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-Thesis in 2006. In my book "Protogeometrie" (Amiras 2014) the actual version of my efforts can be found. A little book concerning the main aspects and presenting them in a more popular scientific manner is already in planning.

     This Website is designed to serve the needs emerging from thefollowing facts:

  1. The historical development of the efforts since Dingler is completely divergent. It is not only that the pupils of Lorenzen follow different approaches. There is also an ignorance of relevant contributions to the subject coming from others, especially critical ones. This can be said about my contributions and those of Bender/Schreiber (Bender/Schreiber 1978, 1984). On this issue I reported 1998 in my doctoral thesis (in the Introduction).

  1. The contributions  to Protogeometry are widespread in journals and for those interested in the subject not easily accessible. Moreover, they follow different approaches and therefore complicate the understanding and access to relevant information. The access for specific needs (systematical, historical or didactical) becomes ineffective.

  1. My own effort is now so extensive that interested addressees (Mathematicians, Philosophers, Teachers) need some orientation. This Website is designed as a knot helping to get first information rapidly and to inform about recent developments.
Dingler and Lorenzen

Recent developments

Dingler and Lorenzen