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 the literature on infinite and infinitesimal idealization in science through an example from mathematical physics that has been largely ignored by philosophers. Specifically, by appealing to John Norton’s distinction between idealization and approximation, I argue that the phenomena of fractional quantum statistics bears negatively on Mary Leng’s proposed path to (...) easy road nominalism, thereby partially defending Mark Colyvan’s claim that there is no easy road to nominalism. (shrink)

Abstract Richard Healey has recently defended an interactive and holistic interpretation of quantum mechanics. The present work focuses on the holistic aspects of this interpretation. Healey claims that symmetric causes are responsible for the experimental violations of the Bell inequalities and that relational holism is a metaphysical implication of these violations. Presented in this way, the holistic features of Healey's interpretation appear to provide metaphysical backing to the physical mechanism of symmetric causes. It is argued that relational holism is not (...) a metaphysical implication at all but is actually a physical component of Healey's interpretation. Seen in this light, Healey's interpretation no longer appears to provide further insight into the violations of the Bell inequalities. (shrink)

This article demonstrates that non-mechanistic, dynamical explanations are a viable approach to explanation in the special sciences. The claim that dynamical models can be explanatory without reference to mechanisms has previously been met with three lines of criticism from mechanists: the causal relevance concern, the genuine laws concern, and the charge of predictivism. I argue, however, that these mechanist criticisms fail to defeat non-mechanistic, dynamical explanation. Using the examples of Haken et al.’s model of bimanual coordination, and Thelen et al.’s (...) dynamical field model of infant perseverative reaching, I show how each mechanist criticism fails once the standards of Woodward’s interventionist framework are applied to dynamical models. An even-handed application of Woodwardian interventionism reveals that dynamical models are capable of producing genuine explanations without appealing to underlying mechanistic details. 1Introduction2Interventionism and Mechanistic Explanation 2.1Causal relevance and ideal interventions2.2Invariance2.3Explanation3Covering-Laws and Dynamical Explanation 3.1Dynamical models3.2Covering-law explanation3.3Prediction4Causal Relevance 4.1The causal relevance concern4.2Intervening on dynamical models4.3Test case I: The Haken–Kelso–Bunz model4.4Test case II: Dynamical field model5Genuine Laws 5.1The genuine laws concern5.2Using invariance in place of laws5.3Test case I: The Haken–Kelso–Bunz model5.4Test case II: Dynamical field model6Prediction 6.1Predictivism6.2Crude and invariant prediction7Interventionist Criticism of the Haken–Kelso–Bunz Model8Dynamical Explanation8Conclusion. (shrink)

This paper is the second of a two-part series on models and theories, the first of which appeared in International Studies in the Philosophy of Science, Vol. 11, No. 2, 1997. It further explores some of themes of the first paper and examines applications, including: the relations between “similarity” and “isomorphism”, and between “model” and “interpretation”, and the notion of structural explanation.

Are there genuine mathematical explanations of physical phenomena, and if so, how can mathematical theories, which are typically thought to concern abstract mathematical objects, explain contingent empirical matters? The answer, I argue, is in seeing an important range of mathematical explanations as structural explanations, where structural explanations explain a phenomenon by showing it to have been an inevitable consequence of the structural features instantiated in the physical system under consideration. Such explanations are best cast as deductive arguments which, by virtue (...) of their form, establish that, given the mathematical structure instantiated in the physical system under consideration, the explanandum had to occur. Against the claims of platonists such as Alan Baker and Mark Colyvan, I argue that formulating mathematical explanations as structural explanations in this way shows that we can accept that mathematics can play an indispensable explanatory role in empirical science without committing to the existence of any abstract mathematical objects. (shrink)

H. Post's conception of quantal particles as non-individuals is set in a formal logico-mathematical framework. By means of this approach certain metaphysical implications of quantum mechanics can be further explored.

