Historians have long sought putative connections between different areas of Newton’s scientific work, while recently scholars have argued that there were causal links between even more disparate fields of his intellectual activity. In this paper I take an opposite approach, and attempt to account for certain tensions in Newton’s ‘scientific’ work by examining his great sensitivity to the disciplinary divisions that both conditioned and facilitated his early investigations in science and mathematics. These momentous undertakings, exemplified by research that he wrote (...) up in two separate notebooks, obey strict distinctions between approaches appropriate to both new and old ‘natural philosophy’ and those appropriate to the mixed mathematical sciences. He retained a fairly rigid demarcation between them until the early eighteenth century. At the same time as Newton presented the ‘mathematical principles’ of natural philosophy in his magnum opus of 1687, he remained equally committed to a separate and more private world or ontology that he publicly denigrated as hypothetical or conjectural. This is to say nothing of the worlds implicit in his work on mathematics and alchemy. He did not lurch from one overarching ontological commitment to the next but instead simultaneously—and often radically—developed generically distinct concepts and ontologies that were appropriate to specific settings and locations as well as to relevant styles of argument. Accordingly I argue that the concepts used by Newton throughout his career were intimately bound up with these appropriate generic or quasi-disciplinary ‘structures’. His later efforts to bring together active principles, aethers and voids in various works were not failures that resulted from his ‘confusion’ but were bold attempts to meld together concepts or ontologies that belonged to distinct enquiries. His analysis could not be ‘coherent’ because the structures in which they appeared were fundamentally incompatible.Author Keywords: Connectionism; Incoherence; Appropriateness; Setting; Discipline; Genre; Structure. (shrink)

The recent discussions on the label “historical epistemology” provide us with an interesting example of branding of concepts, ideas and methods. Given this recent interest in the meaning of the expression “historical epistemology”, a detailed analysis of its genealogy and context of emergence may provide some conceptual clarification in a discussion that is often confused and curiously silent on the long tradition of sociology of knowledge. This essay also sheds light on the difficulty with the international and interdisciplinary circulation of (...) ideas. (shrink)

Achieving understanding of nature is one of the aims of science. In this paper we offer an analysis of the nature of scientific understanding that accords with actual scientific practice and accommodates the historical diversity of conceptions of understanding. Its core idea is a general criterion for the intelligibility of scientific theories that is essentially contextual: which theories conform to this criterion depends on contextual factors, and can change in the course of time. Our analysis provides a general account of (...) how understanding is provided by scientific explanations of diverse types. In this way, it reconciles conflicting views of explanatory understanding, such as the causal-mechanical and the unificationist conceptions. (shrink)

This essay is a think piece that takes a labor and capital perspective on science to discuss two chief concepts: credit and exploitation. Credit, as the symbolic currency of science, has been central to how we understand the moral workings of science in the twentieth century. But our lived experience of changes in the political economy of science also alerts us to the notion that credit may not be applicable to a robust analysis of science in the past and in (...) the present. Scientific exploitation, the evidence of which usually prompts an effort to redistribute credit, may offer only a partial picture of the labor structure of science. Self-exploitation, an implicit understanding of how scientists may approach their work, has never been fully articulated but is nevertheless a useful descriptive notion. (shrink)

There is a tension in Emilie Du Châtelet’s thought on mathematics. The objects of mathematics are ideal or fictional entities; nevertheless, mathematics is presented as indispensable for an account of the physical world. After outlining Du Châtelet’s position, and showing how she departs from Christian Wolff’s pessimism about Newtonian mathematical physics, I show that the tension in her position is only apparent. Du Châtelet has a worked-out defense of the explanatory and epistemic need for mathematical objects, consistent with their metaphysical (...) nonfundamentality. I conclude by sketching how Du Châtelet’s conception of mathematical indispensability differs interestingly from many contemporary approaches. (shrink)

This paper aims to reassess the philosophical puzzle of the “applicability of mathematics to physical sciences” as a misunderstood disciplinary interplay. If the border isolating mathematics from the empirical world is based on appropriate criteria, how does one explain the fruitfulness of its systematic crossings in recent centuries? An analysis of the evolution of the criteria used to separate mathematics from experimental sciences will shed some light on this question. In this respect, we will highlight the historical influence of three (...) major disciplinary paradigms. According to the Aristotelian classification of the sciences, the separation of mathematics from physics is based on their respective objects of study. The Baconian system distinguishes these sciences by the type of knowledge involved in each field. Finally, the Whewellian disciplinary layout categorises these disciplines by their respective methods. In this paper, we argue that the cascading effect of such disciplinary categorisations—based successively on ontological, epistemological, and heuristic criteria—resulted in a profound redefinition of the border between mathematics and physics, with the consequence of obscuring the foundations of the interplay between these fields. Our approach intends to put forward such a mechanism as a constitutive piece of the puzzle of the applicability of mathematics. (shrink)

