Suchergebnisse

19 The dynamical theory of matter and mathematical construction20 The dynamical theory of matter, the mechanical philosophy, and chemistry; 21 The dynamical theory of matter and the categories of quality; Chapter Three Mechanics; 22 Moving force and the communication of motion; 23 Quantity of matter and quantity of motion; 24 Estimating quantity of matter; 25 Material substance and the conservation of matter; 26 Inertia; 27 Action and reaction; 28 Moving force, quantity of matter, and the laws of mechanics; 29 Continuity, time determination, and the categories of relation.

Since the 1930s, philosophy has been divided into two camps: the analytic tradition which prevails in the Anglophone world and the continental tradition which holds sway over the European continent. A Parting of the Ways looks at the origins of this split through the lens of one defining episode: the disputation in Davos, Switzerland, in 1929, between the two most eminent German philosophers, Ernst Cassirer and Martin Heidegger. This watershed debate was attended by Rudlf Carnap, a representative of the Vienna Circle of logical positivists. Michael Friedman shows how philosophical differences interacted with political events. Both Carnap and Heidegger viewd their philosophical efforts as tied to their radical social outlooks, with Carnap on the left and Heidegger on the right, while Cassirer was in the conciliatory classical tradition of liveral republicanism. The rise of Hitler led to the emigration from Europe of most leading philosophers, including Carnap and Cassirer, leaving Heidegger alone on the continent

AbstractHow can metaphors account for the formation of mathematical concepts, for changes in mathematical practices, or for the handling of mathematical problems? Following Hans Blumenberg's thought, this paper aims to unfold a possible answer to these questions by viewing the metaphorical frameworks accompanying these changes as essential for an understanding of how changes in mathematical practices have been accounted for. I will focus especially on cases in which these changes were caused by encounters with a mathematical object which did not yet have a well-defined concept, but also show that such indeterminacy remains with the mathematical concept even after it is considered 'well-defined'. As the paper will show, this 'forefield' [Vorfeld] of the concept is addressed by Blumenberg's account of metaphorology on the one hand, and accompanied by his later account of nonconceptuality [Unbegrifflichkeit] on the other hand. While Blumenberg himself did not develop a full-fledged philosophy of mathematics or of mathematical practices, I aim to show that one can nevertheless extract from his writings a unique position concerning the role metaphors play in mathematics. To this end, Blumenberg's account of nautical and oceanic metaphors and Alexandre Grothendieck's philosophy of mathematical practice provide fruitful starting points.

Three-dimensional material models of molecules were used throughout the 19th century, either functioning as a mere representation or opening new epistemic horizons. In this paper, two case studies are examined: the 1875 models of van 't Hoff and the 1890 models of Sachse. What is unique in these two case studies is that both models were not only folded, but were also conceptualized mathematically. When viewed in light of the chemical research of that period not only were both of these aspects, considered in their singularity, exceptional, but also taken together may be thought of as a subversion of the way molecules were chemically investigated in the 19th century. Concentrating on this unique shared characteristic in the models of van 't Hoff and the models of Sachse, this paper deals with the shifts and displacements between their operational methods and existence: between their technical and epistemological aspects and the fact that they were folded, which was forgotten or simply ignored in the subsequent development of chemistry.

Initially trained as a physicist, Kuhn became a leading and extraordinarily influential figure in the history of science. He saw his work in the history of science as contributing to a novel philosophical conception of the nature of science. At the outset of Structure, for example, Kuhn announces his intention to replace the "development-by-accumulation" model he associates with the philosophical tradition before him—including, in particular, what he calls "early logical positivism"—with a new model of radical conceptual discontinuity or incommensurability. Structure was written during Kuhn's tenure teaching philosophy and history of science at Berkeley, and, shortly after its publication, he took up a new post as professor of philosophy and history of science at Princeton. From 1983 until his death in 1996 Kuhn was professor of philosophy at MIT, where he attempted further to articulate his conception of incommensurability, taking account of developments in linguistics and philosophy of language.