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.

康德对数学的直觉相关理解受到了广泛的批评，即使在今天。 该项目承担了康德数学哲学的“数学重建”。它将表明，康德的意见，即数学知识是“直观的”，而不是discursive，它是综合的，而不是（如预期）分析的先验，可以收到一个富有成效的意义时，这些意见是重建作为一个反映生产作用的可视化在科学思维。为了实现这一点，关于两个主题的辩论将被连接起来：图的认识生产性-而不仅仅是说明性-功能，以及数学哲学中的“行为学”方法，这些方法不再旨在建立数学确定性的绝对基础，而是对整个数学活动范围内的实践进行“适度”的描述和解释。康德的重建步骤包括：（一）发现作为空间增量的“格艮德”（=方向感），（二）探索不一致的对应物，（三）图式和想象在思维中的作用。因此，康德的直觉概念应该被明确为一种行动过程：通过受控的图形方法，使用主观身体现实的轴（右/左，上/下），这种直觉概念使主体间的感知/体验成为可能。因此，康德的“欧几里得性质”不仅是合理的;而且其“线的认识论”也可以创造性地洞察图形在识别中的作用，并激发当前关于数学可视化的辩论。

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.