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)

The ArgumentOne of the earliest arguments for Copernicanism was a widely accepted fact: that on a horizontal plane a body subject to no external resistance can be set in motion by the smallest of all possible forces. This fact was contrary to Aristotelian physics; but it was a physical argument (by abduction) for the possibility of the Copernican world system. For it would be explained if that system was true or at least possible.Galileo argued: only nonviolent motions can be caused (...) by the smallest of all possible forces; hence resistance-free horizontal motions are nonviolent; this confirms Copernicanism insofar as it designates the rotations of celestial spheres (being resistance-free horizontal motions) as nonviolent.Galileo's argument was compatible with (and supportive of) the specific Copernican version of impetus mechanics; but it was also compatible with a (somewhat qualified) principle of inertia. Thus it promoted decisively the transition from impetus mechanics to classical inertial mechanics. (shrink)

The ArgumentOur understanding of the predisposing factors, the nature, and the fate of the Oxford Calculatory tradition can be significantly increased by seeing it in its social and institutional context. For instance, the use of intricate imaginary cases in Calculatory works becomes more understandable if we see the connection of these works to undergraduate logical disputations. Likewise, the demise of the Calculatory tradition is better understood in the light of subsequent efforts at educational reform.Unfortunately, too little evidence remains about the (...) Calculators and their context to enable anything like a full reconstruction of the relation of the Oxford Calculators' work to its context. Nevertheless, seeking out and fitting together the bits of information that do remain can add to our insight. Among the topics worth further research are the relation of training incalculationesto later careers in church or government, and the special features of the Calculatory tradition as a tradition consisting of multiple parallel manifestations closely interconnected with other disciplines, ranging from logic and natural philosophy to theology and medicine. (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 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)

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)

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)

Generally speaking, virtual displacement or work concerns to a timely idea according to which a motion of a certain body is not the unique possible motion. The process of reducing this motion to a particular magnitude and concept, eventually minimizing as a hypothesis, can be traced back to the Aristotelian school. In the history and philosophy of science one finds various enunciations of the Principle of Virtual Laws and its virtual displacement or work applications, i.e., from Aristotle to Leibniz’s vis (...) viva, from Maupertuis’ least action to Euler and Lagrange with calculus of variations to Lazare Carnot’s mechanics. In this case study, I will demonstrate that a particular approach used by Lazare Carnot is original by explaining within the historical context of rival approaches such as the development of the Principle of virtual Laws. I will also discuss Carnot’s geometric motion as one of the possible but invertible movements applied to virtual displacement as employed in his theories of machines and collisions. I will then go on to explore how the originality of an invertible motion within his mechanical and, in general, mathematical research program permitted Carnot to introduce a new way of structuring a scientific theory and making mechanics, with respect to the Newtonian paradigm, to scholars and his students of the École polytechnique de Paris. (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)

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 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).

There is a widely acknowledged, albeit still imprecisely defined, connection between the ‘calculatory’ analyses of local motion developed within the fourteenth century ‘Merton School’ and Galileo Galilei's later treatment of natural motion. The present essay is intended to cast some light on the possible sources and significance of Galileo's putative familiarity with the medieval discussions through a study of the fortunes of the most typical representative of the School, Richard Swineshead. Particular attention is paid to the writings of such scholastic (...) philosophers of Galileo's day as Francisco Toledo, Francesco Piccolomini, Iacopo Zabarella, Francesco Buonamico and Scipione Chiaramonte. Somewhat unexpectedly, it emerges that such authors possessed only the most fragmentary and attenuated knowledge of Swineshead's ideas. The implications of this circumstance, especially insofar as it renders Galileo's familiarity with the Merton tradition even more problematical, are discussed briefly. (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)

: 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)

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 study deals with the school instruction of the concept of weight. The historical review reveals the major steps in changing weight definition reflecting the epistemological changes in physics. The latest change drawing on the operation of weighing has been not widely copied into physics education. We compared the older instruction based on the gravitational definition of weight with the newer one based on the operational definition. The experimental teaching was applied in two versions, simpler and extended. The study examined (...) the impact of this instruction on the middle school students in regular teaching environment. The experiment involved three groups of 14-year-old students. The assessment drew on a written questionnaire and personal interviews. The elicited schemes of conceptual knowledge allowed to evaluate the impact on students’ pertinent knowledge. The advantage of the new teaching manifested itself in the significant decrease of the well-known misconceptions such as “space causes weightlessness,” “weight is an unchanged property of the body considered,” and “heavier objects fall faster”. The twofold advantage—epistemological and conceptual—of the operational definition of weight supports the correspondent curricular changes of its adoption. (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)