Idealizations,essential self-adjointness,and minimal model explanation in the Aharonov–Bohm effect

Two approaches to understanding the idealizations that arise in the Aharonov–Bohm (AB) 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.     

Infinite idealizations in science: an introduction

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.

     

Infinitesimal idealization,easy road nominalism,and fractional quantum statistics

Synthese - 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...