ABSTRACT
This chapter considers the relationship between reflexivity and complexity. Reflexivity has a considerable history as an idea in the social sciences, with many specific meanings and applications, although it generally has involved a mutual interaction between at least two separate agents or groups. Complexity also has many meanings, although often these involve some higher-level emergence, the idea of wholes being greater than the sum of their parts. It has been argued by some in economics especially that there may be a relationship between these two, as the dynamic interactions in reflexive systems may be more likely to bring about forms of complex emergence. The ideas of John B. Davis on this will be especially considered, but those of others will be examined as well, including some of those more critical of the usefulness of these concepts. A new idea put forth in this paper is that some forms of reflexivity may be more conducive to bringing about patterns of complex emergence than others. This may involve more subtle interactions of indirect self-referencing through reflexive systems such as those that underlay proofs of incompleteness. An artistic analogy can be seen in the work of M. C. Escher, with many writing about reflexivity citing his Drawing Hands (Figure 5.1) as an example, which depicts two hands drawing each other. But this may show the sort of reflexivity that is not so associated with complexity. Rather another may do so better: Escher’s Print Gallery (Figure 5.3), which shows a man standing in a picture gallery and looking at a picture of a city that contains a picture gallery that turns out to be the one in which he is standing.
