Introduction to the special issue Hermann Weyl and the philosophy of the ‘New Physics’

This Special Issue Hermann Weyl and the Philosophy of the ‘New Physics’ has two main objectives: first, to shed fresh light on the relevance of Weyl's work for modern physics and, second, to evaluate the importance of Weyl's work and ideas for contemporary philosophy of physics. Regarding the first objective, this Special Issue emphasizes aspects of Weyl's work (e.g. his work on spinors in n dimensions) whose importance has recently been emerging in research fields across both mathematical and experimental physics, as well as in the history and philosophy of physics. Regarding the second objective, this Special Issue addresses the relevance of Weyl's ideas regarding important open problems in the philosophy of physics, such as the problem of characterizing scientific objectivity and the problem of providing a satisfactory interpretation of fundamental symmetries in gauge theories and quantum mechanics. In this Introduction, we sketch the state of the art in Weyl studies and we summarize the content of the contributions to the present volume.     

Theoretical construction in physics – The role of Leibniz for Weyl's ‘Philosophie der Mathematik und Naturwissenschaft’

This paper aims at closing a gap in recent Weyl research by investigating the role played by Leibniz for the development and consolidation of Weyl's notion of theoretical (symbolic) construction. For Weyl, just as for Leibniz, mathematics was not simply an accompanying tool when doing physics—for him it meant the ability to engage in well-guided speculations about a general framework of reality and experience. The paper first introduces some of the background of Weyl's notion of theoretical construction and then discusses particular Leibnizian inheritances in Weyl's ‘Philosophie der Mathematik und Naturwissenschaft’, such as the general appreciation of the principles of sufficient reason and of continuity. Afterwards the paper focuses on three themes: first, Leibniz's primary quality phenomenalism, which according to Weyl marked the decisive step in realizing that physical qualities are never apprehended directly; second, the conceptual relation between continuity and freedom; and third, Leibniz's notion of ‘expression’, which allows for a certain type of (surrogative) reasoning by structural analogy and which gave rise to Weyl's optimism regarding the scope of theoretical construction.     

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.     

Challenging Expertise: Paul Feyerabend vs. Harry Collins & Robert Evans on democracy,public participation and scientific authority: Paul Feyerabend vs. Harry Collins & Robert Evans on scientific authority and public participation

This paper compares Feyerabend's arguments in Science in a Free Society to the controversial theory of expertise proposed by Harry Collins and Robert Evans as a Third Wave of Science Studies. Is the legitimacy of democratic decisions threatened by the unquestioned authority of scientific advice? Or does, on the contrary, science need protection from too much democratic participation in technical decisions? Where Feyerabend's political relativism envisions democratic society as inherently pluralist and demands equal contribution of all traditions and worldviews to public decision-making, Collins and Evans hold a conception of elective modernism, defending the reality and value of technical expertise and arguing that science deserves a privileged status in modern democracies, because scientific values are also democratic values. I will argue that Feyerabend's political relativism provides a valuable framework for the evaluation of Collins' and Evans' theory of expertise. By constructing a dialog between Feyerabend and this more recent approach in Science and Technology Studies, the aim of this article is not only to show where the two positions differ and in what way they might be reconciled, but also how Feyerabend's philosophy provides substantial input to contemporary debate.     

Leibniz on the requisites of an exact arithmetical quadrature

In this paper we will try to explain how Leibniz justified the idea of an exact arithmetical quadrature. We will do this by comparing Leibniz's exposition with that of John Wallis. In short, we will show that the idea of exactitude in matters of quadratures relies on two fundamental requisites that, according to Leibniz, the infinite series have, namely, that of regularity and that of completeness. In the first part of this paper, we will go deeper into three main features of Leibniz's method, that is: it is an infinitesimal method, it looks for an arithmetical quadrature and it proposes a result that is not approximate, but exact. After that, we will deal with the requisite of the regularity of the series, pointing out that, unlike the inductive method proposed by Wallis, Leibniz propounded some sort of intellectual recognition of what is invariant in the series. Finally, we will consider the requisite of completeness of the series. We will see that, although both Wallis and Leibniz introduced the supposition of completeness, the German thinker went beyond the English mathematician, since he recognized that it is not necessary to look for a number for the quadrature of the circle, given that we have a series that is equal to the area of that curvilinear figure.     

