The concept of strong and weak virtual reality

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Theory of Consciousness
Virtual Reality; Sommerhoff’s theory of consciousness; Set theory; Non-wellfounded set theory
Deposited by: 
Dr. Andreas Martin Lisewski
Date of Issue: 
Andreas Martin Lisewski
Journal/Publication Title: 
Minds and Machines
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We approach the virtual reality phenomenon by studying its relationship to set theory. This relationship provides a characterization of virtual reality in set theoretic terms, and we investigate the case where this is done using the wellfoundedness property of sets. Our hypothesis is that non-wellfounded sets (so-called hypersets) give rise to a different quality of virtual reality than do familiar wellfounded sets. A definition of virtual reality is proposed based on Sommerhoff's idea of first and second order self-awareness, with a representation of first and second order self-awareness through sets. These sets, so-called events, originally form a collection of wellfounded sets. Consequently, strong virtual reality refers to 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. Explicit hyperset theories, such as Aczel's hyperset theory, indicate that this definition is not empty because hypersets encompass wellfounded sets already. Moreover, we argue heuristically that weak virtual reality could be realized in human culture through continued progress in computer technology. Finally, in a more general framework, we 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 self-consistent representation.
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