Why and with what justification is Kant a Euclidean? A reconstruction of Kant's conception of mathematics from the perspective of the epistemic functions of diagrammatic visualizations.

• Applicant: Professorin Dr. Sybille Krämer
• Subject Area: Theoretical Philosophy ; Theatre and Media Studies ; History of Science
• Term: from 2014 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 257315058

Kant's intuition-related understanding of mathematics is criticized widely, even nowadays. The project undertakes a 'diagrammatological reconstruction' of Kant's philosophy of mathematics. It will be shown that Kant's views, that mathematical knowledge is "intuitive" and not discursive, that it is synthetic and not (as expected) analytic a priori, can receive a fruitful meaning when these views are reconstructed as a reflection of the productive role of visualisation in scientific thinking. In order to achieve this, debates on two topics will be connected: the epistemically productive - and not just illustrative - function of diagrams, and the 'praxeological' approaches in philosophy of mathematics, which do not any longer aim at an absolute foundation of mathematical certainty, but a 'modest' description and explanation of practices across the whole spectrum of mathematical activities. The steps of the reconstruction of Kant involve (I) his discovery of 'Gegend' (= sense of direction) as the increment of space, (II) his exploration of incongruent counterparts, (III) the role of schematism and imagination in thinking. As a result, the Kantian concept of intuition should be made explicit as a course of action: By means of controlled graphical method, using the axes of subjective corporeality (right / left, up / down), this concept of intuition makes an intersubjective perception / experience possible. Kant's 'Euclidean nature' will thereby not only be plausible; but its 'epistemology of the line' can also give creative insight into the role of diagrams in recognition and inspire current debates about visualization in mathematics.

• DFG Programme: Research Grants
• Participating Institution: Bogazici University ; Philosophy Department ; Kant Group in Turkey; Max-Planck-Institut für Wissenschaftsgeschichte (MPIWG)