Physical and Mathematical Geometry

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


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.


Physical Point Mathematical Point Straight Segment Analytic Geometry Stage Number 
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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Dept. Philosophy & ReligionTruman State UniversityKirksvilleUSA

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