Frege's Dissertation

  • Hans Sluga  “Frege: the early years”, in: Philosophy in History, ed. Q. Skinner et al., Cambridge, Cambridge University Press, 1984


The former[= Frege's dissertation] is devoted to a question arising out of analytic geometry. The equations with which we describe geometrical configurations yield at times imaginary rather than the expected real values. Thus, when we calculate the points at which a straight line lying outside a circle intersects that circle the analytic equations will determine those points as imaginary ones. Gauss had shown how complex numbers can be represented geometrically as points on a plane with a system of coordinates whose one axis represents real and whose other axis represents imagenary values. Frege's project in his dissertation was to find a general geometrical method for representing imaginary figures in real space. The problem had been attacked before him by Christian von Staudt (a student of Gauss), Otto Stolz, and Felix Klein[…]. Frege's attempt, while similar in motivation, is new in the details of its execution[…]*2.


*1:Uber eine geometrische Darstellung der imaginaren Gebilde in der Ebene[On a Geometrical Representation of Imaginary Figures in a Plane]”, Doctoral dissertation, Gottingen, 1873.

*2:Sluga, p.336.