  We approach the virtual reality phenomenon by studying its relationship to
set theory, and we investigate the case where this is done using the
wellfoundedness property of sets. Our hypothesis is that non-wellfounded sets
(hypersets) give rise to a different quality of virtual reality than do
familiar wellfounded sets. We initially provide an alternative approach to
virtual reality based on Sommerhoff's idea of first and second order
self-awareness; both categories of self-awareness are considered as necessary
conditions for consciousness in terms of higher cognitive functions. We then
introduce a representation of first and second order self-awareness through
sets, and assume that these sets, which we call events, originally form a
collection of wellfounded sets. Strong virtual reality characterizes virtual
reality environments which have the limited capacity to create only events
associated with wellfounded sets. In contrast, the more general concept of weak
virtual reality characterizes collections of virtual reality mediated events
altogether forming an entirety larger than any collection of wellfounded sets.
By giving reference to Aczel's hyperset theory we indicate that this definition
is not empty, because hypersets encompass wellfounded sets already. Moreover,
we argue that weak virtual reality could be realized in human history through
continued progress in computer technology. Finally, we reformulate our
characterization into a more general framework, and use Baltag's Structural
Theory of Sets (STS) to show that within this general hyperset theory
Sommerhoff's first and second order self-awareness as well as both concepts of
virtual reality admit a consistent mathematical representation.
