The concept of strong and weak virtual reality

Lisewski, A. M. (2006) The concept of strong and weak virtual reality. Minds and Machines, 16 (2). pp. 201-219.

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Official URL: http://www.springerlink.com/content/e441x7577121v179/

Alternative URL: http://arxiv.org/abs/cs/0312001

Abstract

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.

Comments/Discussion

The paper aims at establishing a formal relationship between set theory and consciousness. It is argued that hypersets, i.e. non-wellfounded sets, naturally incorporate the self-referential nature of consciousness when formulated within Sommerhoff's representational approach.

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