Generative models have been proposed as a new type of non-representational scientific models recently. A generative model is characterized with the capacity of producing new models on the basis of the existing one. The current accounts do not explain sufficiently the mechanism of the generative capacity of a generative model. I attempt to accomplish this task in this paper. I outline two antecedent accounts of generative models. I point out that both types of generative models function to generate new homogenous (...) models in the sense that the latter is a straightforward derivative of the former, both of which share many similar features. Unfortunately, both accounts are implicit about the generative capacity of generative models. Using a case study, I articulate that a two-staged process of abstraction and idealization in modeling may contribute to the generative capacity of a scientific model. I also demonstrate that this two-staged process may go beyond the capacity of generating new homogenous models to generating new heterogeneous models. (shrink)

Drawing on ‘interpretational’ accounts of scientific representation, I argue that the use of so-called ‘toy models’ provides no particular philosophical puzzle. More specifically; I argue that once one gives up the idea that models are accurate representations of their targets only if they are appropriately similar, then simple and highly idealized models can be accurate in the same way that more complex models can be. Their differences turn on trading precision for generality, but, if they are appropriately interpreted, toy models (...) should nevertheless be considered accurate representations. A corollary of my discussion is a novel way of thinking about idealization more generally: idealized models may distort features of their targets, but they needn’t misrepresent them. (shrink)

I argue that fictional models, construed as models that misrepresent certain ontological aspects of their target systems, can nevertheless explain why the latter exhibit certain behaviour. They can do this by accurately representing whatever it is that that behaviour counterfactually depends on. However, we should be sufficiently sensitive to different explanatory questions, i.e., ‘why does certain behaviour occur?’ versus ‘why does the counterfactual dependency invoked to answer that question actually hold?’. With this distinction in mind, I argue that whilst fictional (...) models can answer the first sort of question, they do so in an unmysterious way. Moreover, I claim that the second question poses a dilemma for the defender of the idea that fictions can explain: either these models cannot answer these sorts of explanatory questions, precisely because they are fictional; or they can, but in a way that requires reinterpreting them such that they end up accurately representing the ontological basis of the counterfactual dependency, i.e., reinterpreting them so as to rob them of their fictional status. Thus, the existence of explanatory fictions does not put pressure on the idea that accurate representation of some aspect of a target system is a necessary condition on explaining that aspect. (shrink)

In 1959, mathematician Mark Kac introduced a model, called the Kac ring, in order to elucidate the classical solution of Boltzmann to the problem of macroscopic irreversibility. However, the model is far from being a realistic representation of something. How can it be of any help here? In philosophy of science, it is often argued that models can provide explanations of the phenomenon they are said to approximate, in virtue of the truth they contain, and in spite of the idealisations (...) they are made of. On this view, idealisations are not supposed to contribute to any explaining, and should not affect the global representational function of the model. But the Kac ring is a toy model that is only made of idealisations, and is still used trustworthily to understand the treatment of irreversible phenomena in statistical mechanics. In the paper, my aim is to argue that each idealisation ingeniously designed by the mathematician maintains the representational function of the Kac ring with the general properties of macroscopic irreversibility under scrutiny. Such an active role of idealisations in the representing has so far been overlooked and reflects the art of modelling. (shrink)

We consider various curious features of general relativity, and relativistic field theory, in two spacetime dimensions. In particular, we discuss: the vanishing of the Einstein tensor; the failure of an initial-value formulation for vacuum spacetimes; the status of singularity theorems; the non-existence of a Newtonian limit; the status of the cosmological constant; and the character of matter fields, including perfect fluids and electromagnetic fields. We conclude with a discussion of what constrains our understanding of physics in different dimensions.