Who let the demon out? Laplace and Boscovich on determinism

In this paper, I compare Pierre-Simon Laplace's celebrated formulation of the principle of determinism in his 1814 Essai philosophique sur les probabilités with the formulation of the same principle offered by Roger Joseph Boscovich in his Theoria philosophiae naturalis, published 56 years earlier. This comparison discloses a striking general similarity between the two formulations of determinism as well as certain important differences. Regarding their similarities, both Boscovich's and Laplace's conceptions of determinism involve two mutually interdependent components—ontological and epistemic—and they are both intimately linked with the principles of causality and continuity. Regarding their differences, however, Boscovich's formulation of the principle of determinism turns out not only to be temporally prior to Laplace's but also—being founded on fewer metaphysical principles and more rooted in and elaborated by physical assumptions—to be more precise, complete and comprehensive than Laplace's somewhat parenthetical statement of the doctrine. A detailed analysis of these similarities and differences, so far missing in the literature on the history and philosophy of the concept of determinism, is the main goal of the present paper.     

Tuning up mind's pattern to nature's own idea: Eddington's early twenties case for variational derivatives

This paper sets out to show how Eddington's early twenties case for variational derivatives significantly bears witness to a steady and consistent shift in focus from a resolute striving for objectivity towards “selective subjectivism” and structuralism. While framing his so-called “Hamiltonian derivatives” along the lines of previously available variational methods allowing to derive gravitational field equations from an action principle, Eddington assigned them a theoretical function of his own devising in The Mathematical Theory of Relativity (1923). I make clear that two stages should be marked out in Eddington's train of thought if the meaning of such variational derivatives is to be adequately assessed. As far as they were originally intended to embody the mind's collusion with nature by linking atomicity of matter with atomicity of action, variational derivatives were at first assigned a dual role requiring of them not only to express mind's craving for permanence but also to tune up mind's privileged pattern to “Nature's own idea”. Whereas at a later stage, as affine field theory would provide a framework for world-building, such “Hamiltonian differentiation” would grow out of tune through gauge-invariance and, by disregarding how mathematical theory might precisely come into contact with actual world, would be turned into a mere heuristic device for structural knowledge.     

Instrumental causes and the natural origin of souls in Antonio Ponce Santacruz's theory of animal generation

This article studies the theory of animal seeds as purely material entities in the early seventeenth-century medical writings of Antonio Ponce Santacruz, royal physician to the Spanish king Philipp IV. Santacruz adopts the theory of the eduction of substantial forms from the potentiality of matter, according to which new kinds of causal powers can arise out of material composites of a certain complexity. Santacruz stands out among the late Aristotelian defenders of eduction theory because he applies the concept of an instrument of direction developed by the medieval Avicenna commentator Gentile da Foligno and gives a novel turn to this concept by interpreting animal seeds as separate instruments. The article situates Santacruz's theory in the context of early modern debates about the concept of the eduction of forms, as well as in the context of early modern debates about the concept of separate instruments. Particular attention is paid to Santacruz's responses to the biological views of Julius Caesar Scaliger and Thomas Feyens. Santacruz's response to Scaliger turns out to be central for his explication of the eduction relation, and Santacruz's response to Feyens turns out to be central for his explication of the nature of instrumental causation.     

Mechanics without mechanisms

At the time of Heinrich Hertz's premature death in 1894, he was regarded as one of the leading scientists of his generation. However, the posthumous publication of his treatise in the foundations of physics, Principles of Mechanics, presents a curious historical situation. Although Hertz's book was widely praised and admired, it was also met with a general sense of dissatisfaction. Almost all of Hertz's contemporaries criticized Principles for the lack of any plausible way to construct a mechanism from the “hidden masses” that are particularly characteristic of Hertz's framework. This issue seemed especially glaring given the expectation that Hertz's work might lead to a model of the underlying workings of the ether.In this paper I seek an explanation for why Hertz seemed so unperturbed by the difficulties of constructing such a mechanism. In arriving at this explanation, I explore how the development of Hertz's image-theory of representation framed the project of Principles. The image-theory brings with it an austere view of the “essential content” of mechanics, only requiring a kind of structural isomorphism between symbolic representations and target phenomena. I argue that bringing this into view makes clear why Hertz felt no need to work out the kinds of mechanisms that many of his readers looked for. Furthermore, I argue that a crucial role of Hertz's hypothesis of hidden masses has been widely overlooked. Far from acting as a proposal for the underlying structure of the ether, I show that Hertz's hypothesis ruled out knowledge of such underlying structure.     

‘Working in a new world’: Kuhn,constructivism, and mind-dependence

In The Structure of Scientific Revolutions, Kuhn famously advanced the claim that scientists work in a different world after a scientific revolution. Kuhn's view has been at the center of a philosophical literature that has tried to make sense of his bold claim, by listing Kuhn's view in good company with other seemingly constructivist proposals. The purpose of this paper is to take some steps towards clarifying what sort of constructivism (if any) is in fact at stake in Kuhn's view. To this end, I distinguish between two main (albeit not exclusive) notions of mind-dependence: a semantic notion and an ontological one. I point out that Kuhn's view should be understood as subscribing to a form of semantic mind-dependence, and conclude that semantic mind-dependence does not land us into any worrisome ontological mind-dependence, pace any constructivist reading of Kuhn.     

