The scholastic pendulum

The history of the physics of pendular motion rightly begins with Galileo's discovery of the isochronous character of that motion. There is, however, a ‘pre-history’ of the pendulum, centering on its initial recognition as a significant special case requiring explanation. This occurred in the writings of Jean Buridan and Nicole Oresme in the middle of the fourteenth century. Earlier works that might have been construed as discussing pendular motion are considered, as are the explanations for the scholastic ‘discovery’ of pendular motion put forth by Thomas Kuhn and Piero Ariotti. In contrast to these writers, this paper seeks to account for the pendulum's emergence with reference to an imaginary experiment concerning a body moving past the earth's center, medieval theories of impetus, and the proximate physical model of pendular motion, the late medieval heavy suspended church bell.     

What were the genuine Banach spaces in 1922? Reflection on axiomatisation and progression of the mathematical thought

This paper provides an analysis of the use of axioms in Banach’s Ph.D. and their role in the progression of Banach’s mathematical thought. In order to give a precise account of the role of Banach’s axioms, we distinguish two levels of activity. The first one is devoted to the overall process of creating a new theory able to answer some prescribed problems in functional analysis. The second one concentrates on the epistemological role of axioms. In particular, the notion of norm completeness, as it appears in Banach’s text, can be interpreted as an epistemic linchpin between several a priori inhomogeneous domains of mathematical thought.

     

Edward Gresham’s Astrostereon,or A Discourse of the Falling of the Planet (1603), the Copernican paradox,and the construction of early modern proto-scientific discourse

This paper investigates the functioning of the ‘Copernican paradox’ (stating that the Sun stands still and the Earth revolves around the Sun) in the late sixteenth- and early seventeenth-century England, with particular attention to Edward Gresham's (1565–1613) little-known and hitherto understudied astronomical treatise – Astrostereon, or A Discourse of the Falling of the Planet (1603). The text, which is fully appreciative of the heliocentric system, is analysed within a broader context of the ongoing struggles with the Copernican theory at the turn of the seventeenth century. The article finds that apart from having a purely rhetorical function, the ‘Copernican paradox’ featured in the epistemological debates on how early modern scientific knowledge should be constructed and popularised. The introduction of new scientific claims to sceptical audiences had to be done both through mathematical demonstrations and by referring to the familiar concepts and tools drawn from the inventory of humanist education. As this article shows, Gresham's rhetorical techniques used for the rejection of paradoxicality of heliocentrism are similar to some of the practices which Thomas Digges and William Gilbert employed in order to defend their own findings and assertions.     

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.     

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.     

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.     

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.     

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.     

Incredulity towards Lyotard: a critique of a postmodernist account of science and knowledge

Philosophers of science have paid little attention, positive or negative, to Lyotard’s book The postmodern condition, even though it has been popular in other fields. We set out some of the reasons for this neglect. Lyotard thought that sciences could be justified by non-scientific narratives (a position he later abandoned). We show why this is unacceptable, and why many of Lyotard’s characterisations of science are either implausible or are narrowly positivist. One of Lyotard’s themes is that the nature of knowledge has changed and thereby so has society itself. However much of what Lyotard says muddles epistemological matters about the definition of ‘knowledge’ with sociological claims about how information circulates in modern society. We distinguish two kinds of legitimation of science: epistemic and socio-political. In proclaiming ‘incredulity towards metanarratives’ Lyotard has nothing to say about how epistemic and methodological principles are to be justified (legitimated). He also gives a bad argument as to why there can be no epistemic legitimation, which is based on an act/content confusion, and a confusion between making an agreement and the content of what is agreed to. As for socio-political legitimation, Lyotard’s discussion remains at the abstract level of science as a whole rather than at the level of the particular applications of sciences. Moreover his positive points can be accepted without taking on board any of his postmodernist account of science. Finally we argue that Lyotard’s account of paralogy, which is meant to provide a ‘postmodern’ style of justification, is a failure.     

The rise of western rationalism: Paul Feyerabend's story

I summarize certain aspects of Paul Feyerabend's account of the development of Western rationalism, show the ways in which that account is supposed to run up against an alternative, that of Karl Popper, and then try to give a preliminary comparison of the two. My interest is primarily in whether what Feyerabend called his ‘story’ constitutes a possible history of our epistemic concepts and their trajectory. I express some grave reservations about that story, and about Feyerabend's framework, finding Popper's views less problematic here. However, I also suggest that one important aspect of Feyerabend's material, his treatment of religious belief, can be given an interpretation which makes it tenable, and perhaps preferable to a Popperian approach.     

