Two approaches to understanding the idealizations that arise in the Aharonov–Bohm effect are presented. It is argued that a common topological approach, which takes the non-simply connected electron configuration space to be an essential element in the explanation and understanding of the effect, is flawed. An alternative approach is outlined. Consequently, it is shown that the existence and uniqueness of self-adjoint extensions of symmetric operators in quantum mechanics have important implications for philosophical issues. Also, the alleged indispensable explanatory role of (...) said idealizations is examined via a minimal model explanatory scheme. Last, the idealizations involved in the AB effect are placed in a wider philosophical context via a short survey of part of the literature on infinite and essential idealizations. (shrink)

This volume brings together leading scholars working on understanding and representation in philosophy of science. It features a critical conversation format between contributors that advances debates concerning scientific understanding, scientific representation, and their delicate interplay.

A central goal of the scientific endeavor is to explain phenomena. Scientists often attempt to explain a phenomenon by way of representing it in some manner—such as with mathematical equations, models, or theory—which allows for an explanation of the phenomenon under investigation. However, in developing scientific representations, scientists typically deploy simplifications and idealizations. As a result, scientific representations provide only partial, and often distorted, accounts of the phenomenon in question. Philosophers of science have analyzed the nature and function of how (...) scientists construct representations, deploy idealizations, and provide explanations. As such, our aim in this special issue is to bring these three pillars of research into closer contact with the contributions to it focusing on three main themes. -/- The first set of papers, Alan Baker (2021) and Marc Lange (2021), address mathematical explanations in science. Baker (2021), a proponent of mathematical Platonism, examines its capacity to evade the critique that the so-called Enhanced Indispensability Argument is circular. Lange (2021) examines distinctively mathematical explanations, arguing that neither Platonism nor representationalism are successful paths, and instead argues in favor of Aristotelian realism. A second theme emerging from the papers in this special issue is the impact that various conceptualizations of idealization have on our abilities to offer scientific explanations, to pro- duce an analysis of what explanations are or should be, and to understand scientific representation. Peter Tan (2021) suggests amending inferentialist accounts of scientific representation to account for inconsistent idealizations. Michael Strevens (2021) advocates a view wherein the introduction of idealizations into a model is legitimate so long as it pertains to non-difference-making factors, arguing for a logical reading of the notion of difference-making. Natalia Carrillo and Tarja Knuuttila (2022) offer an alternative account to the idealization-as-distortion view, emphasizing instead the holistic nature of idealization. -/- Finally, contributions by Carrillo and Knuuttila (2022), Terzian (2021), Valente (2021), and Rodriguez (2021) illustrate how issues regarding idealization, representation, and explanation are applied to specific contexts and across various sciences. Carrillo and Knuuttila (2022) examine conceptions of idealization in the context of models of the nerve impulse. Giulia Terzian (2021) extends the discussion of idealizations to the context of generative linguistics. Giovanni Valente (2021) examines how idealizations and evaluations of accurate representation impact capacities to explain phenomena in the context of statistical thermodynamics. Quentin Rodriguez (2021) examines the role of idealizations and analogies in various strategies to explain critical phenomena. -/- In what follows, we offer a brief overview of important philosophical issues connected to representation, idealization, and explanation in science. We then provide short summaries of the eight papers in this special issue. (shrink)

In this essay, I provide an overview of the debate on infinite and essential idealizations in physics. I will first present two ostensible examples: phase transitions and the Aharonov– Bohm effect. Then, I will describe the literature on the topic as a debate between two positions: Essentialists claim that idealizations are essential or indispensable for scientific accounts of certain physical phenomena, while dispensabilists maintain that idealizations are dispensable from mature scientific theory. I will also identify some attempts at finding a (...) middle ground between the essentialists and dispensabilists camps. Finally, I will raise questions for future research on essential and infinite idealizations via the notion of exploration. (shrink)

