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. (shrink)

In their enthusiasm for programming, computational linguists have tended to lose sight of what humansdo. They have conceived of conversations as independent of sound and the bodies that produce it. Thus, implicit in their simulations is the assumption that the text is the essence of talk. In fact, unlike electronic mail, conversations are acoustic events. During everyday talk, human understanding depends both on the words spoken and on fine interpersonal vocal coordination. When utterances are analysed into sequences of word-based forms, (...) however, these prosodic aspects of language disappear. Therefore, to investigate the possibility that machines might talk, we propose acommunion game that includes this interpersonal patterning. Humans and machines would talk together and, based on recordings of them, a panel would appraise the relevant merit of each machine's simulation by how true to life it sounded. Unlike Turing's imitation game, the communion game overtly focuses attention, not on intelligence, but on language. It is designed to facilitate the development of social groups of adaptive robots that exploit complex acoustic signals in real time. We consider how the development of such machines might be approached. (shrink)