Thermodynamic Mathematical Empiricism

This treatise establishes a rigorous philosophical framework positioning mathematics not as a Platonic abstraction or a set of arbitrary axioms, but as a substrate-independent natural language grounded in the thermodynamic necessity of identity differentiation. We posit that foundational mathematics (arithmetic, geometry) emerges from the universal empirical experience of discrete objects and persistent identity patterns ($A=A$), constrained by physical laws rather than cultural convention. Advanced mathematics is formalized as a deterministic inductive extension of these foundational patterns, functioning as a "compressed mechanism" for correcting the computational irreducibility of qualitative human thought. This framework integrates insights from John Stuart Mill's radical empiricism, Imre Lakatos' quasi-empiricism, and Process Philosophy, naturalized through the thermodynamic principles of Fractal Conceptual Fields (FCF).

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