Sorin Bangu

Inference to the best explanation and mathematical realism

Arguing for mathematical realism on the basis of Field’s explanationist version of the Quine–Putnam Indispensability argument, Alan Baker has recently claimed to have found an instance of a genuine mathematical explanation of a physical phenomenon. While I agree that Baker presents a very interesting example in which mathematics plays an essential explanatory role, I show that this example, and the argument built upon it, begs the question against the mathematical nominalist.

Understanding Thermodynamic Singularities: Phase Transitions, Data, and Phenomena*

According to standard (quantum) statistical mechanics, the phenomenon of a phase transition, as described in classical thermodynamics, cannot be derived unless one assumes that the system under study is infinite. This is naturally puzzling since real systems are composed of a finite number of particles; consequently, a well‐known reaction to this problem was to urge that the thermodynamic definition of phase transitions (in terms of singularities) should not be “taken seriously.” This article takes singularities seriously and analyzes their role by using the well‐known distinction between data and phenomena, in an attempt to better understand the origin of the puzzle.

Indispensability and Explanation

The question as to whether there are mathematical explanations of physical phenomena has recently received a great deal of attention in the literature. The answer is potentially relevant for the ontology of mathematics; if affirmative, it would support a new version of the indispensability argument for mathematical realism. In this article, I first review critically a few examples of such explanations and advance a general analysis of the desiderata to be satisfied by them. Second, in an attempt to strengthen the realist position, I propose a new type of example, drawing on probabilistic considerations. 1 Introduction 2 Mathematical Explanations   2.1 ‘Simplicity’ 3 An Average Story: The Banana Game   3.1 Some clarifications   3.2 Hopes and troubles for the nominalist   3.3 New hopes?   3.4 New troubles 4 Conclusion 1 Introduction 2 Mathematical Explanations   2.1 ‘Simplicity’   2.1 ‘Simplicity’ 3 An Average Story: The Banana Game   3.1 Some clarifications   3.2 Hopes and troubles for the nominalist   3.3 New hopes?   3.4 New troubles   3.1 Some clarifications   3.2 Hopes and troubles for the nominalist   3.3 New hopes?   3.4 New troubles 4 Conclusion

On the Role of Bridge Laws in Intertheoretic Relations

What is the role of bridge laws in intertheoretic relations? An assumption shared by many views about these relations is that bridge laws enable reductions. In this article, I acknowledge the naturalness of this assumption, but I question it by presenting a context within thermal physics (involving phase transitions) in which the bridge laws, puzzlingly, seem to contribute to blocking the reduction.

Why Does Water Boil? Fictions in Scientific Explanation

A lot of attention has been devoted lately to the philosophical questions raised by phase transitions, and for a good reason. The topic is not only conceptually intriguing, but also generous, inviting interesting connections to issues such as emergence and reduction, idealizations and modeling, as well as the status of fictions in scientific explanations. Here I address this latter topic, and sketch a novel approach to understanding the role of a certain type of fiction (an infinite system) in the explanation of the phenomena of phase-change.

Numerical Methods, Complexity, and Epistemic Hierarchies

Modern mathematical sciences are hard to imagine without appeal to efficient computational algorithms. We address several conceptual problems arising from this interaction by outlining rival but complementary perspectives on mathematical tractability. More specifically, we articulate three alternative characterizations of the complexity hierarchy of mathematical problems that are themselves based on different understandings of computational constraints. These distinctions resolve the tension between epistemic contexts in which exact solutions can be found and the ones in which they cannot; however, contrary to a persistent myth, we conclude that having an exact solution is not generally more epistemologically beneficial than lacking one.

On ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’

I present a reconstruction of Eugene Wigner’s argument for the claim that mathematics is ‘unreasonable effective’, together with six objections to its soundness. I show that these objections are weaker than usually thought, and I sketch a new objection.

Neither Weak, Nor Strong? Emergence and Functional Reduction

The clarification of the concept of emergence has long been on the agenda of the metaphysics of science; notions such as ‘irreducibility’, ‘novelty’ and ‘unpredictability’ have been invoked in an attempt to better circumscribe this notoriously elusive idea. This paper joins this effort, by examining a class of familiar physical processes, such as boiling and freezing—generically called ‘phase transitions’—since many philosophers and physicists take them to be good candidates of emergent phenomena. While I am broadly sympathetic to this view, in this paper I ask what kind of emergence they instantiate. I am asking this question because I would like to argue that the two kinds of emergence currently identified in the metaphysics literature, ‘weak’ and ‘strong’, do not adequately characterize these phenomena.

Scientific Progress, Understanding and Unification

I review critically several accounts of scientific progress and discuss in some detail the most recent one, which I call the ‘knowledge-accumulation’ account. While I am sympathetic to it, I argue that it leaves out an important component of the notion of progress, namely the role of scientific understanding. A sketch of a complementary account (‘understanding-accumulation’) is offered, which construes understanding in terms of unification.

Discontinuities and singularities, data and phenomena: for Referentialism

The paper rebuts a currently popular criticism against a certain take on the referential role of discontinuities and singularities in the physics of first-order phase transitions. It also elaborates on a proposal I made previously on how to understand this role within the framework provided by the distinction between data and phenomena.