Studies on the role of imagination and the mechanism of mathematical knowledge in Leibniz's philosophy of mathematics

本研究旨在阐明数学知识的机制和本质以及想象力在莱布尼茨数学哲学中的作用。主要是通过对17世纪70年代的手稿的研究，发现莱布尼茨符号观的框架是什么。此外，在他的普遍数学思想中，莱布尼茨考虑到了符号的各个方面，例如清晰度和排列。因此，莱布尼茨在数学研究中利用数学概念和符号的模糊性，意在利用符号的各种功能。这种解释将为莱布尼茨的数学哲学提供新的视角。

This study aims to explicate the mechanism and nature of mathematical knowledge and the role of imagination in Leibniz's philosophy of mathematics. Mainly based on the research on manuscripts written in1670s, it turned out that what the framework of Leibniz's view of symbols consists in. Moreover, in his idea of mathesis universalis, Leibniz takes into account various aspects of symbols, for example sharpness and arrangement. So, it could be concluded that in mathematical study, Leibniz utilizes mathematical concept and symbol ambiguity intended to utilize various function of symbol. This interpretation would provide new perspective of Leibniz's philosophy of mathematics.