In his 1918 book Das Kontinuum, Weyl aimed at a wholesale reworking of the foundations of analysis. While his general ideas have been very influential, several of the specific ways he pursues those ideas remain very puzzling today. After a brief and generally accessible introduction to Weyl's theory, I will discuss one puzzle about how he chose to develop the theory. Specifically, Weyls thinks that sets are formed by reifying the extensions of concepts and relations. In principle, this process of set-formation could then be iterated, but Weyl chooses not to do so. Why? I will suggest that an answer to this question can be found in Weyl's remarks about the nature of mathematics and its role vis a vis natural science.