This paper introduces the Empirical-Axiomatic Framework, a conceptual framework designed to clarify the relationships between empirical reality, abstract space, knowledge, epistemic capacity, and representation. The framework begins from a strict separation: empirical reality is physical, causal, and mind-independent, while knowledge consists of abstract structures that exist in abstract space independently of their use, discovery, or interpretation. Knowledge is not representation, not epistemic activity, and not reducible to models or theories. Representation arises only when an empirical system with epistemic capacity selects and applies abstract structures under interpretive rules to model aspects of empirical reality. Epistemic capacity itself is treated as an empirical property of physical systems, constrained, finite, and causally instantiated, which enables selection and use of abstract structures without creating or defining them. Using physics as a primary case study, the paper demonstrates that scientific progress is driven by the need for increasingly expressive abstract structures as empirical reality reveals features that cannot be represented within existing mathematical frameworks. The progression from classical mechanics to quantum mechanics, quantum field theory, and modern theoretical approaches is analyzed as a sequence of epistemic responses to representational failure, each requiring axiomatic enrichment of mathematics. Mathematical advancement is shown to consist in the introduction of new axioms and structures, expanding representational capacity while remaining inherently open-ended, as guaranteed by Gödel’s incompleteness for sufficiently strong formal systems. Consequently, physical models can achieve increasing accuracy without ever attaining completeness. The framework further clarifies the role of empirical limits, showing how epistemic saturation produces the illusion of finality and motivates the mistaken notion of a theory of everything. This illusion reflects practical constraints on empirical access, not exhaustion of abstract space or closure of reality. Finally, the framework is applied to the concept of self, distinguishing the empirical self as a physical system from multiple axiomatic selves as abstract models, including experiential and enlightenable selves, without introducing new ontological categories. By enforcing strict conceptual discipline between empirical reality and abstract representation, the Empirical-Axiomatic Framework dissolves persistent confusions in epistemology, philosophy of science, and philosophy of mind while preserving the reality of experience, the success of science, and the open-ended nature of epistemic progress.
Akash Pawar (Sun,) studied this question.