The central aim of this chapter was to answer questions related to the ontology, semantics, and methodology of computer simulations. The chapter first focused on distinguishing between analogical simulations and computer simulations, drawing important ontological and semantic differences for use in future chapters. Once I established the general category of simulation, the next step was to distinguish the representational capacity of computer simulations over mere reckoning power as the most prominent epistemic virtue. Another important conceptual distinction was to narrow down the class of computer simulations of interest to equation-based simulations, excluding in this way cellular automata, agent-based simulations, and complex systems from the scope of this work. This distinction is paramount for the analysis of the explanatory power of computer simulation, mainly due to the specific representational characteristics that an equation-base simulation offers.
Finally, my analysis focused on the methodology of computer simulations. These analyses were illustrated with a concrete example of a computer simulation as used in current scientific practice. Finally, I proposed a working conceptualization of
computer simulations which corresponds to current scientific uses of equation-based simulations.
Notes
1A recent comparison between the computer and the brain shows that even though computers are faster to calculate and can store more information, a human brain is much more efficient (Fischetti, 2011).
2Cf. (Humphreys, 2004, 110).
3For instance, (Guala, 2002; Parker, 2009; Winsberg, 2009b).
4On this last point, (cf. Kitcher, 1993, 27). More specifically, these structures are understood as natural kinds, objective causal relationships, objective natural necessities, and similar concepts that philosophers use to account for the metaphysics of science. See (Kitcher, 1986, 1994).
5In this work, I shall not make any conceptual difference among terms such as ‘describing,’ ‘rep-resenting,’ ‘standing for,’ and the like. There is a vast literature on the topic. See, for instance, (Frigg, 2009a; Hughes, 1997; Giere, 2009).
6Other philosophers and scientists that take the same stand on this distinction are (Haugeland, 1981; Von Neumann, 1958; Wiener, 1961).
7Cf. (Goodman, 1968, 159-160).
8Cf. (Goodman, 1968, 161).
9Cf. (Lewis, 1971, 324).
10Cf. (Lewis, 1971, 327).
11Virtually every philosopher of experimentation shares these ideas. A shortlist includes (Brown, 1991, 1994; Franklin, 1986; Galison, 1997; Hacking, 1983, 1988; Woodward, 2003).
12Cf. (Pylyshyn, 1984, 144).
13The controversial point here is the idea of ‘parallel causal-structures isomorphic to the phe-nomenon.’ For a closer look, please refer to (Trenholme, 1994, 118). For the sake of the argument, I will take it simply as a way to describe two system sharing the same causal relations. I base my interpretation on what the author says in the appendix: “the simulated system causally af-fects the simulating system through sensory input thereby initiating a simulation run whose causal structure parallels that of the run being undergone by the simulated system” (Trenholme, 1994, 128). All things considered, it is not clear what the author takes as causal-structures. Also, the introduction of ‘isomorphism’ as the relation of representation can be problematic. On this last point, see (Suárez, 2003).
14Cf. (Trenholme, 1994, 118).
15Unfortunately, the author leaves the notion ofintentional concepts undefined. Given that these terms belong to the terminological canon of the cognitive sciences, and given that Trenholme is following Pylyshyn in many respects, it seems appropriate to suggest that a definition could be found in Pylyshyn’s work. However, it is not possible to find a clear definition in Pylyshyn’s work that could be of help. Instead, Pylyshyn talks ofintentional terms (cf. Pylyshyn, 1984, 5), intentional explanation (cf. Pylyshyn, 1984, 212), intentional objects (cf. Pylyshyn, 1984, 262), intentional descriptions (cf. Pylyshyn, 1984, 20), and similar concepts, but no direct reference to intentional concepts whatsoever.
16On this point (cf. Trenholme, 1994, 119). Let it be noted that this claim is the equivalent to Pylyshyn’s description of physical manipulation processes. See (Trenholme, 1994, 144).
17Trenholme uses the notions ofsymbolic process andsymbolic computationindistinguishably. Cf.
(Trenholme, 1994, 118).
18Ian Hacking coined the term ‘life of its own’ to refer to laboratory practice that is independent and not driven by higher level theories (Hacking, 1983, 150). My concept here emphasizes the other side, that is, that the results of the simulation depend on the model, and it is only because some models represent an empirical system that those results can be related to the external world.
19Humphreys calls this view ‘selective entity realism.’ Cf. (Humphreys, 2004, 84).
20For more discussion on this issue, see (Durán, 2013a). The remainder of this section is a part of that paper.
