By carefully examining one of the most famous thought experiments in the history of science—that by which Galileo is said to have refuted the Aristotelian theory that heavier bodies fall faster than lighter ones—I attempt to show that thought experiments play a distinctive role in scientific inquiry. Reasoning about particular entities within the context of an imaginary scenario can lead to rationally justified concluusions that—given the same initial information—would not be rationally justifiable on the basis of a straightforward argument.

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)

There is substantial evidence that traditional instructional methods have not been successful in helping students to restructure their commonsense conceptions and learn the conceptual structures of scientific theories. This paper argues that the nature of the changes and the kinds of reasoning required in a major conceptual restructuring of a representation of a domain are fundamentally the same in the discovery and in the learning processes. Understanding conceptual change as it occurs in science and in learning science will require the (...) development of a common cognitive model of conceptual change. The historical construction of an inertial representation of motion is examined and the potential instructional implications of the case are explored. (shrink)

Science has always engaged with the worldviews of societies and cultures. The theme is of particular importance at the present time as many national and provincial education authorities are requiring that students learn about the nature of science (NOS) as well as learning science content knowledge and process skills. NOS topics are being written into national and provincial curricula. Such NOS matters give rise to at least the following questions about science, science teaching and worldviews: -/- What is a worldview? (...) -/- Does science have a worldview? -/- Are there specific ontological, epistemological and ethical prerequisites for the conduct of science? -/- Does science lack a worldview but nevertheless have implications for worldviews? -/- How can scientific worldviews and practice be reconciled with seemingly discordant religious and cultural worldviews? -/- In which ways do the worldviews of students impact on their interest and learning of science? -/- Should science teachers engage with the worldviews of students? -/- In addition to the NOS curricular impetus for refining understanding of science and worldviews, there are also pressing cultural and social forces that give prominence to questions about science, worldviews and education. There is something of an avalanche of popular literature on the subject that teachers and students are variously engaged by. Additionally the modernisation and science-based industrialisation of huge non-Western populations whose traditional religions and beliefs are different from those that have been associated with orthodox science make very pressing the questions of whether, and how, science is committed to and hence promotes particular worldviews and contradicts others. Hopefully this chapter, and others in the section, will contribute to a more informed understanding of the relationship between science, worldviews and education and provide assistance to teachers who are routinely engaged with the subject. (shrink)

The notions of conservation and relativity lie at the heart of classical mechanics, and were critical to its early development. However, in Newton’s theory of mechanics, these symmetry principles were eclipsed by domain-specific laws. In view of the importance of symmetry principles in elucidating the structure of physical theories, it is natural to ask to what extent conservation and relativity determine the structure of mechanics. In this paper, we address this question by deriving classical mechanics—both nonrelativistic and relativistic—using relativity and (...) conservation as the primary guiding principles. The derivation proceeds in three distinct steps. First, conservation and relativity are used to derive the asymptotically conserved quantities of motion. Second, in order that energy and momentum be continuously conserved, the mechanical system is embedded in a larger energetic framework containing a massless component that is capable of bearing energy (as well as momentum in the relativistic case). Imposition of conservation and relativity then results, in the nonrelativistic case, in the conservation of mass and in the frame-invariance of massless energy; and, in the relativistic case, in the rules for transforming massless energy and momentum between frames. Third, a force framework for handling continuously interacting particles is established, wherein Newton’s second law is derived on the basis of relativity and a staccato model of motion-change. Finally, in light of the derivation, we elucidate the structure of mechanics by classifying the principles and assumptions that have been employed according to their explanatory role, distinguishing between symmetry principles and other types of principles (such as compositional principles) that are needed to build up the theoretical edifice. (shrink)

By briefly reviewing three well-known scientific revolutions in fundamental physics (the discovery of inertia, of special relativity and of general relativity), I claim that problems that were supposed to be crying for a dynamical explanation in the old paradigm ended up receiving a structural explanation in the new one. This claim is meant to give more substance to Kuhn’s view that revolutions are accompanied by a shift in what needs to be explained, while suggesting at the same time the existence (...) of a pattern that is common to all of the discussed case-studies. It remains to be seen whether also quantum mechanics, in particular entanglement, conforms to this pattern. (shrink)

In Making Sense of Life , Keller emphasizes several differences between biology and physics. Her analysis focuses on significant ways in which modelling practices in some areas of biology, especially developmental biology, differ from those of the physical sciences. She suggests that natural models and modelling by homology play a central role in the former but not the latter. In this paper, I focus instead on those practices that are importantly similar, from the point of view of epistemology and cognitive (...) science. I argue that concrete and abstract models are significant in both disciplines, that there are shared selection criteria for models in physics and biology, e.g. familiarity, and that modelling often occurs in a similar fashion. (shrink)

