A new hypothesis on the basic features characterising the Foundations of Mathematics is suggested. By means of them the entire historical development of Mathematics before the 20th Century is summarised through a table. Also the several programs, launched around the year 1900, on the Foundations of Mathematics are characterised by a corresponding table. The major difficulty that these programs met was to recognize an alternative to the basic feature of the deductive organization of a theory - more precisely, to Hilbert’s (...) main tenet. Ironically, already half a century before the births of these programs the alternative organization has been substantially represented by Lobachevsky's theory on parallel lines. Moreover, although each program’s founder recognised the basic features in a partial way only, all together these programs represented just the four possible foundational approaches. (shrink)

This paper provides a survey of several philosophical issues arising in classical electrodynamics arguing that there is a philosophically rich set of problems in theories of classical physics that have not yet received the attention by philosophers that they deserve. One issue, which is connected to the philosophy of causation, concerns the temporal asymmetry exhibited by radiation fields in the presence of wave sources. Physicists and philosophers disagree on whether this asymmetry reflects a fundamental causal asymmetry or is due to (...) statistical or thermodynamic considerations. I suggest that an explanation appealing to the asymmetry of causation is more promising. Another issue concerns the conceptual structure of the theory. Despite its empirical success, classical electrodynamics faces serious foundational problems. Models of charged particles involve what by the theory's own lights are idealizations, I maintain, and this is a feature that is not readily captured by traditional philosophical accounts of scientific theories. Other issues I discuss concern (i) the relation between Lorentz's theory of the electron and Einstein's Theory of Special Relativity; (ii) the notion of the domain of a theory, the question of theory reduction, and the relation between classical and more fundamental quantum theories; and (iii) the role of locality constraints, their relation to the concept of causation; and the status of locality conditions in the semi-classical theory of the Aharanov-Bohm effect. (shrink)

According to a view widely held among philosophers of science, the notion of cause has no legitimate role to play in mature theories of physics. In this paper I investigate the role of what physicists themselves identify as causal principles in the derivation of dispersion relations. I argue that this case study constitutes a counterexample to the popular view and that causal principles can function as genuine factual constraints. 1. Introduction2. Causality and Dispersion Relations3. Norton's Skepticism4. Conclusion.

In his book, Physical Relativity, Harvey Brown challenges the orthodox view that special relativity is preferable to those parts of Lorentz's classical ether theory it replaced because it revealed various phenomena that were given a dynamical explanation in Lorentz's theory to be purely kinematical. I want to defend this orthodoxy. The phenomena most commonly discussed in this context in the philosophical literature are length contraction and time dilation. I consider three other phenomena of this kind that played a role in (...) the early reception of special relativity in the physics literature: the Fresnel drag effect in the Fizeau experiment, the velocity dependence of electron mass in beta-ray deflection experiments by Kaufmann and others, and the delicately balanced torques on a moving charged capacitor in the Trouton-Noble experiment. I offer historical sketches of how Lorentz's dynamical explanations of these phenomena came to be replaced by their now standard kinematical explanations. I then take up the philosophical challenge posed by the work of Harvey Brown and Oliver Pooley and clarify how those kinematical explanations work. (shrink)

If physics is a science that unveils the fundamental laws of nature, then the appearance of mathematical concepts in its language can be surprising or even mysterious. This was Eugene Wigner’s argument in 1960. I show that another approach to physical theory accommodates mathematics in a perfectly reasonable way. To explore unknown processes or phenomena, one builds a theory from fundamental principles, employing them as constraints within a general mathematical framework. The rise of such theories of the unknown, which I (...) call blackbox models, drives home the unsurprising effectiveness of mathematics. I illustrate it on the examples of Einstein’s principle theories, the S-matrix approach in quantum field theory, effective field theories, and device-independent approaches in quantum information. (shrink)

I examine Harvey Brown’s account of relativity as dynamic and constructive theory and Michel Janssen recent criticism of it. By contrasting Einstein’s principle-constructive distinction with a related distinction by Lorentz, I argue that Einstein's distinction presents a false dichotomy. Appealing to Lorentz’s distinction, I argue that there is less of a disagreement between Brown and Janssen than appears initially and, hence, that Brown’s view presents less of a departure from orthodoxy than it may seem. Neither the kinematics-dynamics distinction nor Einstein’s (...) principle- and constructive theory distinction ultimately capture their disagreement, which may instead be a disagreement about the role of modality in science and the explanatory force of putatively nomic constraints. (shrink)

