In 1768 Immanuel Kant presented an argument showing the necessity of absolute space, i.e. substantivalism in contrast to relationalism, based on the property of handedness. While there is large consensus about the fallacy of Kant’s argument, a more recent debate exists – mainly stimulated by John Earman – about the status of the Kantian argument in view of modern physics and its fundamentally built-in parity violation, which leads to a preferred handedness. According to Earman the relationalist has no means to (...) distinguish one handedness in the cosmos without reference to an absolute structure of space. After recapitulating the historical background of the Newton/Leibniz debate on the ontological status of space as well as the Kantian argument, this paper offers a systematic consideration of arguments about handedness in modern physics. The goal is to show that “Earman’s challenge” can be rejected. (shrink)

The article attempts to reconsider the relationship between Leibniz’s and Kant’s philosophy of geometry on the one hand and the nineteenth century debate on the foundation of geometry on the other. The author argues that the examples used by Leibniz and Kant to explain the peculiarity of the geometrical way of thinking are actually special cases of what the Jewish-German mathematician Felix Hausdorff called “transformation principle”, the very same principle that thinkers such as Helmholtz or Poincaré applied in a more (...) general form in their celebrated philosophical writings about geometry. The first two parts of the article try to show that Leibniz’s and Kant’s philosophies of geometry, despite their differences, appear to be preoccupied with the common problem of the impossibility to grasp conceptually the intuitive difference between two figures (such as a figure and its scaled, displaced or mirrored copy). In the third part, it is argued that from the perspective of Hausdorff’s philosophical-geometrical reflections, this very same problem seems to find a more radical application in Helmholtz’s or Poincaré’s thought experiments on the impossibility of distinguishing distorted copies of our universe from the original one. I draw the conclusion that in Hausdorff’s philosophical work, which has received scholarly attention only recently, one can find not only an original attempt to frame these classical arguments from a set-theoretical point of view, but also the possibility of considering the history of philosophy of geometry from an uncommon perspective, where especially the significance of Kant’s infamous appeal to “intuition” can be judged by more appropriate standards. (shrink)

Se defiende la tesis de que la teoría kantiana del espacio, en el contexto del idealis-mo trascendental, constituye un marco adecuado para solucionar la paradoja de las contrapartidas incongruentes. Se incluyen dos hipótesis: a) la solución kantiana implica una referencia a la conciencia de la propia corporalidad, para comprender cómo poseemos la capacidad para orientarnos en el espacio; b) no existe contradicción en el uso kantiano de las contrapartidas incongruentes en diferentes estadios de su pensamiento. La solución kantiana de 1768 (...) constituye una versión germinal del desarrollo que culminará en la teoría idealista trascendental acerca del espacio como una forma de nuestra sensibilidad. (shrink)

RESUMEN Se defiende la tesis de que la teoría kantiana del espacio, en el contexto del idealismo trascendental, constituye un marco adecuado para solucionar la paradoja de las contrapartidas incongruentes. Se incluyen dos hipótesis: a) la solución kantiana implica una referencia a la conciencia de la propia corporalidad, para comprender cómo poseemos la capacidad para orientarnos en el espacio; b) no existe contradicción en el uso kantiano de las contrapartidas incongruentes en diferentes estadios de su pensamiento. La solución kantiana de (...) 1768 constituye una versión germinal del desarrollo que culminará en la teoría idealista trascendental acerca del espacio como una forma de nuestra sensibilidad. ABSTRACT The article argues that the Kantian theory of space, in the context of transcendental idealism, constitutes an adequate framework to resolve the paradox of incongruent counterparts. Two hypotheses are considered: a) the Kantian solution implies a reference to the awareness of one's corporeity in order to understand how we have the capacity to orient ourselves in space; b) there is no contradiction in the Kantian use of incongruent counterparts throughout the different stages of his thought. The Kantian solution of 1768 is a germinal version of the development leading up to the transcendental idealist theory of space as a form of our sensibility. (shrink)

Kant uses incongruent counterparts in his work before and after 1781, but not in the first Critique. Given the relevance that incongruent counterparts had for his thought on space, and their persistence in his work during the 1780s, it is plausible to think that he had a reason for leaving them out of both editions of the Critique. Two implausible conjectures for their absence are here considered and rejected. A more plausible alternative is put forth, which explains that textual absence (...) as a result of the synthetic method of presentation intended for the Critique. (shrink)