INTO THE OTHERS' MIND. REMARKS ON THE PHILOSOPHY OF GEOMETRY FROM KANT ONWARDS

The post-Kantian debate on the philosophy of geometry prevalently revolved around the question whether axioms are synthetic or analytic. In my view, this suggests that even though Kant's philosophy often appeared as a critical target, it nonetheless provided a general frame of discussion. In this paper, I aim to expand on this and to show that along with this frame, Kant's agonists inherited the structure of his transcendental argument for the foundation of spatial cognition. After a short introduction, in the second section, I will thus reconstruct Kant's transcendental claim, by highlighting that the supposition of the existence of extra-terrestrial minds is pivotal to ground the 'infra-subjective' character of the intuition of space. In this respect, I will also show that this hypothesis allows us, at least to a certain degree, to lower the importance of the unicity of intuition and thus the apodicticity of Euclidean geometry. In the third section, I will deal with von Helmholtz's revision of Kantianism and explain that the endorsement of empiricism is nevertheless coupled with an example whose structure is undoubtedly Kantian. In the fourth section, I will dwell upon Poincare's reflection on similar examples and present the idea that conventionalism is in resonance with Kant's infra-subjectivity. The final section contains concluding remarks.