主讲人介绍

Johan van Benthem，清华大学哲学系金岳霖讲席教授，阿姆斯特丹大学逻辑、语言与计算研究所（ILLC）教授，美国斯坦福大学哲学系教授，欧洲科学院院士，荷兰皇家艺术与科学院院士

讲座摘要

Reasoning patterns in natural language combine logical and arithmetical features, transcending divides between qualitative and quantitative. This natural practice blends into inference patterns in ‘grassroots mathematics’ such as pigeon-hole principles. And extrapolating from these basic abilities that everyone has, experts can of course ascend to the pinnacles of abstract mathematics.

In the historical foundations of science and philosophy, one has often assumed a hierarchy: either ‘logic first, arithmetic later”, or the other way around. However, our topic is the cooperation of logic and counting on a par, studied with small formal systems and gradually extending these. We will see what can be expressed, and where computational complexity barriers arise. After this, we return to the basic reasoning practices in natural language, confronting our formal systems with linguistic quantifier vocabulary, monotonicity reasoning, and so-called procedural semantics. We conclude with some pointers to cognitive psychology on the topic of acquisition of mathematical reasoning.

海报｜周润杰

排版 | 郭悠然

审核 | 王小芳