Both Philosophy and Mathematics study abstract concepts and structures, and they share an intertwined early history. On the one hand, a lot of mathematical tools are used in the frontier philosophical research on the concepts such as infinity, necessity, possibility, existence, truth, meaning, knowledge, belief, causality, and so on, which makes the philosophical discussions more precise. On the other hand, in facing the past three crises in mathematics in history, philosophical ideas played a key role in the development of mathematics. In particular, the early 20th century witnessed the development of mathematical logic which deepened our understanding of mathematics and its foundation. Philosophical Mathematics Week is aimed at presenting the connections between modern (technical) philosophy and mathematics in a comprehensive way, showing the role of mathematical tools played in the current philosophical research. At the same time, we also hope to be able to demonstrate the lively connections between philosophy and other related disciplines such as theoretical computers, artificial intelligence, linguistics, and so on.