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The first theorist, who explicitly makes the practical procedure of producing flat surfaces ("primal production", german: "Urzeugung", "3-plates-procedure") a basis of a terminological determination of the term "plane" is Hugo Dingler (1881-1954). He has the idea to terminologically use the terms of a description of  the procedure (touch relations, fitting) to give a definition of "plane surface" as a specifically formed surface (1911). For five decades Dingler´s effort directed at the constitution of a pre-theory of geometry in order to derive from that the axioms of geometry remains without success. Furthermore, the deficiencies of his contributions are also tremendous.


Paul Lorenzen (1915-1994) takes over the Dingler´s idea and gives it a precise logical form as homogeneity principle. He proposes a construction of geometric theory on this basis, a mathematical sound task, but of very questionable relevance to the foundational problem undertaken by Dingler himself. After some repairing efforts Lorenzen later abandons this approach.

Dingler and Lorenzen

Recent developments From Lobatchevsky to Poincaré Recent developments From Lobatchevsky to Poincaré