Carnap on unified science

Unified science is a recurring theme in Carnap's work from the time of the Aufbau until the end of the 1930's. The theme is not constant, but knows several variations. I shall extract three quite precise formulations of the thesis of unified science from Carnap's work during this period: from the Aufbau, from Carnap's so-called syntactic period, and from Testability and Meaning and related papers. My main objective is to explain these formulations and to discuss their relation, both to each other and to other aspects of Carnap's work.     

Inference to the best explanation and Norton's material theory of induction

I argue that we should consider Norton's material theory of induction as consisting of two largely independent claims. First, there is the claim that material facts license inductions - a claim which I interpret as a type of contextualism about induction. Second, there is the claim that there are no universal rules of induction. While a good case can be made for the first claim, I believe that Norton's arguments for the second claim are lacking. In particular, I spell out Norton's argument against the claim that all induction may be reduced to inference to the best explanation, and argue that it is not persuasive. Rejecting this part of Norton's theory does not however require us to abandon the first claim that material facts license inductions. In this way, I distinguish the parts of the material theory of induction we should happily accept from the parts about which we should be more skeptical.     

Fresnel's laws,ceteris paribus

This article is about structural realism, historical continuity, laws of nature, and ceteris paribus clauses. Fresnel's Laws of optics support Structural Realism because they are a scientific structure that has survived theory change. However, the history of Fresnel's Laws which has been depicted in debates over realism since the 1980s is badly distorted. Specifically, claims that J. C. Maxwell or his followers believed in an ontologically-subsistent electromagnetic field, and gave up the aether, before Einstein's annus mirabilis in 1905 are indefensible. Related claims that Maxwell himself did not believe in a luminiferous aether are also indefensible. This paper corrects the record. In order to trace Fresnel's Laws across significant ontological changes, they must be followed past Einstein into modern physics and nonlinear optics. I develop the philosophical implications of a more accurate history, and analyze Fresnel's Laws' historical trajectory in terms of dynamic ceteris paribus clauses. Structuralists have not embraced ceteris paribus laws, but they continue to point to Fresnel's Laws to resist anti-realist arguments from theory change. Fresnel's Laws fit the standard definition of a ceteris paribus law as a law applicable only in particular circumstances. Realists who appeal to the historical continuity of Fresnel's Laws to combat anti-realists must incorporate ceteris paribus laws into their metaphysics.     

Between relativism and pluralism: Philosophical and political relativism in Feyerabend's late work

Relativism is one of the most problematic terms associated with philosophical discourse, with Feyerabend considered among the most important twentieth century theorists subscribing to it. This paper provides a detailed overview of relativist positions advanced in Feyerabend's mid-to-late work and investigates the associated epistemic and political applications. Emphasis is placed on how Feyerabend supported certain aspects of relativism, and at what stage he rejected others. It is noted that Feyerabend had already imposed limitations on relativism in Farewell to Reason, in which he entertained the possibility of epistemic definition within stable contexts, and advanced the notion that opportunities and equality associated with political and cultural units could only be valid within a democratic system. In Conquest of Abundance, political relativism is largely discarded, while epistemological relativism is increasingly treated as an appeal for diversity in all areas.In this re-reading of his work, it becomes clear that Feyerabend was already advocating a moderate form of epistemic and political relativism in the middle of his career, which he subsequently developed in the direction of “ontological pluralism” in his later work. This paper thus shows that Feyerabend's relativism should not be completely rejected, but rather that it continues to offer interesting food for thought.     

The diagrammatic dimension of William Gilbert's De magnete

In De magnete (1600), Gilbert frequently appealed to diagrams. As result of a focus on the experimental methodology of the treatise, its diagrammatic dimension has been overlooked in the scholarship. This paper argues that, in De magnete, at least some diagrams are epistemically relevant; specifically, Gilbert moves from experiments to concepts and theories through diagrams. To show this, I analyze the role that the “Diagram of motions in magnetick orbes” plays in the formulation of Gilbert's rule of alignment of magnetic bodies within the orb of virtue (the space around a magnet where its influence is exerted). If it turns out that diagrams play a genuine role in Gilbert's magnetic investigations, then his investigative strategy goes beyond mere experimentalism.     

