Preamble to an analysis of the relevance of Ernst Kummer’s studies on factorization to the history of theories of language.

Abstract

One of the cornerstones upon which contemporary linguistic theory lies, whether it knows or not, is made up by the studies by Ernst Kummer on the unique factorization of an integer number into primes. It comes then hardly as a surprise that some well-known discrepancies between linguistic schools may be traced back to differences regarding this crucial issue. The present paper seeks to provide insight, with help from some of the original sources, into the different mathematical meanings underlying the use of the concept of factorization both within American structuralism and generative grammar. An enlightening parallelism is established between Ernst Kummer and Zellig Harris, on the one side, and Richard Dedekind and Noam Chomsky on the other. This first instalment includes: 1) a brief historical overview of the factorization of integers into primes, 2) a presentation of its usage in some of Zellig Harris’s work, and 3) an annex with Harris’s quotations on the matter of graph decomposition, which advances the main topic dealt with in the forthcoming sequel.