The first part of this paper consists of an exposition of the views expressed by Pierre Duhem in his Aim and Structure of Physical Theory concerning the philosophy and historiography of mathematics. The second part provides a critique of these views, pointing to the conclusion that they are in need of reformulation. In the concluding third part, it is suggested that a number of the most important claims made by Duhem concerning physical theory, e.g., those relating to the Newtonian method, (...) the limited falsifiability of theories, and the restricted role of logic, can be meaningfully applied to mathematics. (shrink)

Although Hegel is generally not known as a philosopher of mathematics, he maintained a deep interest in the history of mathematics, especially in its transformations between antiquity and the modern age. Charles S. Peirce, who was the son of a distinguished mathematician and was involved in developments in mathematics in the second half of the nineteenth century, was critical of what he perceived as Hegel’s lack of mathematical acumen. Nevertheless, he recognized in Hegel’s Science of Logic structural features of his (...) own mathematically informed philosophy. In this article, I look to Hegel’s discussion of magnitude in The Science of Logic, and especially to his conception of the relation between continuous and discrete magnitudes, in order to articulate a solution he might have offered to difficulties encountered by Peirce in his opposition to Cantor’s set-theoretical analysis of the continuum. It is argued that Hegel’s interest in the ancient Platonic/Pythagorean tradition in mathematics provided him with crucial resources in this regard. (shrink)

Com este trabalho pretende dar-se um panorama do que foi a actividade científica, no domínio da Matemática e das ciências que lhe andavam ligadas (Geografia, Astronomia, Mecânica), no grande centro cultural que foi o Museu e a Biblioteca de Alexandria, nos tempos áureos e até ao declínio definitivo da ciência nesse espaço. Pretende-se igualmente sublinhar as descobertas e progressos que abriram caminho para posteriores estádios de desenvolvimento da Matemática, assim como dar conta do cruzamento de saberes e da grande mobilidade (...) de cientistas matemáticos e relações entre si, alguns provenientes de muitos espaços e sediados em Alexandria, outros formados em Alexandria e regressados ao seu espaço de origem. (shrink)