Émilie Du Châtelet's interpretation of the laws of motion in the light of 18th century mechanics

Émilie Du Châtelet is well known for her French translation of Newton's Philosophiae Naturalis Principia Mathematica. It is the first and only French translation of Newton's magnum opus. The complete work appeared in 1759 under the title Principes mathématiques de la philosophie naturelle, par feue Madame la Marquise Du Chastellet. Before translating Newton's Principia, Du Châtelet worked on her Institutions de physique. In this book she defended the Leibnizian concept of living forces – vis viva. This paper argues that both of these works were part of a critical transformation and consolidation of post-Newtonian mechanics in the early 18th century, beyond Newton and Leibniz. This will be shown by comparing Du Châtelet's translation of Newton's axioms with her own formulations of the laws of motion in light of Thomas Le Seur's and François Jacquier's Geneva edition which holds a special place among the several editions of the Principia that appeared in the early 18th century.     

Zweideutigkeit about “Zweideutigkeit”: Sommerfeld,Pauli, and the methodological origins of quantum mechanics

In early 1925, Wolfgang Pauli (1900–1958) published the paper for which he is now most famous and for which he received the Nobel Prize in 1945. The paper detailed what we now know as his “exclusion principle.” This essay situates the work leading up to Pauli's principle within the traditions of the “Sommerfeld School,” led by Munich University's renowned theorist and teacher, Arnold Sommerfeld (1868–1951). Offering a substantial corrective to previous accounts of the birth of quantum mechanics, which have tended to sideline Sommerfeld's work, it is suggested here that both the method and the content of Pauli's paper drew substantially on the work of the Sommerfeld School in the early 1920s. Part One describes Sommerfeld's turn away from a faith in the power of model-based (modellmässig) methods in his early career towards the use of a more phenomenological emphasis on empirical regularities (Gesetzmässigkeiten) during precisely the period that both Pauli and Werner Heisenberg (1901–1976), among others, were his students. Part two delineates the importance of Sommerfeld's phenomenology to Pauli's methods in the exclusion principle paper, a paper that also eschewed modellmässig approaches in favour of a stress on Gesetzmässigkeiten. In terms of content, a focus on Sommerfeld's work reveals the roots of Pauli's understanding of the fundamental Zweideutigkeit (ambiguity) involving the quantum number of electrons within the atom. The conclusion points to the significance of these results to an improved historical understanding of the origin of aspects of Heisenberg's 1925 paper on the “Quantum-theoretical Reformulation (Umdeutung) of Kinematical and Mechanical Relations.”     

English engineer John Smeaton's experimental method(s): Optimisation,hypothesis testing and exploratory experimentation

In this paper I provide a detailed account of eighteenth-century engineer John Smeaton's experimental methods, with the aim of bringing our understanding of his work into line with recent research in the history and philosophy of science. Starting from his use of the technique of parameter variation, I identify three distinct methodological aims in the research he carried out on waterwheels, windmills and hydraulic mortars. These aims are: optimisation, hypothesis testing and maxim generation. The main claim of this paper is that Smeaton did more than merely improve engineering methods by systematising earlier artisanal approaches, which is the classic view of Smeaton's method developed by historians of technology in the 1990s. I argue instead that his approach bridged the divide between science and technology, by integrating both hypothesis testing and exploratory experimentation. This is borne out, in particular, by the way that Smeaton emphasised the exploratory side of the work he published in the Philosophical Transactions, in contrast to his account of the construction of the Eddystone lighthouse, which was aimed at a broader, non-specialist public. I contribute to recent research on exploratory experimentation by showing – in line with other work on this topic – that exploratory experimentation is not incompatible with hypothesis testing. This new perspective on Smeaton's method will hopefully lead to further research and new insights into the relation between science and technology at the start of the Industrial Revolution.     

Saving the mutual manipulability account of constitutive relevance

Constitutive mechanistic explanations are said to refer to mechanisms that constitute the phenomenon-to-be-explained. The most prominent approach of how to understand this relation is Carl Craver's mutual manipulability approach (MM) to constitutive relevance. Recently, MM has come under attack (Baumgartner and Casini 2017; Baumgartner and Gebharter 2015; Harinen 2014; Kästner 2017; Leuridan 2012; Romero 2015). It is argued that MM is inconsistent because, roughly, it is spelled out in terms of interventionism (which is an approach to causation), whereas constitutive relevance is said to be a non-causal relation. In this paper, I will discuss a strategy of how to resolve this inconsistency—so-called fat-handedness approaches (Baumgartner and Casini 2017; Baumgartner and Gebharter 2015; Romero 2015). I will argue that these approaches are problematic. I will present a novel suggestion for how to consistently define constitutive relevance in terms of interventionism. My approach is based on a causal interpretation of manipulability in terms of causal relations between the mechanism's components and what I will call temporal EIO-parts of the phenomenon. Still, this interpretation accounts for the fundamental difference between constitutive relevance and causal relevance.