I present a novel approach to the scholarly debate that has arisen with respect to the philosophical import one should infer from scientific accounts of phase transitions by appealing to a distinction between representation understood as denotation, and faithful representation understood as a type of guide to ontology. It is argued that the entire debate is misguided, for it stems from a pseudo-paradox that does not license the type of claims made by scholars and that what is really interesting about (...) phase transitions is the manner by which they force us to rethink issues regarding scientific representation, idealizations, and realism. (shrink)

This paper looks at the nature of idealizations and representational structures appealed to in the context of the fractional quantum Hall effect, specifically, with respect to the emergence of anyons and fractional statistics. Drawing on an analogy with the Aharonov–Bohm effect, it is suggested that the standard approach to the effects— the topological approach to fractional statistics—relies essentially on problematic idealizations that need to be revised in order for the theory to be explanatory. An alternative geometric approach is outlined and (...) endorsed. Roles for idealizations in science, as well as consequences for the debate revolving around so-called essential idealizations, are discussed. (shrink)

In this paper I show how certain requirements must be set on any tenable account of scientific representation, such as the requirement allowing for misrepresentation. I then continue to argue that two leading accounts of scientific representation— the inferential account and the interpretational account—are flawed for they do not satisfy such requirements. Through such criticism, and drawing on an analogy from non-scientific representation, I also sketch the outline of a superior account. In particular, I propose to take epistemic representations to (...) be intentional objects that come with reference, semantic contents and a representational code, and I identify faithful representations as representations that act as guides to ontology. (shrink)

In this article we argue that idealizations and limiting cases in models play an exploratory role in science. Four senses of exploration are presented: exploration of the structure and representational capacities of theory; proof-of-principle demonstrations; potential explanations; and exploring the suitability of target systems. We illustrate our claims through three case studies, including the Aharonov-Bohm effect, the emergence of anyons and fractional quantum statistics, and the Hubbard model of the Mott phase transitions. We end by reflecting on how our case (...) studies and claims compare to accounts of idealization in the philosophy of science literature such as Michael Weisberg’s three-fold taxonomy. (shrink)

Various claims regarding intertheoretic reduction, weak and strong notions of emergence, and explanatory fictions have been made in the context of first-order thermodynamic phase transitions. By appealing to John Norton’s recent distinction between approximation and idealization, I argue that the case study of anyons and fractional statistics, which has received little attention in the philosophy of science literature, is more hospitable to such claims. In doing so, I also identify three novel roles that explanatory fictions fulfill in science. Furthermore, I (...) scrutinize the claim that anyons, as they are ostensibly manifested in the fractional quantum Hall effect, are emergent entities and urge caution. Consequently, it is suggested that a particular notion of strong emergence signals the need for the development of novel physical–mathematical research programs. (shrink)

It has been recently debated whether there exists a so-called “easy road” to nominalism. In this essay, I attempt to fill a lacuna in the debate by making a connection with the literature on infinite and infinitesimal idealization in science through an example from mathematical physics that has been largely ignored by philosophers. Specifically, by appealing to John Norton’s distinction between idealization and approximation, I argue that the phenomena of fractional quantum statistics bears negatively on Mary Leng’s proposed path to (...) easy road nominalism, thereby partially defending Mark Colyvan’s claim that there is no easy road to nominalism. (shrink)

Historical inductions, that is, the pessimistic metainduction and the problem of unconceived alternatives, are critically analyzed via John D. Norton’s material theory of induction and subsequently rejected as noncogent arguments. It is suggested that the material theory is amenable to a local version of the pessimistic metainduction, for example, in the context of some medical studies.