In physics education, equations are commonly seen as calculation tools to solve problems or as concise descriptions of experimental regularities. In physical science, however, equations often play a much more important role associated with the formulation of theories to provide explanations for physical phenomena. In order to overcome this inconsistency, one crucial step is to improve physics teacher education. In this work, we describe the structure of a course that was given to physics teacher students at the end of their (...) master’s degree in two European universities. The course had two main goals: To investigate the complex interplay between physics and mathematics from a historical and philosophical perspective and To expand students’ repertoire of explanations regarding possible ways to derive certain school-relevant equations. A qualitative analysis on a case study basis was conducted to investigate the learning outcomes of the course. Here, we focus on the comparative analysis of two students who had considerably different views of the math-physics interplay in the beginning of the course. Our general results point to important changes on some of the students’ views on the role of mathematics in physics, an increase in the participants’ awareness of the difficulties faced by learners to understand physics equations and a broadening in the students’ repertoire to answer “Why?” questions formulated to equations. Based on this analysis, further implications for physics teacher education are derived. (shrink)

: This paper first discusses the current historical and philosophical framework forged during the last century to account for both the history and the epistemic status of Newton's theory of general gravitation. It then examines the conflict surrounding this theory at the close of the seventeenth century and the first steps towards the revolutionary shift in rational mechanics in the eighteenth century. From a historical point of view, it shows the crucial contribution of the Cartesian mechanistic philosophy and Leibnizian analytic (...) methods to the emergence of so-called Newtonian mechanics which can also be fairly characterized as a synthetic theory of attraction. From a philosophical standpoint, the paper suggests that the reworking of Newton's theory in the 18th century is better understood in a theoretical framework that reconciles Kuhn's notion of "invisible revolution" rather than his notion of "normal science" with Whewell's ascription of the completion of dynamical studies to the post Newtonian period. (shrink)

In this chapter we will argue, firstly, that Bacon’s engages in a pecu-liar form of mathematization of nature that develops a quali-quantitative methodology of measurement. Secondly, we will show that medicine is one of the disciplines where that dual way of measurement is practiced. In the first section of the chapter, we will expose the ontology involved in the Baconian proposal of measurement of nature. The second section will address the place that mixed mathematics occupies in Bacon’s scheme of scientific (...) branches and will suggest that a proper advancement of medicine can generate a new branch of mixed mathematics. The next section will reconstruct Bacon’s approach to measurement and expose its quali-quantitative import. In the last section, we will show some examples of medicine in which this quali-quantitative measurement is applied. (shrink)

Este artículo analiza las condiciones a través de las cuales las matemáticas pasan de un estado de subordinación a desempeñar un papel rector frente a la filosofía natural. Esta transformación se manifestó esencialmente en un cambio de actitud frente al pensamiento tradicional, mediante la sustitución de la explicación cualitativa de los fenómenos naturales por una explicación cuantitativa. En el texto se abordarán los aspectos epistemológicos e institucionales que están implicados en el debate sobre la cientificidad de las matemáticas. A su (...) vez, se hará un recorrido historiográfico señalando las diferentes posturas que tuvieron lugar en la polémica, para ofrecer elementos históricos y conceptuales de análisis respecto de las matemáticas como herramienta de la ciencia moderna. (shrink)

The widespread and long-lived failings of academic economics are due to an over-reliance on largely inappropriate mathematical methods of analysis. This is an assessment I have long maintained. Many heterodox economists, however, appear to hold instead that the central problem is a form of political-economic ideology. Specifically, it is widely contended in heterodox circles that the discipline goes astray just because so many economists are committed to a portrayal of the market economy as a smoothly or efficiently functioning system or (...) some such, a portrayal that, whether sincerely held or otherwise, is inconsistent with the workings of social reality. Here I critically examine the contention that a form of political-economic ideology of this sort is the primary problem and assess its explanatory power. I conclude that the contention does not fare very well. I do not, though, deny that ideology of some sort has a major impact on the output of the modern economics academy. However it is of a different nature to the form typically discussed, and works in somewhat indirect and complex ways. Having raised the question of the impact of ideology I take the opportunity to explore its play in the economics academy more generally. (shrink)

