Mathematics as a quasi-empirical science

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

Abstract

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).

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,616

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

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.

Analytics

Added to PP
2009-01-28

Downloads
87 (#178,790)

6 months
7 (#175,814)

Historical graph of downloads
How can I increase my downloads?

References found in this work

Naturalism in mathematics.Penelope Maddy - 1997 - New York: Oxford University Press.
Foundations of Set Theory.Abraham Adolf Fraenkel & Yehoshua Bar-Hillel - 1973 - Atlantic Highlands, NJ, USA: Elsevier.
Mathematical Thought from Ancient to Modern Times.M. Kline - 1978 - British Journal for the Philosophy of Science 29 (1):68-87.
From Frege to Gödel.Jean van Heijenoort - 1968 - Philosophy of Science 35 (1):72-72.
Philosophical papers.Imre Lakatos - 1978 - New York: Cambridge University Press.

View all 22 references / Add more references