in the investigation on the one hand, and the real-world
systems that are the targets of the investigation on the other. In
cases of both experiment and simulation, therefore, it takes an
argument of some substance to establish the 'external
validity' of the investigation - to establish that what is
learned about the system being manipulated is applicable to the system
of interest. Mendel, for example, manipulated pea plants, but he was
interested in learning about the phenomenon of heritability
generally. The idea of a *model organism* in biology makes this
idea perspicuous. We experiment on *Caenorhabditis elegans*
because we are interested in understanding how organism in general use
genes to control development and genealogy. We experiment
on *Drosophila melanogaster*, because it provides a
useful model of mutations and genetic inheritance. But the idea is not
limited to biology. Galileo experimented with inclined planes because
he was interested in how objects fall and how they would behave in the
absence of interfering forces--phenomena that the inclined plane
experiments did not even actually instantiate.




Of course, this view about experiments is not uncontested. It is
true that, quite often, experimentalists infer something about a system
distinct from the system they interfere with. However, it is not clear
whether this inference is proper part of the original experiment.
Peschard (2010) mounts a criticism along these lines, and hence can be
seen as a defender of Gilbert and Troitzsch. Peschard argues that the
fundamental assumption of their critics--that in experimentation,
just as in simulation, what is manipulated is a system standing in for
a target system--is confused. It confuses, Peschard argues, the
*epistemic target* of an experiment with its *epistemic
motivation.* She argues that while the epistemic motivation for
doing experiments on *C. elegans* might be quite far-reaching,
the proper epistemic target for any such experiment is the worm
itself. In a simulation, according to Peschard, however, the
epistemic target is never the digital computer itself. Thus,
simulation is distinct from experiment, according to her, in that its
epistemic target (as opposed to merely its epistemic motivation) is
distinct from the object being manipulated. Roush (2017) can also be
seen as a defender of the Gilbert and Troitzsch line, but Roush
appeals to sameness of natural kinds as the crucial feature that
separates experiments and simulations. Other opponents of the identity
thesis include Giere (2009) and Beisbart and Norton (2012, Other
Internet Resources).




It is not clear how to adjudicate this dispute, and it seems to
revolve primarily around a difference of emphasis. One can
emphasize the *difference* between experiment and simulation,
following Gilbert and Troitzsch and Peschard, by insisting that
experiments teach us first about their epistemic targets and only
secondarily allow inferences to the behavior of other systems. 
(I.e., experiments on worms teach us, in the first instance, about
worms, and only secondarily allow us to make inferences about genetic
control more generally.) This would make them conceptually
different from computer simulations, which are not thought to teach us,
in the first instance, about the behavior of computers, and only in the
second instance about storms, or galaxies, or whatever.




Or one can emphasize *similarity* in the opposite way. One can
emphasize the degree to which experimental targets are always chosen
as surrogates for what's really of interest. Morrison, 2009 is
probably the most forceful defender of emphasizing this aspect of the
similarity of experiment and simulation. She argues that most
experimental practice, and indeed most measurement practice, involve
the same kinds of modeling practices as simulations. In any case,
pace Peschard, nothing but a debate about nomenclature--and maybe
an appeal to the ordinary language use of scientists; not always the
most compelling kind of argument--would prevent us from saying
that the epistemic target of a storm simulation is the computer, and
that the storm is merely the epistemic motivation for studying the
computer.




Be that as it may, many philosophers of simulation, including those
discussed in this section, have chosen the latter path--partly as
a way of drawing attention to ways in which the message lurking behind
Gilbert and Troitzsch's quoted claim paints an overly simplistic
picture of experiment. It does seem overly simplistic to paint a
picture according to which experiment gets a *direct grip* on
the world, whereas simulation's situation is *exactly
opposite*. And this is the picture one seems to get from the
Gilber and Troitzsch quotation. Peschard's more sophisticated picture
involving a distinction between epistemic targets and epistemic
motivations goes a long way towards smoothing over those concerns
without pushing us into the territory of thinking that simulation and
experiment are *exactly the same*, in this regard.




Still, despite rejecting Gilbert and Troitzsch's
characterization of the difference between simulation and experiment,
Guala and Morgan both reject the identity thesis. Drawing on the
work of Simon (1969), Guala argues that simulations differ
fundamentally from experiments in that the object of manipulation in an
experiment bears a material similarity to the target of interest, but
in a simulation, the similarity between object and target is merely
formal. Interestingly, while Morgan accepts this argument against the
identity thesis, she seems to hold to a version of the
*epistemological dependency thesis*. She argues, in other words,
that the difference between experiments and simulations identified by
Guala implies that simulations are epistemologically inferior to real
experiments - that they have intrinsically less power to warrant
belief in hypotheses about the real world *because* they are not
experiments.




