It is contended that one of the promising directions for brooding over the problem of incommensurability of paradigms, coined by T. Kuhn and P. Feyerabend, may be associated with the trend of neo-Kantian epistemology, embodied by the writings of Ernst Cassirer. According to Cassirer, the statements fixing connections and relationships between mathematical ideal constructs render a reliable ‘neutral language’ that can serve as a firm ground for comparing the ‘old’ and ‘new’ paradigms. The aim of the paper is to offer (...) Maxwell’s work as a test case against the incommensurability thesis. A case study of the genesis and functioning of a neutral mathematical language related to the Maxwellian solid synthesis of optics and electromagnetism is provided. It is elicited that its basis is constituted by stodgy language of continuum mechanics. The main function of the neutral language was to project the consequences of all the unified partial theoretical schemes (‘old’ rival paradigms) of Ampѐre, Faraday, Biot, Savar et al. onto the grand mathematical model, ‘rewrite’ all known laws in this pervasive mathematical language, compare their conclusions with each other to eliminate contradictions. Eventually the stuff was generalized in a self-consistent system of Maxwell’s equations. (shrink)