Descartes on Corporeal Substances

Descartes' carton--On plausibility.

n t odern healthcare operates under the banner of “evidencebased” medicine. The pursuit of such evidence, however, is ot exclusively driven by need, but by the vailability of funds, which in turn deends partly on the likelihood of profit. ore portentously, the pursuit of data is ounded by the prevailing conceptions of iological plausibility. This essay makes he case that such borders are not re...

Descartes on the Logical Properties of Ideas

There is a problem in Descartes’s writings about the logical nature of the contents of his understanding, his ideas. On the one hand it seems that such things can be true, for as is well known, Descartes argues in Meditation III that any idea he very clearly and distinctly perceives is bound to be true. However, in the same Meditation, he seems to say something incompatible with this: he says t...

The Descartes Rule of Sweeps and the Descartes Signature

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 ...

Arithmetic Multivariate Descartes' Rule Arithmetic Multivariate Descartes' Rule

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...

Descartes on love and/as error.