Grundlagen , Section 64: Frege's Discussion of Definitions by Abstraction in Historical Context.

I offer in this paper a contextual analysis of Frege'sGrundlagen, section 64. It is surprising that with so much ink spilled on that section, the sources of Frege's discussion of definitions by abstraction have remained elusive. I hope to have filled this gap by providing textual evidence coming from, among other sources, Grassmann, Schlömilch, and the tradition of textbooks in geometry for secondary schools (including a textbook Frege had used when teaching in a Privatschule in Jena in 1882–1884). In addition, I put Frege's considerations in the context of a widespread debate in Germany on ‘directions’ as a central notion in the theory of parallels. [ABSTRACT FROM PUBLISHER]