Hobbes on natural philosophy as “True Physics” and mixed mathematics

In this paper, I offer an alternative account of the relationship of Hobbesian geometry to natural philosophy by arguing that mixed mathematics provided Hobbes with a model for thinking about it. In mixed mathematics, one may borrow causal principles from one science and use them in another science without there being a deductive relationship between those two sciences. Natural philosophy for Hobbes is mixed because an explanation may combine observations from experience (the ‘that’) with causal principles from geometry (the ‘why’). My argument shows that Hobbesian natural philosophy relies upon suppositions that bodies plausibly behave according to these borrowed causal principles from geometry, acknowledging that bodies in the world may not actually behave this way. First, I consider Hobbes's relation to Aristotelian mixed mathematics and to Isaac Barrow's broadening of mixed mathematics in Mathematical Lectures (1683). I show that for Hobbes maker's knowledge from geometry provides the ‘why’ in mixed-mathematical explanations. Next, I examine two explanations from De corpore Part IV: (1) the explanation of sense in De corpore 25.1-2; and (2) the explanation of the swelling of parts of the body when they become warm in De corpore 27.3. In both explanations, I show Hobbes borrowing and citing geometrical principles and mixing these principles with appeals to experience.     

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.     

Hilbert's axiomatic method and Carnap's general axiomatics

This paper compares the axiomatic method of David Hilbert and his school with Rudolf Carnap's general axiomatics that was developed in the late 1920s, and that influenced his understanding of logic of science throughout the 1930s, when his logical pluralism developed. The distinct perspectives become visible most clearly in how Richard Baldus, along the lines of Hilbert, and Carnap and Friedrich Bachmann analyzed the axiom system of Hilbert's Foundations of Geometry—the paradigmatic example for the axiomatization of science. Whereas Hilbert's axiomatic method started from a local analysis of individual axiom systems in which the foundations of mathematics as a whole entered only when establishing the system's consistency, Carnap and his Vienna Circle colleague Hans Hahn instead advocated a global analysis of axiom systems in general. A primary goal was to evade, or formalize ex post, mathematicians' ‘material’ talk about axiom systems for such talk was held to be error-prone and susceptible to metaphysics.     

Henry More and the development of absolute time

This paper explores the nature, development and influence of the first English account of absolute time, put forward in the mid-seventeenth century by the ‘Cambridge Platonist’ Henry More. Against claims in the literature that More does not have an account of time, this paper sets out More's evolving account and shows that it reveals the lasting influence of Plotinus. Further, this paper argues that More developed his views on time in response to his adoption of Descartes' vortex cosmology and cosmogony, providing new evidence of More's wider project to absorb Cartesian natural philosophy into his Platonic metaphysics. Finally, this paper argues that More should be added to the list of sources that later English thinkers – including Newton and Samuel Clarke – drew on in constructing their absolute accounts of time.     

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.     

Kant and the scope of the analytic method

The paper investigates Kant's pre-critical views on the use of analytic and synthetic methods in Newtonian science and in philosophical reasoning. In his 1755/56 writings, Kant made use of two variants of the analytic method, i.e., conceptual analysis in a Cartesian (or Leibnizean) sense, and analysis of the phenomena in a Newtonian sense. His Prize Essay (1764) defends Newton's analytic method of physics as appropriate for philosophy, in contradistinction to the synthetic method of mathematics. A closer look, however, shows that Kant does not identify Newton's method with conceptual analysis, but just suggests a methodological analogy between both methods. Kant’s 1768 paper on incongruent counterparts also fits in with his pre-critical use of conceptual analysis. Here, Kant criticizes Leibniz’ relational concept of space, arguing that it is incompatible with the phenomenon of chiral objects. Since this result was in conflict with his pre-critical views about space, Kant abandoned the analytic method of philosophy in favour of his critical method. The paper closes by comparing Kant's pre-critical analytic method and the way in which he once again took up the methodological analogy between Newtonian science and metaphysics, in the preface B to the Critique of Pure Reason, in the context of his thought experiment of pure reason.     

The Replication of Hertz's Cathode Ray Experiments

I reappraise in detail Hertz's cathode ray experiments. I show that, contrary to Buchwald's (1995) evaluation, the core experiment establishing the electrostatic properties of the rays was successfully replicated by Perrin (probably) and Thomson (certainly). Buchwald's discussion of ‘current purification’ is shown to be a red herring. My investigation of the origin of Buchwald's misinterpretation of this episode reveals that he was led astray by a focus on what Hertz ‘could do’—his experimental resources. I argue that one should focus instead on what Hertz wanted to achieve—his experimental goals. Focusing on these goals, I find that his explicit and implicit requirements for a successful investigation of the rays’ properties are met by Perrin and Thomson. Thus, even by Hertz's standards, they did indeed replicate his experiment.     

