Abstract
It is contended that one of the promising directions for solving the problem of incommensurability of paradigms, coined by T. Kuhn and P. Feyerabend, can be associated with the trend of advancement of neo-Kantian epistemology, presented by the writings of Ernst Cassirer. According to Cassirer, the statements fixing connections and relationships between mathematical ideal constructs form a “neutral language” that can serve as a firm ground for comparing the “old” and “new” paradigms. A case study of the genesis and functioning of a neutral mathematical language related to the Maxwellian synthesis of optics and electromagnetism isprovided. It is elicited that its basis is constituted by the mathematical language of continuum mechanics. The main function of the neutral language was to project the consequences of all the unified theories onto the mathematical model, “rewrite” all known laws in this mathematical language, compare their conclusions with each other to eliminate contradictions and generalize the stuff in a self-consistent system of equations.
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