21Cf. (Humphreys, 1991, 497-498).
22Cf. (Humphreys, 1991, 500).
23For the rest of this work, ‘to be analytically solvable,’ ‘to be solved by an analytic method,’ or similar assertions refer to finding solutions of a model by pen-and-paper mathematics.
24Cf. (Humphreys, 1991, 502).
25A notable exception is (García and Velasco, 2013).
26See (Guala, 2002).
27This is the opinion of (Humphreys, 2004; Morgan, 2005; Winsberg, 2003).
28For each one of these uses, cf. (Hartmann, 1996).
29Cf. (Humphreys, 2004, 60).
30Cf. (Humphreys, 2004, 68).
31Cf. (Wolfram, 1984a, vii).
32Cf. (Vichniac, 1984, 113).
33See, for instance, (Omohundro, 1984; Wolfram, 2002).
34Of course, not every proponent of cellular automata defends these assumptions. There is, how-ever, a special branch of philosophy known as ‘pan-computationalism’ that defends most of the metaphysical assumptions (Wootters and Langton, 1990; Smith et al., 1984; Hillis, 1984; Gosper, 1984).
35For instance, (Lesne, Online).
36Tommaso Toffoli is of this opinion. See (Toffoli, 1984).
37See, for instance, (Bedau and Humphreys, 2008; Bedau, 1997; Humphreys, 1997).
38For further reading on this topic, see (Wootters and Langton, 1990; Toffoli, 1984).
39A good example of this kind of work is (Omohundro, 1984).
40(Lotka, 1910).
41For a more detailed analysis on the distinctionprecision andaccuracy, see the Lexicon.
42For examples of the uses of theoretical simulations, see (Tymoczko, 1979; Babuska et al., 2000).
43A ‘word’ represents the minimum unit of data used by a particular processor design. It is a fixed sized group of bits that are handled as a unit by the hardware of the processor.
44For more on numerical methods see, for instance (Press et al., 2007).
45The prefix ‘pseudo’ is important here for at least two reasons: first, because these methods are based on an algorithm that produces numbers on a recursive basis, possibly repeating the series of numbers produced. Second, because computers make use of words that are finite in size, reducing significantly the amount of numbers generated. In any case, pure randomness in computers can never be achieved.
46Arguably, it is the only stochastic method. Any other so-called stochastic method (stratified sampling, importance sampling, etc.) is an adaptation of the original Monte Carlo. See (Metropolis and Ulam, 1949; Metropolis, 1987).
47For more on the Monte Carlo methods, see (Grimmett and Stirzaker, 1992).
48See (Oberkampf et al., 2003).
49See (Oberkampf and Roy, 2010; Oberkampf and Trucano, 2008).
50For a complete list, see (Atkinson et al., 2009; Gould et al., 2007).
51See the Lexicon and (Butcher, 2008).
52A good example of this, but at the level of computer hardware, is von Neumann’s architecture that has been the same since his 1945 report (von Neumann, 1945).
53I have slightly modified Woolfson and Pert’s example. Cf. (Woolfson and Pert, 1999, 20). In the original example, the authors indicate four bodies where one is the planet, and the satellite is divided into the other three (the three positions of the satellite under tidal stress). The modification clarifies a source of possible confusion that the simulation is about a 4-body problem, when in reality it is only a two body problem. I also reduce the mass of the first body. It originally was the size of Jupiter (i.e.,1.8986x1027kg), but in such a case the satellite would collapse into it.
54Thanks to Dr. Ing. Wolfgang Nowak for discussion on this point.
55Also known as ‘internal validity’ and ‘external validity,’ respectively.
56Cf. (Oberkampf and Roy, 2010, Preface).
57See (Oberkampf et al., 2003).
58See (Oberkampf and Roy, 2010, 21-29) for an analysis on the diversity of concepts. Also, see (Salari, 2003; Sargent, 2007; Naylor et al., 1967b).
59Cf. (Morrison, 2009, 43).
60See also (ASME, 2006, 10) and (Mihram, 1972; Nelson, 1992; Oberkampf et al., 2003; Oreskes et al., 1994; Sargent, 2007).
61Also referred to assolution verification in (Oberkampf and Roy, 2010, 26), or asnumerical error estimation in (Oberkampf et al., 2003, 26).
62Cf. (Oberkampf et al., 2003, 26).
63Cf. (MacKenzie, 2006, 130).
64For a more detailed discussion on Figure 3.5, see (Oberkampf and Roy, 2010, 23-31).