When evaluating the success of causal theories of explanation the focus has typically been on the legitimacy of causal relations and on putative examples of explanations that we cannot capture in causal terms. Here I motivate the existence of a third kind of problem: the difficulty of accounting for explanatory disputes. Moreover, I argue that this problem remains even if the first two are settled and that it threatens to undercut one of the central motivations for causal accounts of explanation, (...) namely, the causal account of the directionality of scientific explanation. (shrink)

The aim of this paper is to analyse the role that the distinction between principle and constructive theories have in the question of the explanatory power of Special Relativity. We show how the distinction breaks down at the explanatory level. We assess Harvey Brown’s (2005) claim that, as a principle theory, Special Relativity lacks of explanatory power and criticize it, as, we argue, based upon an unrealistic picture of the kind of explanations provided by principle (and constructive) theories. Finally, we (...) claim that the structural account of explanation (Hughes 1989b) captures the explanatory success of Special Relativity. (shrink)

In his recent book Bananaworld. Quantum mechanics for primates, Jeff Bub revives and provides a mature version of his influential information-theoretic interpretation of Quantum Theory (QT). In this paper, I test Bub’s conjecture that QT should be interpreted as a theory about information, by examining whether his information-theoretic interpretation has the resources to explain (or explain away) quantum conundrums. The discussion of Bub’s theses will also serve to investigate, more in general, whether other approaches succeed in defending the claim that (...) QT is about quantum information. First of all, I argue that Bub’s interpretation of QT as a principle theory fails to fully explain quantum non-locality. Secondly, I argue that a constructive interpretation, where the quantum state is interpreted ontically as information, also fails at providing a full explanation of quantum correlations. Finally, while epistemic interpretations might succeed in this respect, I argue that such a success comes at the price of rejecting some in between the most basic scientific standards of physical theories. (shrink)

This paper investigates the relationship between structural explanation and the New Mechanistic account of explanation. The aim of this paper is twofold: firstly, to argue that some phenomena in the domain of fundamental physics, although mechanically brute, are structurally explained; and secondly, by elaborating on the contrast between SE and mechanistic explanation to better clarify some features of SE. Finally, this paper will argue that, notwithstanding their apparently antithetical character, SE and ME can be reconciled within a unified account of (...) general scientific explanation. (shrink)

By briefly reviewing three well-known scientific revolutions in fundamental physics (the discovery of inertia, of special relativity and of general relativity), I claim that problems that were supposed to be crying for a dynamical explanation in the old paradigm ended up receiving a structural explanation in the new one. This claim is meant to give more substance to Kuhn’s view that revolutions are accompanied by a shift in what needs to be explained, while suggesting at the same time the existence (...) of a pattern that is common to all of the discussed case-studies. It remains to be seen whether also quantum mechanics, in particular entanglement, conforms to this pattern. (shrink)

Scientific models invariably involve some degree of idealization, abstraction, or nationalization of their target system. Nonetheless, I argue that there are circumstances under which such false models can offer genuine scientific explanations. After reviewing three different proposals in the literature for how models can explain, I shall introduce a more general account of what I call model explanations, which specify the conditions under which models can be counted as explanatory. I shall illustrate this new framework by applying it to the (...) case of Bohr's model of the atom, and conclude by drawing some distinctions between phenomenological models, explanatory models, and fictional models. (shrink)

In semiclassical mechanics one finds explanations of quantum phenomena that appeal to classical structures. These explanations are prima facie problematic insofar as the classical structures they appeal to do not exist. Here I defend the view that fictional structures can be genuinely explanatory by introducing a model-based account of scientific explanation. Applying this framework to the semiclassical phenomenon of wavefunction scarring, I argue that not only can the fictional classical trajectories explain certain aspects of this quantum phenomenon, but also that (...) an explanation that does not make reference to these classical structures is, in a certain sense, deficient. (shrink)

Ontic structural realism constitutes a promising take on scientific realism, one that avoids the well‐known issues that realist stances have with underdetermination and theory change. In its most radical versions, ontic structural realism proposes a type of eliminativism about theoretical entities, ascribing ontological commitment only to the structures, and not to the objects appearing in our theories. More moderate versions of ontic structural realism have also been proposed, allowing for ‘thin’ objects in the ontology. This work connects these takes on (...) structural realism with the independent notion that there are two categorically different kinds of scientific theories, namely those that deal with interactions and those that deal with structural constraints – what are known as interaction and framework theories, respectively. By taking this classification seriously, one can arrive at a selective version of ontic structural realism which is better adapted to our scientific knowledge, in which eliminativist ontic structural realism constitutes a natural fit to framework theories, whereas the moderate version is connected to interaction theories. (shrink)