Knowing what would happen: The epistemic strategies in Galileo's thought experiments

While philosophers have subjected Galileo's classic thought experiments to critical analysis, they have tended to largely ignored the historical and intellectual context in which they were deployed, and the specific role they played in Galileo's overall vision of science. In this paper I investigate Galileo's use of thought experiments, by focusing on the epistemic and rhetorical strategies that he employed in attempting to answer the question of how one can know what would happen in an imaginary scenario. Here I argue we can find three different answers to this question in Galileo later dialogues, which reflect the changing meanings of ‘experience’ and ‘knowledge’ (scientia) in the early modern period. Once we recognise that Galileo's thought experiments sometimes drew on the power of memory and the explicit appeal to ‘common experience’, while at other times, they took the form of demonstrative arguments intended to have the status of necessary truths; and on still other occasions, they were extrapolations, or probable guesses, drawn from a carefully planned series of controlled experiments, it becomes evident that no single account of the epistemological relationship between thought experiment, experience and experiment can adequately capture the epistemic variety we find Galileo's use of imaginary scenarios. To this extent, we cannot neatly classify Galileo's use of thought experiments as either ‘medieval’ or ‘early modern’, but we should see them as indicative of the complex epistemological transformations of the early seventeenth century.     

A history of entanglement: Decoherence and the interpretation problem

This paper examines the interweaving of the history of quantum decoherence and the interpretation problem in quantum mechanics through the work of two physicists—H. Dieter Zeh and Wojciech Zurek. In the early 1970s Zeh anticipated many of the important concepts of decoherence, framing it within an Everett-type interpretation. Zeh has since remained committed to this view; however, Zurek, whose papers in the 1980s were crucial in the treatment of the preferred basis problem and the subsequent development of density matrix formalism, has argued that decoherence leads to what he terms the ‘existential interpretation’, compatible with certain aspects of both Everett's relative-state formulation and the Bohr's ‘Copenhagen interpretation’. I argue that these different interpretations can be traced back to the different early approaches to the study of environment-induced decoherence in quantum systems, evident in the early work of Zeh and Zurek. I also show how Zurek's work has contributed to the tendency to see decoherence as contributing to a ‘new orthodoxy’ or a reconstruction of the original Copenhagen interpretation.     

The National Science Foundation and philosophy of science's withdrawal from social concerns

At some point during the 1950s, mainstream American philosophy of science began increasingly to avoid questions about the role of non-cognitive values in science and, accordingly, increasingly to avoid active engagement with social, political and moral concerns. Such questions and engagement eventually ceased to be part of the mainstream. Here we show that the eventual dominance of ‘value-free’ philosophy of science can be attributed, at least in part, to the policies of the U.S. National Science Foundation's “History and Philosophy of Science” sub-program. In turn, the sub-program's policies were set by logical empiricists who espoused value-free philosophy of science; these philosophers' actions, we also point out, fit a broad pattern, one in which analytic philosophers used institutional control to marginalize rival approaches to philosophy. We go on to draw on existing knowledge of this pattern to suggest two further, similar, contributors to the withdrawal from value-laden philosophy of science, namely decisions by the editors of Philosophy of Science and by the editors of The Journal of Philosophy. Political climate was, we argue, at most an indirect contributor to the withdrawal and was neither a factor that decided whether it occurred nor one that was sufficient to bring it about. Moreover, we argue that the actions at the National Science Foundation went beyond what was required by its senior administrators and are better viewed as part of what drove, rather than as what was being driven by, the adoption of logical empiricism by the philosophy of science community.     

Quantum metaphysical indeterminacy and the ontological foundations of orthodoxy

This paper develops quantum state individualism, a fundamental ontology for what is usually known as ‘orthodox quantum mechanics.’ The central import of this ontology is that allows for a systematic evaluation of some of the main conclusions of the recent literature on quantum metaphysical indeterminacy. In particular, quantum state individualism supports the ‘gappy’ version of Jessica Wilson's determinable-based account of metaphysical indeterminacy; it implies that fundamental reality is perfectly precise; and third, it provides a non-disjunctive definition of determinables and thereby shields Wilson's account against the charge that it requires either a departure from classical logic or a revision of the quantum formalism.     

Between Cassirer and Kuhn. Some remarks on Friedman’s relativized a priori

This paper provides a critical evaluation of Friedman’s arguments in favour of a relativized a priori resting on Cassirer’s Neo-Kantianism, Reichenbach’s and Carnap’s constitutive a priori, and finally Kuhn’s account of scientific paradigms change. The main objection concerns Cassirer’s own view of dynamic and historical moveable a priori categories, which Friedman seems to underestimate and recasts in a merely regulative function. However, Cassirer conception of a “liberalized” a priori can shed new light on the process of scientific change and his transcendental method may be considered as a still stimulating alternative to Kuhn’s and post-Kuhnian relativism in the philosophy of science.     

