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.

即使在今天，康德对数学的直觉性理解仍受到广泛批评。该项目对康德的数学哲学进行了“图解重建”。康德认为数学知识是“直观的”而不是话语的，是综合的而不是（如预期的那样）先验的分析的观点，当这些观点被重构为可视化在科学思维中的生产作用的反映时，将会得到富有成效的意义。为了实现这一目标，关于两个主题的辩论将被联系起来：图表的认识论生产性（而不仅仅是说明性）功能，以及数学哲学中的“行为学”方法，它不再以数学确定性的绝对基础为目标，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。重构康德的步骤包括：(1)他发现了作为空间增量的“方向感”，(2)他对不一致对应物的探索，(3)图式和想象在思维中的作用。因此，康德的直觉概念应该作为一个行动过程被明确地表达出来：通过受控的图形方法，使用主观形体的轴线（右/左，上/下），直觉概念使主体间感知/体验成为可能。因此，康德的“欧几里得性质”不仅是似是而非的；但它的“线的认识论”也可以创造性地洞察图表在识别中的作用，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.