Natural selection and the ‘antiquity of man’: Intellectual impacts in the Australian colonies

Two months before the publication of Charles Darwin's On the Origin of Species (1859), Scottish geologist Charles Lyell announced a consensus on ‘the antiquity of man.’ Although stemming from separate intellectual traditions, human antiquity and natural selection had such a powerful influence on nineteenth century science that the former is often thought to be an inevitable conceptual and chronological consequence of the latter. Various scholars have argued it was in fact the acceptance of human antiquity that provided a foundation for the intelligibility and eventual acceptance of evolution by natural selection. This article investigates how these two interwoven theories affected understandings of human antiquity in Australia; itself an under-examined topic in Australian scholarship. Indeed, most historians maintain Australia's human antiquity was not ‘discovered’ or broadly understood until the advent of radiocarbon dating and professional archaeology in the 1960s. This over-simplified narrative has only recently begun to be reassessed. To contribute to this reassessment, and to the broader reclamation of human antiquity as a historical subject, this article focuses on the early decades of human antiquity's dissemination in Australia, examines its complex relationship with natural selection, and ultimately challenges narratives of its ‘recent’ discovery.     

Chemist,entomologist, Darwinian,and man of affairs: Raphael Meldola and the making of a scientific career

In 1925 a debate erupted in the correspondence columns of the British Medical Journal concerning the effectiveness of eating raw pancreas as a treatment for diabetes. Enthusiasts were predominantly general practitioners (GPs), who claimed success for the therapy on the basis of their clinical impressions. Their detractors were laboratory‐oriented ‘biochemist‐physicians,’ who considered that their own experiments demonstrated that raw pancreas therapy was ineffective. The biochemist‐physicians consistently dismissed the GPs' observations as inadequately ‘controlled’. They did not define the meaning of ‘control’ in this context, although it clearly did not have the term's present‐day meaning of a trial employing an untreated comparison group of patients. Rather, the physician‐biochemists' ‘properly controlled’ experiments involved careful regulation of their patients' diet and other environmental factors, and evaluation of the therapy's success through biochemical, rather than just clinical, criteria. However, my analysis suggests that these factors alone are inadequate to account for the biochemist‐physicians' dismissal of the GPs' work as ‘uncontrolled’. I suggest that the biochemist‐physicians were deliberately exploiting the powerful rhetorical connotations of the term ‘control’. Ultimately, they implied that only a trial which they themselves had conducted could be deemed ‘adequately controlled’.     

Duncan F. Gregory,William Walton and the development of British algebra: ‘algebraical geometry’, ‘geometrical algebra’, abstraction

This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on ‘algebraical geometry’ and ‘geometrical algebra’ in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the ‘abstract algebra’ and ‘abstract geometry’ of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to ‘algebraical geometry’ and ‘geometrical algebra’ of the second generation of ‘scientific’ symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s–1840s.     

Craft,money and mercy: an apothecary's self-portrait in sixteenth-century Bologna1

The apothecary occupied a liminal position in early modern society between profit and healing. Finding ways to distance their public image from trade was a common problem for apothecaries across Europe. This article uses the case of a Bolognese apothecary, Filippo Pastarino, to address the question of how early modern apothecaries chose to represent themselves to political authorities and to the wider public. ‘Mercy’, alongside ‘craft’, was a pillar of apothecaries’ social identity. By contrast, no matter how central financial transactions (‘money’) were to their activity, apothecaries did not want to be perceived as merchants. Thus, the assistance and advice apothecaries provided to patients and customers resulted as central aspects of their social role. In this context, Bolognese apothecaries aimed to defend their current status, which had been challenged by naturalist Ulysses Aldrovandi, city authorities and local monasteries. However, Pastarino's claims can also be seen as antecedents to the self-legitimizing strategy that seventeenth-century artisans deployed when faced with the need to enhance their new status as natural philosophers. The present study attributes a name, a date of birth and a shop to Filippo Pastarino, revising previous interpretations. More broadly, by focusing on how these artisans defended their position in the city it enriches our understanding of the self-representation of apothecaries.