Newton's methodology is significantly richer than the hypothetico-deductive model. It is informed by a richer ideal of empirical success that requires not just accurate prediction but also accurate measurement of parameters by the predicted phenomena. It accepts theory-mediated measurements and theoretical propositions as guides to research. All of these enrichments are exemplified in the classical response to Mercury's perihelion problem. Contrary to Kuhn, Newton's method endorses the radical transition from his theory to Einstein's. The richer themes of Newton's method are (...) strikingly realized in a challenge to general relativity from a new problem posed by Mercury's perihelion. †To contact the author, please write to: Talbot College, University of Western Ontario, London, Ontario, Canada N6A 3K7; e-mail: [email protected]. (shrink)

This article seeks to provide a historically well-informed analysis of an important post-Newtonian area of research in experimental physics between 1798 and 1898, namely the determination of the mean density of the earth and, by the end of the nineteenth century, the gravitational constant. Traditionally, research on these matters is seen as a case of “puzzle solving.” In this article, the author shows that such focus does not do justice to the evidential significance of eighteenth- and nineteenth-century experimental research on (...) the mean density of the earth and the gravitational constant. As Newton’s theory of universal gravitation was mainly based on astronomical observation, it remained to be shown that Newton’s law of universal gravitation did not break down at terrestrial distances. In this context, Cavendish’ experiment and related nineteenth-century experiments played a decisive role, for they provided converging and increasingly stronger evidence for the universality of Newton’s theory of gravitation. More precisely, the author shall argue that, as the accuracy and precision of the experimental apparatuses and the procedures to eliminate external disturbances involved increasingly improved, the empirical support for the universality of Newton’s theory of gravitation improved correspondingly. (shrink)

In this essay, I attempt to assess Henk de Regt and Dennis Dieks recent pragmatic and contextual account of scientific understanding on the basis of an important historical case-study: understanding in Newton’s theory of universal gravitation and Huygens’ reception of universal gravitation. It will be shown that de Regt and Dieks’ Criterion for the Intelligibility of a Theory (CIT), which stipulates that the appropriate combination of scientists’ skills and intelligibility-enhancing theoretical virtues is a condition for scientific understanding, is too strong. (...) On the basis of this case-study, it will be shown that scientists can understand each others’ positions qualitatively and quantitatively, despite their endorsement of different worldviews and despite their convictions as what counts as a proper explanation. (shrink)

In this paper an analysis of Newton’s argument for universal gravitation is provided. In the past, the complexity of the argument has not been fully appreciated. Recent authors like George E. Smith and William L. Harper have done a far better job. Nevertheless, a thorough account of the argument is still lacking. Both authors seem to stress the importance of only one methodological component. Smith stresses the procedure of approximative deductions backed-up by the laws of motion. Harper stresses “systematic dependencies” (...) between theoretical parameters and phenomena. I will argue that Newton used a variety of different inferential strategies: causal parsimony considerations, deductions, demonstrative inductions, abductions and thought-experiments. Each of these strategies is part of Newton’s famous argument. (shrink)

In this essay I argue against I. Bernard Cohen's influential account of Newton's methodology in the Principia: the 'Newtonian Style'. The crux of Cohen's account is the successive adaptation of 'mental constructs' through comparisons with nature. In Cohen's view there is a direct dynamic between the mental constructs and physical systems. I argue that his account is essentially hypothetical-deductive, which is at odds with Newton's rejection of the hypothetical-deductive method. An adequate account of Newton's methodology needs to show how Newton's (...) method proceeds differently from the hypothetical-deductive method. In the constructive part I argue for my own account, which is model based: it focuses on how Newton constructed his models in Book I of the Principia. I will show that Newton understood Book I as an exercise in determining the mathematical consequences of certain force functions. The growing complexity of Newton's models is a result of exploring increasingly complex force functions (intra-theoretical dynamics) rather than a successive comparison with nature (extra-theoretical dynamics). Nature did not enter the scene here. This intra-theoretical dynamics is related to the 'autonomy of the models'. (shrink)

I examine Popper’s claims about Newton’s use of induction in Principia with the actual contents of Principia and draw two conclusions. Firstly, in common with most other philosophers of his generation, it appears that Popper had very little acquaintance with the contents and methodological complexities of Principia beyond what was in the famous General Scholium. Secondly Popper’s ideas about induction were less sophisticated than those of Newton, who recognised that it did not provide logical proofs of the results obtained using (...) it, because of the possibilities of later, contrary evidence. I also trace the historical background to commonplace misconceptions about Newton’s method.Author Keywords: Newton; Popper; Induction; Principia; Kepler’s laws. (shrink)