Galileo’s quanti: understanding infinitesimal magnitudes

In On Local Motion in the Two New Sciences, Galileo distinguishes between ‘time’ and ‘quanto time’ to justify why a variation in speed has the same properties as an interval of time. In this essay, I trace the occurrences of the word quanto to define its role and specific meaning. The analysis shows that quanto is essential to Galileo’s mathematical study of infinitesimal quantities and that it is technically defined. In the light of this interpretation of the word quanto, Evangelista Torricelli’s theory of indivisibles can be regarded as a natural development of Galileo’s insights about infinitesimal magnitudes, transformed into a geometrical method for calculating the area of unlimited plane figures.     

Jean-François Pilˆatre de Rozier

A translation of Kant's early paper, ‘Die Frage, ob die Erde veralte, physikalisch erwogen’ (‘The question, whether the Earth is ageing, considered physically’) is presented, and the main features of his position on this question in 1754 are summarized. In that year, Kant believed that the Earth was ageing, and that it was about 6000 years old. The paper allows us to understand the approximate outline of Kant's general ‘theory of the Earth’, and the relation of this theory to the cosmogony that he propounded in 1755. His ideas on the processes of erosion, and the formation of rivers, deltas and sandbanks, are noteworthy, and provide a contribution to the eighteenth-century literature on the denudation dilemma. Kant's general theory of erosion and deposition was, it seems, based to a significant extent on his knowledge of the geographical features of the Königsberg district. The general teleological position underpinning his philosophy may be discerned in this early paper, and he may be thought of as having been trying to orientate himself in space and time, so to speak, before undertaking his major reconstructions in philosophy.     

The benefits of acquiring interactional expertise: Why (some) philosophers of science should engage scientific communities

Philosophers of science are increasingly arguing for and addressing the need to do work that is socially and scientifically engaged. However, we currently lack well-developed frameworks for thinking about how we should engage other expert communities and what the epistemic benefits are of doing so. In this paper, I draw on Collins and Evans' concept of ‘interactional expertise’ – the ability to speak the language of a discipline in the absence of an ability to practice – to consider the epistemic benefits that can arise when philosophers engage scientific communities. As Collins and Evans argue, becoming an interactional expert requires that one ‘hang out’ with members of the relevant expert community in order to learn crucial tacit knowledge needed to speak the language. Building on this work, I argue that acquiring interactional expertise not only leads to linguistic fluency, but it also confers several ‘socio-epistemic’ benefits such as the opportunity to cultivate trust with scientific communities. These benefits can improve philosophical work and facilitate the broader uptake of philosophers' ideas, enabling philosophers to meet a variety of epistemic goals. As a result, having at least some philosophers of science acquire interactional expertise via engagement will likely enhance the diversity of epistemic capacities for philosophy of science as a whole. For some philosophers of science, moreover, the socio-epistemic benefits identified here may be more important than the ability to speak the language of a discipline, suggesting the need for a broader analysis of interactional expertise, which this paper also advances.     

Feyerabend on politics,education, and scientific culture

The purpose of this paper is to offer a sympathetic reconstruction of the political thought of Paul Feyerabend. Using a critical discussion of the idea of the ‘free society’ it is suggested that his political thought is best understood in terms of three thematic concerns—liberation, hegemony, and the authority of science—and that the political significance of those claims become clear when they are considered in the context of his educational views. It emerges that Feyerabend is best understood as calling for the grounding of cognitive and cultural authorities—like the sciences—in informed deliberation, rather than the uncritical embrace of prevailing convictions. It therefore emerges that a free society is best understood as one of epistemically responsible citizenship rather than epistemically anarchistic relativism of the ‘anything goes’ sort—a striking anticipation of current debates about philosophy of science in society.     

Realism without tears II: The structuralist legacy of sensory physiology

This paper examines the implications of the Doctrine of Specific Nerve Energies for contemporary philosophy and psychology. Part I analyzed Johannes Peter Müller’s canonical formulation of the Doctrine, arguing that it follows from empirical results combined with methodological principles. Here, I argue that these methodological principles remain valid in psychology today, consequently, any naturalistic philosophy of perception must accept the Doctrine’s skeptical conclusion, that the qualities of our perceptual experience are not determined by, and thus do not reveal the nature of, their causes in the world. Nevertheless, this does not mean that we must be global skeptics; rather, I argue that contemporary epistemology of perception should embrace Müller’s own response to the Doctrine: epistemic structural realism. As articulated by Müller’s student, Helmholtz, structural realism follows from the Doctrine once we recognize that active exploration constitutes part of the mechanism that determines perceptual experience, a view congenial to contemporary theories of embodied perception in cognitive science. Structural realists in philosophy of science should likewise heed the lessons of the Doctrine, as it played a critical part in the early history of their view, and may still serve a constructive role as exemplar today.