Computer Simulations: An Inferential Conception

1. IntroductionComputer simulations are crucial to various aspects of scientific practice. In some cases, they are a source of data about situations in which direct empirical information is hard, or even impossible, to reach. In other cases, simulations guide scientific theorizing.1 In this paper, I offer an inferential account of computer simulations that highlights the significant role simulations play as inferential devices to represent features of empirical phenomena. I argue that the inferential conception accommodates the integration of empirical and theoretical data; it makes sense of the role that is played by false traits in a simulation, and highlights the similarities and differences between simulations and scientific instruments.2. An Inferential Conception of SimulationsThe account proposed here expands on the inferential conception of the application of mathematics (Bueno and Colyvan 2011). According to the inferential conception, the application of mathematics, and scientific representation more generally, involve three basic steps. First, certain features of the empirical set up are selected for representation by immersing them into a given model (the immersion step). By exploring the mathematical resources of the model, results are then derived from the initial information that was embedded into the model (derivation step). Finally, these results are interpreted back into the empirical set up (interpretation step).Here are two illustrations of the inferential conception. Consider, first, the representation of quantum states in (nonrelativistic) quantum mechanics. In the immersion step, quantum states are associated with certain vectors in a Hilbert space. In the derivation step, the evolution of the system is determined by Schrodinger's equation, and the superposition of states emerges, in part, as a feature of the mathematics. Finally, in the interpretation step, the results are then interpreted back into the empirical set up, and the measurement problem needs to be addressed.As a second illustration, consider the representation of economic behavior in neoclassical economics. In the immersion step, the behavior of economic agents is associated with maximization principles (e.g. the maximization of profit). In the derivation step, maximization techniques are then used to determine the agent's best choice outcome. In the interpretation step, the results are then interpreted back into the empirical set up. It turns out that actual economic agents do not in fact follow such maximization requirements. Different norms are then introduced, such as Herbert Simon's satisficing (Simon 1982).In the case of simulations, instead of simply having a model into which certain features of the empirical set up are embedded, we have a dynamic process in which not only the relevant features of the empirical set up are introduced (immersion step), but also theoretical assumptions are incorporated in order to give structure and dynamics to the simulation. Theoretical assumptions are crucial to the simulation, and in terms of them it is determined what follows from the particular empirical conditions (derivation step). Once the results are obtained, they need to be interpreted, and corrections are introduced, so that these results can be made relevant to the empirical set up (interpretation and correction step). (See figure 1.)The inferential conception generalizes Hughes's (2010) account of representation in terms of denotation, demonstration, and interpretation. Whereas Hughes takes denotation to be a particular relation between the empirical set up and the model (namely, the denotation function from model-theoretic semantics), the inferential conception emphasizes that there are several such relations between the empirical set up and the relevant models: a variety of different mappings can be used, such as (partial) isomorphism, (partial) homomorphism, etc. This is highlighted in the immersion step. …