Infinite idealizations in science: an introduction

Abstract

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.

Reckoning with Continuum Idealizations: Some Lessons from Soil Hydrology

“…In these cases, the limiting relations span the gap between discrete, finitely valued models of the target system at the molecular level to continuous, infinitely valued models of the target system at the continuum level. Problematically, however, this constitutes a misrepresentation of the target system since the systems under consideration do not include infinite molecules at the micro-scale (Fletcher et al 2019). Responses to this problem have spawned two positions: the indispensabilists who argue that the infinite idealizations are necessary for capturing real, emergent phenomena, thus adopting a top-down approach to the issue of inter-theoretic reduction and the dispensabilists who have argued that infinite idealizations do not substantively feature in mature scientific theory and are explanatorily dispensable in principle, adopting a bottom-up approach 2 (Shech 2018).…”

“…The indispensabilist position to continuum idealizations can be glossed as follows: For some property or phenomena, there exists a lower scale theory or model which accurately represents this property or phenomena as occurring at the lower scale. However, the prediction, explanation or understanding of this property or phenomena requires a continuum idealization and the corresponding continuum scale model or theory is indispensable; that is, the continuum scale model or theory is not reducible (derivable, deducible, or explainable from the lower scale model or theory) (Fletcher et al 2019). The indispensabilists or essentialists claim that the indispensability or irreducible nature of the phenomena or property at the continuum scale to the lower scale can be accounted for in at least two ways: first, by that property or phenomena's being emergent at the continuum scale or second, by the ineliminable role that continuum idealizations play in isolating the counterfactual dependencies requisite for explanation (Woodward 2003).…”

Multi-model approaches to phylogenetics: Implications for idealization

“…Relatedly, there is a debate, primarily within the philosophy of physics, over whether certain idealizations are dispensable or essential to theory (see especially Shech, 2018, but also Shech, 2019Fletcher et al, 2019;Strevens, 2019). Those who argue that idealizations are essential, such as Batterman (2002) and Bokulich (2008), among others, point to the ways in which our understanding of and explanations for certain phenomena (such as phase transitions) depend on idealizations.…”

Hypothetical Frequencies as Approximations

“…On a von Mises-styled approach, limiting frequencies are meant to account for the objective probabilities appearing in scientific theories, with statistical mechanics serving as a paradigm. And lately, philosophers of physics have become increasingly more attuned to the subtleties of using infinite limits in various physical theories (Earman 2019;Fletcher et al 2019;Palacios and Valente 2021;Valente 2019). Of particular importance to this literature is Norton's (2012) distinction between limits used as mere approximations and those used to construct idealizations.…”