What Role Plays Intuition in Mathematics and Science? On the Borders Between Several Conceptions of What It Means to Intuit

  • Johan Arnt MyrstadEmail author
Part of the Springer Geography book series (SPRINGERGEOGR)


In discussions about Euclidean and non-Euclidean geometries, to take one central example, the notion of intuition plays a decisive role. According to Immanuel Kant, no geometry is possible without being based in a priori or pure intuition of space. The arrival of non-Euclidean geometries has generally been understood to falsify this claim, in particular according to Henri Poincaré’s introduction of conventionalism in the philosophy of mathematics. However, even on the surface, qualifications are introduced into the discussion, such as “the intuition of representative space” and “rational intuition”, indicating that the term “intuition” covers up serious ambiguities. Furthermore, the models of so-called non-Euclidean geometries, allegedly based in conventionally chosen sets of formal axioms, are directly or indirectly the very same objects claimed to be given to intuition in Euclidean space. The paper explores the nuances in the use of the term “intuition” in Kant and Poincaré, thereby discovering deep paralogisms in the discussion about geometry and hence resolving some of the problems pestering modern epistemology, by focusing on the border zones of conceptions covered by the same or similar terms.


  1. de Abreu R, Guerra V (2015) Speakable and unspeakable in special relativity: time readings and clock rhythms. Elect J Theor Phys 12:183–204Google Scholar
  2. Andersen F (2017) Experience and theory: a defense of the kantian a priori and Kepler’s philosophy of science in light of modern space-time physics, PhD Thesis 2017: 70, Norwegian University of Life Sciences, Faculty of Social Sciences, School of Economics and BusinessGoogle Scholar
  3. Cellucci (2013) Rethinking logic, logic in relation to mathematics, evolution and method. SpringerGoogle Scholar
  4. Guerra V, de Abreu R (2008) On the consistency between the assumption of a special system of reference and special relativity. Found Phys 36:1820–1845CrossRefGoogle Scholar
  5. Stump DJ (2015) Conceptual change and the philosophy of science. Alternative interpretations of the a priori. RoutledgeGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Nord UniversityBodøNorway

Personalised recommendations