Husserl and hilbert on completeness and husserl's term rewrite-based theory of multiplicity

Mitsuhiro Okada

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

Hilbert and Husserl presented axiomatic arithmetic theories in different ways and proposed two different notions of "completeness" for arithmetic, at the turning of the 20th Century (1900- 1901). The former led to the completion axiom, the latter completion of rewriting. We look into the latter in comparison with the former. The key notion to understand the latter is the notion of definite multiplicity or manifold (Mannigfaltigkeit). We show that his notion of multiplicity is understood by means of term rewrite theory in a very coherent manner, and that his notion of "definite" multiplicity is understood as the relational web (or tissue) structure, the core part of which is a "convergent" term rewrite proof structure. We examine how Husserl introduced his term rewrite theory in 1901 in the context of a controversy with Hilbert on the notion of completeness, and in the context of solving the justification problem of the use of imaginaries in mathematics, which was an important issue in the foundations of mathematics in the period.

Original languageEnglish
Title of host publication24th International Conference on Rewriting Techniques and Applications, RTA 2013
EditorsFemke van Raamsdonk
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages4-19
Number of pages16
ISBN (Electronic)9783939897538
ISBN (Print)9783939897538, 9783939897538
DOIs
Publication statusPublished - 2013
Event24th International Conference on Rewriting Techniques and Applications, RTA 2013 - Eindhoven, Netherlands
Duration: 2013 Jun 242013 Jun 26

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume21
ISSN (Print)1868-8969

Other

Other24th International Conference on Rewriting Techniques and Applications, RTA 2013
CountryNetherlands
CityEindhoven
Period13/6/2413/6/26

Keywords

  • Hilbert
  • History of term rewrite theory
  • Husserl
  • Knuth- bendix completion
  • Proof theory

ASJC Scopus subject areas

  • Software

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