Abstract

Scientific understanding proceeds through experiments that reveal how systems behave and through abstract models constructed to account for those behaviours. Persistent conceptual and philosophical confusions arise, however, when the distinction between empirical reality and its abstract representations is left implicit. This issue is particularly evident in the study of light, where multiple, mutually non-equivalent models coexist, each successful within specific limits, yet none capable of exhausting all observed phenomena. In this work, light is analysed as a case study using the empirical–axiomatic self-framework. Light is treated first as an empirical self: a system that exists and behaves in reality and constrains observation through experimental interaction. Experimental outcomes are taken as empirical facts, understood not as explanations but as constraints imposed by reality on representation. From these constraints, multiple axiomatic selves ray, wave, classical electromagnetic, particle, quantum, and quantum field models are constructed as abstract, internally coherent structures, each defined by assumptions and restricted domains of validity. The analysis shows that domains of validity are determined directly by experimental results and indirectly by comparison with more general axiomatic selves, though experimental constraint remains the ultimate authority. More general models clarify, but do not replace, earlier ones, explaining their success within restricted regimes. No axiomatic self, regardless of generality, is identified with the empirical self itself. By maintaining a strict distinction between empirical reality and abstract representation, the framework dissolves several long-standing philosophical confusions, including realism versus instrumentalism, wave–particle duality, theory replacement, determinism versus probability, and the measurement problem. These issues are shown to arise from category mistakes rather than from deep features of nature. Although light serves as the central example, the principles extracted are not specific to optical phenomena. The empirical–axiomatic distinction applies broadly across physical systems and extends naturally to complex systems. The work thus offers a clarified account of scientific understanding: to understand a system is to know the empirical constraints it imposes, the axiomatic structures used to represent it, the domains in which those structures apply, and the limits beyond which they fail.