The modal-Hamiltonian interpretation and the Galilean covariance of quantum mechanics

The aim of this paper is to analyze the modal-Hamiltonian interpretation of quantum mechanics in the light of the Galilean group. In particular, it is shown that the rule of definite-value assignment proposed by that interpretation has the same properties of Galilean covariance and invariance as the Schrödinger equation. Moreover, it is argued that, when the Schrödinger equation is invariant, the rule can be reformulated in an explicitly invariant form in terms of the Casimir operators of the Galilean group. Finally, the possibility of extrapolating the rule to quantum field theory is considered.     

On Understanding: Maxwell on the Methods of Illustration and Scientific Metaphor

In this paper I examine the notion and role of metaphors and illustrations in Maxwell's works in exact science as a pathway into a broader and richer philosophical conception of a scientist and scientific practice. While some of these notions and methods are still at work in current scientific research—from economics and biology to quantum computation and quantum field theory—, here I have chosen to attest to their entrenchment and complexity in actual science by attempting to make some conceptual sense of Maxwell's own usage; this endeavour includes situating Maxwell's conceptions and applications in his own culture of Victorian science and philosophy. I trace Maxwell's notions to the formulation of the problem of understanding, or interpreting, abstract representations such as potential functions and Lagrangian equations. I articulate the solution in terms of abstract-concrete relations, where the concrete, in tune with Victorian British psychology and engineering, includes the muscular as well as the pictorial. This sets the basis for a conception of understanding in terms of unification and concrete modelling, or representation. I examine the relation of illustration to analogies and metaphors on which this account rests. Lastly, I stress and explain the importance of context-dependence, its consequences for realism-instrumentalism debates, and Maxwell's own emphasis on method.     

Galilean argumentation and the inauthenticity of the Cigoli letter on painting vs. sculpture

This essay is partly a case study of the role of logic in historiography. It is also partly a test case for the thesis of a Galilean correspondence between aesthetic attitude and scientific thought, advanced by Panofsky, Koyré, and Heilbron. Intrinsically, it is a discussion of the authenticity of the letter to Cigoli dated 26 June 1612, widely attributed to Galileo, containing argumentation about the relative aesthetic merits of painting and sculpture. I undertake a systematic analysis of the letter’s method of argument, comparing and contrasting it with Galileo’s. I argue that the letter does have some Galilean characteristics: critical reasoning; ad hominem argumentation, in the seventeenth-century sense; and appeal to experimentation. However, the letter falls short of the typical Galilean open-mindedness, fair-mindedness, and clarity; crucially, it uses several illative terms which Galileo never uses, and does not use the one he uses most often. The latter features outweigh the former. Moreover, I discuss some aspects of the letter’s substantive content, primarily a theory of vision that disregards the dynamics of perspective and the faculty of binocularity, which Galileo understood and exploited very well. My novel argument vindicates an old judgment of Favaro, who doubted the letter’s authenticity.     

The bounded heavens: defining the limits of astrological practice in the Iberian indices

ABSTRACT

This paper explores the rules for the expurgation of texts of astrology in the Iberian Indices of forbidden books. It addresses the prohibitions put forward in Rule IX of the Index of Trent and the bull Coeli et terrae of Sixtus V, and studies its impact on the rules and their interpretation in the Spanish and Portuguese Indices, in particular, those published in the first decades of the seventeenth century: the Spanish Index librorum prohibitorum et expurgatorum of 1612 and the Portuguese Index auctorum damnatae memoriae of 1624. It shows how these indices offer a more meticulous examination of the prohibitions providing not only more detail regarding the different practices of astrology, but also explicitly accept the doctrine of inclinations of Thomas Aquinas as a central rule to deal with astrological judgments on human behaviour. It also highlights some specific details of the practice of censorship of astrological books by examining case studies of censored Portuguese and Spanish astrological publications. These provide new dimensions and highlight significant differences between the theoretical rules, practical guidelines, and actual restriction of astrological content.     

The problem of the invariance of dimension in the growth of modern topology,part II

Summary This work examines the historical origins of topological dimension theory with special reference to the problem of the invariance of dimension. Part I, comprising chapters 1–4, concerns problems and ideas about dimension from ancient times to about 1900. Chapter 1 deals with ancient Greek ideas about dimension and the origins of theories of hyperspaces and higher-dimensional geometries relating to the subsequent development of dimension theory. Chapter 2 treatsCantor's surprising discovery that continua of different dimension numbers can be put into one-one correspondence and his discussion withDedekind concerning the discovery. The problem of the invariance of dimension originates with this discovery. Chapter 3 deals with the early efforts of 1878–1879 to prove the invariance of dimension. Chapter 4 sketches the rise of point set topology with reference to the problem of proving dimensional invariance and the development of dimension theory. Part II, comprising chapters 5–8, concerns the development of dimension theory during the early part of the twentieth century. Chapter 5 deals with new approaches to the concept of dimension and the problem of dimensional invariance. Chapter 6 analyses the origins ofBrouwer's interest in topology and his breakthrough to the first general proof of the invariance of dimension. Chapter 7 treatsLebesgue's ideas about dimension and the invariance problem and the dispute that arose betweenBrouwer andLebesgue which led toBrouwer's further work on topology and dimension. Chapter 8 offers glimpses of the development of dimension theory afterBrouwer, especially the development of the dimension theory ofUrysohn andMenger during the twenties. Chapter 8 ends with some concluding remarks about the entire history covered. Dedicated to Hans Freudenthal     

Minimal length in quantum gravity and the fate of Lorentz invariance

The paper highlights a recent debate in the quantum gravity community on the status of Lorentz invariance in theories that introduce a fundamental length scale, and in particular in deformed special relativity. Two arguments marshaled against that theory are examined and found wanting.     

