Implizite Definitionen—Eine Verwechselungsgeschichte

Abstract

Summary The concept of implicit definition has played a central role in the controversies about the foundations of geometry. The history of this concept, however, exhibits several important confusions. The term has been used in at least three different senses—Gergonne's position, Hilbert's position of the so-called definitions by axioms (postulates), and that of Pasch and Dubislav in the sense of Russell's contextual definition. Frege's contribution to the explication of Hilbert's view has occasioned an adequate appraisal in recent years. A summary account is given. The main purpose of the paper is to present some details about the historical development of the transfer of Gergonne's term ‘implicit definition’ to the Hilbert position, a transfer which goes back to the Peano School and was disseminated by Enriques.