In his recent 2018 book, Resisting Scientific Realism, K. Brad Wray provides a detailed, full-fledged defense of anti-realism about science. In this paper, I argue against the two main claims that constitute Wray’s positive and novel argument for his position, viz., his suggested Darwinian-selectionist explanation of the success of science and his skepticism about unobservables based on radical theory change. My goal is not wholly negative though. Instead, I aim to identify the type of work that an anti-realist like Wray (...) would need to undertake in order to further substantiate their position, viz., taking a stance on inductive inference and support, and the type of realist and anti-realist positions that seem viable. (shrink)

In this essay, I provide an overview of the debate on infinite and essential idealizations in physics. I will first present two ostensible examples: phase transitions and the Aharonov–Bohm effect. Then, I will describe the literature on the topic as a debate between two positions: Essentialists claim that idealizations are essential or indispensable for scientific accounts of certain physical phenomena, while dispensabilists maintain that idealizations are dispensable from mature scientific theory. I will also identify some attempts at finding a middle (...) ground between the essentialists and dispensabilists camps. Finally, I will raise questions for future research on essential and infinite idealizations via the notion of exploration. (shrink)

We examine arguments for distinguishing between ontological and epistemological concepts of fundamentality, focusing in particular on the role that scale plays in these concepts. Using the fractional quantum Hall effect as a case study, we show that we can draw a distinction between ontologically fundamental and non-fundamental theories without insisting that it is only the fundamental theories that get the ontology right: there are cases where non-fundamental theories involve distinct ontologies that better characterize real systems than fundamental ones do. In (...) order to reconcile these distinct ontologies between fundamental and non-fundamental theories, we suggest that ontology must be understood as scale-dependent. (shrink)

In this paper, I appeal to a distinction made by David Lewis between identifying and determining semantic content in order to defend a complementarity thesis expressed by Anjan Chakravartty. The thesis states that there is no conflict between informational and functional views of scientific modeling and representation. I then apply the complementarity thesis to well-received theories of pictorial representation, thereby stressing the fruitfulness of drawing an analogy between the nature of fictions in art and in science. I end by attending (...) to the problem of depicting impossible fictions. It is suggested that progress can be made by understanding the role of impossible fictions in science, namely, allowing researchers to probe into the possible structure and representational capacities of scientific theory. (shrink)

Arguments from perceptual variation challenge the view that colors are objective properties of objects, properties that objects have independent of how they are perceived. This paper attempts, first, to diagnose one central reason why arguments from perceptual variation seem especially challenging for objectivists about color. Second, we offer a response to this challenge, claiming that once we focus on determinate colors rather than the determinables they determine, a response to arguments from perceptual variation becomes apparent. Third, our nominal opponents are (...) relationalist (like Cohen in The red and the real: an essay on color ontology, Oxford University Press, Oxford, 2009) and we will argue that the main argument for rejecting objectivism commits the relationalist to a position that is more radical than the one he would wish to endorse. Fourth, we suggest that insight into which properties could be relational may be found by looking to our best scientific theories. (shrink)

We look to mitonuclear ecology and the phenomenon of Mother’s Curse to argue that the sex of parents and offspring among populations of eukaryotic organisms, as well as the mitochondrial genome, ought to be taken into account in the conceptualization of evolutionary fitness. Subsequently, we show how characterizations of fitness considered by philosophers that do not take sex and the mitochondrial genome into account may suffer. Last, we reflect on the debate regarding the fundamentality of trait versus organism fitness and (...) gesture at the idea that the former lies at the conceptual basis of evolutionary theory. (shrink)

Kevin Davey claims that the justification of the second law of thermodynamics as it is conveyed by the “standard story” of statistical mechanics, roughly speaking, that lowentropy microstates tend to evolve to high-entropy microstates, is “unhelpful at best and wrong at worst.” In reply, I demonstrate that Davey’s argument for rejecting the standard story commits him to a form of skepticism that is more radical than the position he claims to be stating and that Davey places unreasonable demands on the (...) notion of justification in the physical sciences. (shrink)

Practical ability manifested through robust and reliable task performance, as well as information relevance and well-structured representation, are key factors indicative of understanding in the philosophical literature. We explore these factors in the context of deep learning, identifying prominent patterns in how the results of these algorithms represent information. While the estimation applications of modern neural networks do not qualify as the mental activity of persons, we argue that coupling analyses from philosophical accounts with the empirical and theoretical basis for (...) identifying these factors in deep learning representations provides a framework for discussing and critically evaluating potential machine understanding given the continually improving task performance enabled by such algorithms. (shrink)

We present the problem of perceptual agreement (of determinate color) and submit that it proves to be a serious and long overlooked obstacle for those insisting that colors are not objective features of objects, viz., nonobjectivist theories like C. L. Hardin’s (2003) eliminativism and Jonathan Cohen’s (2009) relationalism.

