Dialectic and diagonalization

Abstract

This essay is about mathematics as a written or literate language. Through historical and anthropological observations drawn from the history of Greek mathematics and the oral tradition preceding the rise of literacy in Greece, as well as considerations on the nature of alphabetic writing, it is argued that three essential linguistic features of mathematical discourse are jointly possible only through written, alphabetic language. The essay concludes with a discussion of how both alphabetic principles and issues related to literacy faced by the Greeks in the axiomatization of geometry play a central role in some specific metamathematical theories. Drawing extensively on the work of ArpSd Szatx5, Eric Havelock, and Albert Lord, the implications developed between Szab6's history of Greek mathematics and Havelock and Lord's theories of writing and oral traditions (Homer's in particular) are the author's own, as are the applications to modern logic.