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Textual Theory and Complex Belief Systems: Topological Theory

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Abstract

In order to establish patterns of materialization of the beliefs we are going to consider that these have defined mathematical structures. It will allow us to understand better processes of the textual, architectonic, normative, educative, etc., materialization of an ideology. The materialization is the conversion by means of certain mathematical correspondences, of an abstract set whose elements are beliefs or ideas, in an impure set whose elements are material or energetic. Text is a materialization of ideology and it is any representation of the Reality represented by symbolic means. In all text T we can observe diverse topological structures: Metric Textual Space, Textual Topology and a Textual Lattice.

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Notes

  1. Impure sets are sets whose referential elements (absolute beings) are not counted as abstract objects and have the following conditions: a) They are real (material or energetic absolute beings). b) They exist independently of the Subject. c) S develops \(p\)-significances on them. d) True things can be said about them. e) Subject can know these true things about them. f) They have properties that support a robust notion of mathematical truth. A simple impure system-linkage \(\Sigma \equiv \) (M, R) is a semiotic system consisting of the pair formed by an impure object set M the elements of which are \(p\)-significances (relative beings) of entities belonging to Reality (absolute beings) or certain attributes of these, and a set of binary relations, such that \(\hbox {R }\, \subset \,\hbox { P}(\hbox {M} \times \hbox {M}) = \,\hbox { P}(\hbox {M}^{2})\). That is \(\forall \hbox {r} \in \hbox {R}/\hbox {r} \subset \hbox {M } \times \hbox { M }\) being \(r=\left\{ \left( x_{i},\,y_{j}\right) \in M \times M/x_{i},\,y_{j} \in M\right\} \) An impure system-linkage defined within an impure object set M is a simple system S = (M, R) or a finite union of simple systems-linkage \(\Sigma =\cup ^{\hbox {n}}_{\mathrm{i}=1} \Sigma _{\mathrm{i}}\) such that \(\Sigma _{\mathrm{i}}\) are simple systems. This shall be denoted as \(\Sigma \equiv \left( {\hbox {M},\hbox { R}} \right) \) such that \(\hbox {R}\subset \hbox {P}(\cup _{\mathrm{finite}} \hbox {M}^{2})\). A Deontical system is an organization of knowledge on the part of the subject S that fulfils the following ones: a) Other subjects (human beings) are elements of the system. b) Some existing relations between elements have Deontic modalities. c) There is purpose (purposes).

  2. In any process, we can distinguish between having a signifier as inherent property, and having significance when it is related to other processes of Reality that the Subject considers as system. The existence of information is independent of the fact that there is a Subject able to decode the message, which it is wished to communicate. This objective information is termed signifier. The information in a message acquires meaning if a Subject decodes the message. This subjective information is termed significance.

  3. Connotation is the sum of all the cultural units that the signifier can evoke institutionally in the mind of the addressee Subject whose only psychic possibility is cultural availability.

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  1. Department of Applied Mathematics, University of Alicante, Alicante, Spain

    J. Nescolarde-Selva & J. L. Usó-Doménech

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Nescolarde-Selva, J., Usó-Doménech, J.L. Textual Theory and Complex Belief Systems: Topological Theory. Found Sci 21, 153–175 (2016). https://doi.org/10.1007/s10699-015-9410-6

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