Arguments for the effectiveness, and even the indispensability, of mathematics in scientific explanation rely on the claim that mathematics is an effective or even a necessary component in successful scientific predictions and explanations. Well-known accounts of successful mathematical explanation in physical science appeals to scientists’ ability to solve equations directly in key domains. But there are spectacular physical theories, including general relativity and fluid dynamics, in which the equations of the theory cannot be solved directly in target domains, and yet (...) scientists and mathematicians do effective work there (McLarty 2023, Elder 2023). Building on extant accounts of structural scientific explanation (Bokulich 2011, Leng 2021), I argue that philosophical accounts of the role of equations in scientific explanation need not rely on scientists’ ability to solve equations independently of their understanding of the empirical or experimental context. For instance, the process of formulating solutions to equations can involve significant appeal to information about experimental contexts (Curiel 2010) or of physically similar systems (Sterrett 2023). Working from a close analysis of work in fluid mechanics by Martin Bazant and Keith Moffatt (2005), I propose an account of heuristic structural explanation in mathematics (Einstein 1921, Pincock 2021), which explains how physical explanations can be constructed even in domains where basic equations cannot be solved directly. (shrink)

According to a widely held view, scientific modelling consists in entertaining a set of model descriptions that specify a model. Rather than studying the phenomenon of interest directly, scientists investigate the phenomenon indirectly via a model in the hope of learning about some of the phenomenon’s features. I call this view the description-driven modelling (DDM) account. I argue that although an accurate description of much of scientific research, the DDM account is found wanting as regards the mechanistic modelling found in (...) many branches of biology. By analysing research practices in cancer immunology concerning the development of mechanistic models of the process of cancer metastasis, this paper presents and argues for a complementary account of scientific modelling, herein called the experimentation-driven modelling (EDM) account. In EDM, scientists investigate a set of experimental systems and then integrate the results obtained from experiments into a mechanistic model. While EDM shares some key features with DDM, the two are epistemically very different approaches to research. (shrink)

It is a well-known fact that mathematics plays a crucial role in physics; in fact, it is virtually impossible to imagine contemporary physics without it. But it is questionable whether mathematical concepts could ever play such a role in psychology or philosophy. In this paper, we set out to examine a rather unobvious example of the application of topology, in the form of the theory of persons proposed by Kurt Lewin in his Principles of Topological Psychology. Our aim is to (...) show that this branch of mathematics can furnish a natural conceptual system for Gestalt psychology, in that it provides effective tools for describing global qualitative aspects of the latter’s object of investigation. We distinguish three possible ways in which mathematics can contribute to this: explanation, explication and metaphor. We hold that all three of these can be usefully characterized as throwing light on their subject matter, and argue that in each case this contrasts with the role of explanations in physics. Mathematics itself, we argue, provides something different from such explanations when applied in the field of psychology, and this is nevertheless still cognitively fruitful. (shrink)

In this paper we explore the hypothesis that constrained uses of imagination are crucial to economic modeling. We propose a theoretical framework to develop this thesis through a number of specific hypotheses that we test and refine through six new, representative case studies. Our ultimate goal is to develop a philosophical account that is practice oriented and informed by empirical evidence. To do this, we deploy an abductive reasoning strategy. We start from a robust set of hypotheses and leave space (...) for the generation of further hypotheses and theoretical claims based on the qualitative analysis of new empirical data. (shrink)

This paper provides a conceptual framework that allows for distinguishing between different kinds of generalisation and applicability. It is argued that generalising models may bring epistemic benefits. They do so if they show that restrictive and unrealistic assumptions do not threaten the credibility of results derived from models. There are two different notions of applicability, generic and specific, which give rise to three different kinds of generalizations. Only generalising a result brings epistemic benefits concerning the truth of model components or (...) results. Abstracting the model and applying the model into new systems are not intrinsically epistemically beneficial in this way. The Dixit-Stiglitz model of monopolistic competition is used as an illustration. (shrink)

The recent discussion of fictional models has focused on imagination, implicitly considering fictions as something nonconcrete. We present two cases from synthetic biology that can be viewed as concrete fictions. Both minimal cells and alternative genetic systems are modal in nature: they, as well as their abstract cousins, can be used to study unactualized possibilia. We approach these synthetic constructs through Vaihinger’s notion of a semi-fiction and Goodman’s notion of semifactuality. Our study highlights the relative existence of such concrete fictions. (...) Before their realizations neither minimal cells nor alternative genetic systems were any well-defined objects, and the subsequent experimental work has given more content to these originally schematic imaginings. But it is as yet unclear whether individual members of these heterogeneous groups of somewhat functional synthetic constructs will eventually turn out to be fully realizable, remain only partially realizable, or prove outright impossible. (shrink)

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. (shrink)

