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)

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.

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)

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)

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)

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)

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)

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 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)

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)

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)

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)

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)