Philosophical Issues Concerning Phase Transitions and Anyons: Emergence, Reduction, and Explanatory Fictions

Scientific understanding in the Aharonov‐Bohm effect

“…Last, idealisations in the form of the two‐dimensional limit allow for the exploration of the full spectrum of the quantum exchange phase and corresponding quantum statistics (Shech, 2015, 2019; Shech & Gelfert, 2019; Shech & McGivern, 2021). Specifically, in two dimensions quantum theory has the representational capacity to characterise anyons, which are particles that obey fractional quantum statistics and are contrasted with bosons and fermions (Wilczek, 1982, 1990).…”

Infinite idealizations in science: an introduction

“…However, since this topic was already discussed in Sect. 1, we will not comment on it further [but see Palacios (2017Palacios ( , 2018 and Shech (2018b) for recent contributions, as well as the papers by Robertson (Sect. 3.6), Feintzeig (Sect.…”

Infinite idealizations in physics

“…Other ostensible examples of infinite or infinitesimal idealizations include fractional quantum statistics as portrayed by anyons in the fractional quantum Hall effect (Shech, 2015a, 2018a, 2018b), superselection rules (Butterfield, ; Earman, ), fractals (Butterfield, ), catastrophe optics (Batterman, ), semiclassical mechanics (Batterman, ; Bokulich, ; Landsman, ), point‐particle idealizations in general relativity (Tamir, ; Wayne, ), thermodynamically reversible processes (Norton, ; Valente, ), and systems portraying indeterminism such as a dome with infinite curvature at its peak, an infinite array of masses and springs, and an infinite domino cascade (see Norton, , for these examples), as well as various supertasks (Manchak & Roberts, ).…”

“…Also see Bangu (, 2015a, 2015b), where he argues that the PT case study shows us (i) how bridge laws may impede reduction, as opposed to facilitate it, (ii) that PT are emergent in a manner that signals the need for refinement of the well‐known distinction between strong and weak emergence, and (iii) how the acceptance of fictions among the expalanans (of an explanation) is sometimes justified, since they are required by the special nature of the fictional explananda. Shech (2018b) criticizes these claims in the context of PT but suggests that they are perhaps warranted in the context of the case study of anyons and fractional quantum statistics.…”

“…The idea is that, perhaps, as dispensabilists urge, idealizations are not essential for the explanation of phenomena like PT, SSB, and the Aharonov–Bohm effect, but it does not follow that idealizations play no substantive and indispensible role in science, i.e., this does not mean that idealizations are just there to “make the math easier.” Instead, it is suggested that infinite idealizations may play an indispensible role in the exploration of scientific theories, intertheoretic relations, and phenomena, and that possibly such exploration is needed for deep sense of scientific understanding. Such lines of thought have been investigated by, among others, Butterfield (), Earman (), Gelfert (), Ruetsche (), Shech and Gelfert (), Shech (2015a, 2015b, , , 2018b), and Yi () and can be traced back to work by Redhead () and Wimsatt (). Since this is a current and developing area of research, my goal in this section is just to outline some interesting senses of exploration and identify avenues of future study.…”