Conclusion

one special kind of computer software, namely, computer simulations. I will study them from a methodological and epistemic point of view.

Notes

1See, for instance, (Hartmann, 1995; Humphreys, 1991; Parker, 2009; Winsberg, 2003).

2Admittedly I am only concerned about the specification of the instrument, in a broader context, though specifications of the experimental setup are also relevant for the understanding of results.

3For a more detailed analysis on the distinction between precision andaccuracy, see the Lexicon.

4For a more thorough study onspecifications, see (Raymond, 2006; Severi and Szasz, 2001; Turner, 2005).

5On this point, see (Arbab and Sirjani, 2009; Jalote, 2008; Pfleeger and Atlee, 2009).

6I discuss errors in Section 3.3.3.

7See the Lexicon for a definition of each one of these terms.

8See Section 3.3.2.

9See also (Humphreys, 2009).

10See, for instance, (Hoare, 1969) and (Olsen, 2005) respectively.

11For more technical details on algorithms, see (Eden and Turner, 2005, 2007; Kao, 2008).

12See (Knuth, 1974, 1973) and (Dijkstra, 1974).

13These two notions were coined by (Humphreys, 2004, 95).

14Cf. (Humphreys, 2004, 97).

15Alternatives to isomorphism are also discussed in the literature (see, for instance, (Blass et al., 2009; Blass and Gurevich, 2003)). Let it be noted, however, that isomorphism is the only -morphism that could warrant total equivalency between algorithms.

16For CASL, see for instance (Bidoit and Mosses, 2004). For VDM, see for instance, (Bjørner and Jones, 1978; Bjørner and Henson, 2007). For Z notation, see for instance (Jacky, 1996; Spivey, 2001, 1992).

17See, for instance, (Queille and Sifakis, 1982; McMillan, 1992).

18I do not address the question about the computational architecture on which the computer software is run. However it should be clear from the context that I assume silicon-based computers (as opposed to quantum computers, biological computers, etc.). It must also be clear that other architectures represent a host of other philosophical problems (Berekovic et al., 2008; Rojas and Hashagen, 2000).

19See (von Neumann, 1945, 1948). Also, for an historical approach to this architecture, see (Aspray, 1990a; Eigenmann and Lilja, 1998).

20See, for instance (Cohn, 1989; Ciletti, 2010; Mermet, 1993).

21See also (Guttag et al., 1978; Hoare, 1999; Rapaport, 1995, 2003; Hayes, 1988; Nelson, 1992).

22For a discussion on errors in computer science, see Section 3.3.3.

23For instance, in (Fetzer, 1988, 1991, 1997).

24For instance (Ashenhurst, 1989).

25I discuss reliability in more detail in Section 4.2.1.

26This is the general claim in specialized literature on foundations of computer science. See, for instance, (Gruska, 1997; Eden, 2007; Eden and Turner, 2007; Hoare, 2004; Hoare and Jifeng, 1998;

Hoare and Jones, 1989).

Chapter 3

Computer simulations: towards their conceptualization

3.1 Introduction

Current philosophical literature takes computer simulations as aids for over-coming imperfections and limitations of human cognition. Such imperfections and limitations have one common source: humans cannot process the enormous amount of information that current scientific activity manages.¹ Margaret Morrison, for in-stance, considers that although computer simulations are another form of modeling,

“given the various functions of simulation [. . . ] one could certainly characterize it as a type of ‘enhanced’ modelling” (Morrison, 2009, 47). In a similar sense, Paul Humphreys conceives a computer simulation as an ‘amplification instrument,’ one that speeds up what an unaided human could not do²

I believe that these philosophers’ claims are fundamentally correct. Computer simulations do represent novel ways of practicing science precisely because of their high speed processing and accumulation of information. However, the idea of com-puter simulations as ‘cognitive enhancers’ depends on the existence of the few fea-tures that computers can offer as physical instruments, such as speed, memory, or computational power. If the epistemic power of computer simulations is analyzed in this way, as many philosophers have,³ I believe we are missing a more interest-ing characteristic of computer simulations that exhibits their true epistemic power, namely, their capacity to successfully investigate the behavior of a host of target sys-tems (empirical or otherwise). My proposal, then, is to relate the epistemic power of computer simulations to specific activities that exploit their capacity as devices that are analytic and inquisitive about our empirical world, such as explaining phenom-ena, predicting future states of the target system, or offering evidence for scientific

hypothesis.

