In an interesting new paper, my colleague Paul Lewis discusses the origins of Hayek's views on emergence in his work on theoretical psychology and The Sensory Order. Hayek published The Sensory Order in 1952, but he developed the core ideas in the book very early in his career while studying law, and reading economics and psychology at University of Vienna.
Emergence is central to a Hayekian understanding of spontaneous order and properties of the price system. In the market, prices are "of human action, but not of human design" - they emerge from the buying and selling of the many individuals at the micro level, but settle on values that balance the quantity demanded with the supplied of a particular good. Prevailing market prices are reflective of individual decisions, but not necessarily reducible to any particular bid / ask. Moreover, the vast array of prices in an economic system are far too complex and interdependent for anyone to be capable of accurate, detailed future predictions. This idea that in complex systems we are limited to what Hayek called "explanation of principle" or pattern prediction builds from his earlier work concerning the classification system of the mind.
In his paper, Lewis traces the early development of Hayek's ideas in the German psychologist Wilhelm Wundt and goes on to make the argument that it was in reading the organic biologists Joseph Woodger and Ludwig von Bertalanffy that Hayek was "able to develop his appreciation of how the arrangement of certain parts or elements so as to form a particular relational order can give rise to structural properties that are quite distinct from the properties of those elements taken in isolation. Quite literally, this is emergence in all but name" (pg. 141).