Styles of reasoning are important devices to understand scientific practice. As I use the concept, a style of reasoning is a pattern of inferential relations that are used to select, interpret, and support evidence for scientific results. In this paper, I defend the view that there is a plurality of styles of reasoning: different domains of science often invoke different styles. I argue that this plurality is an important source of disunity in scientific practice, and it provides additional arguments in (...) support of the disunity claim. I also contrast Ian Hacking’s broad characterization of styles of reasoning with a narrow understanding that I favor. Drawing on examples from molecular biology, chemistry and mathematics, I argue that differences in style of reasoning lead to differences in the way the relevant results are obtained and interpreted. The result is a pluralist view about styles of reasoning that is sensitive to nuances of inferential relations in scientific activity. (shrink)

Algunos especialistas de Newton han sostenido que la metodología con la que éste demuestra la existencia de la fuerza se fundamenta en el tratamiento matemático de los fenómenos del movimiento, lo que se ha convertido en la lectura clásica del asunto. No obstante, esta interpretación presenta amplias limitaciones si se examina a la luz de la lectura que intérpretes como Guicciardini y Guerlac proponen. Este artículo muestra las limitaciones de la lectura clásica a la luz de esta lectura más reciente, (...) explorando los aspectos metodológicos de la demostración de la fuerza. (shrink)

Kant is well known for his restrictive conception of proper science. In the present paper I will try to explain why Kant adopted this conception. I will identify three core conditions which Kant thinks a proper science must satisfy: systematicity, objective grounding, and apodictic certainty. These conditions conform to conditions codified in the Classical Model of Science. Kant’s infamous claim that any proper natural science must be mathematical should be understood on the basis of these conditions. In order to substantiate (...) this reading, I will show that only in this way it can be explained why Kant thought (1) that mathematics has a particular foundational function with respect to the natural sciences and (2) as such secures their scientific status. (shrink)

This article examines Newton’s method of induction and its connection to methodological atomism. The article argues that Newton’s Rule III for the Study of Natural Philosophy is a criterion for isolating the primary qualities of the atomic parts; in other words, it interprets Rule III as a transductive inference. It is shown that both the standard inductive and invariance interpretations of Rule III can be subsumed under the transductive view, although the invariance criterion is reinterpreted; by qualities “that cannot be (...) intended or remitted,” Newton means qualities that are invariant under changes in the configuration of the atomic parts. (shrink)

How Galileo Galilei discovered the law of fall, and the difference that this makes Galileo’s law of fall is one of the crucial building blocks of classical mechanics. The question how this law was discovered has often been a topic of debate. This article offers a reconstruction of the developments within Galileo’s research that led to the discovery of the law. This reconstruction is offered to make a philosophical point regarding the epistemic status of experimental results: Galileo’s experiments can offer (...) sufficient justification for the acceptance of the law of fall only because of their place in a broad research programme. (shrink)

Newton’s Principia introduces four rules of reasoning for natural philosophy. Although useful, there is a concern about whether Newton’s rules guarantee truth. After redirecting the discussion from truth to validity, I show that these rules are valid insofar as they fulfill Goodman’s criteria for inductive rules and Newton’s own methodological program of experimental philosophy; provided that cross-checks are used prior to applications of rule 4 and immediately after applications of rule 2 the following activities are pursued: (1) research addressing observations (...) that systematically deviate from theoretical idealizations and (2) applications of theory that safeguard ongoing research from proceeding down a garden path. (shrink)

This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the (...) field, it lays down a much-needed marker of progress to date and provides a platform for informed and coherent future analysis and research of the subject. -/- The publication comes at a time of heightened worldwide concern over the standard of science and mathematics education, attended by fierce debate over how best to reform curricula and enliven student engagement in the subjects There is a growing recognition among educators and policy makers that the learning of science must dovetail with learning about science; this handbook is uniquely positioned as a locus for the discussion. -/- The handbook features sections on pedagogical, theoretical, national, and biographical research, setting the literature of each tradition in its historical context. Each chapter engages in an assessment of the strengths and weakness of the research addressed, and suggests potentially fruitful avenues of future research. A key element of the handbook’s broader analytical framework is its identification and examination of unnoticed philosophical assumptions in science and mathematics research. It reminds readers at a crucial juncture that there has been a long and rich tradition of historical and philosophical engagements with science and mathematics teaching, and that lessons can be learnt from these engagements for the resolution of current theoretical, curricular and pedagogical questions that face teachers and administrators. (shrink)

