Abstract
English translation of Moritz Pasch,“Die Begriffswelt des Mathematikers in der Vorhalle der Geometrie,” Annalen der Philosophie mit besonderer Rücksicht auf die Probleme der Als-Ob-Betrachtung 3 (1922), pp. 155–187. This prelude to geometry, “does not pretend to be an axiomatic presentation of the subject.” Instead, Pasch offers a window into the mind of a mathematician struggling to identify the most fundamental principles governing bodily shapes . He guides us through a series of thought experiments involving the manipulation of physical objects.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
This sort of surface is not to be confused with the exterior “surface” of a block .
- 2.
[Form a segment with two endpoints \(a,c\) and just one interior point b. Place a fourth point c ′ adjacent to b. Every decomposition of this line into natural parts yields two individual points and a segment consisting of two points. This is the “one way” of decomposing it naturally – though there are three such decompositions: \(ab+c+c',\;cb+a+c',\;c'b+a+c\).]
- 3.
As in no. 16, this sort of surface is not to be confused with the exterior “surface” of a block .
References
Pasch, Moritz. 1921. Implicit definition and the proper grounding of mathematics. Annalen der Philosophie 2:145–162.
Pasch, Moritz. 1922. Rigid bodies in geometry. Annalen der Philosophie 3:188–199.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Pollard, S. (2010). Prelude to Geometry: The Essential Ideas. In: Pollard, S. (eds) Essays on the Foundations of Mathematics by Moritz Pasch. The Western Ontario Series in Philosophy of Science, vol 83. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9416-2_7
Download citation
DOI: https://doi.org/10.1007/978-90-481-9416-2_7
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-9415-5
Online ISBN: 978-90-481-9416-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)