Sixteenth-century Philosophy of Mathematics in Historical and Philosophical Perspective

该研究项目旨在揭示16世纪数学哲学的历史和哲学意义。迄今为止，这个问题一直是从科学史，特别是科学革命史的角度来看待的。这种方法从根本上是有偏见的：它忽视了这样一个事实，即对数学学科性质的思考构成了一个独特的哲学传统，始于希腊古代。为了更多地关注这一传统中的传统拓朴，我们研究了M.A.齐马拉和A.皮科洛米尼的相关文本，以及他们从中得出问题的古代、阿拉伯和中世纪来源。我们还试图将数学哲学与文艺复兴时期的其他科学理论进行比较，例如法律-医学辩论或弗朗西斯科·彼得拉卡的科学批判。

The research project was aimed at shedding light on the historical and philosophical significance of the philosophy of mathematics during the 16th century. The subject has hitherto been treated from the viewpoint of the history of science, especially of the history of the Scientific Revolution. This approach is fundamentally biased: it neglects the fact that reflections on the nature of the mathematical disciplines constituted a distinct philosophical tradition beginning in Greek Antiquity. In paying more attention to traditional topoi in this tradition, we have studied relevant texts by M. A. Zimara and A. Piccolomini, as well as the Ancient, Arabic and Medieval sources from which they derived their problems. We have also attempted comparisons between the philosophy of mathematics and other theories of science during the Renaissance, such as the legal-medical debates or the critique of science by Francesco Petrarca.