Klein-Weyl's program and the ontology of gauge and quantum systems

We distinguish two orientations in Weyl's analysis of the fundamental role played by the notion of symmetry in physics, namely an orientation inspired by Klein's Erlangen program and a phenomenological-transcendental orientation. By privileging the former to the detriment of the latter, we sketch a group(oid)-theoretical program—that we call the Klein-Weyl program—for the interpretation of both gauge theories and quantum mechanics in a single conceptual framework. This program is based on Weyl's notion of a “structure-endowed entity” equipped with a “group of automorphisms”. First, we analyze what Weyl calls the “problem of relativity” in the frameworks provided by special relativity, general relativity, and Yang-Mills theories. We argue that both general relativity and Yang-Mills theories can be understood in terms of a localization of Klein's Erlangen program: while the latter describes the group-theoretical automorphisms of a single structure (such as homogenous geometries), local gauge symmetries and the corresponding gauge fields (Ehresmann connections) can be naturally understood in terms of the groupoid-theoretical isomorphisms in a family of identical structures. Second, we argue that quantum mechanics can be understood in terms of a linearization of Klein's Erlangen program. This stance leads us to an interpretation of the fact that quantum numbers are “indices characterizing representations of groups” ((Weyl, 1931a), p.xxi) in terms of a correspondence between the ontological categories of identity and determinateness.     

The balance between immunity and tolerance: The role of Langerhans cells

Langerhans cells are immature skin-homing dendritic cells that furnish the epidermis with an immune surveillance system, and translate information between the internal and external milieu. Dendritic cells, in particular Langerhans cells, are gaining prominence as one of the potential principal players orchestrating the decision between immunity and tolerance. Langerhans cells capture aberrant self-antigen and pathogen-derived antigen for display to the efferent immune response. Recent evidence suggests redundancy in the antigen-presenting function of Langerhans cells, with dermal dendritic subsets capable of fulfilling an analogous role. There is mounting evidence that Langerhans cells can cross-prime T cells to recognize antigens. Langerhans cells are proposed to stimulate T regulatory cells, and are implicated in the pathogenesis of cutaneous T cell lymphoma.The phenotype of Langerhans cells, which may be tolerogenic or immunogenic, appears to depend on their state of maturity, inciting immunogen and cytokine environment, offering the potential for manipulation in immunotherapy. Received 6 August 2008; received after revision 18 September 2008; accepted 13 October 2008     

Reconsidering the Fresnel–Maxwell theory shift: how the realist can have her cake and EAT it too

This paper takes another look at a case study which has featured prominently in a variety of arguments for rival realist positions. After critically reviewing the previous commentaries of the theory shift that took place in the transition from Fresnel’s ether to Maxwell’s electromagnetic theory of optics, it will defend a slightly different reading of this historical case study. Central to this task is the notion of explanatory approximate truth, a concept which must be carefully analysed to begin with. With this notion properly understood, it will be finally argued, the popular Fresnel–Maxwell case study points towards a novel formulation of scientific realism.     

The NOX toolbox: validating the role of NADPH oxidases in physiology and disease

Reactive oxygen species (ROS) are cellular signals but also disease triggers; their relative excess (oxidative stress) or shortage (reductive stress) compared to reducing equivalents are potentially deleterious. This may explain why antioxidants fail to combat diseases that correlate with oxidative stress. Instead, targeting of disease-relevant enzymatic ROS sources that leaves physiological ROS signaling unaffected may be more beneficial. NADPH oxidases are the only known enzyme family with the sole function to produce ROS. Of the catalytic NADPH oxidase subunits (NOX), NOX4 is the most widely distributed isoform. We provide here a critical review of the currently available experimental tools to assess the role of NOX and especially NOX4, i.e. knock-out mice, siRNAs, antibodies, and pharmacological inhibitors. We then focus on the characterization of the small molecule NADPH oxidase inhibitor, VAS2870, in vitro and in vivo, its specificity, selectivity, and possible mechanism of action. Finally, we discuss the validation of NOX4 as a potential therapeutic target for indications including stroke, heart failure, and fibrosis.     

Making the abstract concrete: The role of norms and values in experimental modeling

Experimental modeling is the construction of theoretical models hand in hand with experimental activity. As explained in Section 1, experimental modeling starts with claims about phenomena that use abstract concepts, concepts whose conditions of realization are not yet specified; and it ends with a concrete model of the phenomenon, a model that can be tested against data. This paper argues that this process from abstract concepts to concrete models involves judgments of relevance, which are irreducibly normative. In Section 2, we show, on the basis of several case studies, how these judgments contribute to the determination of the conditions of realization of the abstract concepts and, at the same time, of the quantities that characterize the phenomenon under study. Then, in Section 3, we compare this view on modeling with other approaches that also have acknowledged the role of relevance judgments in science. To conclude, in Section 4, we discuss the possibility of a plurality of relevance judgments and introduce a distinction between locally and generally relevant factors.