Logicism and Mathematics

The prototype of the Proposition in modern Science is the Newtonian Law, and, hence, entails the application of Mathematics.  Accordingly, in both Kantian and Russellian Logicisms, Mathematics mediates between Logic and Empirical propositions.  In the former, that mediation is effected by the Temporalization of the Categories, which, concomitantly, facilitates the enumerability of Experience.  In the latter, Logic and Mathematics are conceived as identical, e. g. Conjunction and Disjunction are equated with Arithmetical Multiplication and Addition, respectively, and with Set Theoretical Intersection and Union, respectively.  In remarkable contrast with both, in his project of founding Science, Husserl asserts that "the mathematician is not really the pure theoretician, but only the ingenious technician" (Logical Investigations, Prolegomena, #71).  So, not only is Mathematics extrinsic to his Logicism, his Instrumentalism predates that of both Heidegger and Wittgenstein by decades, contrary to standard interpretations of those relations.  Furthermore, this affinity with the later Wittgenstein is another indication of the greater hospitability of his Logicism, than of Russell's, to a Semantics of 'ordinary language'.