A phenomenon in which, whenever movement is made upwards or downwards through the levels of some heirarchial system, the system unexpectedly arrives back where it started. Hofstadter (1987) uses the strange loop as a paradigm in which to interpret paradoxes in logic (such as Grelling's Paradox and Russell's Paradox) and calls a system in which a strange loop appears a Tangled Hierarchy.
See also Grelling's Paradox, Russell's Paradox, Tangled Hierarchy
Hofstadter, D. R. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Vintage Books, p. 10, 1989.