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

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).
Keywords quasi-empiricism and mathematics  lakatos  mathematical research programme  Cantor–Zermelo set theory  philosophy of mathematics  mathematical knowledge
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Reprint years 2006
DOI 10.1007/s10699-004-5912-3
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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.

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

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