I analyze the extent to which classical phase transitions, both first order and continuous, pose a challenge for intertheoretic reduction. My contention is that phase transitions are compatible with a notion of reduction that combines Nagelian reduction and what Thomas Nickles called Reduction2. I also argue that, even if the same approach to reduction applies to both types of phase transitions, there is a crucial difference in their physical treatment: in addition to the thermodynamic limit, in continuous phase transitions there (...) is a second infinite limit involved, which marks an important difference in the reduction of first-order and continuous phase transitions. (shrink)

This paper presents an in-depth analysis of the anatomy of both thermodynamics and statistical mechanics, together with the relationships between their constituent parts. Based on this analysis, using the renormalization group and finite-size scaling, we give a definition of a large but finite system and argue that phase transitions are represented correctly, as incipient singularities in such systems. We describe the role of the thermodynamic limit. And we explore the implications of this picture of critical phenomena for the questions of (...) reduction and emergence. (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.

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)

According to the free energy principle, life is an “inevitable and emergent property of any random dynamical system at non-equilibrium steady state that possesses a Markov blanket” :20130475, 2013). Formulating a principle for the life sciences in terms of concepts from statistical physics, such as random dynamical system, non-equilibrium steady state and ergodicity, places substantial constraints on the theoretical and empirical study of biological systems. Thus far, however, the physics foundations of the free energy principle have received hardly any attention. (...) Here, we start to fill this gap and analyse some of the challenges raised by applications of statistical physics for modelling biological targets. Based on our analysis, we conclude that model-building grounded in the free energy principle exacerbates a trade-off between generality and realism, because of a fundamental mismatch between its physics assumptions and the properties of actual biological targets. (shrink)

Richard Levins’s (Am Sci 54(4):421–431, 1966) paper sets a landmark for the significance of scientific model-making in biology. Colombo and Palacios (Biol Philos 36(5):1–26. 10.1007/s10539-021-09818-x, 2021) have recently built their critique of the explanatory power of the Free Energy Principle on Levins’s insight into the relationship between generality, realism, and precision. This paper addresses the issue of the plausibility of biological explanations that are grounded in the Free Energy Principle (FEP) and deals with the question of the realist fortitude of (...) FEP’s theoretical framework. It indicates that what is required for establishing the plausibility of the explanation of a target system given a model of that system is the dosage or the harmony between the generality and accuracy of explanatory models. This would also provide a basis for seeing how scientific realism could be a viable option with respect to FEP. (shrink)