This paper examines the role of Kant's theory of mathematical cognition in his phoronomy, his pure doctrine of motion. I argue that Kant's account of how we can construct the composition of motion rests on the construction of extended intervals of space and time, and the representation of the identity of the part–whole relations the construction of these intervals allow. Furthermore, the construction of instantaneous velocities and their composition also rests on the representation of extended intervals of space and time, (...) reflecting the general approach to instantaneous velocity in the eighteenth century. (shrink)

The first attempted derivation by Galileo of the law relating space and time in free fall that has survived is preserved on an otherwise unidentified sheet bound among his manuscripts preserved at Florence. It is undoubtedly closely associated with a letter from Galileo to Paolo Sarpi, dated 16 October 1604, which somehow found its way into the Seminary of Pisa, where it is still preserved. Those two documents, together with the letter from Sarpi to Galileo which seems to have inspired (...) them, are translated in full below. Sarpi's letter, dated 9 October 1604, suggests that recent oral discussions of problems of motion had recently taken place between the two men. It reads as follows:“In sending you the enclosure, it occurs to me to propose to you a problem to resolve, and another that seems to me paradoxical. (shrink)

The article investigates the role of symbolic means of knowledge representation in concept development using the historical example of medieval diagrams of change employed in early modern work on the motion of fall. The parallel cases of Galileo Galilei, Thomas Harriot, and René Descartes and Isaac Beeckman are discussed. It is argued that the similarities concerning the achievements as well as the shortcomings of their respective work on the motion of fall can to a large extent be attributed to their (...) shared use of means of knowledge representation handed down from antiquity and the Middle Ages. While the interpretation of medieval diagrams was unproblematic in the scholastic context from which they arose, in the early modern context, which was characterized by the confluence of natural philosophy and practical mathematics, it became ambiguous. It was the early modern mathematicians’ work within this contradictory framework that brought about a new conceptualization of motion which, in particular, eventually led to an infinitesimal concept of velocity. In this process, the diagrams themselves remained largely unchanged and thus functioned as a catalyst for concept development. (shrink)

At the end of the last century Paul Tannery published an article on geometry in eleventh-century Europe, which he began with the following statement:“This is not a chapter in the history of science; it is a study of ignorance, in a period immediately before the introduction into the West of Arab mathematics.”.

The concept of energy, the premier concept of physics and indeed of all science, is here investigated from the standpoint of its early historical origin and the philosophical implications thereof. The fundamental assumption is made that the root of the concept is the notion of invariance or constancy in the midst of change. Salient points in the development of this idea are presented from ancient times up to the publication of Lagrange'sMécanique Analytique (1788).

The aim of this paper is to report some little-known aspects of sixteenth-century physics as these relate to the development of mechanics in the seventeenth century. The research herein reported grew out of a study on the mechanics of Domingo de Soto, a sixteenth-century Spanish scholastic,1 which has been concerned, in part, with examining critically Pierre Duhem's thesis that the English “Calculatores” of the fourteenth century were a primary source for Galileo's science.2 The conclusion to which this has come, thus (...) far, is that Duhem had important insights into the late medieval preparation for the modern science of mechanics, but that he left out many of the steps. And the steps are important, whether one holds for a continuity theory or a discontinuity theory vis-à-vis the connection between late medieval and early modern science. (shrink)

The problem analysed in this paper is whether we can gain knowledge by using valid inferences, and how we can explain this process from a model-theoretic perspective. According to the paradox of inference (Cohen & Nagel 1936/1998, 173), it is logically impossible for an inference to be both valid and its conclusion to possess novelty with respect to the premises. I argue in this paper that valid inference has an epistemic significance, i.e., it can be used by an agent to (...) enlarge his knowledge, and this significance can be accounted in model-theoretic terms. I will argue first that the paradox is based on an equivocation, namely, it arises because logical containment, i.e., logical implication, is identified with epistemological containment, i.e., the knowledge of the premises entails the knowledge of the conclusion. Second, I will argue that a truth-conditional theory of meaning has the necessary resources to explain the epistemic significance of valid inferences. I will explain this epistemic significance starting from Carnap’s semantic theory of meaning and Tarski’s notion of satisfaction. In this way I will counter (Prawitz 2012b)’s claim that a truth-conditional theory of meaning is not able to account the legitimacy of valid inferences, i.e., their epistemic significance. (shrink)

