Ideological Complex Systems: Mathematical Theory

Abstract

The goal of this article is to build an abstract mathematical theory rather than a computational one of the process of transmission of ideology. The basis of much of the argument is Patten's Environment Theory that characterizes a system with its double environment (input or stimulus and output or response) and the existing interactions among them. Ideological processes are semiotic processes, and if in Patten's theory, the two environments are physical, in this theory ideological processes are physical and semiotic, as are stimulus and response. V C 2014 Wiley Periodicals, Inc. Complexity 21: [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65] 2015

What Are Ideological Systems?

“…In the Deontical Impure Systems (DIS) (Impure sets and their mathematical properties have been previously defined in Nescolarde Selva et al [27]) approach, the superstructure of social systems has been divided in two [27][28][29][30][31][32][33][34][35][36][37][38][39][40].…”

“…The believers work together and then experts work out what is the correct behavior, the "right" values and so on; (4) Language. A language L is the logical expression of an ideology relating one substantive (Substantive beliefs [36,37] make up a system's axioms, and most of the beliefs make up their theorems) belief [27][28][29][30][31][32][33][34][35][36][37][38][39] to the others in the belief system. Language is understood from repeated patterns in the use of sets of beliefs.…”

Structure and Superstructures in Complex Social Systems

“…This Doxical Space or belief space is a normative superstructure and includes ways of thinking about the economic and legal normative structures. Two superstructures are involved in this approach to DIS [1][2][3][4][5][6][7][8][9][10]:…”

“…Let r i k be a doxical relation belonging to a k sheaf [1][2][3][4][5][6][7][8][9][10] ( ) , with Ù being the function "and". We define the systemic significance s and there will also be a denotative significance d-s which is what we know of the significance s of an object in Reality that we call an absolute being.…”

“…In previous works, the authors have defined social systems as Deontic Impure Systems (DIS) [1][2][3][4][5][6][7][8][9][10], and provided mathematical properties of their structure. These systems are considered impure because their elements are either living things or materials and what we know of them is constrained by our ways of thinking and may vary from person to person.…”