David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Foundations of Science 11 (1-2):41-79 (2006)
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)|
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
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Robert A. Holland (1992). Apriority and Applied Mathematics. Synthese 92 (3):349 - 370.
Thomas Tymoczko (1991). Mathematics, Science and Ontology. Synthese 88 (2):201 - 228.
Davide Rizza (2010). Mathematical Nominalism and Measurement. Philosophia Mathematica 18 (1):53-73.
Edmund Nierlich (1990). Eine Konstruktivistische Grundlegung der Objekte Empirisch-Wissenschaftlicher Theorien. Journal for General Philosophy of Science 21 (1):75 - 104.
Otávio Bueno (2000). Quasi-Truth in Quasi-Set Theory. Synthese 125 (1-2):33-53.
Susan Vineberg (1996). Confirmation and the Indispensability of Mathematics to Science. Philosophy of Science 63 (3):263.
Stojan Obradović & Slobodan Ninković (2009). The Heuristic Function of Mathematics in Physics and Astronomy. Foundations of Science 14 (4):351-360.
Krzysztof Wójtowicz (2006). Independence and Justification in Mathematics. Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):349-373.
Nicolas D. Goodman (1991). Modernizing the Philosophy of Mathematics. Synthese 88 (2):119 - 126.
Gianluigi Oliveri (1997). Criticism and Growth of Mathematical Knowledge. Philosophia Mathematica 5 (3):228-249.
Added to index2009-01-28
Total downloads21 ( #90,899 of 1,413,453 )
Recent downloads (6 months)1 ( #154,636 of 1,413,453 )
How can I increase my downloads?