Infinities and natural philosophy in Leibniz (1672-1676)
Abstract
In this paper, we will consider the theoretical aspects of Leibniz’s thought on infinitely small and infinite quantities in the context of the natural philosophy developed by him in the Parisian period (1672-1676). We will hold that in the texts of this period an attempt of problematizing concepts of infinitary mathematics is found, which is not in the strictly mathematical texts. In this perspective, we also propose that there is in Leibniz a “double methodological record” concerning the question of the infinity and of the infinitesimal. As a mathematician, Leibniz is concerned about technical questions related to the construction of the infinitesimal calculus, in its different aspects, without be concerned about the philosophical challenges its adoption implies. However, as a philosopher and a metaphysician, Leibniz is obliged to deal with epistemological and ontological problems that emerge from the adoption of technical resources in matters of infinitesimal mathematics.
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