The concept of strong and weak virtual reality

TL;DR

This paper explores the philosophical and mathematical foundations of virtual reality by linking it to set theory, distinguishing between wellfounded and non-wellfounded sets, and proposing a formal framework for understanding different virtual reality qualities.

Contribution

It introduces a novel set-theoretic model of virtual reality based on hypersets and self-awareness, providing a formal mathematical framework for strong and weak virtual reality.

Findings

Strong virtual reality involves wellfounded sets.

Weak virtual reality encompasses non-wellfounded hypersets.

Mathematical formalization using Baltag's Structural Theory of Sets.

Abstract

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.