Scholarlink

<p>We provide an interpretation of Husserl’s 1901 <i>Doppelvortrag</i> in Göttingen from the viewpoint of the modernist transformation of mathematics. We emphasise the dialectical aspects of the <i>Doppelvortrag</i>, and especially the underlying conflict between <i>abstraction</i> and <i>intuition</i>, which often resurfaces in Husserl’s philosophy. We focus on three key aspects: (1) the relation between Husserl’s idea of pure logic and Hilbert’s axiomatic method; (2) the concept of <i>Definitheit</i> and the early developments of model theory; (3) the nature of imaginary numbers and their justification in arithmetic and algebra. We stress that, in contrast to Hilbert’s Completeness Axiom from his <i>Grundlagen</i>, Husserl viewed the <i>Definitheit</i> as a statement requiring a proof, and he believed that one could be provided in the cases of arithmetic and geometry.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Some remarks on Husserl’s Doppelvortrag

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年5月10日

查看全文
  • Davide Emilio Quadrellaro

摘要

We provide an interpretation of Husserl’s 1901 Doppelvortrag in Göttingen from the viewpoint of the modernist transformation of mathematics. We emphasise the dialectical aspects of the Doppelvortrag, and especially the underlying conflict between abstraction and intuition, which often resurfaces in Husserl’s philosophy. We focus on three key aspects: (1) the relation between Husserl’s idea of pure logic and Hilbert’s axiomatic method; (2) the concept of Definitheit and the early developments of model theory; (3) the nature of imaginary numbers and their justification in arithmetic and algebra. We stress that, in contrast to Hilbert’s Completeness Axiom from his Grundlagen, Husserl viewed the Definitheit as a statement requiring a proof, and he believed that one could be provided in the cases of arithmetic and geometry.