Outline of a dynamical inferential conception of the application of mathematics

We outline a framework for analyzing episodes from the history of science in which the application of mathematics plays a constitutive role in the conceptual development of empirical sciences. Our starting point is the inferential conception of the application of mathematics, recently advanced by Bueno and Colyvan (2011). We identify and discuss some systematic problems of this approach. We propose refinements of the inferential conception based on theoretical considerations and on the basis of a historical case study. We demonstrate the usefulness of the refined, dynamical inferential conception using the well-researched example of the genesis of general relativity. Specifically, we look at the collaboration of the physicist Einstein and the mathematician Grossmann in the years 1912–1913, which resulted in the jointly published “Outline of a Generalized Theory of Relativity and a Theory of Gravitation,” a precursor theory of the final theory of general relativity. In this episode, independently developed mathematical theories, the theory of differential invariants and the absolute differential calculus, were applied in the process of finding a relativistic theory of gravitation. The dynamical inferential conception not only provides a natural framework to describe and analyze this episode, but it also generates new questions and insights. We comment on the mathematical tradition on which Grossmann drew, and on his own contributions to mathematical theorizing. The dynamical inferential conception allows us to identify both the role of heuristics and of mathematical resources as well as the systematic role of problems and mistakes in the reconstruction of episodes of conceptual innovation and theory change.     

From sunspots to the Southern Oscillation: confirming models of large-scale phenomena in meteorology

The epistemic problem of assessing the support that some evidence confers on a hypothesis is considered using an extended example from the history of meteorology. In this case, and presumably in others, the problem is to develop techniques of data analysis that will link the sort of evidence that can be collected to hypotheses of interest. This problem is solved by applying mathematical tools to structure the data and connect them to the competing hypotheses. I conclude that mathematical innovations provide crucial epistemic links between evidence and theories precisely because the evidence and theories are mathematically described.     

Failure of ontological excess baggage as a criterion of the ontic approaches to quantum theory

This article presents a discussion of the notion of quantum ontological excess baggage, first proposed by Hardy. It is argued here that this idea does not have the significance suggested in his paper. It is shown that if this concept is properly analyzed, it fails to pose any threat to the ontic approach to quantum theory in general.     

From Helmholtz to Schlick: The evolution of the sign-theory of perception

Efforts to trace the influence of fin de siècle neo-Kantianism on early 20th Century philosophy of science have led scholars to recognize the powerful influence on Moritz Schlick of Hermann von Helmholtz, the doyen of 19th Century physics and a leader of the zur?ck zu Kant movement. But Michael Friedman thinks that Schlick misunderstood Helmholtz' signature philosophical doctrine, the sign-theory of perception. Indeed, Friedman has argued that Schlick transformed Helmholtz' Kantian view of spatial intuition into an empiricist version of the causal theory of perception. However, it will be argued that, despite the key role the sign-theory played in his epistemology, Schlick thought the Kantianism in Helmholtz' thought was deeply flawed, rendered obsolete by philosophical insights which emerged from recent scientific developments. So even though Schlick embraced the sign-theory, he rejected Helmholtz' ideas about spatial intuition. In fact, like his teacher, Max Planck, Schlick generalized the sign-theory into a form of structural realism. At the same time, Schlick borrowed the method of concept-formation developed by the formalist mathematicians, Moritz Pasch and David Hilbert, and combined it with the conventionalism of Henri Poincaré. Then, to link formally defined concepts with experience, Schlick's introduced his ‘method of coincidences’, similar to the ‘point-coincidences’ featured in Einstein's physics. The result was an original scientific philosophy, which owed much to contemporary scientific thinkers, but little to Kant or Kantianism.     

Experimental : The double standard in the quantum-information approach to the foundations of quantum theory

Among the alternatives of non-relativistic quantum mechanics (NRQM) there are those that give different predictions than quantum mechanics in yet-untested circumstances, while remaining compatible with current empirical findings. In order to test these predictions, one must isolate one's system from environmental induced decoherence, which, on the standard view of NRQM, is the dynamical mechanism that is responsible for the ‘apparent’ collapse in open quantum systems. But while recent advances in condensed-matter physics may lead in the near future to experimental setups that will allow one to test the two hypotheses, namely genuine collapse vs. decoherence, hence make progress toward a solution to the quantum measurement problem, those philosophers and physicists who are advocating an information-theoretic approach to the foundations of quantum mechanics are still unwilling to acknowledge the empirical character of the issue at stake. Here I argue that in doing so they are displaying an unwarranted double standard.     

