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Robert Batterman and others have argued that certain idealizing explanations have an asymptotic form: they account for a state of affairs or behavior by showing that it emerges \"in the limit\". Asymptotic idealizations are interesting in many ways, but is there anything special about them as idealizations? To understand their role in science, must we augment our philosophical theories of idealization? This paper uses simple examples of asymptotic idealization in population genetics to argue for an affirmative answer and proposes a general schema for asymptotic idealization, drawing on insights from Batterman's treatment and from John Norton's subsequent critique.

Idealization and abstraction are central concepts in the philosophy of science and in science itself. My goal in this paper is suggest an account of these concepts, building on and refining an existing view due to Jones (in: Jones MR, Cartwright N (eds) Idealization XII: correcting the model. Idealization and abstraction in the sciences, vol 86. Rodopi, Amsterdam, pp 173–217, 2005) and Godfrey-Smith (in: Barberousse A, Morange M, Pradeu T (eds) Mapping the future of biology: evolving concepts and theories. Springer, Berlin, 2009). On this line of thought, abstraction —which I call, for reasons to be explained, abstractness—involves the omission of detail, whereas idealization consists in a deliberate mismatch between a description (or a model) and the world. I will suggest that while the core idea underlying these authors’ view is correct, they make several assumptions and stipulations that are best avoided. For one thing, they tie abstractness too close to truth. For another, they do not allow sufficient room to the difference between idealization and error. Taking these points into account leads to a refined account of the distinction, in which abstractness is seen in terms of relative richness of detail, and idealization is seen as closely connected with the knowledge and intentions of idealizers. I lay out these accounts in turn, and then discuss the relationship between the two concepts, and several other upshots of the present way of construing the distinction.

Recent results demonstrate that inducing an abstract representation of target analogs at retrieval time aids access to analogous situations with mismatching surface features (i.e., the late abstraction principle ). A limitation of current implementations of this principle is that they either require the external provision of target-specific information or demand very high intellectual effort. Experiment 1 demonstrated that constructing an idealized situation model of a target problem increases the rate of correct solutions compared with constructing either concrete simulations or no simulations. Experiment 2 confirmed that these results were based on an advantage for accessing the base analog, and not merely an advantage of idealized simulations for understanding the target problem in its own terms. This target idealization strategy has broader applicability than prior interventions based on the late abstraction principle because it can be achieved by a greater proportion of participants and without the need to receive target-specific information. We present a computational model, SampComp, that predicts successful retrieval of a stored situation to understand a target based on the overlap of a random, but potentially biased, sample of features from each. SampComp is able to account for the relative benefits of base and target idealization, and their interaction.

Recent results demonstrate that inducing an abstract representation of target analogs at retrieval time aids access to analogous situations with mismatching surface features (i.e., the late abstraction principle'). A limitation of current implementations of this principle is that they either require the external provision of target-specific information or demand very high intellectual effort. Experiment 1 demonstrated that constructing an idealized situation model of a target problem increases the rate of correct solutions compared with constructing either concrete simulations or no simulations. Experiment 2 confirmed that these results were based on an advantage for accessing the base analog, and not merely an advantage of idealized simulations for understanding the target problem in its own terms. This target idealization strategy has broader applicability than prior interventions based on the late abstraction principle because it can be achieved by a greater proportion of participants and without the need to receive target-specific information. We present a computational model, SampComp, that predicts successful retrieval of a stored situation to understand a target based on the overlap of a random, but potentially biased, sample of features from each. SampComp is able to account for the relative benefits of base and target idealization, and their interaction.

How does mathematics apply to something non-mathematical? We distinguish between a general application problem and a special application problem. A critical examination of the answer that structural mapping accounts offer to the former problem leads us to identify a lacuna in these accounts: they have to presuppose that target systems are structured and yet leave this presupposition unexplained. We propose to fill this gap with an account that attributes structures to targets through structure generating descriptions. These descriptions are physical descriptions and so there is no such thing as a solely mathematical account of a target system.

Deidealization as a topic in its own right has attracted remarkably little philosophical interest despite the extensive literature on idealization. One reason for this is the often implicit assumption that idealization and deidealization are, potentially at least, reversible processes. We question this assumption by analyzing the challenges of deidealization within a menu of four broad categories: deidealizing as recomposing, deidealizing as reformulating, deidealizing as concretizing, and deidealizing as situating. On closer inspection, models turn out much more inflexible than the reversal thesis would have us believe, and deidealization emerges as a creative part of modeling.

I argue that we cannot adequately characterize idealization and abstraction and the distinction between the two on the grounds that they have distinct semantic properties. By doing so, on the one hand, we focus on the conceptual products of the two processes in making the distinction and we overlook the importance of the nature of the thought processes that underlie model-simplifying assumptions. On the other hand, we implicitly rely on a sense of abstraction as subtraction, which is unsuitable for explicating scientific model construction. Instead, I argue that a sense of abstraction as extraction is more suitable. Finally, I suggest a different way to distinguish the two processes that avoids these problems. Namely, that both idealization and abstraction could be understood as particular modes of application of the same cognitive process: selective attention.

Commensality (the act of eating together) is studied in a range of disciplines and often considered important for social communion, order, health and well-being, while simultaneously being understood as in decline (especially the family meal). However, such claims are also contested in various ways. In this paper, we discuss the expanding field of commensality research and critically reflect on the debates surrounding its social functions, including its role in public health. We illuminate the deep social and cultural significance of commensality, through time and space, and conclude that whether or not commensality is the preferred social form of eating for any given individual, it is difficult to escape its sociocultural desirability and idealization. As a cross-cultural phenomenon in both past, present, and future, we suggest that commensality deserves further research. This includes commensality as a research topic in itself and as an entry point to unveil different dimensions of social relations between people, as well as interactions between humans and material objects.

In this paper I begin with a recent challenge to the Semantic Approach and identify an underlying assumption, namely that identity conditions for theories should be provided. Drawing on previous work, I suggest that this demand should be resisted and that the Semantic Approach should be seen as a philosophical device that we may use to represent certain features of scientific practice. Focussing on the partial structures variant of that approach, I then consider a further challenge that arises from a concern with the role of idealisations in that practice. I argue that the partial structures approach is capable of meeting this challenge and I conclude with some broader observations about the role of such formal accounts within the philosophy of science.