JOURNAL ARTICLE

Is Iteration an Object of Intuition?

  • Published In: Philosophia Mathematica, 2025, v. 33, n. 1. P. 69 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Bentzen, Bruno 3 of 3

Abstract

The article critiques Mark van Atten's interpretation of L.E.J. Brouwer's philosophy, specifically his claim that iteration is an object of intuition. The author argues that van Atten's arguments are unconvincing, highlighting tensions with Brouwer's views on second-order mathematics and the differing understandings of succession in Brouwer's and Husserl's philosophies. The critique emphasizes that while Brouwer acknowledges the role of intuition in iteration, he does not support the notion that iteration itself can be intuitively grasped as an object. The author concludes that van Atten's phenomenological approach fails to accurately reconstruct Brouwer's ideas due to fundamental differences in their conceptual frameworks. [Extracted from the article]

Additional Information

  • Source:Philosophia Mathematica. 2025/02, Vol. 33, Issue 1, p69
  • Document Type:Article
  • Subject Area:Literature and Writing
  • Publication Date:2025
  • ISSN:0031-8019
  • DOI:10.1093/philmat/nkae019
  • Accession Number:185320531
  • Copyright Statement:Copyright of Philosophia Mathematica is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Looking to go deeper into this topic? Look for more articles on EBSCOhost.