Prima facie, accounts of scientific representation should illuminate how models support justified surrogative reasoning while remaining neutral on the nature of inductive inference. We argue that doing both at once is harder than it first appears. Accounts like “DEKI,” which distinguish justified and unjustified surrogative inferences by appealing to a distinction between derivational and factual correctness, cannot accommodate non-formal, non-rule-based accounts of inference such as John Norton’s material theory of induction. In contrast, a recent expressivist-inferentialist account appears compatible with material (...) inference, but at the cost of abandoning inductive neutrality. (shrink)

By appealing to resources found in the scientific understanding literature, I identify in what senses idealisations afford understanding in the context of the (magnetic) Aharonov-Bohm effect. Three types of concepts of understanding are discussed: understanding-what, which has to do with understanding a phenomenon; understanding-with, which has to do with understanding a scientific theory; and understanding-why, which has to do with the reason some phenomenon occurs. Consequently, I outline an account of understanding-with that is suggested by the historical controversy surrounding the (...) Aharonov-Bohm effect. (shrink)

Idealizations are ubiquitous in physics. They are distortions or falsities that enter into theories, laws, models, and scientific representations. Various questions suggest themselves: What are idealizations? Why do we appeal to idealizations and how do we justify them? Are idealizations essential to physics and, if so, in what sense and for which purpose? How can idealizations provide genuine understanding? If our motivation for believing in the existence of unobservable entities like electrons and quarks is that they are indispensable to our (...) best theories, should we also believe in the existence of indispensable idealizations? This Element will tackle such questions and offer an opinionated and selective introduction to philosophical issues concerning idealizations in physics. Topics to be covered include the concept of and reasons for introducing idealization, abstraction, and approximation, possible taxonomy and justification, and application to issues of mathematical Platonism, scientific realism, and scientific understanding. (shrink)

Contemporary scholars are engaged in a debate over whether Charles Augustin Coulomb’s results that he presented in his 1785 and 1787 memoirs to the Paris Academy of Sciences were attained experimentally or theoretically. In this paper, we study Coulomb’s famous 1785 electric torsion balance experiment through analysis of relevant texts and, more importantly, through a replication that is more faithful to Coulomb’s original design than previous attempts. We show that, despite recent claims, it has so far proved impossible to obtain (...) the same results reported by Coulomb in his paper of 1785, Coulomb’s published results are most likely atypical, and electric torsion balance experiments degenerate quickly when parameters are altered by small amounts. Acknowledgements: We wish to thank Jed Buchwald for generously making available the glass pieces of a torsion balance identical to that used by Alberto Martinez. Special thanks also to Paolo Palmieri for his important roles in replicating the electric torsion balance, discussing results and recording trials, as well as for the invaluable comments given on earlier drafts of this paper. A part of this paper was presented at the 2008 History of Science Society Annual Meeting in Pittsburgh, PA. We thank the participants of that meeting, especially Alberto A. Martinez, for helpful discussion and comments. Thank you also to Peter Heering for recent discussion and feedback. This research was supported by the Wesley C. Salmon fund, History and Philosophy of Science department, University of Pittsburgh. (shrink)

Idealizations are ubiquitous in physics. They are distortions or falsities that enter into theories, laws, models, and scientific representations. Various questions suggest themselves: What are idealizations? Why do we appeal to idealizations and how do we justify them? Are idealizations essential to physics and, if so, in what sense and for which purpose? How can idealizations provide genuine understanding? If our motivation for believing in the existence of unobservable entities like electrons and quarks is that they are indispensable to our (...) best theories, should we also believe in the existence of indispensable idealizations? This Element will tackle such questions and offer an opinionated and selective introduction to philosophical issues concerning idealizations in physics. Topics to be covered include the concept of and reasons for introducing idealization, abstraction, and approximation, possible taxonomy and justification, and application to issues of mathematical Platonism, scientific realism, and scientific understanding. (shrink)

We offer a framework for organizing the literature regarding the debates revolving around infinite idealizations in science, and a short summary of the contributions to this special issue.

