Foundations of Science

, Volume 11, Issue 1–2, pp 41–79 | Cite as

Mathematics as a Quasi-Empirical Science



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, ..., T n in which Ti+1, for 1 ≤ i < n, supersedes T i . 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).


quasi-empiricism and mathematics lakatos mathematical research programme Cantor–Zermelo set theory philosophy of mathematics mathematical knowledge 


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© Springer 2006

Authors and Affiliations

  1. 1.Dipartimento di Filosofia e Critica dei SaperiUniversità di PalermoPalermoItalia

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