Cartesianos

Cartesianos, or Cartesians, is a term used in Spanish and Portuguese to refer to followers of René Descartes or to concepts derived from his work. The label can indicate philosophical commitments associated with Cartesianism as well as mathematical ideas that carry Descartes’s name.

In philosophy, Cartesianism denotes a program of rationalist inquiry initiated by Descartes (1596–1650). It emphasizes methodical doubt, the primacy of reason, and the provable nature of knowledge. Central themes include the existence of the thinking self (cogito), mind-body dualism (the distinction between res cogitans and res extensa), and a mechanical philosophy of nature. Cartesianism profoundly influenced later rationalist and realist traditions and interacted with empirical approaches during the Scientific Revolution.

In mathematics, Cartesian often refers to analytic geometry and the Cartesian coordinate system. Descartes’s invention linked algebra and geometry by describing geometric loci with algebraic equations expressed in a coordinate frame. The Cartesian plane uses perpendicular axes, conventionally labeled x and y, to locate points by ordered pairs; this method extends to three dimensions with a z-axis. Cartesian coordinates underpin much of modern geometry, physics, and computer science, and give rise to related concepts such as the Cartesian product in set theory.

The term also appears in broader scientific and educational contexts, sometimes describing grids, coordinate-based models, or algorithmic thinking that follows a systematic, rationalist approach associated with Cartesian methodology.