How can reasons explain actions? What is the force of "because" in "He did this because..." followed by a statement of the agent's intentions? The answer involves some concept of what can count as explanation, and the history of science indicates that the acceptability of explanations depends, in part, on a scientific community which has decided to pursue its inquiries in one direction rather than another. The first part of this paper examines this pragmatic aspect of explanations; the second part (...) draws on this examination in the hope of elucidating the way reasons explain actions. The possibility of eliminating our ordinary, "purposive," explanations of actions in favor of some "mechanistic," neuro-physiological, account is then considered. (shrink)

in this paper we return to Marshall Clagett’s view about the existence of an ancient Greek geometry of motion. It can be read in two ways. As a basic presentation of ancient Greek geometry of motion, followed by some aspects of its further development in landmark works by Galileo and Newton. Conversely, it can be read as a basic presentation of aspects of Galileo’s and Newton’s mathematics that can be considered as developments of a geometry of motion that was first (...) conceived by ancient Greek mathematicians. (shrink)

O propósito deste artigo é analisar a expressão que assegura a presença de partes da cosmologia de Empédocles no Ocidente latino nos séculos XII-XIII, qual seja, creatio mundi, esta que é a tradução do termo κοσμοποιία. A análise centra-se, por um lado, em três traduções latinas da Física II, 4, 196a 20-24, de Aristóteles, texto no qual aparece o termo κοσμοποιία e, por outro lado, em partes da obra de Tomás de Aquino na qual o autor discute a cosmologia de (...) Empédocles. Para tanto, o texto é composto de três partes. Na primeira apresento o problema suscitado pela tradução de κοσμοποιία como creatio mundi e como factura mundi respectivamente. Na segunda, por seu turno, exponho os termos que viabilizam uma certa visão de conjunto da cosmologia de Empédocles no século XIII. Enfim, na terceira parte, apresento brevemente o sentido da noção de mundo e sua possível configuração para Empédocles. (shrink)

: Following Aristotle, medieval natural philosophers believed that knowledge was ultimately based on perception and observation; and like Aristotle, they also believed that observation could not explain the "why" of any perception. To arrive at the "why," natural philosophers offered theoretical explanations that required the use of the imagination. This was, however, only the starting point. Not only did they apply their imaginations to real phenomena, but expended even more intellectual energy on counterfactual phenomena, both extracosmic and intracosmic, extensively discussing, (...) among other themes, the possible existence of other worlds and the possibility of an infinite extracosmic space. The application of the imagination to scientific problems during the Middle Ages was not an empty exercise, but, as I shall show, played a significant role in the development of early modern science. (shrink)

Through an analysis of conditions under which the question of spatial anisotropy can be raised, the present paper brings out intimate conceptual relationships between the scientific concept of space and the concepts of entities, behavior, and explanation specified by scientific theories. Thus scientific departures from ordinary usage (or from usage in other scientific theories) of the term "space" entail corresponding shifts in the use of other terms not generally seen to be connected. As a case study of the relations between (...) these terms, and of the refusal to allow the possibility of spatial anisotropy, Newtonian mechanics is examined. (shrink)

This paper aims at a partial rehabilitation of E. A. Moody''s characterization of the 14th century as an age of rising empiricism, specifically by contrasting the conception of the natural science of psychology found in the writings of a prominent 13th-century philosopher (Thomas Aquinas) with those of two 14th-century philosophers (John Buridan and Nicole Oresme). What emerges is that if the meaning of empiricism can be disengaged from modern and contemporary paradigms, and understood more broadly in terms of a cluster (...) of epistemic doctrines concerned with the methodology of knowing, it characterizes very appropriately some of the differences between the ways in which late-medieval thinkers both understood and practised the science of psychology. In particular, whereas Aquinas thinks psychology is about reasoning demonstratively to the real nature of the soul from its evident operations (thereby assimilating psychology to metaphysics), Buridan and Oresme, both of whom doubt whether real animate natures can be known empirically, focus on giving detailed accounts of those operations themselves (thereby assimilating psychology to physics). (shrink)

El tratado hidrostático fue uno de los primeros textos de Descartes, fruto de su decisivo encuentro con Isaac Beeckman. En este artículo, analizaremos cómo fue concebido y los motivos que llevaron a Descartes a cuestionar alguno de los aspectos fundamentales de la física matemática de Beeckman. Este episodio está íntimamente relacionado con la independencia de las disciplinas matemáticas y su aplicación a cuestiones propias de la filosofía natural.Descartes’ hydrostatic treatise was one of his first text, fruit of his crucial meeting (...) with Isaac Beeckman. In this article, we will analyse how it was conceived and the reasons which leaded Descartes to question some fundamental aspects of Beeckman’s Physico-mathematics. This subject is closely connected with theautonomy and implementation of mathematical sciences to typical matters of natural philosophy. (shrink)