This chapter gives an overview of the various themes and issues discussed in the volume. It includes summaries of all chapters and places the contributions, some of which are part of a critical conversation format, in the context of the larger literature and debates.

This chapter responds to Michael Tamir and Elay Shech’s chapter “Understanding from Deep Learning Models in Context.”.

Elay Shech and John Earman have recently argued that the common topological interpretation of the Aharonov–Bohm (AB) effect is unsatisfactory because it fails to justify idealizations that it presupposes. In particular, they argue that an adequate account of the AB effect must address the role of boundary conditions in certain ideal cases of the effect. In this paper I defend the topological interpretation against their criticisms. I consider three types of idealization that might arise in treatments of the (...) effect. First, Shech takes the AB effect to involve an idealization in the form of a singular limit, analogous to the thermodynamic limit in statistical mechanics. But, I argue, the AB effect itself features no singular limits, so it doesn’t involve idealizations in this sense. Second, I argue that Shech and Earman’s emphasis on the role of boundary conditions in the AB effect is misplaced. The idealizations that are useful in connecting the theoretical description of the AB effect to experiment do interact with facts about boundary conditions, but none of these idealizations are presupposed by the topological interpretation of the effect. Indeed, the boundary conditions for which Shech and demands justification are incompatible with some instances of the AB effect, so the topological interpretation ought not justify them. Finally, I address the role of the non-relativistic approximation usually presumed in discussions of the AB effect. This approximation is essential if—as the topological interpretation supposes—the AB effect constrains and justifies a relativistic theory of the electromagnetic interaction. In this case the ends justify the means. So the topological view presupposes no unjustified idealizations. (shrink)

A one-page editorial including one-sentence summaries of papers authored by Carsten Held, Elise Crull, Johanna Wolff, Elay Shech, Richard Dawid, and Gábor Hofer-Szabó.

This special issue includes papers authored by Carsten Held, Elise Crull, Johanna Wolff, Elay Shech, Richard Dawid, and Gábor Hofer-Szabó.

Shech (2022) offers a critical assessment of my defense of anti-realism, developed in Resisting Scientific Realism. Induction and inductive inferences play a central role in Shech’s critical analysis of my defense of realism. I argue that Shech’s criticisms that relate to induction and inductive inference are problematic, and do not constitute a threat to my defense of anti-realism. Contrary to what Shech claims, the anti-realist does not need to explain why inductive inferences are successful. That is (...) not part of contemporary realism/anti-realism debate. Further, such a demand fails to recognise that some anti-realists do not put much stock in induction. (shrink)

In recent decades, philosophers of science have devoted considerable efforts to understand what models represent. One popular position is that models represent fictional situations. Another position states that, though models often involve fictional elements, they represent real objects or scenarios. Though these two positions may seem to be incompatible, I believe it is possible to reconcile them. Using a threefold distinction between different signs proposed by Peirce, I develop an argument based on a proposal recently made by Kralemann and Lattman (...) (in Synthese 190:3397–3420, 2013) that shows that the two aforementioned positions can be reconciled by distinguishing different ways in which a model representation can be used. In particular, on the basis of Peirce’s distinction between icons, indices and symbols, I argue that models can sometimes function as icons, sometimes as indexes and sometimes as symbols, depending on the context in which they are considered and the use that they are developed for because they all have iconic, indexical and symbolic features. In addition, I show that conceiving models as signs enables us to develop an account of scientific representation that meets the main desiderata that Shech (in Synthese 192:3463–3485, 2015) presents. (shrink)