The epistemic value of models has traditionally been approached from a representational perspective. This paper argues that the artifactual approach evades the problem of accounting for representation and better accommodates the modal dimension of modeling. From an artifactual perspective, models are viewed as erotetic vehicles constrained by their construction and available representational tools. The modal dimension of modeling is approached through two case studies. The first portrays mathematical modeling in economics, while the other discusses the modeling practice of synthetic biology, (...) which exploits and combines models in various modes and media. Neither model intends to represent any actual target system. Rather, they are constructed to study possible mechanisms through the construction of a model system with built-in dependencies. (shrink)

Idealization is commonly understood as distortion: representing things differently than how they actually are. In this paper, we outline an alternative artifactual approach that does not make misrepresentation central for the analysis of idealization. We examine the contrast between the Hodgkin-Huxley (1952a, b, c) and the Heimburg-Jackson (2005, 2006) models of the nerve impulse from the artifactual perspective, and argue that, since the two models draw upon different epistemic resources and research programs, it is often difficult to tell which features (...) of a system the central assumptions involved are supposed to distort. Many idealizations are holistic in nature. They cannot be locally undone without dismantling the model, as they occupy a central position in the entire research program. Nor is their holistic character mainly related to the use of mathematical and statistical modeling techniques as portrayed by Rice (2018, 2019). We suggest that holistic idealizations are implicit theoretical and representational assumptions that can only be understood in relation to the conceptual and representational tools exploited in modeling and experimental practices. Such holistic idealizations play a pivotal role not just in individual models, but also in defining research programs. -/- . (shrink)

This paper examines two parallel discussions of scientific modeling which have invoked experimentation in addressing the role of models in scientific inquiry. One side discusses the experimental character of models, whereas the other focuses on their exploratory uses. Although both relate modeling to experimentation, they do so differently. The former has considered the similarities and differences between models and experiments, addressing, in particular, the epistemic value of materiality. By contrast, the focus on exploratory modeling has highlighted the various kinds of (...) exploratory functions of models in the early stages of inquiry. These two perspectives on modeling are discussed through a case study in the field of synthetic biology. The research practice in question explores biological control by making use of an ensemble of different epistemic means: mathematical models and simulations, synthetic genetic circuits and intracellular measuring devices, and finally electronic circuits. We argue that the study of exploratory modeling should trace the ways different epistemic means, in different materialities, are being combined over time. Finally, the epistemic status of such novel investigative objects as synthetic genetic circuits is evaluated, with the conclusion that they can function as both experiments and models. (shrink)

The aim of this article is to use a model from the origin of life studies to provide some depth and detail to our understanding of exploratory models by suggesting that some of these models should be understood as indeterminate. Models that are indeterminate are a type of exploratory model and therefore have extensive potential and can prompt new lines of research. They are distinctive in that, given the current state of scientific understanding, we cannot specify how and where the (...) model will be useful in understanding the natural world: in this case, the origin of life on Earth. The purpose of introducing indeterminacy is to emphasize the epistemic uncertainty associated with modeling, a feature of this practice that has been under emphasized in the literature in favor of attempts to understand the more specific epistemic successes afforded by models. (shrink)

Philosophy of science has undergone a naturalistic turn, moving away from traditional idealized concerns with the logical structure of scientific theories and toward focusing on real-world scientific practice, especially in domains such as modeling and experimentation. As part of this shift, recent work has explored how the project of philosophically understanding science as a natural phenomenon can be enriched by drawing from different fields and disciplines, including niche construction theory in evolutionary biology, on the one hand, and ecological and enactive (...) views in embodied cognitive science, on the other. But these insights have so far been explored in separation from each other, without clear indication of whether they can work together. Moreover, the focus on particular practices, however insightful, has tended to lack consideration of potential further implications for a naturalized understanding of science as a whole (i.e., above and beyond those particular practices). Motivated by these developments, here we sketch a broad-ranging view of science, scientific practice and scientific knowledge in terms of ecological-enactive co-construction. The view we propose situates science in the biological, evolutionary context of human embodied cognitive activity aimed at addressing the demands of life. This motivates reframing theory as practice, and reconceptualizing scientific knowledge in ecological terms, as relational and world-involving. Our view also brings to the forefront of attention the fundamental link between ideas about the nature of mind, of science and of nature itself, which we explore by outlining how our proposal differs from more conservative, and narrower, conceptions of “cognitive niche construction.”. (shrink)

A powerful idea put forward in the recent philosophy of science literature is that scientific models are best understood as instruments, tools or, more generally, artifacts. This idea has thus far been developed in combination with the more traditional representational approach: accordingly, current artifactualist accounts treat models as representational tools. But artifactualism and representationalism are independent views, and adopting one does not require acceptance of the other. This paper argues that a leaner version of artifactualism, free of representationalist assumptions, is (...) both desirable and viable. Taking seriously the idea that models are artifacts can help us philosophically to make sense of how and why scientific modeling works even without reference to representation. (shrink)