The object of this paper is to look at the extent and nature of the uses of analogy during the ªrst century following the so-called scientiªc revolution. Using the research tool provided by JSTOR we systematically analyze the uses of “analog” and its cognates (analogies, analogous, etc.) in the Philosophical Transactions of the Royal Society of London for the period 1665–1780. In addition to giving the possibility of evaluating quantitatively the proportion of papers explicitly using analogies, this approach makes it (...) possible to go beyond the maybe idiosyncratic cases of Descartes, Kepler, Galileo, and other much studied giants of the so-called Scientiªc Revolution. As a result a classiªcation of types of uses is proposed. Relations between types of analogies and research ªelds are also established. In this paper we are less interested in discussing the “real nature” or “essence” or even the cognitive limitations of analogical thinking than in describing its various uses and different meanings as they changed over the course of a century. (shrink)

In the seventeenth and eighteenth centuries, mathematicians and physical philosophers managed to study, via mathematics, various physical systems of the sublunar world through idealized and simplified models of these systems, constructed with the help of geometry. By analyzing these models, they were able to formulate new concepts, laws and theories of physics and then through models again, to apply these concepts and theories to new physical phenomena and check the results by means of experiment. Students’ difficulties with the mathematics of (...) high school physics are well known. Science education research attributes them to inadequately deep understanding of mathematics and mainly to inadequate understanding of the meaning of symbolic mathematical expressions. There seem to be, however, more causes of these difficulties. One of them, not independent from the previous ones, is the complex meaning of the algebraic concepts used in school physics, as well as the complexities added by physics itself. Another source of difficulties is that the theories and laws of physics are often applied, via mathematics, to simplified, and idealized physical models of the world and not to the world itself. This concerns not only the applications of basic theories but also all authentic end-of-the-chapter problems. Hence, students have to understand and participate in a complex interplay between physics concepts and theories, physical and mathematical models, and the real world, often without being aware that they are working with models and not directly with the real world. (shrink)

Today, Larry Laudan is known predominantly for his work on the pessimistic metainduction and for his discussion of science and values. This essay examines a less familiar part of Laudan’s work, his typology of historical methodologies from the late 1970s. My aim is to elucidate Laudan’s typology and to examine one of the types in more depth, namely, the “pragmatic, symbiotic” model of historical methodology. Laudan expounded the model in the essays that eventually became his 1981 book Science and Hypothesis. (...) Laudan himself characterized this approach to methodology as “history of philosophy of science” and described a number of historiographical guidelines for this history. Several of Laudan’s questions about past scientific methodologies are still worth pursuing, although—and in part because—the concept of scientific methodology changed dramatically as philosophers turned to experimentation in the late twentieth century. Moreover, the study of Laudan’s work in the historical context in which it was devised can shed light on the historical turn in philosophy of science. (shrink)

Explaining is one of the most important everyday practices in science education. In this article, we examine how scientific explanations could serve as cultural tools for members of a group of pre-service physics teachers. Specifically, we aim at their use of explanations about forces of inertia in non-inertial frames of reference. A basic assumption of our study is that explanatory tools (e.g., typical explanations learned) shape the ways we think and speak about the world. Drawing on the theory of mediated (...) action, analysis illustrates three major claims on scientific explanations: (1) explaining is an act of actively responding to explanations presented by others (and not only to evidence itself); (2) the actual experience of explaining involves the enactment of power and authority; (3) resistance (not acknowledging an explanation as one’s own) might be a constitutive part of learning how to explain (hence, teachers could approach scientific explanation in a less dogmatic way). These assertions expand the possibilities of dialogue between studies of scientific explanations and the social sciences. Implications for science teaching and research in science education are presented. (shrink)

Mathematics is so common-place in modern physics and chemistry that one may not realise how controversial its admittance was to these fields in the eightieth and ninetieth centuries respectively. This paper deals with the controversy during the formation of physical chemistry as a discipline in the late ninetieth and early twentieth centuries and sketches more recent criticisms of the way mathematics has been used in solution chemistry. The controversy initially related particularly to electrolyte chemistry and its emerging use of mathematics (...) to support Arrhenius’ theory of ionic dissociation. The impact of mathematics on the field is divided into three phases: that from 1880 to 1920 which was a period of heightened controversy; that from 1920 to 1990 which was a period of relative calm and mathematical development; and finally, that from 1990 to the present which has been a time of reflective criticism of the extensive use of empirical parameters in the emergent mathematics of the twentieth century. It is argued that the current solution to the criticism, as proposed by Heyrovska, is best viewed in the light of the historical development of the controversy. (shrink)