On the depth of Gödel's incompleteness theorem

英文摘要：

In this paper, we use Gödel's incompleteness theorem as a case study for investigating mathematical depth. We take for granted the widespread judgment by mathematical logicians that Gödel's incompleteness theorem is deep, and focus on the philosophical question of what its depth consists in. We focus on the methodological study of the depth of Gödel's incompleteness theorem, and propose three criteria to account for its depth: influence, fruitfulness, and unity. Finally, we give some explanations for our account of the depth of Gödel's incompleteness theorem.