One of the chief concerns of the young Descartes was with what he, and others, termed “physico-mathematics”. This signalled a questioning of the Scholastic Aristotelian view of the mixed mathematical sciences as subordinate to natural philosophy, non explanatory, and merely instrumental. Somehow, the mixed mathematical disciplines were now to become intimately related to natural philosophical issues of matter and cause. That is, they were to become more ’physicalised’, more closely intertwined with natural philosophising, regardless of which species of natural philosophy (...) one advocated. A curious, short-lived yet portentous epistemological conceit lay at the core of Descartes’ physico-mathematics—the belief that solid geometrical results in the mixed mathematical sciences literally offered windows into the realm of natural philosophical causation—that in such cases one could literally “see the causes”. Optics took pride of place within Descartes’ physico-mathematics project, because he believed it offered unique possibilities for the successful vision of causes. This paper traces Descartes’ early physico-mathematical program in optics, its origins, pitfalls and its successes, which were crucial in providing Descartes resources for his later work in systematic natural philosophy. It explores how Descartes exploited his discovery of the law of refraction of light—an achievement well within the bounds of traditional mixed mathematical optics—in order to derive—in the manner of physico-mathematics—causal knowledge about light, and indeed insight about the principles of a “dynamics” that would provide the laws of corpuscular motion and tendency to motion in his natural philosophical system. (shrink)

ABSTRACT Francis Bacon and René Descartes have traditionally been presented as leaders of opposed philosophical currents. However, more and more studies show important continuities between their philosophies. This article explores one of them: their perspectives on medicine. The dominion over nature and the instinct for self-preservation are the central elements of the theoretical framework within which they inserted their assessments of medicine. Medicine is valued as the most outstanding discipline for its benefits for the care of the human being. Departing (...) from this start-point, one finds further coincidences about the status, practice, and reform of medicine. (shrink)

In 1626, René Descartes and Claude Mydorge worked closely together on the problem of refraction, apparently discovering what is now known as the sine law of refraction. They constructed a plano-hyperbolic lens in order to test out the truth of this mathematical relationship. In 1637, Descartes finally published the sine method of determining refractions in his Dioptrique, which also demonstrated, on the basis of this relationship, that the hyperbola and ellipse were anaclastic lines (that is, that a lens with their (...) profile would refract rays perfectly to a single point) without mentioning Mydorge. Mydorge himself wrote a short manuscript on the subject of refraction and lenses, which is found in a copy among Mersenne’s papers. Scholars have usually assumed that this treatise was written as Mydorge and Descartes worked together in 1626. However, other evidence shows that only the first part of the treatise records the two men’s early collaboration. Subsequently, Mydorge and Descartes completed their arguments separately, Descartes with the help of Isaac Beeckman. (shrink)

Descartes’s most extensive discussion of the law of refraction and the shape of the anaclastic lens is contained in Rule 8 of "Rules for the Direction of the Mind". Few reconstructions of Descartes’s discovery of the law of refraction take Rule 8 as their basis. In Rule 8, Descartes denies that the law of refraction can be discovered by purely mathematical means, and he requires that the law of refraction be deduced from physical principles about natural power or force, the (...) nature of the action of light, and the behavior of light rays in a variety of transparent media. For over a century, however, there has been broad agreement that Descartes discovered the law of refraction by purely mathematical means, and that he only later provided the relevant physical rationale (via comparisons or analogies) in Dioptrics II. I execute each step in Descartes’s proposed deduction of the law of refraction and the shape of the anaclastic lens in Rule 8 and concretely show how Descartes could have discovered the law of refraction and the shape of the anaclastic by its means. Rule 8, I argue, reflects Descartes’s actual path to the discovery of the law of refraction and the shape of the anaclastic lens. (shrink)

Es muy habitual que se presenten los grandes lineamientos de la filosofía moderna en el marco del paradigma epistemológico y apelando a la distinción de dos corrientes filosóficas fundamentales, el empirismo y el racionalismo. Se trata de categorías analíticas construidas para interpretar y caracterizar retrospectivamente a ciertos filósofos de la modernidad. Pero no fueron términos ni conceptos utilizados por los actores mismos6. John Locke, George Berkeley y David Hume no se llamaban a sí mismos empiristas, ni René Descartes, Baruch Spinoza (...) y Gottfried W. Leibniz se autodenominaban racionalistas. En este capítulo, profundizaremos algunos puntos esbozados en el capítulo anterior. En primer lugar, expondremos las definiciones que han recibido el empirismo y el racionalismo dentro del paradigma epistemológico, que si bien ha sido criticado y redefinido en las últimas décadas, sigue siendo sostenido en la actualidad. En esa misma sección, analizaremos en qué medida las figuras del canon moderno establecido por el paradigma sostienen o no las tesis racionalistas y empiristas que les atribuyen esas definiciones tradicionales. Finalmente, resumiremos algunas críticas que ha recibido la narrativa tradicional y presentaremos una propuesta de resignificación de ambas categorías que nos parece más atinada. (shrink)