S. Gaukroger (Ed.) (1980): Descartes: Philosophy, Mathematics and Physics. Harvester Readings in the History of Science and Philosophy, No. 1. Brighton and New Jersey: The Harvester Press and Barnes & Noble Books. $28. Pp. xi + 329.

In the history of science there have been many cases where former students have broken with their mentor, often in the process of establishing their own ideas and pursuits. The resulting ambivalence and conflict can be likened to that which occurs in a family when offspring separate from parents and establish their own identities. However, there are relatively few instances in the history of science when this process has taken place in a context in which both mentor and students were women. Such was the case with Florence Bascom and her protégées at Bryn Mawr College, Anna Jonas (Stose) and Eleanora Bliss (Knopf). The controversy began over the relative age of the Wissahickon schist/gneiss, which was referred to the Ordovician in a paper on the Piedmont district of Pennsylvania published by Bascom in 1905. Jonas and Bliss became involved following the publication in 1916 of their joint doctoral dissertation on the relation of the Wissahickon to other formations in the Doe Run-Avondale region of Pennsylvania. In subsequent papers that came out in the 1920s, they sought to establish the existence of a pre-Cambrian "Glenarm series," including the Wissahickon, and introduced the concept of the Martic overthrust. This hypothesized fault was eventually extended by them and George Stose northward to New Jersey and southward to Alabama; the argument, which peaked in the 1930s, eventually extended to everyone concerned with Appalachian geology.

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Force, Mathematics, and Physics in Newton's Principia: A New Approach to Enduring Issues

Science in Context ◽

10.1017/s0269889707001457 ◽

2007 ◽

Vol 20 (4) ◽

pp. 571-600 ◽

Cited By ~ 4

Author(s):

Koffi Maglo

Keyword(s):

Mathematical Modeling ◽

History Of Science ◽

Philosophy Of Mathematics ◽

Epistemic Status ◽

New Approach ◽

Philosophical Standpoint ◽

History Of ◽

Axiomatic Systems ◽

Mathematical Construct ◽

Mathematics And Physics

ArgumentThis paper investigates the conceptual treatment and mathematical modeling of force in Newton's Principia. It argues that, contrary to currently dominant views, Newton's concept of force is best understood as a physico-mathematical construct with theoretical underpinnings rather than a “mathematical construct” or an ontologically “neutral” concept. It uses various philosophical and historical frameworks to clarify interdisciplinary issues in the history of science and draws upon the distinction between axiomatic systems in mathematics and physics, as well as discovery patterns in science. It also dwells on Newton's “philosophy” of mathematics, described here in terms of mathematical naturalism. This philosophy considers mathematical quantities to be physically significant quantities whose motions are best mapped by geometry. It then shows that to understand the epistemic status of force in the Principia, it is important to scrutinize both Newton's mathematical justificatory strategies and his background assumptions about force – without constructing, however, an overarching metaphysical framework for his science. Finally, the paper studies scientific attempts to redefine or eliminate force from science during the period between Newton and Laplace. From a philosophical standpoint, the paper implicitly suggests that questions about the reality of force be distinguished from questions about the validity of force, and that both sets of questions be distinguished from questions about the utility of the concept of force in science.

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Notes on the historical conceptual streams for mathematics and physics teaching

Lietuvos matematikos rinkinys ◽

10.15388/lmr.a.2013.02 ◽

2013 ◽

Vol 54 ◽

Cited By ~ 3

Author(s):

Raffaele Pisano

Keyword(s):

History Of Science ◽

Mathematics Teaching ◽

Physics Teaching ◽

Teaching Process ◽

History Of ◽

And Mathematics ◽

The Relationship ◽

Mathematics And Physics

Based on recent researches of mine concerning history and epistemology of sciences (physics and mathematics) one side and foundations of sciences within my physics and mathematics teaching other side, in this paper I briefly discuss and report the role played by history of science within physics and mathematics teaching. Some case-study on the relationship between mathematics, physics and logics in the history and teaching process are presented, as well.

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REFLECTIONS ON LEARNING MATHEMATICS IN PHYSICS PHENOMENOLOGY AND HISTORICAL CONCEPTUAL STREAMS

Problems of Education in the 21st Century ◽

10.33225/pec/12.46.93 ◽

2012 ◽

Vol 46 (1) ◽

pp. 93-100

Author(s):

Maria Mellone ◽

Raffaele Pisano

Keyword(s):

Science Education ◽

History Of Science ◽

Euclidean Geometry ◽

History Of Mathematics ◽

Point Of View ◽

Mathematical Education ◽

Epistemology Of Science ◽

History Of ◽

Mathematical Sciences ◽

Mathematics And Physics

Although several efforts produced by new mathematical education approaches for improving education systems and teaching, yet the results are not sufficient to adsorb the totality of innovations proposed, both in the contents and management. In this sense constructive debates and new ideas were welcomed and appreciated upon new aspects of science education, side new learning and Cognitive Modelling, for our interests. A parallel effort was produced by scientist-epistemologist-historians concerning the history of science and its foundations in science education. Historical foundations represent the most important intellectual part of the science, even if sometimes they were avoided or limited to specialist disciplines such as history of mathematics, history of physics, only. Nevertheless some results, such as the operative concept of mass by Mach, rather the coherence and validity of an algebraic–geometric group in a Euclidean geometry and in non-Euclidean geometry was firstly appointed by epistemological point of view by (e.g.,) Poincaré, etc... Thus, what kind of concrete relationship between science education (mathematics and physics) and history of science (idem) one can discuss correlated with foundations of science? and above all, how this relationship can be appointed? The history and epistemology of science help to understand evolution/involution of mathematical and physical sciences in the interpretation-modelling of a phenomenon and its interpretation-didactic-modelling, and how the interpretation can change for a different use of mathematical: e.g., mathematics à la Cauchy, non-standard analysis, constructive mathematics in physics. Based on previous studies, a discussion concerning mathematics education and history of science is presented. In our paper we will focus on learning modelling to discuss its efficacy and power both from educational point of view and the need of mathematics and physics teachers education. Some case–studies on the relationship between physics and mathematics in the history are presented, as well. Particularly we focus on a possible learning modelling activity within physics phenomenology to create a resonance among the above poles and mathematical modelling cycle to argue its efficacy, power and related with historical foundations of physical, mathematical sciences. Key words: modelling, mathematics, physics, history of foundations, epistemology of science.

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