ヴィトゲンシュタイン数学哲学の意義と可能な応用に関する再検討

基于对工作数学家的采访结果，我开始进一步调查数学实践的多个方面，这些方面是最近数学哲学家特别关注的，比如数学证明的可视化，数学在自然科学中的作用。我发现，与20世纪40年代的其他哲学家只关注数学的基础不同，维特根斯坦留下了许多关于数学实践的评论，比如在数学证明中使用图表。我正在起草一篇论文，考虑维特根斯坦关于图表本身是否可以在没有形式语言或自然语言的帮助下成为证明的观点。此外，我还对数学知识与自然科学知识之间的认识论进行了广泛的考察，特别是比较了拉卡托斯、维特根斯坦以及菲利普·基彻等当代哲学家的思想。我的论文提案被伦敦经济学院支持的大师班“Lakatos’s未完成的工作”接受。

Based on the results from interviews with working mathematicians, I started to investigate further on multiple aspects of mathematical practice that recent philosophers of mathematics are paying particular attention, such as visualization of mathematical proof, the role mathematics plays in natural science. I found that unlike other philosophers from 1940s, who merely focused on the foundation of mathematics, Wittgenstein left multiple remarks regarding practices of mathematics, such as the use of diagram in mathematical proof. I am drafting a paper considering Wittgenstein's view on whether diagram can be a proof itself without the help of formal or natural language. Moreover, I also did extensive examination on the epistemology between mathematical knowledge and natural science knowledge, in particular, I focus on comparing the thoughts of Lakatos, Wittgenstein and other contemporary philosophers, such as Philip Kitcher. My paper proposal was accepted by the masterclass "Lakatos's Undone Work" supported by London School of Economics.