Interpretation neutrality in the classical domain of quantum theory

I show explicitly how concerns about wave function collapse and ontology can be decoupled from the bulk of technical analysis necessary to recover localized, approximately Newtonian trajectories from quantum theory. In doing so, I demonstrate that the account of classical behavior provided by decoherence theory can be straightforwardly tailored to give accounts of classical behavior on multiple interpretations of quantum theory, including the Everett, de Broglie–Bohm and GRW interpretations. I further show that this interpretation-neutral, decoherence-based account conforms to a general view of inter-theoretic reduction in physics that I have elaborated elsewhere, which differs from the oversimplified picture that treats reduction as a matter of simply taking limits. This interpretation-neutral account rests on a general three-pronged strategy for reduction between quantum and classical theories that combines decoherence, an appropriate form of Ehrenfest׳s Theorem, and a decoherence-compatible mechanism for collapse. It also incorporates a novel argument as to why branch-relative trajectories should be approximately Newtonian, which is based on a little-discussed extension of Ehrenfest׳s Theorem to open systems, rather than on the more commonly cited but less germane closed-systems version. In the Conclusion, I briefly suggest how the strategy for quantum-classical reduction described here might be extended to reduction between other classical and quantum theories, including classical and quantum field theory and classical and quantum gravity.     

Weyl’s ‘agens theory’ of matter and the Zurich Fichte

This paper investigates Hermann Weyl’s reception of philosophical concepts stemming from the German Idealist Johann Gottlieb Fichte. In particular, Weyl’s ‘agens theory’ of matter, which he held around 1925, will be looked at. In the extant literature, the—admittedly also important—influence of Husserl on Weyl has mainly been addressed. Thus, apart from investigating some detailed Fichtean inheritances in Weyl’s concepts of causality, chance and continuity, the general difference which Weyl saw between the philosophies of Fichte and Husserl will also be discussed. For Weyl this is above all a difference between an active constructivism and a rather passive phenomenological seeing (Schau). Further, the paper shows in some detail the way Weyl was drawn into a certain reading of Fichte by his Zurich colleague, the philosopher Fritz Medicus. The methodological frame of the paper is that of Konstellationsforschung, a historical and systematic approach which proves to be particularly fruitful when investigating a (broadly speaking) German Idealist context and which allows special attention to be given to the acting subjects within the constellation under investigation. Conversely, Weyl’s agens theory suggests amendments to this methodology.     

How not to integrate the history and philosophy of science: a reply to Chalmers

Alan Chalmers uses Robert Boyle’s mechanical philosophy as an example of the irrelevance of ‘philosophy’ to ‘science’ and criticizes my 2006 book Atoms and alchemy for overemphasizing Boyle’s successes. The present paper responds as follows: first, it argues that Chalmers employs an overly simplistic methodology insensitive to the distinction between historical and philosophical claims; second, it shows that the central theses of Atoms and alchemy are untouched by Chalmers’s criticisms; and third, it uses Boyle’s analysis of subordinate causes and his debate with Henry More in the 1670s to demonstrate the inadequacy of Chalmers’s construal of the mechanical philosophy.     

Putting pragmatism to work in the Cold War: Science, technology, and politics in the writings of James B. Conant

This paper examines James Conant’s pragmatic theory of science—a theory that has been neglected by most commentators on the history of 20^th-century philosophy of science—and it argues that this theory occupied an important place in Conant’s strategic thinking about the Cold War. Conant drew upon his wartime science policy work, the history of science, and Quine’s epistemological holism to argue that there is no strict distinction between science and technology, that there is no such thing as “the scientific method,” and that theories are better interpreted as policies rather than creeds. An important consequence that he drew from these arguments is that science is both a thoroughly value-laden, and an intrinsically social, enterprise. These results led him to develop novel proposals for reorganizing scientific and technological research—proposals that he believed could help to win the Cold War. Interestingly, the Cold War had a different impact upon Conant’s thinking than it did upon many other theorists of science in postwar America. Instead of leading him to “the icy slopes of logic,” it led him to develop a socially- and politically-engaged theory that was explicitly in the service of the American Cold War effort.