However in the finance areas the term reflexivity has been popularised largely by one man, George Soros.
The basic idea is that:
1. The market is made up of people.
2. People have a conception of the economic reality (which is inevitably false or incomplete) and base their actions on these conceptions.
3. These conceptions then have a feedback loop with "economic fundamentals"..
4. In certain historical circumstances this feedback loop leads to outcomes that are initially self fulfilling but inevitably self defeating in a boom/bust sequence.
5. Generally this reflexive boom/bust sequence initially builds on a pre-existing trend based on sound economic fundamentals.
Examples of factors that may give rise to this the feedback loop in point 4 include
(a) increasing lending against appreciating assets without understanding that one of the main reasons for the increased asset price is the increased lending.
(b) the trend-following habits of investors or speculators (including adaptive expectations formation).
A current example of reflexivity in modern financial markets is that of the debt and equity of housing markets. I would argue that both the factors (a) and (b) above contributed to this damaging boom bust cycle in the following way.
a. Lenders began to make more money available to more people in the 1990s to buy houses. More people bought houses with this larger amount of money, thus increasing the prices of these houses. Lenders looked at their balance sheets which not only showed that they had made more loans, but that their equity backing the loans - the value of the houses, had gone up (because more money was chasing almost the same amount of housing). Thus they lent out more money because their balance sheets looked good, and prices went up more, and they lent more, etc. Prices increased rapidly, and lending standards were relaxed.
b. Ever larger numbers of potential investors in housing markets grew increasingly confident that house prices would continue to increase based on their past experience (i.e. adaptive expectations) and thus scrambled to bid up the prices of houses.
Reflexivity in simply an inescapable fact of life in all arenas of social action. The reflexive boom/bust sequence is one consequence of this and only occurs in certain historical settings. In this conception financial markets are not necessarily in, or indeed close to, equilibrium.
Soros perspective is that the housing boom and bust has been superimposed on a larger global "super bubble" for that last 25-30 years. This super bubble is base on so called global "market fundamentalism" regarding financial markets. i.e the belief that free financial markets work well and when left to their own devices tend towards equilibrium. This belief lead to three main trends: (a) unchecked credit expansion, (b) an explosion in the value and type of unregulated financial instruments (derivatives, leveraged instruments, securitised instruments, synthetic instruments etc.), (c) globalization of financial markets with the financing of US consumption (private and government) by foreign lenders (China etc). This bubble has now burst and we are now in the beginning of the bust phase. Given that the boom took 25 years to unfold I would not be surprised if the bust lasts more than a year or two.
For more information on the broad idea of reflexivity see the follows chapter from a book on the reflexivity http://www.springer.com/cda/content/document/cda_downloaddocument/9783790820911-c1.pdf?SGWID=0-0-45-624115-p173844610.
For more information on George Soros and his thoughts on reflexivity and the current financial crisis see http://www.georgesoros.com/.