While the majority of Descartes’ medical writings detail the machinery and mechanics of the human body – its material parts, their organization, and their lawful operations – Descartes’ correspondence with Princess Elisabeth highlights what is ultimately at stake in his medicine, namely, the health of the human being. Medicine is a significant theme in their correspondence, and their discussion...

The Descartes Rule of Signs, which establishes a bound on the number of positive roots of a polynomial with real coefficients, is extended to polynomials with complex coefficients. The extension is modified to bound the number of complex roots in a given direction on the complex plane, giving rise to the Descartes Signature of a polynomial. The search for the roots of a polynomial is sometimes ...

Université Paris Descartes, Service de Maladies Infectieuses et Tropicales, Centre d’Infectiologie Necker-Pasteur, IHU Imagine, Hôpital Necker-Enfants Malades, Assistance Publique-Hôpitaux de Paris, Paris, France; Université Paris Descartes, Service d’Hématologie, IHU Imagine, Hôpital Necker-Enfants Malades, Assistance Publique-Hôpitaux de Paris, Paris, France; Université Paris Descartes, Servi...

modern age due to its epistemological virtue has a special important, since it defined a new relation between human and truth, in which some modern philosophers, like descartes, kant and nietzsche have more roles. in this thought, human could take place as the center and criterion of understanding and interpretation of truth. in fact, human’s subjectivism has been of more important role in unde...

We summarize the results of the cross-benchmarks for two univariate algebraic kernels (AK) developed in ACS. The kernels, developed at INRIA and MPI, were tested on 6 types of univariate polynomials of various degrees and bitsizes. The methods included were: Sturm, Sleeve, CF, NCF, NCF2 for the INRIA kernel, and Descartes and Bitstream-Descartes for the MPI kernel. NCF, NCF2, Descartes and Bits...

Let L be any number field or p-adic field and consider F := (f1, . . . , fk) where fi∈L[x ±1 1 , . . . , x ±1 n ]\{0} for all i and there are exactlym distinct exponent vectors appearing in f1, . . . , fk. We prove that F has no more than 1+ ( σm(m− 1)2n2 logm )n geometrically isolated roots in Ln, where σ is an explicit and effectively computable constant depending only on L. This gives a sign...

C. Rodriguez-Régent, S. Mouchet-Mages, S. Rodrigo, M-O. Krebs, C. Oppenheim, and J-F. Meder Department of Morphologic and Functional Imaging, University Paris Descartes, Sainte Anne Hospital, PARIS, France, Pathophysiology of Psychiatric Diseases, University Paris Descartes, Sainte Anne Hospital, PARIS, France, Department of Morphologic and Functional Imaging, University Paris Descartes, Sainte...

Phenomenology questions the basic foundations of Modernity. In particular, it challenges Descartes‘ attempt to found the scientific method with absolute certainty. Phenomenology is defined by the work of Husserl, Heidegger, and Merleau-Ponty. Even though each of them developed their own way within Phenomenology, their theories are determined by a critique of the Cartesian method. For them, Desc...

Cathay Ming Lih Liu: Descartes' Philosophical Grounds for Algebra and Geometry (Under the direction of Alan Nelson) Though neither Descartes nor Fermat developed analytic geometry as we understand the mathematical discipline today, they each developed a different central feature of it. But history of mathematics has not explained their differences in mathematical aims and practice in terms of p...

In an influential article, Anthony Kenny charged that (a) the view of freedom in Descartes’ “1645 letter to Mesland” is incoherent, and (b) that this incoherence was present in Descartes’ thought from the beginning. Against (b), I argue that such incoherence would rather support Gilson’s suspicions that the 1645 letter is dishonest. Against (a), I offer a close reading of the letter, showing th...