A defense of the epistemic power of simulations against Morgan's
(2002) argument could come in the form of a defense of the identity
thesis, or in the form of a rejection of the epistemological
dependency thesis. On the former front, there seem to be two problems
with Guala's (2002) argument against the identity thesis. The
first is that the notion of material similarity here is too weak, and
the second is that the notion of mere formal similarity is too vague,
to do the required work. Consider, for example, the fact that it is
not uncommon, in the engineering sciences, to use simulation methods
to study the behavior of systems fabricated out of silicon. The
engineer wants to learn about the properties of different design
possibilities for a silicon device, so she develops a computational
model of the device and runs a simulation of its behavior on a digital
computer. There are deep material similarities between, and some of
the same material causes are at work in, the central processor of the
computer and the silicon device being studied. On Guala's line
of reasoning, this should mark this as an example of a real
experiment, but that seems wrong. The peculiarities of this example
illustrate the problem rather starkly, but the problem is in fact
quite general: any two systems bear some material similarities to each
other and some differences.




On the flip side, the idea that the existence of a formal similarity
between two material entities could mark anything interesting is
conceptually confused. Given any two sufficiently complex entities,
there are many ways in which they are formally identical, not to
mention similar. There are also ways in which they are formally
completely different. Now, we can speak loosely, and say that two
things bear a formal similarity, but what we really mean is that our
best formal representations of the two entities have formal
similarities. In any case, there appear to be good grounds for rejecting both
the Gilbert and Troitzsch and the Morgan and Guala grounds for
distinguishing experiments and simulations. 




Returning to the defense of the epistemic power of simulations, there
are also grounds for rejecting the epistemological dependence thesis.
As Parker (2009a) points out, in both experiment and simulation, we
can have relevant similarities between computer simulations and target
systems, and that's what matters. When the relevant background
knowledge is in place, a simulation can provide more reliable
knowledge of a system than an experiment. A computer simulation of the
solar system, based on our most sophisticated models of celestial
dynamics, will produce better representations of the planets'
orbits than any experiment. 



Parke (2014) argues against the epistemological dependency thesis by
undermining two premises that she believes support it: first, that
experiments generate greater inferential power than simulations, and
second, that simulations cannot surprise us in the same way that
experiments can. The argument that simulations cannot surprise us
comes from Morgan (2005). Pace Morgan, Parke argues that
simulationists are often surprised by their simulations, both because
they are not computationally omniscient, and because they are not
always the sole creators of the models and code they use. She argues,
moreover, that '[d]ifferences in researcher's epistemic states, alone,
seem like the wrong grounds for tracking a distinction between
experiment and simulation' (258). Adrian Curry (2017) defends
Morgan's original intuition by making two friendly amendments. He
argues that the distinction Morgan was really after was between two
different kinds of surprise, and in particular to what the source of
surprise is: surprise due to bringing out theoretical knowledge into
contact with the world are distinctive of experiment. He also more
carefully defines surprise in a non-psychological way such that it is
a "quality the attainment of which constitutes genuine epistemic
progress" (p. 640).


## 6. Computer Simulation and the structure of scientific theories




Paul Humphreys (2004) has argued that computer simulations
have profound implications for our understanding of the structure of
theories; he argues that they reveal inadequacies with both the
semantic and syntactic views of scientific theories. This claim has
drawn sharp fire from Roman Frigg and Julian Reiss (2009). Frigg and
Reiss argue that whether a model admits of analytic solution or not has
no bearing on how it relates to the world. They use the example of the
double pendulum to show this. Whether or not the pendulum's inner
fulcrum is held fixed (a fact which will determine whether the relevant
model is analytically solvable) has no bearing on the semantics of the
elements of the model. From this, they conclude that the semantics of a
model, or how it relates to the world, is unaffected by whether or not
the model is analytically solvable.




 This was not responsive, however,
to the most charitable reading of what Humphreys was pointing at. The
syntactic and semantic views of theories, after all, were not just
accounts of how our abstract scientific representations relate to the
world. More particularly, they were not stories about the
relation between particular models and the world, but rather about the
relation between *theories* and the world, and the role, if any,
that models played in that relation.




