The Topos of Virtuality
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 th...
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| Format: | Article |
| Language: | English |
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Paderborn University: Media Systems and Media Organisation Research Group
2009-07-01
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| Series: | tripleC: Communication, Capitalism & Critique |
| Subjects: | |
| Online Access: | https://www.triple-c.at/index.php/tripleC/article/view/70 |
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| _version_ | 1849400612833198080 |
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| author | Rainer Zimmermann Wolfgang Hofkirchner |
| author_facet | Rainer Zimmermann Wolfgang Hofkirchner |
| author_sort | Rainer Zimmermann |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-91cfc5cdafdf4f5cb2cabb3f5bef259d |
| institution | Kabale University |
| issn | 1726-670X |
| language | English |
| publishDate | 2009-07-01 |
| publisher | Paderborn University: Media Systems and Media Organisation Research Group |
| record_format | Article |
| series | tripleC: Communication, Capitalism & Critique |
| spelling | doaj-art-91cfc5cdafdf4f5cb2cabb3f5bef259d2025-08-20T03:37:57ZengPaderborn University: Media Systems and Media Organisation Research GrouptripleC: Communication, Capitalism & Critique1726-670X2009-07-017110.31269/triplec.v7i1.7070The Topos of VirtualityRainer ZimmermannWolfgang HofkirchnerGeneralizing 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.https://www.triple-c.at/index.php/tripleC/article/view/70Topos theoryTopologySocial SpaceCognitionEvolutionary Systems |
| spellingShingle | Rainer Zimmermann Wolfgang Hofkirchner The Topos of Virtuality tripleC: Communication, Capitalism & Critique Topos theory Topology Social Space Cognition Evolutionary Systems |
| title | The Topos of Virtuality |
| title_full | The Topos of Virtuality |
| title_fullStr | The Topos of Virtuality |
| title_full_unstemmed | The Topos of Virtuality |
| title_short | The Topos of Virtuality |
| title_sort | topos of virtuality |
| topic | Topos theory Topology Social Space Cognition Evolutionary Systems |
| url | https://www.triple-c.at/index.php/tripleC/article/view/70 |
| work_keys_str_mv | AT rainerzimmermann thetoposofvirtuality AT wolfganghofkirchner thetoposofvirtuality AT rainerzimmermann toposofvirtuality AT wolfganghofkirchner toposofvirtuality |