Foundations of Science 11 (1-2):41-79 (2004)

The present paper aims at showing that there are times when set theoretical knowledge increases in a non-cumulative way. In other words, what we call ‘set theory’ is not one theory which grows by simple addition of a theorem after the other, but a finite sequence of theories T1, ..., Tn in which Ti+1, for 1 ≤ i < n, supersedes Ti. This thesis has a great philosophical significance because it implies that there is a sense in which mathematical theories, like the theories belonging to the empirical sciences, are fallible and that, consequently, mathematical knowledge has a quasi-empirical nature. The way I have chosen to provide evidence in favour of the correctness of the main thesis of this article consists in arguing that Cantor–Zermelo set theory is a Lakatosian Mathematical Research Programme (MRP).
Keywords quasi-empiricism and mathematics  lakatos  mathematical research programme  Cantor–Zermelo set theory  philosophy of mathematics  mathematical knowledge
Categories (categorize this paper)
Reprint years 2006
DOI 10.1007/s10699-004-5912-3
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: 51,304
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

Naturalism in Mathematics.Penelope Maddy - 1997 - Oxford University Press.
Mathematical Thought From Ancient to Modern Times.M. Kline - 1978 - British Journal for the Philosophy of Science 29 (1):68-87.
Philosophical Papers.Imre Lakatos - 1978 - Cambridge University Press.

View all 16 references / Add more references

Citations of this work BETA

O filozofii matematyki Imre Lakatosa.Krzysztof Wójtowicz - 2007 - Roczniki Filozoficzne 55 (1):229-247.

Add more citations

Similar books and articles

Apriority and Applied Mathematics.Robert A. Holland - 1992 - Synthese 92 (3):349 - 370.
Mathematics, Science and Ontology.Thomas Tymoczko - 1991 - Synthese 88 (2):201 - 228.
Mathematical Nominalism and Measurement.Davide Rizza - 2010 - Philosophia Mathematica 18 (1):53-73.
Eine Konstruktivistische Grundlegung der Objekte Empirisch-Wissenschaftlicher Theorien.Edmund Nierlich - 1990 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 21 (1):75 - 104.
Quasi-Truth in Quasi-Set Theory.Otávio Bueno - 2000 - Synthese 125 (1-2):33-53.
Independence and Justification in Mathematics.Krzysztof Wójtowicz - 2006 - Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):349-373.
Criticism and Growth of Mathematical Knowledge.Gianluigi Oliveri - 1997 - Philosophia Mathematica 5 (3):228-249.


Added to PP index

Total views
67 ( #137,836 of 2,330,100 )

Recent downloads (6 months)
4 ( #193,234 of 2,330,100 )

How can I increase my downloads?


My notes