They were also stories that had a lot to say about where the
philosophically interesting action is when it comes to scientific
theorizing. The syntactic view suggested that scientific practice could
be adequately rationally reconstructed by thinking of theories as
axiomatic systems, and, more importantly, that logical deduction was a
useful regulative ideal for thinking about how inferences from theory
to the world are drawn. The syntactic view also, by omission, made if
fairly clear that modeling played, if anything, only a
*heuristic* role in science. (This was a feature of the
syntactic view of theories that Frederick Suppe, one of its most ardent
critics, often railed against.) Theories themselves had nothing
to do with models, and theories could be compared *directly* to
the world, without any important role for modeling to play.




The semantic view of theories, on the other hand, did emphasize an
important role for models, but it also urged that theories were
non-linguistic entities. It urged philosophers not to be distracted by
the contingencies of the particular form of linguistic expression a
theory might be found in, say, a particular textbook.




Computer simulations, however, do seem to illustrate that both of
these themes were misguided. It was profoundly wrong to think that
logical deduction was the right tool for rationally reconstructing the
process of theory application. Computer simulations show that there are
methods of theory application that vastly outstrip the inferential
power of logical deduction. The space of solutions, for example, that
is available via logical deduction from the theory of fluids is
microscopic compared with the space of applications that can be
explored via computer simulation. On the flip side, computer
simulations seem to reveal that, as Humphreys (2004) has urged, syntax
matters. It was wrong, it turns out, to suggest, as the semantic
view did, that the particular linguistic form in which a scientific
theory is expressed is philosophically uninteresting. The syntax of the
theory's expression will have a deep effect on what inferences
can be drawn from it, what kinds of idealizations will work well with
it, etc. Humphreys put the point as follows: "the
specific syntactic representation used is often crucial to the
solvability of the theory's equations" (Humphreys 2009,
p.620). The theory of fluids can be used to
emphasize this point: whether we express that theory in Eulerian or
Lagrangian form will deeply affect what, in practice, we can calculate
and how; it will affect what idealizations, approximations, and
calculational techniques will be effective and reliable in which
circumstances. So the epistemology of computer simulation needs
to be sensitive to the particular syntactic formulation of a theory,
and how well that particular formulation has been credentialed. 
Hence, it does seem right to emphasize, as Humphreys (2004) did, that
computer simulations have revealed inadequacies with both the syntactic
and semantic theories.


## 7. Emergence




Paul Humphreys (2004) and Mark Bedau (1997, 2011) have argued that
philosophers interested in the topic of emergence can learn a great
deal by looking at computer simulation. Philosophers
interested in this topic should consult the entry on 
 emergent properties,
where the contributions of all these philosophers have been
discussed. 




The connection between emergence and simulation was perhaps best
articulated by Bedau in his (2011). Bedau argued that any
conception of emergence must meet the twin hallmarks of explaining how
the whole depends on its parts and how the whole is independent of its
parts. He argues that philosophers often focus on what he calls
"strong" emergence, which posits brute downward causation that is
irreducible in principle. But he argues that this is a
mistake. He focuses instead on what he calls "weak"
emergence, which *allows* for reducibility of wholes to parts
*in principle* but not *in practice*. Systems that
produce emergent properties are mere mechanisms, but the mechanisms are
very complex (they have very many independently interacting parts). As
a result, there is no way to figure out exactly what will happen given
a specific set of initial and boundary conditions, except to "crawl the
causal web". It is here that the connection to computer
simulation arises. Weakly emergent properties are characteristic
of complex systems in nature. And it is also characteristic of
complex computer simulations that there is no way to predict what they
will do except to let them run. Weak emergence explains, according to
Bedau, why computer simulations play a central role in the
science of complex systems. The best way to understand and predict how
real complex systems behave is to simulate them by crawling the
micro-causal web, and see what happens.


## 8. Fictions


 Models of course involve idealizations. But it has been argued
that some kinds of idealization, which play an especially prominent
role in the kinds of modeling involved in computer simulation, are
special--to the point that they deserve the title of
"fiction." This section will discuss attempts to define
fictions and explore their role in computer simulation.




There are two different lines of thinking about the role of fictions
in science. According to one, all models are fictions. This line of
thinking is motivated by considering the role, for example, of
"the ideal pendulum" in science. Scientists, it is argued,
often make claims about these sorts of entities (e.g., "the
ideal pendulum has a period proportional to the square-root of its
length") but they are nowhere to be found in the real world;
hence they must be fictional entities. This line of argument about
fictional entities in science does not connect up in any special way
with computer simulation--readers interested in this topic should
consult the entry on
 scientific representation
 [forthcoming].




