 In explicitly embracing late nineteenth-century work on the foundations of mathematics, Cassirer comes into very close proximity with early twentieth-century analytic philosophy. Indeed, Cassirer takes the modern mathematical logic implicit in the work of Dedekind and Hilbert, and explicit in the work of Gottlob Frege and the early Bertrand Russell, as providing us with our primary tool for moving beyond the empiricist abstractionism due ultimately to Aristotelian syllogistic. The modern “theory of the concept,” accordingly, is based on the fundamental notions of function, series, and order (relational structure) – where these notions, from the point of view of pure mathematics and pure logic, are entirely formal and abstract, having no intuitive relation, in particular, to either space or time. Nevertheless, and here is where Cassirer diverges from most of the analytic tradition, this modern theory of the concept only provides us with a genuine and complete alternative to Aristotelian abstractionism and philosophical empiricism when it is embedded within the genetic conception of knowledge. What is primary is the generative historical process by which modern mathematical natural science successively develops or evolves, and pure mathematics and pure logic only have philosophical significance as elements of or abstractions from this more fundamental developmental process of “productive synthesis” aimed at the application of such pure formal structures in empirical knowledge (see especially [Cassirer 1907b]).