A central issue arising here is the notion of computer simulation. Instead of envisaging computer simulations as ‘cognitive enhancers,’ then, I take them as in-struments for studying the patterns of behavior of a target system. The shift in emphasis leads to a different way of approaching the philosophical study of com-puter simulations. Specifically, instead of focusing on their mechanistic features as the means of studying their epistemic power, I focus the analysis on the kind of sci-entific activities that a computer simulation can perform. In this vein, to simulate the dynamics of a biological system is, to me, to simulate the patterns of behavior of a predator-prey system in order to explain or predict some behavior. Following Philip Kitcher, I take the notion ofpatterns as one which reflects the structures, the performance, and thebehavior of the target system.⁴ The advantage of conceptual-izing computer simulations in this way is that the physical features of the computer are no longer their primary epistemic virtue, but rather, it is their capacity to repre-sent or describepatterns of behavior of the target system that entrenches computer simulations as epistemically powerful.⁵

Of course, this shift of emphasis is not meant to downplay the role of com-puter simulations as cognitive enhancers. On the contrary, computational power still makes the computation of scientific models possible, and it is at the core of the claim for the novelty of computer simulations in the sciences. But here the computational power of simulations is considered a second-level epistemic feature.

In this sense, instead of locating the epistemic virtues of computer simulation in their capacity for crunching large amounts of data, these virtues come from de-scribing patterns among systems from which we obtain understanding of the world.

The challenge, then, is to show how and in what way computer simulations yield understanding of the world.

Given that the universe of simulations is significantly large, I propose to first nar-row it down to computer simulations (Section 3.2). In this first analysis, I will be distinguishing analogical simulations from digital or computer simulations. There are two valuable lessons from this analysis: first, to establish that computer simula-tions are not causally related as analogical simulasimula-tions are. This result is important for the discussion on scientific explanations. In particular, ontic theories of scientific explanation are excluded on grounds that computer simulations lack the necessary causal chain traceable in an explanation. Second, the analysis of analogical sim-ulations and digital simsim-ulations provides the notion of ‘symbolic simulation’ as a two stage mapping affair. The first mapping relates the symbolic simulation to the states of the hardware, whereas the second mapping relates the symbolic simulation

to the representation of the target system. Such a conceptualization furnishes the intuition that a computer simulation is a ‘world of its own’ in the sense that its results are directly related to the simulation model that has been computed, but only indirectly to the empirical phenomenon.

Next, I will be addressing different notions of computer simulation in current literature. The purpose of this discussion is to set the grounds for my own working conceptualization, which I elaborate later in the chapter (see Section 3.3.1.1). Sec-tion 3.2.2 also includes a discussion on cellular automata, agent-based simulaSec-tions, and complex systems as computer simulations that are excluded from this work. The reason for excluding them is based on the diverse ontological, methodological, and epistemic characteristics that each kind of simulation has to offer. For instance, an agent-based simulation consists in a set of rules that describe the emerging behavior of systems. These features can be used for different epistemic or methodological purposes, such as the dynamism of sociological systems, or for self-reproducing bio-logical systems. Since these features are not relevant in equation-based simulations, my analysis on the epistemic power of computer simulations will not take this class of computer simulation into account. In Section 3.2.3 I narrow down the class of computer simulations to equation-based simulations, such as Ordinary Differential Equations, or Partial Differential Equations (henceforth ODE and PDE, respec-tively).

Finally, I discuss the methodology of computer simulations and present an ex-ample of a satellite under tidal stress which I will use for the remainder of this work as a paradigmatic example of the class of computer simulations of interest (Section 3.3).