Towards a complex theory of information — extended abstract

Publicado: 2025-10-05

This is the abstract for a talk I will give at ICPHILCOMP25.

We give the foundations for a complex theory of information. It is complex in the sense that it accounts for both qualitative and quantitative aspects of information, therefore beholding both subjective and objective informational phenomena. It is also complex in the sense that approaches a layer of abstraction structuring information as such, thus, a layer meta-structuring any kind of discourse. By its nature, abstractions made here through a schematic approach, allow simple formal and graphical representations, coming with a rich and novel top-down visual reasoning methodology grounded in a complex theory of duality. On these grounds, our theory departs from the code-theoretical and algorithmic approaches of Shannon and Chaitin respectively, by instead adopting a phenomenological and semiotic perspective.

We began with the initial observation that everything is information to us. Thus, our point of departure is phenomenological. From the pure experience of reality arise mental phenomena, and from there a subjective—and intersubjective—process of categorization. Information is therefore the outcome of a phenomenological reduction synthesizing formal abstraction and subjective interpretation of experience in any form of reality. Such a perspective places us within a layer of an abstract categorical framework in which information resides and structures itself. Also, it further advances us into a new metaphysics of schematic abstraction as foundational grounds.

The link between the purity of abstraction and the pragmatics of visual reasoning lies in a complex theory of duality. Complex duality abstracts the intentionality of discursive duality through a categorical approach, wherein we observe categories as complex discursive universes encompassing any kind of discourse—or argumentation—exhibiting qualities associated with a hypostasis or simple abstract term. Accordingly, we approach the phenomenological reduction process as one of categorizing phenomena. Furthermore, this process must proceed by differentiation, as it results in dual categories that distinguish a particular phenomenon from others.

This categorical standpoint lays out the first informational contention schema. The categorical schema divides the universe of discourse in two by generating a subcategory of discourses—that is, the simplifications we derive from the complexity of the universe. Thus, a universe of discourse may contain discourses that define other universes, and complexity may encompass its own simplifications. Moreover, by referring to those composite universes, we also distinguish them from others, thereby naming a third containing category within a transcendent universe.

What we approach with this contention triad is the base for a foundational archetype: an intentional structure of information according to its own complexity qualities, in such a manner that gives a schematic meta-structure to discursive complexity. This approach not only turns categories into composable intensional entities, but also opens local windows to complexity by means of schematic intensional relations.

This schematic approach has a geometrical dual simplifying contention into oppositions. As a matter of fact, we derive it from an abstract geometrical operation: we evert contention outwards as abstract oppositions, where containing universes become intensional or complex, and contained ones become extensional or simple. It should be clear that these dual pairs are not sufficient to describe qualitatively any kind of abstract quality. This is because the schematic approach abstracts the quality of opposition itself into relation, position, contention or structure. The result is that the more abstract a pair of dual terms are, the more they can be used as structural intension for other pairs of dual terms. Intension-extension, complex-simple, theory-practice, game-strategy, spirit-matter, etc., become, together or separately, the structural intentionality of more complex dualities.

Our third transcendent category also acquires an abstract quality that must meet its dual within the same transcendent —i.e., more complex— universe of discourse. Here, we note that the archetypal essence of our schematic approach ensures that the schema applies to all information, including itself. This archetypal foundation establishes an abstract categorical framework by ensuring that any pair of dual terms we may structure must also have a dual pair of opposite quality within the same universe of discourse. Moreover, this triadic arrangement forms the foundation of schematic abstract dialectics emerging from opposition and quality abstraction.

If for every duality there exists—metaphysically—another one of opposite quality, then also one of those becomes the structural intentionality of the other. Thus, an oppositional square emerges where every term (node) is opposite in abstract quality to its two neighbors. The transcendent oppositions also conform then a new square, more complex than the previous one. Of course, if archetypal duality schematically applies to duality itself, then also applies to these new squares, and as we can continue abstracting and synthesizing as far as we wish, this applies also to new squares and to any intensional grouping or arrangement we can come up from them by following their oppositional abstract qualities.

Fractality, together with a new ontology of complexity, emerges then as a consequence of the schematic meta-structuring approach. Every binary, triadic, or tetradic arrangement based on these oppositional qualities will delimit a universe of discourse of increasing complexity, relative to our abstractions of the oppositional structure itself. Other complex structures preserving aforementioned properties may become a pragmatical representation of more complex archetypes that . Through graph-theoretic or semiotic approaches, this approach foresee a fruitful path of varied applications.

We present advances on the philosophical and pragmatical aspects of the theory. The methodology that emerges has been applied to the theory itself, resulting in a proper ontology of generic categories of information. Advances into akin ontology of computer programming, and others, are also presented. Future work includes the mathematical and graph-theoretic analysis of these abstract structures, and also further research on the computational-theoretic aspects of the theory.

tags:: Ensayo, Metafísica, Abstracción, Arquetipo, Dualidad, Complejidad, Teoría de la información