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Physical and Mathematical Geometry

  • Stephen Pollard
Chapter
Part of the The Western Ontario Series in Philosophy of Science book series (WONS, volume 83)

Abstract

English translation of Moritz Pasch,“Physikalische und mathematische Geometrie,” Annalen der Philosophie mit besonderer Rücksicht auf die Probleme der Als-Ob-Betrachtung 3 (1922), pp. 362–374. Pasch discusses “the fundamental differences that separate physical from mathematical geometry.” In the former, points are understood to be physical objects. In the latter, the term “point” is an undefined expression in a system of axioms. Physical points can move. Mathematical points cannot, although, in mathematical geometry, “intuitive” motions have “purely intellectual” counterparts: transformations. Because our instruments are not infinitely precise, one physical point can be represented equally well by distinct coordinates. In mathematical geometry, distinct coordinates always represent distinct points.

Keywords

Physical Point Mathematical Point Straight Segment Analytic Geometry Stage Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Pasch, Moritz. 1882. Lectures on modern geometry. Leipzig: B.G. Teubner.Google Scholar
  2. 2.
    Pasch, Moritz. 1904. On the introduction of imaginary numbers. Archiv der Mathematik und Physik 7:102–108.Google Scholar
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    Pasch, Moritz. 1909. Foundations of analysis. Leipzig: B.G. Teubner.Google Scholar
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    Pasch, Moritz. 1912. Lectures on modern geometry, 2nd edn. Leipzig: B.G. Teubner.Google Scholar
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    Pasch, Moritz. 1914. Variable and function. Leipzig: B.G. Teubner.Google Scholar
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    Pasch, Moritz. 1921. Implicit definition and the proper grounding of mathematics. Annalen der Philosophie 2:145–162.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Dept. Philosophy & ReligionTruman State UniversityKirksvilleUSA

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