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Abstract
From the time of Aristotle until the time of the Enlightenment, intension and remission of forms was mostly considered as a problem of change of a specific type of accidental forms (qualities). The problem appeared in various disciplines such as theology (the infusion of charity), philosophy of nature (changes in qualities), medicine (the problem of proportion of elements in the body and the compounding of drug effects), optics (the intensification of light), and methodology and mathematics (the representation of change). During the fourteenth century, the intension and remission of forms became one of the central issues of philosophical debate. Various theories offered by a group of Oxonian thinkers, the so-called Oxford Calculators, contributed to the development of mathematical physics. The most elaborate and influential theory of geometrical representation of the configurations of qualities and motion, however, was presented, by the French natural philosopher – Nicholas Oresme.
Starting from the fourteenth century, “intension” (intensio) and “remission” (remissio) became terms linked to the philosophical attempt at quantifying qualitative changes. Although this attempt proved to some extent useful for the seventeenth-century emergence of a mathematized study of motion, its scope can only be understood within a frame of reference where “motion” has a broad, Aristotelian, sense. Also, intension and remission did not pertain to natural philosophy only – in fact, their meaning grew in philosophical importance within the purview of theology, metaphysics, and medicine. The doctrine of intension and remission has been hitherto studied especially with relation to late middle ages. Some studies have shed light on single instances of Renaissance developments, but a comprehensive study in this regard is yet to be done. A possibly deeper lacuna affects the study of its eighteenth-century legacy. This being the case, the entry is meant to provide the essential coordinates to contextualize Renaissance contributions to intension and remission. The latter are considered in three aspects: university teaching; Aristotelian and non-Aristotelian criticisms; natural philosophy and medicine.
By way of introduction, the chapter considers aspects of Galileo’s considerations regarding motion and mechanics prior to his conceptual shift toward the assumption that motion of fall is naturally accelerated. The aspects discussed have been selected for the relevance they assumed when, from 1602 onward, Galileo started to engage in the investigations which eventually led to the establishment of his new science of motion. In particular, his understanding of the free fall of heavy bodies and of acceleration is being presented as it is reflected in a compilation of early manuscripts, which have come to be referred to as De Motu Antiquiora. One of these manuscripts, commonly designated as On Motion, contains a chapter in which Galileo investigated the dynamics of motion along inclined planes and, in particular, provided a proof for the law of the inclined plane relating the inclination of the plane to the force along this plane experienced by a body placed upon it. Galileo’s arguments in this chapter are discussed in some detail.
This chapter consists of a systematic introduction to the nature and function of habitus in Latin medieval philosophy. Over the course of this introduction, several topics are treated: the theoretical necessity to posit habitus; their nature; their causal contribution to the production of internal and external acts; how and why habitus can grow and decay; what makes their unity when they can have multiple objects and work in clusters. Finally, we examine two specific questions: why intellectual habitus represent a special case that triggered considerable debate; how human beings can be said to be free if their actions are determined by moral habitus.
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 (e.g. variables, parameters, functions), as well as the complexities added by physics itself (e.g. that equations’ symbols represent magnitudes with empirical meaning and units instead of pure numbers). 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.
Etude de la question de l'intension et de la remission des qualites dans le commentaire de la «Physique» d'Aristote par Oresme. Examinant les theories scolastiques de l'addition et de la succession des formes, l'A. montre que Oresme defend une position originale concernant le statut ontologique des accidents.
Godefroid de Fontaines et la theorie de la succession dans l’intensification des formes. Chemis de la pensée médiévale
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