Irreducible complexity is an argument by proponents of intelligent design that certain biological systems are too complex to have evolved from simpler, or ‘less complete’ predecessors, through natural selection acting upon a series of advantageous naturally occurring, chance mutations.
The argument is central to intelligent design, and is rejected by the scientific community at large, which overwhelmingly regards intelligent design as pseudoscience. Irreducible complexity is one of two main arguments (both discredited) used by intelligent design proponents, the other being specified complexity (which singles out patterns that are both specified and complex as markers of design by an intelligent agent).
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The Daily Omnivore 