Cartesisch

Cartesisch, or Cartesian, is an adjective used to denote ideas associated with the 17th-century French philosopher René Descartes or systems named after him. The term appears in mathematics, geometry, logic, and philosophy.

In mathematics, Cartesian coordinates allow a correspondence between algebraic equations and geometric shapes. The two-dimensional Cartesian plane uses perpendicular axes, labeled x and y, with points given by ordered pairs (x, y). Three dimensions add z. The Cartesian coordinate system underpins analytic geometry, graphical representations of equations, and many numerical methods.

The Cartesian product of two sets A and B is the set of all ordered pairs (a, b) with a in A and b in B, denoted A × B. It forms the basis of relations and functions in set theory and computer science.

In philosophy, the Cartesian method of doubt is associated with Descartes’ search for certainty. He proposed dualism, distinguishing mind (res cogitans) from body (res extensa), and famously argued “I think, therefore I am” (cogito). His philosophy influenced epistemology, metaphysics, and science.

The term Cartesian is widely used to describe Descartes’ influence on mathematics and philosophy, and to label coordinate systems, products, and methods that reflect his analytic approach.