Abstract
T he topic announced by my title may seem perverse, since Frege never developed an account of complex numbers. Even his treatment of the reals is incomplete, and we have only recently begun to get a reasonable understanding of how it works.2 Presumably for that reason, the secondary literature simply does not discuss how complex numbers might fit into Frege's project.3 As I will show, we can be quite confident from what little he does say that Frege intended his logicist program to extend to complex numbers. What we do not know is how he might have gone about it. I will try to show that however he approached this task, he was bound to fail. This fact has profound implications, not just for his approach to arithmetic, but for his whole understanding of mathematics-and indeed, for his understanding of what is required to secure reference to particular objects generally.
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