A persistent criticism of radical embodied cognitive science is that it will be impossible to explain “real cognition” without invoking mental representations. This paper provides an account of explicit, real-time thinking of the kind we engage in when we imagine counter-factual situations, remember the past, and plan for the future. We first present a very general non-representational account of explicit thinking, based on pragmatist philosophy of science. We then present a more detailed instantiation of this general account drawing on nonlinear (...) dynamics and ecological psychology. (shrink)

Scientific research is constrained by limited resources, so it is imperative that it be conducted efficiently. This paper introduces the notion of epistemic expression, a kind of representation that expedites the solution of research problems. Epistemic expressions are representations that (i) contain information in a way that enables more reliable information to place the most stringent constraints on possible solutions and (ii) make new information readily extractible by biasing the search through that space. I illustrate these conditions using historical and (...) contemporary examples of biomolecular structure determination. Then, I argue that the notion of epistemic expression parts ways with pragmatic accounts of scientific representation and an understanding of models as artifacts, neither of which require models to accurately represent. Explicating epistemic expression thus fills a gap in our understanding of scientific practice, extending Morrison and Morgan's (1999) conception of models as investigative instruments. (shrink)

Experiments in particle physics have hitherto failed to produce any significant evidence for the many explicit models of physics beyond the Standard Model (BSM) that had been proposed over the past decades. As a result, physicists have increasingly turned to model-independent strategies as tools in searching for a wide range of possible BSM effects. In this paper, we describe the Standard Model Effective Field Theory (SM-EFT) and analyse it in the context of the philosophical discussions about models, theories, and (bottom-up) (...) effective field theories. We find that while the SM-EFT is a quantum field theory, assisting experimentalists in searching for deviations from the SM, in its general form it lacks some of the characteristic features of models. Those features only come into play if put in by hand or prompted by empirical evidence for deviations. Employing different philosophical approaches to models, we argue that the case study suggests not to take a view on models that is overly permissive because it blurs the lines between the different stages of the SM-EFT research strategies and glosses over particle physicists' motivations for undertaking this bottom-up approach in the first place. Looking at EFTs from the perspective of modelling does not require taking a stance on some specific brand of realism or taking sides in the debate between reduction and emergence into which EFTs have recently been embedded. (shrink)

ArgumentAgent-based social simulations have historically been evaluated using two criteria: verification and validation. This article questions the adequacy of this dual evaluation scheme. It claims that the scheme does not conform to everyday practices of evaluation, and has, over time, fostered a theory-practice gap in the assessment of social simulations. This gap originates because the dual evaluation scheme, inherited from computer science and software engineering, on one hand, overemphasizes the technical and formal aspects of the implementation process and, on the (...) other hand, misrepresents the connection between the conceptual and the computational model. The mismatch between evaluation theory and practice, it is suggested, might be overcome if practitioners of agent-based social simulation adopt a single criterion evaluation scheme in which: i) the technical/formal issues of the implementation process are tackled as a matter of debugging or instrument calibration, and ii) the epistemological issues surrounding the connection between conceptual and computational models are addressed as a matter of validation. (shrink)

Even though the philosophy of simulation is intended as a comprehensive reflection about the practice of computer simulation in contemporary science, its output has been disproportionately shaped by research on equation-based simulation in the physical and climate sciences. Hence, the particularities of alternative practices of computer simulation in other scientific domains are not sufficiently accounted for in the current philosophy of simulation literature. This article centres on agent-based social simulation, a relatively established type of simulation in the social sciences, to (...) exemplify this claim. The analysis advanced has a twofold goal. First, it shows that the philosophy of agent-based social simulation, mostly developed by practitioners themselves, is, on one hand, heavily influenced by the methodological features of agent-based modelling and by the loose and fragmented character of social theory and, on the other hand, distinctively shaped by contrasting views of what it implies to do social research with virtual or artificial societies. Second, it suggests ways in which cross-fertilisation could enrich the philosophical understanding of computer simulation both in agent-based social simulation and in the philosophy of simulation. (shrink)

There are two traditions of thinking about idealization offering almost opposite views on their functioning and epistemic status. While one tradition views idealizations as epistemic deficiencies, the other one highlights the epistemic benefits of idealization. Both of these, however, identify idealization with misrepresentation. In this article, we instead approach idealization from the artifactual perspective, comparing it to the distortion-to-reality accounts of idealization, and exemplifying it through the case of the Hodgkin and Huxley model of nerve impulse. From the artifactual perspective, (...) the epistemic benefits and deficiencies introduced by idealization frequently come in a package due to the way idealization draws together different resources in model construction. Accordingly, idealization tends to be holistic in that it is not often easily attributable to just some specific parts of the model. Instead, the idealizing process tightly embeds theoretical concepts and formal tools into the construction of a model. (shrink)