Predictive Set Theory: A Generative Framework for Cognitive Architecture with Operationalized Core Mechanisms
TL;DR
Predictive Set Theory is introduced, a formal generative framework that reconstructs cognitive architecture from first principles that offers novel resolutions to classical problems such as Russell's paradox, the cognitive status of G\"{o}delian incompleteness, the grounding of negative feedback, and the comprehension of film editing.
Abstract
Predictive processing theories portray the brain as a hierarchical prediction engine that minimizes prediction error, yet they lack operational definitions for the structure of a"prediction,"the standardized response to a prediction error, and the mechanism that maintains consistency across successive updates. Bayesian cognitive science attempts to subsume all uncertainty under probabilistic belief updating, but it presupposes a closed hypothesis space and provides no generative account of how the objects over which probabilities are distributed become discrete, identifiable referents in the first place. This paper introduces Predictive Set Theory (PST), a formal generative framework that reconstructs cognitive architecture from first principles. PST anchors cognition in a minimal set of operations---a sensor formalized as an identity function, set-theoretic state refresh, and three fundamental forms of reference chains (reference, counter-reference, and semi-reference)---and rigorously derives core cognitive functions including state sequences, demand, comparison, efficiency, and finite-horizon probabilistic planning. Rather than modeling neural mechanisms, PST constitutes a design specification for any system that must maintain internal consistency while acting under incomplete information and irreversible risk. The framework offers novel resolutions to classical problems such as Russell's paradox, the cognitive status of G\"{o}delian incompleteness, the grounding of negative feedback, and the comprehension of film editing. The primary purpose of this paper is to establish, through the public academic record, the originality and completeness of the Predictive Set Theory framework.