According to conventional wisdom, local gauge symmetry is not a symmetry of nature, but an artifact of how our theories represent nature. But a study of the so-called theta-vacuum appears to refute this view. The ground state of a quantized non-Abelian Yang-Mills gauge theory is characterized by a real-valued, dimensionless parameter theta—a fundamental new constant of nature. The structure of this vacuum state is often said to arise from a degeneracy of the vacuum of the corresponding classical theory, which degeneracy (...) allegedly arises from the fact that “large” (but not “small”) local gauge transformations connect physically distinct states of zero field energy. If that is right, then some local gauge transformations do generate empirical symmetries. In defending conventional wisdom against this challenge I hope to clarify the meaning of empirical symmetry while deepening our understanding of gauge transformations. I distinguish empirical from theoretical symmetries. Using Galileo’s ship and Faraday’s cube as illustrations, I say when an empirical symmetry is implied by a theoretical symmetry. I explain how the theta-vacuum arises, and how “large” gauge transformations differ from “small” ones. I then present two analogies from elementary quantum mechanics. By applying my analysis of the relation between empirical and theoretical symmetries, I show which analogy faithfully portrays the character of the vacuum state of a classical non-Abelian Yang-Mills gauge theory. The upshot is that “large” as well as “small” gauge transformations are purely formal symmetries of non-Abelian Yang-Mills gauge theories, whether classical or quantized. It is still worth distinguishing between these kinds of symmetries. An analysis of gauge within the constrained-Hamiltonian formalism yields the result that “large” gauge transformations should not be classified as gauge transformations; indeed, nor should “global” gauge transformations. In a theory in which boundary conditions are modeled dynamically, “global” gauge transformations may be associated with physical symmetries, corresponding to translations of these extra dynamical variables. Such translations are symmetries if and only if charge is conserved. But it is hard to argue that these symmetries are empirical, and in any case they do not correspond to any constant phase change in a quantum state. (shrink)

The problems that exist in relating quantum mechanical phenomena to classical concepts like properties, causes, or entities like particles or waves are well-known and still open to question, so that there is not yet an agreement on what kind of metaphysics lies at the foundations of quantum mechanics. However, physicists constantly use the formal resources of quantum mechanics in order to explain quantum phenomena. The structural account of explanation, therefore, tries to account for this kind of mathematical explanation in physics, (...) and hinges on the following claims: i) scientific models are central in scientific explanation; ii) in some cases the relevant information for the explanation/understanding of a phenomenon P consists in the sole structural properties of the (models displayed by the) theory; iii) in these cases, the interpretation of the formalism in terms of a categorial framework is unessential for the explanation of P and a mathematical model can be at the base of an objective and effective scientific explanation. The present paper will carry a reflection about some issues arising from R.I.G. Hughes and Robert Clifton’s works in the attempt to outline some details of structural explanation. (shrink)

In this paper we argue that structural explanations are an effective way of explaining well known relativistic phenomena like length contraction and time dilation, and then try to understand how this can be possible by looking at the literature on scientific models. In particular, we ask whether and how a model like that provided by Minkowski spacetime can be said to represent the physical world, in such a way that it can successfully explain physical phenomena structurally. We conclude by claiming (...) that a partial isomorphic approach to scientific representation can supply an answer only if supplemented by a robust injection of pragmatic factors. (shrink)

In this paper we argue that quantum mechanics provides a genuine kind of structural explanations of quantum phenomena. Since structural explanations only rely on the formal properties of the theory, they have the advantage of being independent of interpretative questions. As such, they can be used to claim that, even in the current absence of one agreed-upon interpretation, quantum mechanics is capable of providing satisfactory explanations of physical phenomena. While our proposal clearly cannot be taken to solve all interpretive issues (...) raised by quantum theory, we will argue that it can be successfully applied to some of its most puzzling phenomena, such Heisenberg's uncertainty relations and quantum non-locality. The discussion of these two case studies will also serve to illustrate the main properties of structural explanations and compare them to the DN and the unificationist models. Finally, we briefly discuss how structural explanations might relate to structural realism. (shrink)