Knowledge and Information in Epistemic Dynamics

Abstract

This paper proposes a general theory of cognitive systems that inverts the conventional relationship between information and knowledge. While classical approaches define knowledge as the byproduct of processed information, we establish knowledge as a primitive concept and formulate information as a measure emerging from the process of assimilating knowledge. The epistemic measure of information provides a formal counterpart to Piaget’s assimilation-accommodation paradigm, expressed in terms of knowledge encoding costs. We present a general axiomatic definition of a cognitive system, along with its corresponding epistemic information measure, and demonstrate that Shannon’s source information, artificial neural networks, and formal logical theories are all concrete realizations of this unified framework. A central theoretical result is the proof of the Epistemic Inaccessibility Theorem, which establishes an intrinsic form of cognitive incompleteness. As a major consequence, we prove Gödel’s First Incompleteness Theorem for Peano Arithmetic directly from epistemic inaccessibility. Finally, we discuss the role of multi-level knowledge encodings, highlighting how artificial intelligence and Large Language Models suggest new avenues for modeling reflexivity, reasoning, and autonomous cognitive evolution.