David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Minds and Machines 16 (2):201-219 (2006)
We approach the virtual reality phenomenon by studying its relationship to set theory. This approach offers a characterization of virtual reality in set theoretic terms, and we investigate the case where this is done using the wellfoundedness property. Our hypothesis is that non-wellfounded sets (so-called hypersets) give rise to a different quality of virtual reality than do familiar wellfounded sets. To elaborate this hypothesis, we describe virtual reality through Sommerhoff’s categories of first- and second-order self-awareness; introduced as necessary conditions for consciousness in terms of higher cognitive functions. We then propose 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 logically weaker and 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, within a more general framework, we use Baltag’s structural theory of sets (STS) to show that within this hyperset theory Sommerhoff’s first- and second-order self-awareness as well as both concepts of virtual reality admit a consistent mathematical representation. To illustrate our ideas, several examples and heuristic arguments are discussed.
|Keywords||Virtual Reality ZFC set theory Non-wellfounded set theory Sommerhoff’s theory of consciousness|
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References found in this work BETA
Uriah Kriegel (2006). The Same-Order Monitoring Theory of Consciousness. In Uriah Kriegel & Kenneth Williford (eds.), Self-Representational Approaches to Consciousness. MIT Press 143--170.
Gerd Sommerhoff (1990). Life, Brain, and Consciousness: New Perceptions Through Targeted Systems Analysis. Distributors for the U.S. And Canada, Elsevier Science Pub. Co..
A. Baltag (1999). Sts: A Structural Theory Of Sets. Logic Journal of the IGPL 7 (4):481-515.
G. Sommerhoff & Karl F. MacDorman (1994). An Account of Consciousness in Physical and Functional Terms: A Target for Research in the Neurosciences. Integrative Physiological and Behavioral Science 29:151-81.
Paul Bernays (1954). A System of Axiomatic Set Theory--Part VII. Journal of Symbolic Logic 19 (2):81-96.
Citations of this work BETA
Garry Young & Monica Whitty (2011). Progressive Embodiment Within Cyberspace: Considering the Psychological Impact of the Supermorphic Persona. Philosophical Psychology 24 (4):537 - 560.
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