Skip to main content

Francesca Biagioli: Space, Number, and Geometry from Helmholtz to Cassirer

Springer, Dordrecht, 2016, 239 pp, $109.99 (Hardcover), ISBN: 978-3-319-31777-9

This is a preview of subscription content, access via your institution.


  1. Even as those mentioned continue to break new ground on themes including the formulation and defense of ‘scientific philosophy’ and the Unity of Science program, they are joined by a group of researchers who bring formal expertise and historical sensibility to an expanded set of questions. Marco Giovanelli, Flavia Padovani, Michela Massimi, Katherine Brading, Elise Crull, David Hyder, Scott Edgar, Joshua Eisenthal, Matthias Neuber, and their allies focus on the history and philosophy of physics, physiology, or mathematics. Erich Reck, Georg Schiemer, Dirk Schlimm, Jeremy Heis, Audrey Yap, and Paula Cantù delve into structuralism and formalism in nineteenth and twentieth century mathematics. Martin Kusch, Pierre Keller, Samantha Matherne, Katherina Kinzel, Paul Roth, and Frederick Beiser are among the mainstays of a circle studying the philosophy of history itself during this period.

  2. A translation of Dedekind (1872) can be found in Dedekind (1963).

  3. There is no requirement of comprehensiveness in a project such as this one. I should mention that Flavia Padovani’s work on Hans Reichenbach on measurement and time would be an excellent complement to much of what is achieved in Space, Time, and Geometry, as would Elise Crull’s and Erik Banks’s work on Grete Hermann.


  • Biagioli, F. (2014). What does it mean that “Space can be transcendental without the axioms being so”? Journal for General Philosophy of Science, 45(1), 1–21.

    Article  Google Scholar 

  • Biagioli, F. (2018). Articulating space in terms of transformation groups: Helmholtz and Cassirer. Journal for the History of Analytical Philosophy, 6(3), 115–131.

    Article  Google Scholar 

  • Dedekind, R. (1872). Stetigkeit und irrationale Zahlen. Braunschweig: Friedrich Vieweg und Sohn.

    Google Scholar 

  • Dedekind, R. (1963). Continuity and irrational numbers. In W. W. Beman (Trans.), Essays on the theory of numbers (pp. 1–30). New York: Dover.

  • Halsted, G. (1899). Report on progress in non-Euclidean geometry. The American Mathematical Monthly, 6(10), 219–233.

    Article  Google Scholar 

  • Neuber, M. (2018). Perception and coincidence in Helmholtz’s theory of measurement. Journal for the History of Analytical Philosophy, 6(3), 79–94.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Lydia Patton.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Patton, L. Francesca Biagioli: Space, Number, and Geometry from Helmholtz to Cassirer. J Gen Philos Sci 50, 311–315 (2019).

Download citation

  • Published:

  • Issue Date:

  • DOI: