Open AccessThe Topos of Virtuality
Author(s) -
Rainer Zimmermann,
Wolfgang Hofkirchner
Publication year - 2009
Publication title -
triplec
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.564
H-Index - 21
ISSN - 1726-670X
DOI - 10.31269/triplec.v7i1.70
Subject(s) - topos theory , category theory , domain theory , mathematics , space (punctuation) , representation (politics) , computer science , algebra over a field , epistemology , pure mathematics , discrete mathematics , art , literature , philosophy , politics , political science , law , operating system
Generalizing the conceptual approach to a theory of biosemiotics which is primarily based on insight from mathematical topology , we discuss here the relevance of the cognitive representation of the category of space in terms of the consequences implied by topos theory: In this sense, it is shown that a topos is a Lindenbaum-Tarski algebra for a logical theory whose models are the points of a space. We also show what kind of epistemic conclusions can be drawn from this result with a view to model theory and by doing so establish important relationships among the concepts of social space, networks, systems and evolutionary games on the one hand and semiosis on the other. We can thus achieve a suitable reconciliation of both the onto-epistemic approach of the Kassel group and the evolutionary approach of the Salzburg group, respectively, carrying us forward among other things to fundamental aspects of a unified theory of information. This first paper deals with the mentioned relationships in general spaces, the second deals with applications to virtual space proper.