Copyright © Lucas Amiras 2020
Lorenzen and his pupil Rüdiger Inhetveen on the one side and Peter Janich on the other try to pursue the program of a "operative foundation of geometry" following different approaches. Janich´s efforts are directed towards an operational founded "homogeneity geometry" , whereas Lorenzen and Inhetveen make far reaching proposals for a reconstruction of Euclidean geometry as a theory of forms. Lorenzen calls the fundamental part of this theory, which has to establish the primitive geometrical notions, "Protogeometry". I have adopted his denomination for obvious reasons.
Critical discussions and analyses of all efforts since Dingler can be found in my
Ph.D. Thesis (Amiras 1998). As a result of my investigations there are numerous and
serious deficiencies in the terminology and conception of all approaches. The hole
program of protogeometry appeared to me therefore as demanding a thorough revision.
This revision accompanied by extensive historical investigations and a didactical
part dealing with an introduction of elementary geometric notions at learning geometry
is carried out in my Habilitation-
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