In previous work I have argued that classical electrodynamics is beset by deep conceptual problems, which result from the problem of self-interactions. Symptomatic of these problems, I argued, is that the main approach to modeling the interactions between charges and fields is inconsistent with the principle of energy–momentum conservation. Zuchowski reports a formal result that shows that the so-called ‘Abraham model' of a charged particle satisfies energy–momentum conservation and argues that this result amounts to a refutation of my inconsistency claim. (...) In this paper I defend my claims against her criticism and argue that she has succeeded neither in refuting my inconsistency argument nor in showing that the conceptual problems of classical electrodynamics have been solved. (shrink)

In his Zur Einstein’schen Relativitätstheorie, Ernst Cassirer presents relativity theory as the last manifestation of the tradition of the “physics of principles” that, starting from the nineteenth century, has progressively prevailed over that of the “physics of models.” In particular, according to Cassirer, the relativity principle plays a role similar to the energy principle in previous physics. In this article, I argue that this comparison represents the core of Cassirer’s neo-Kantian interpretation of relativity. Cassirer pointed out that before and after (...) Kant, the history of physics presents significant instances in which the search for formal conditions that the laws of nature must satisfy preceded and made possible the direct search for such laws. In his earlier years, Cassirer seems to have regarded principles like the energy principle, the relativity principle, and the principle of least action as a constitutive but provisional form of a priori, imposing specific limitations on the form of the allowable laws of nature. Only in his later years, by attributing an autonomous status to these statements of principle, did Cassirer attribute a definitive but merely regulative meaning to the a priori. This does not impose specific requirements on natural laws but only a motivation to search for them. (shrink)

If physics is a science that unveils the fundamental laws of nature, then the appearance of mathematical concepts in its language can be surprising or even mysterious. This was Eugene Wigner’s argument in 1960. I show that another approach to physical theory accommodates mathematics in a perfectly reasonable way. To explore unknown processes or phenomena, one builds a theory from fundamental principles, employing them as constraints within a general mathematical framework. The rise of such theories of the unknown, which I (...) call blackbox models, drives home the unsurprising effectiveness of mathematics. I illustrate it on the examples of Einstein’s principle theories, the S-matrix approach in quantum field theory, effective field theories, and device-independent approaches in quantum information. (shrink)

Authoritative appraisals have qualified this book as an “axiomatic” theory. However, given that its essential content is no more than an analogy, its theoretical organization cannot be axiomatic. Indeed, in the first edition Dirac declares that he had avoided an axiomatic presentation. Moreover, I show that the text aims to solve a basic problem (How quantum mechanics is similar to classical mechanics?). A previous paper analyzed all past theories of physics, chemistry and mathematics, presented by the respective authors non-axiomatically. Four (...) characteristic features of a new model of organizing a theory were recognized. A careful examination of Dirac’s text shows that it actually applied this kind of organization of a theory, confirming formally what Kronz and Lupher suggested through intuitive categories (pragmatism and rigour), i.e. Dirac’s formulation of Quantum mechanics represents a distinct theoretical approach from von Neumann’s axiomatic approach. However, since the second edition Dirac has changed his approach: although relying again on analogy, his theory refers to the axiomatic method. Some considerations on the odd paths which led to the present formulation of QM are added. They suggest that a new foundation of this theory needs to be found. (shrink)

An overview of the German philosophy of science community is given for the years 1992–2012, based on a survey in which 159 philosophers of science in Germany participated. To this end, the institutional background of the German philosophy of science community is examined in terms of journals, centers, and associations. Furthermore, a qualitative description and a quantitative analysis of our survey results are presented. Quantitative estimates are given for: (a) academic positions, (b) research foci, (c) philosophers’ of science most important (...) publications, and (d) externally funded projects, where for (c) all survey participants had indicated their five most important publications in philosophy of science. In addition, the survey results for (a)–(c) are also qualitatively described, as they are interesting in their own right. With respect to (a), we estimated the gender distribution among academic positions. Concerning (c), we quantified philosophers’ of science preference for (i) journals and publishers, (ii) publication format, (iii) language, and (iv) coauthorship for their most important publications. With regard to research projects, we determined their (i) prevalence, (ii) length, and (iii) trend (an increase in number?) as well as their most frequent (iv) research foci and (v) funding organizations. We also distinguished between German-based and non-German-based journals, publishers, and funding institutions, making it thereby possible to evaluate the involvement of the German philosophy of science community in the international research landscape. Finally, we discuss some implications of our findings. (shrink)

In a notable article entitled “What is the Theory of Relativity?” written at the request of The Times and published in its November 28, 1919 edition, Albert Einstein famously distinguished “theories of principle” from “constructive theories.” Einstein placed relativity theory among the principle theories. His distinction has recently received increased attention, especially as it relates to scientific explanation. In particular, there has been considerable discussion of how to explain why there obtain the Lorentz transformations as well as of how to (...) account for the Lorentz covariance of the dynamical laws. Some .. (shrink)