The didactics of astronomy is a relatively young field with respect to that of other sciences. Historical issues have most often been part of the teaching of astronomy, although that often does not stem from a specific didactics. The teaching of astronomy is often subsumed under that of physics. One can easily consider that, from an educational standpoint, astronomy requires the same mathematical or physical strategies. This approach may be adequate in many cases but cannot stand as a general principle (...) for the teaching of astronomy. This chapter offers in a first part a brief overview of the status of astronomy education research and of the role of the history and philosophy of science (HPS) in astronomy education. In a second part, it attempts to illustrate possible ways to structure the teaching of astronomy around its historical development so as to pursue a quality education and contextualized learning. (shrink)

This paper considers the importance of unification in the context of developing scientific theories. I argue that unifying hypotheses are not valuable simply because they are supported by multiple lines of evidence. Instead, they can be valuable because they guide experimental research in different domains in such a way that the results from those experiments inform the scope of the theory being developed. I support this characterization by appealing to the early development of quantum theory. I then draw some comparisons (...) with discussions of robustness reasoning. (shrink)

The Akaike Information Criterion can be a valuable tool of scientific inference. This statistic, or any other statistical method for that matter, cannot, however, be the whole of scientific methodology. In this paper some of the limitations of Akaikean statistical methods are discussed. It is argued that the full import of empirical evidence is realized only by adopting a richer ideal of empirical success than predictive accuracy, and that the ability of a theory to turn phenomena into accurate, agreeing measurements (...) of causally relevant parameters contributes to the evidential support of the theory. This is illustrated by Newton's argument from orbital phenomena to the inverse-square law of gravitation. (shrink)

This paper analyzes Deborah Mayo's error-statistical (ES) account of scientific evidence in order to clarify the kinds of "material postulates" it requires and to explain how those assumptions function. A secondary aim is to explain and illustrate the importance of the security of an inference. After finding that, on the most straightforward reading of the ES account, it does not succeed in its stated aims, two remedies are considered: either relativize evidence claims or introduce stronger assumptions. The choice between these (...) approaches turns on the value attached to two aims of inquiry that are in tension: drawing strong, informative conclusions and reasoning securely. (shrink)

This paper considers the importance of unification in the context of developing scientific theories. I argue that unifying hypotheses are not valuable simply because they are supported by multiple lines of evidence. Instead, they can be valuable because they guide experimental research in different domains in such a way that the results from those experiments inform the scope of the theory being developed. I support this characterization by appealing to the early development of quantum theory. I then draw some comparisons (...) with discussions of robustness reasoning. (shrink)

In Kaplan and Winther’s recent article (Biol Theory. doi:10.1007/s13752-012-0048-0, 2012) they argue for three bold theses: first, that “it is illegitimate to read any ontology about ‘race’ off of biological theory or data”; second, that “using biological theory to ground race is a pernicious reification”; and, third, that “race is fundamentally a social rather than a biological category.” While Kaplan and Winther’s theses are thoughtful, I show that the arguments that their theses rest on are unconvincing. In order to be (...) constructive, I go on to show exactly how one can use biological theory and data to legitimately infer an ontological view of race, to infer a biological view of race that is not a reification, and to argue that race is both socially constructed and biologically real. (shrink)

The purpose of this dissertation is to contribute to our understanding of scientific theory pursuit by providing a detailed case study on the development of early quantum theory, from roughly 1900 to 1916. I first elaborate on why this case should be considered an instance of piecemeal pursuit by presenting the historical quantum conjectures that were being used in different contexts. These conjectures gave varied interpretations of quantization. By comparing these conjectures, I identify a general quantum postulate that captures the (...) underlying assumption common to all the cases. I argue that it is possible to consider a general postulate about quantization even when its proper application is ambiguous in a given context, and that the postulate can be separated from different elements of the framework being used to investigate it. I show that the quantum postulate can be deemed promising by analysing the support it gains using a Bayesian framework. I first defend the use of such a framework by considering the purported inconsistencies in Planck's introduction of his quantum conjecture and how we should handle these. I then explicate two cases of support for the postulate. First, I show how we can use a particular solution to the Bayesian problem of old evidence to interpret the support the quantum postulate received by accounting for phenomena that had no previous explanation. Finally, I show that the quantum postulate is also supported by a unification argument, where unification is interpreted as informational relevance between the different domains of inquiry. (shrink)

Kant is well known for his restrictive conception of proper science. In the present paper I will try to explain why Kant adopted this conception. I will identify three core conditions which Kant thinks a proper science must satisfy: systematicity, objective grounding, and apodictic certainty. These conditions conform to conditions codified in the Classical Model of Science. Kant’s infamous claim that any proper natural science must be mathematical should be understood on the basis of these conditions. In order to substantiate (...) this reading, I will show that only in this way it can be explained why Kant thought (1) that mathematics has a particular foundational function with respect to the natural sciences and (2) as such secures their scientific status. (shrink)