caa a22 4500 467901783 CHVBK 20180406152820.0 cr unu---uuuuu 170328e20060301xx s 000 0 eng 10.1007/s10699-004-5912-3 doi (NATIONALLICENCE)springer-10.1007/s10699-004-5912-3 Oliveri Gianluigi Dipartimento di Filosofia e Critica dei Saperi, Università di Palermo, viale delle Scienze, 90128, Palermo, Italia aut Mathematics as a Quasi-Empirical Science [Elektronische Daten] [Gianluigi Oliveri] 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). Springer, 2006 quasi-empiricism and mathematics nationallicence lakatos nationallicence mathematical research programme nationallicence Cantor-Zermelo set theory nationallicence philosophy of mathematics nationallicence mathematical knowledge nationallicence Foundations of Science Kluwer Academic Publishers 11/1-2(2006-03-01), 41-79 1233-1821 11:1-2<41 2006 11 10699 https://doi.org/10.1007/s10699-004-5912-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10699-004-5912-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Oliveri Gianluigi Dipartimento di Filosofia e Critica dei Saperi, Università di Palermo, viale delle Scienze, 90128, Palermo, Italia aut NATIONALLICENCE 773 0- Foundations of Science Kluwer Academic Publishers 11/1-2(2006-03-01), 41-79 1233-1821 11:1-2<41 2006 11 10699 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer