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 T(1),..., T(n) in which T(i+1) supersedes T(i). This thesis has 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).
|Data di pubblicazione:||2006|
|Titolo:||MATHEMATICS AS A QUASI-EMPIRICAL SCIENCE|
|Autori interni:||OLIVERI, Gianluigi|
|Tipologia:||Articolo su rivista|
|Citazione:||OLIVERI G (2006). MATHEMATICS AS A QUASI-EMPIRICAL SCIENCE. FOUNDATIONS OF SCIENCE, 11, 41-79.|
|Digital Object Identifier (DOI):||10.1007/s10699-004-5912-3|
|Appare nelle tipologie:||01 - Articolo su rivista|