65For a recent philosophical work on errors, see (Parker, 2008).
66See (Franklin, 1990, 109).
67For a cogent history of computation, see (Rojas and Hashagen, 2000; Ceruzzi, 1998).
68See (Cipra, 1995; Moler, 1995). Also see http://www.cs.earlham.edu/~dusko/cs63/fdiv.html.
69See, for instance (Cohn, 1989).
70See, for instance (Koren and Krishna, 2007; Al-Arian, 1992; Lee and Anderson, 1990).
71See, for instance (Tanenbaum and Woodhull, 2006; Tews et al., 2009; Klein et al., 2009).
72For more on this point, see (Jason, 1989; Mayo and Spanos, 2010; Mayo, 2010).
Chapter 4
Theoretical assumptions behind scientific explanation
4.1 Introduction
In previous chapters, my efforts have been focused on elucidating the notion of computer simulation. These efforts are now going to be cashed out in my defense of the epistemic power of computer simulations. When philosophers discuss the epistemic power of computer simulations, they are interested in questions such as
“what can we learn by running a computer simulation?” or “what kind of knowledge about the world does a computer simulation yield?” This chapter begins my attempt to answer these questions in a qualitative and systematic way. The motivation is that by showing that computer simulations have explanatory power, I will also be defending their epistemic value. In other words, since scientific explanation is an epistemic activity par excellence, then showing how computer simulations explain will be emphasizing precisely their epistemic value.
The many aspects of scientific explanation which must be addressed force me to divide my findings into two chapters. The current chapter discusses theoretical assumptions behind scientific explanation. This chapter also analyzes suitable the-ories of scientific explanation as candidates for computer simulations. One of the results of analyzing these candidates is that the unificationist theory of scientific explanation emerges as the most suitable conceptual framework for explanation in computer simulations. However, it is not until the next chapter that I discuss the unificationist approach.
A central issue arising here, then, is related to the metaphysics of scientific explanation. Indeed, to answer the question‘why p?’ requires the semantics ofp to be an empirical phenomenon.1 A realist theory of scientific explanation is interested
in explaining a phenomenon that is ‘out there,’ for in this way one can say that we gain some understanding of the world by explaining it. However, in Section 3.2 I argued that computer simulations do not necessarily represent empirical systems, for they can be heuristic or merely imaginary, and therefore lacking any representational content. I even borrow the term ‘world of their own’ from Ian Hacking to depict this feature of computer simulations. Given that my purpose is to confer epistemic power on computer simulations by showing how they are explanatory devices, I must find the conditions under which there is genuine representation of an empirical target system. These conditions work as the epistemic guarantees that explaining results of a computer simulation applies equally to an empirical phenomenon and, thereby, yields understanding of the world. Let me illustrate these issues with an example.
Consider for instance the spikes in Figure 3.3 which are the result of computing one particular simulation. A successful explanation of why the simulated spikes occur must also be applicable as an explanation of why the spikes occur in the empirical world. In order to justify that this is one and the same explanation, we must first justify that the computer simulation is a reliable process that produces genuine results in the sense that they are a good representation of the target system.
Clarifying these issues is the first task of this chapter, and it is addressed in Section 4.2.1.
In Section 4.2.2 I address the notion ofunderstanding and how it relates to scien-tific explanation. This is a short but important discussion that aims at establishing scientific explanation as an epistemic notion. Next, I address a classification for the-ories of scientific explanation that divides them into two kinds; namely,explanatory internalist accounts, and explanatory externalists accounts. I use this classifica-tion for narrowing down the kind of theory of explanaclassifica-tion of interest for computer simulations to fourinternalist accounts.
Finally, Section 4.3 aims at analyzing which internalist account provides the most suitable conceptual framework for computer simulations as explanatory devices. It also raises the following question: could computer simulations stand by themselves as a new theory of scientific explanation? I answer this question negatively and outline my reasons in Section 4.3.1. The remainder of the chapter is a discussion of three internalist accounts that I reject based on theoretical assumptions that prove to be incompatible with computer simulations. I finally endorse the unificationist account as elaborated by Philip Kitcher as the most suitable for computer simu-lations. Due to the importance and breadth of this discussion, I address it more extensively in Chapter 5.
Before getting into the analysis of scientific explanation, let me briefly introduce some of the basic terminology still in use in the contemporary literature. According to Carl Hempel, a scientific explanation consists of two major constituents: an explanans, or the description that accounts for the phenomenon to be explained, and the explanandum, or the description of the phenomenon to be explained.2