Logicism is the name commonly given to what is considered the best strategy to defend a certain grand philosophical vision of mathematics. But logicism is famously problematic. It has been widely rejected, and with it the grand vision has been abandoned. But nonetheless, we can hold onto this grand vision of mathematics, and defend logicism, properly understood. The failure of logicism, as commonly conceived, can be tied to giving logic a too central role in various parts of the project. I will argue that the greatest threat to the grand vision is a certain picture of the source of mathematical objectivity, and that this picture is false at least in the case of arithmetic. Once this is seen we can hope to defend the grand vision, in part by conceiving of logicism as a form of rationalism.