Specified complexity is a concept proposed by William Dembski and used by him and others to promote the pseudoscientific arguments of intelligent design. According to Dembski, the concept can formalize a property that singles out patterns that are both specified and complex, in specific senses defined by Dembski. Dembski states that specified complexity is a reliable marker of design by an intelligent agent—a central tenet to intelligent design, which Dembski argues for in opposition to modern evolutionary theory. The concept of specified complexity is widely regarded as mathematically unsound and has not been the basis for further independent work in information theory, in the theory of complex systems, or in biology. Proponents of intelligent design use specified complexity as one of their two main arguments, alongside irreducible complexity.
In Dembski's terminology, a specified pattern is one that admits short descriptions, whereas a complex pattern is one that is unlikely to occur by chance. Dembski argues that it is impossible for specified complexity to exist in patterns displayed by configurations formed by unguided processes. Therefore, Dembski argues, the fact that specified complex patterns can be found in living things indicates some kind of guidance in their formation, which is indicative of intelligence. Dembski further argues that one can rigorously show by applying no-free-lunch theorems the inability of evolutionary algorithms to select or generate configurations of high specified complexity.
In intelligent-design literature, an intelligent agent is one that chooses between different possibilities and has, by supernatural means and methods, caused life to arise. Specified complexity is what Dembski terms an "explanatory filter" which can recognize design by detecting "complex specified information" (CSI). The filter relies on the premise that the categories of regularity, chance, and design are, according to Dembski, "mutually exclusive and exhaustive". Complex specified information detects design because it detects what characterizes intelligent agency; it detects the actualization of one among many competing possibilities.