Year: 2026
Type: article
Abstract: 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.
Author: Davide Emilio Quadrellaro
Language: English
Subfield: Theoretical Computer Science
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W7160775246