Synthese 193 (3):937-969 (2016)

The paper traces the development and the role of syntactic reduction in Edmund Husserl’s early writings on mathematics and logic, especially on arithmetic. The notion has its origin in Hermann Hankel’s principle of permanence that Husserl set out to clarify. In Husserl’s early texts the emphasis of the reductions was meant to guarantee the consistency of the extended algorithm. Around the turn of the century Husserl uses the same idea in his conception of definiteness of what he calls “mathematical manifolds.” The paper argues that the notion anticipates the notion of reduction in term rewrite theory in computer science. The role of the reduction for Husserl is, however, primarily epistemological: its purpose is to impart clarity to formal mathematics
Keywords Husserl  Hermann Hankel  Principle of permanence   Equational computation  Term rewriting  Definite manifolds
Categories (categorize this paper)
DOI 10.1007/s11229-015-0779-0
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 70,091
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Formalism.Michael Detlefsen - 2005 - In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press. pp. 236--317.

View all 10 references / Add more references

Citations of this work BETA

Maddy On The Multiverse.Claudio Ternullo - 2019 - In Deniz Sarikaya, Deborah Kant & Stefania Centrone (eds.), Reflections on the Foundations of Mathematics. Berlin: Springer Verlag. pp. 43-78.
Husserl on Completeness, Definitely.Mirja Hartimo - 2018 - Synthese 195 (4):1509-1527.

Add more citations

Similar books and articles

Mathematical Roots of Phenomenology: Husserl and the Concept of Number.Mirja Hartimo - 2006 - History and Philosophy of Logic 27 (4):319-337.
Husserl’s Phenomenology.Dan Zahavi - 2002 - Stanford University Press.


Added to PP index

Total views
50 ( #226,621 of 2,506,348 )

Recent downloads (6 months)
2 ( #277,420 of 2,506,348 )

How can I increase my downloads?


My notes