TY - GEN

T1 - Husserl and hilbert on completeness and husserl's term rewrite-based theory of multiplicity

AU - Okada, Mitsuhiro

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Hilbert

KW - History of term rewrite theory

KW - Husserl

KW - Knuth- bendix completion

KW - Proof theory

UR - http://www.scopus.com/inward/record.url?scp=84889566383&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84889566383&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.RTA.2013.4

DO - 10.4230/LIPIcs.RTA.2013.4

M3 - Conference contribution

AN - SCOPUS:84889566383

SN - 9783939897538

SN - 9783939897538

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 4

EP - 19

BT - 24th International Conference on Rewriting Techniques and Applications, RTA 2013

A2 - van Raamsdonk, Femke

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 24th International Conference on Rewriting Techniques and Applications, RTA 2013

Y2 - 24 June 2013 through 26 June 2013

ER -