Frege's objects of a quite special kind

A previous version of this paper was read at the universities of Glasgow, Munich, Oxford and St. Andrews; the penultimate version was presented at the universities of Bologna, Erlangen-Nürnberg, Minnesota, Puerto Rico and at University College, London. I am grateful to Verena Mayer, Eva Picardi, Peter Clark, Michael Dummett, Bill Hart, Andreas Kemmerling, Brian McGuinness, Guillermo E. Rosado Haddock, Joachim Schulte, Leslie Stevenson and especially to Christian Thiel and Crispin Wright for helpful comments.