Another line of thinking about fictions is concerned with the question
of what sorts of representations in science ought to be regarded as
fictional. Here, the concern is not so much about the ontology of
scientific model entities, but about the representational character of
various postulated model entities. Here, Winsberg (2009c) has argued
that fictions do have a special connection to computer simulations. Or
rather, that some computer simulations contain elements that best
typify what we might call fictional representations in science, even
if those representations are not uniquely present in simulations. 




He notes that the first conception of a fiction--mentioned
above--which makes "any representation that contradicts
reality a fiction" (p. 179), doesn't correspond to our ordinary
use of the term: a rough map is not fiction. He then proposes an
alternative definition: nonfiction is offered as a "good
enough" guide to some part of the world (p. 181); fiction is
not. But the definition needs to be refined. Take the fable of the
grasshopper and the ant. Although the fable offers lessons about how
the world is, it is still fiction because it is "a useful guide
to the way the world is in some general sense" rather than a
specific guide to the way a part of the world is, its "prima
facie representational target", a singing grasshopper and
toiling ant. Nonfictions, on the other hand, "point to a certain
part of the world" and are a guide to that part of the world
(p. 181).




These kinds of fictional components of models are
paradigmatically exemplified in certain computer simulations. Two of
his examples are the "silogen atom" and "artificial
viscosity." Silogen atoms appear in certain nanomechanical models
of cracks in silicon--a species of the kind of multiscale models
that blend quantum mechanics and molecular mechanics mentioned in
section 2.3. The silogen containing models of crack propagation in
silicon work by describing the crack itself using quantum mechanics and
the region immediately surrounding the crack using classical molecular
dynamics. To bring together the modeling frameworks in the two regions,
the boundary gets treated as if it contains 'silogen'
atoms, which have a mixture of the properties of silicon and those of
hydrogen. Silogen atoms are fictions. They are not offered as even a
'good enough' description of the atoms at the
boundary--their prima facie representational targets. But they are
used so that the overall model can be hoped to get things right. Thus
the overall model is not a fiction, but one of its components is.
Artificial viscosity is a similar sort of example. Fluids with abrupt
shocks are difficult to model on a computational grid because the
abrupt shock hides inside a single grid cell, and cannot be resolved by
such an algorithm. Artificial viscosity is a technique that pretends
that the fluid is highly viscous--a fiction--right were the
shock is, so that he shock becomes less abrupt, and blurs over several
grid cells. Getting the viscosity, and hence the thickness of the
shock, wrong, helps to get the overall model to work "well
enough." Again, the overall model of the fluid is not a fiction,
it is a reliable enough guide to the behavior of the fluid. But the
component called artificial viscosity is a fiction--it is not
being used to reliably model the shock. It is being incorporated into a
larger modeling framework so as to make that larger framework,
"reliable enough."




This account has drawn two sorts of criticisms. Toon (2010) has
argued that this definition of a fiction is too narrow. He gives
examples of historical fictions like *I, Claudius*, and
*Schindler's Ark*, which he argues are fictions, despite
the fact that "they are offered as 'good enough'
guides to those people, places and events in certain respects and we
are entitled to take them as such." (p. 286-7). Toon, presumably,
supports a broader conception of the role of fictions in science, then,
according to which they do not play a particularly prominent or
heightened role in computer simulation.




Gordon Purves (forthcoming) argues that there are examples of
fictions in computational models (his example is so-called
"imaginary cracks"), and elsewhere, that do not meet the
strict requirements discussed above. Unlike Toon, however, he also
wants to delineate fictional modeling elements from the non-fictional
ones. His principal criticism is of the criterion of fictionhood in
terms of social norms of use--and Purves argues that we ought to
be able to settle whether or not some piece of modeling is a fiction in
the absence of such norms. Thus, he wants to find an intrinsic
characterization of a scientific fiction. His proposal takes as
constitutive of model fictions that they fail to have the
characteristic that Laymon (1985) called "piecewise
improvability" (PI). PI is a characteristic of many models that
are idealizations; it says that as you de-idealize, your model becomes
more and more accurate. But as you de-idealize a silogen atom, you do
not get a more and more accurate simulation of a silicon crack. But
Purves takes this failure of PI to be constitutive of a fiction, rather
than merely symptomatic of them.