 Compared to Frege, Dedekind also has much more to say about the infinite, not just by formulating a definition of that notion, but also by exploring the possibility of different infinite cardinalities with Cantor. And he shows more awareness of the challenge posed by Kroneckerian computational and constructivist strictures to logicism. The differences between Frege’s and Dedekind’s respective treatments of the natural and real numbers are noteworthy too. As we saw, Dedekind conceives of the natural numbers primarily as ordinal numbers; he also identifies them purely  “structurally”. Frege makes their application as cardinal numbers central; and he insists on building this application into the very nature of the natural numbers, thus endowing them with non-structural, “intrinsic” properties.  The case of the real numbers illustrates this divergence further. Finally, Frege’s and Dedekind’s underlying conceptions of logic and language differ significantly.  (The latter is one of the main reasons for why Dedekind is not  interpreted as a logicist in Sinaceur 2008, 2015, 2017.)