The present PhD dissertation aims to examine the relation between modality and change in Aristotle’s metaphysics. -/- On the one hand, Aristotle supports his modal realism (i.e., worldly objects have modal properties - potentialities and essences - that ground the ascriptions of possibility and necessity) by arguing that the rejection of modal realism makes change inexplicable, or, worse, banishes it from the realm of reality. On the other hand, the Stagirite analyses processes by means of modal notions (‘change is the (...) actuality of what is virtual insofar as it is virtual’). In other words: to grasp what change is, one has to resort to the modal idiom of potentialities, while the fact that there is change is indicative of the fact that nature is full of modal properties. -/- Aristotle’s modal and kinetic realism finds a negative in the figure of the Megaric Diodorus Kronus. The polemical situation of Greek philosophy has indeed the dialectical advantage of not opposing the Aristotelian position to a sui generis straw man. Both in its reduction of modal judgements to temporal quantifications and in its dissolution of the reality of the state-of-being-in-motion in favour of a cinematographic view of processes, the philosophical figure of reductionist antirealism embodied by Diodorus constitutes an alternative that takes the opposite view of Aristotle’s realism. -/- The present study is structured as a discussion between these two positions. In the face of Diodorus’ antirealist challenges, Aristotle articulates modal and kinetic considerations: the answers he gives to Diodorus’ puzzles thus provide valuable insight into his metaphysics. Moreover, the examination of Aristotle’s and Diodorus’ metaphysics, because of their insight and originality, will not fail to interest the philosopher concerned with the metaphysical foundations of modern physics, insofar as the entanglement between modalities and processes is nowadays at the core of mechanics (phase spaces, path integrals, etc.). (shrink)

Quantum gravity is supposed to be the most fundamental theory, including a quantum theory of the metrical field (spacetime). However, it is not clear how a quantum theory of gravity could account for classical phenomena, including notably measurement outcomes. But all the evidence that we have for a physical theory is based on measurement outcomes. We consider this problem in the framework of canonical quantum gravity, pointing out a dilemma: all the available accounts that admit classical phenomena presuppose entities with (...) a well-defined spatio-temporal localization (“local beables” in John Bell's terms) as primitive. But there seems to be no possibility to include such primitives in canonical quantum gravity. However, if one does not do so, it is not clear how entities that are supposed to be ontologically prior to spacetime could give rise to entities that then are spatio-temporally localized. (shrink)

Making a history of the principle of inertia, as of any other principle or concept, is a complex but still possible operation. In this work it has been chosen to make a back story which seemed the most natural way for a reconstruction. On the way back, it has been decided to stop at the 6th century CE with the contribution of Ioannes Philoponus. The principle he stated, although very different from the modern one, is certainly associated with it. Going (...) back in time it is still possible and of course one could proceed to the origins of the homo sapiens who perhaps posed the problem of why a club thrown with his hand could go so far from him. But the similarities that one can find with the modern principle are very vague, too perhaps. Without going so far one could see an embryonic idea of the principle of inertia in the atomistic theory of Democritus in the 5th century BCE. The motion of atoms whirling with no apparent reason can suggest the idea that a body can also move with no reason. But the transition from the atom, a metaphysical being, to the body, an empirical being, is far from immediate. (shrink)

RESUMO Este artigo apresenta a noção de valor aplicado à análise da moeda, elaborada por Nicole Oresme, em 1355, e Nicolau Copérnico, em 1526. Mostramos que, para os autores, o valor da moeda deve ser estável e determinado pela comunidade em atividades de compra e venda. Também mostramos como esses autores opõem-se à instabilidade do valor, especialmente a desvalorização promovida pelo governante. Argumentamos que ambos os autores criam sistemas de medição e controle do valor da moeda em tempos de turbulência (...) monetária. De acordo com Oresme e Copérnico, a instabilidade no valor da moeda não só mantém o comércio distante, em outros reinos ou repúblicas, mas também revela a má conduta do príncipe, aquele que é investido de autoridade política e monetária nas sociedades europeias dos séculos XIV e XVI. ABSTRACT This paper presents the notion of value applied to the analysis of currency, elaborated by Nicole Oresme, in 1355, and Nicolas Copernicus, in 1526. It shows that, to these authors, currency value must be stable and determined by the community engaged in activites of buying and selling. It also shows how they are opposed to instability of value, especially to its devaluation promoted by the government. It argues that both authors create systems for measuring and controlling of currency value in times of monetary turmoil. According to Oresme and Copernicus, instability of currency value not only keeps commerce faraway, in other kingdoms or republics, but also reveals the misconduct of the prince, the one who is invested with political and monetary authority in European societies of the fourteenth and sixteenth centuries. (shrink)

