Yichen Luo

There is a question of whether de-idealization is needed for justified use of -- for 'checking' -- idealizations. We argue that the standard philosophical account of de-idealization has become too idealized, but that this does not preclude the possibility of justificatory practices which show how models can be used to make inferences about the world. In turn, motivated by examples in physics, we provide a more expansive and practice-driven account of de-idealization by relaxing the standards for closeness to more realistic theoretical items, identifying at least three kinds of procedures for de-idealization: intra-model, inter-model, and measurement de-idealizations. These examples highlight how idealizations can be -- and indeed have been -- scrutinized within physics without appealing to the philosopher's idealized notion of de-idealization.

The axiomatization of physical theories is a fundamental issue of science. The first-order axiomatic system SpecRel for special relativity proposed recently by Andréka et al. is not enough to explain all the main results in the theory, including the twin paradox and energy-mass relation. In this paper, from a four-dimensional spacetime perspective, we introduce the concepts of world-line, proper time and four-momentum to our axiomatic system SpecRel+. Then we introduce an axiom of mass (AxMass) and take four-momentum conservation as an axiom (AxCFM) in SpecRel+. It turns out that the twin paradox and energy-mass relation can be derived from SpecRel+ logically. Hence, as an extension of SpecRel, SpecRel+ is a suitable first-order axiomatic system to describe the kinematics and dynamics of special relativity.

This thesis explores the conceptual foundations of black hole physics through two interconnected aims. First, drawing on philosophical work on scientific modeling, explanation, and idealization, I elucidate the mathematical and methodological bases of black hole physics, thereby clarifying the physical significance of black holes across various theoretical contexts. Second, by examining physicists’ attempts to understand black holes, I critically engage with ongoing debates in the philosophy of science. I argue that black holes are physically robust and indispensable entities, serving as crucial junctions between gravity, quantum physics, and thermodynamics. Chapter 2 identifies three primary but different approaches to modeling classical black holes: exact solutions, topological-causal analyses, and the initial-value formulation. I argue that the distinct mathematical techniques in each of these approaches are mutually integrable and jointly support the physical significance of black holes—in particular, among other things, in substantiating the final state conjecture, which posits that Kerr-Newman family of solutions represent possible end states of gravitational collapse. In Chapter 3, building on these idealized black hole models, I offer a nuanced account of scientific idealization and de-idealization. In light of asymptotic methods, I propose a tripartite framework for de-idealizing de-idealization: intra-model, inter-model, and measurement de-idealizations. These, in turn, reveal how the three main modeling strategies de-idealize black hole models in productive and interrelated ways. Chapter 4 addresses the philosophical notion of universality, prompted by Chandrasekhar’s view of black holes as the simplest and most perfect macroscopic objects in the universe. I identify three complementary forms of black hole universality. I argue that explaining black hole universality requires both (1) the abstract, mathematical operation (idealization) used in topological proofs of uniqueness theorems and (2) the dynamical and causal details revealed in stability theorems. The latter justifies and de-idealizes the former, countering the claim that there are always essential and ineliminable idealizations in universality explanation. The final chapter reinforces the physical status of black holes by analyzing black hole thermodynamics. I focus on the frameworks of quasi-local horizons, particularly isolated and dynamical horizons, arguing that they provide a more solid physical foundation for black hole thermodynamics than traditional arguments based on event horizons.