ArgumentThis paper discusses the theory of motion of the philosopher Honoré Fabri (1608–1688), a senior representative of early modern Jesuit scientists. It argues that the consensus prevailing among historians – according to which Fabri's theory of impetus is diametrically opposed to Galileo's or Descartes' concept of inertia – is false. It shows: that Fabri carefully constructed his concept of impetus in order to easily incorporate the principle of linear conservation of motion (designated here as “limited inertia”), by adopting formal (rather (...) than efficient) causality between impetus and motion and by allowing impetus to act only along straight lines; that he explicitly deemed Aristotle's famous “inertial paradox” not as a paradox at all; and that linear conservation of motion was not limited to “counterfactual” circumstances but played a significant part in his discrete theory of free fall and constituted an integral component of his general physical (and even mathematical) philosophy. However, the paper also shows that Fabri's notion of inertia was restricted to one dimension only, and therefore should indeed be considered “limited.” In his analysis of horizontal projectiles, Fabri explicitly rejected Galileo's important principle of superposition, and thus revealed significant constraints to his “inertial” thinking. (shrink)

Abstract The grammar of spatial and temporal concepts cannot, it is argued, be the same in their application to the (manifest) world as perceived and to the (nether) world of unobservable causes as modelled in physics. A parallel case is the dual meaning of colour words, for hues and for material dispositions. The keys to differentiating the two main ranges of uses of ?s? and ?t? are: differences in criteria of numerical and qualitative identity in the two ?worlds'; differences in (...) the logic of indexicals in each context; the explanatory role of powers. The differences can be illustrated in a close analysis of the concept of velocity. (shrink)

Albert of Saxony, master of Arts at Paris from 1351 until 1361/62, has left two commentaries on the Physics of Aristotle. Since he was well aware of the tradition, his writings may serve for an analysis of the transmision of ideas from the ancient and Arabic philosophers into the fourteenth century. In this paper, this is exemplified by the problems of place and space, especially by those of the definition of place and of the immobility of place, of natural place (...) and of the location of the last and outermost sphere. As a result, four modes emerge how an author of the fourteenth century may have been influenced by tradition. Ancient Greek or Pre-Socratic philosophers were mainly known through Aristotle, and thus their opinions were mostly refuted; the same holds true for later ancient or Arabic authors known through the commentaries of Averroes; the influence of the authors of the thirteenth century was present though their texts may not have been directly consulted; and, finally, the contemporary authors were known, but nearly never quoted. Thus, though there was a line of tradition from Aristotle into the fourteenth century, there was also room for proper solutions. (shrink)

This paper deals with Ágnes Heller’s suggestion, in A Theory of Modernity (1999), to ascribe to science a central role in the ongoing development of modernity. As we shall argue, this is not merely a historical issue but, rather, a historical-philosophical one that entails the problem of defining modernity, science and technology and their mutual interconnections. As for modernity, according to Heller, it is a free developmental project without any foundations other than freedom itself. In particular, the evolution of science (...) and technology is one of its main developmental tendencies. Science, she argues, has become the dominant world explanation while technological thought is the corresponding dominant (but not unique) imaginary institution. Her attempt to isolate the essential cultural features of science-technology owes much to Habermas’s analyses of the 1960s on the technocratic developments of contemporary societies legitimized through an ideological employment of science. Like Habermas, Heller embraces an instrumental and problem-solving conception of technology and ‘normal’ science which appears questionable, however, in the light of conclusions on the intrinsic creativity of the science-technology interface deriving from historical epistemology and an externalist history of science. Considerations and examples derived from the recent agenda of historical epistemology could integrate Heller’s philosophical and cultural analysis of the role of science in modernity while challenging some of her assumptions. (shrink)

The history of mechanics has been extensively investigated in a number of historical works. The full story from the Greeks and medievals through the Scientific Revolution to the modern era is long and complex. But it is also incomplete. Studies to date have been admirably thorough in putting empirical discoveries into proper perspective and in making clear the great importance of mathematical innovations. But there has been surprisingly little regard for the role of thought experiments in the development of mechanics. (...) We attempt to rectify this, at least in part. After a brief account of Greek ideas of space and motion, we focus on late medieval and early modern physics, especially the development of inertial motion. In particular, we examine the thought experiments of Buridan, Oresme, and Galileo, which did so much to undermine Aristotle’s account of motion and lead the way to the modern concept of inertia. (shrink)