6533b86ffe1ef96bd12cd49b
RESEARCH PRODUCT
MATHEMATICS AS A QUASI-EMPIRICAL SCIENCE
Gianluigi Oliverisubject
Set (abstract data type)Philosophy of mathematicsPhilosophy of scienceMultidisciplinaryCorrectnessHistory and Philosophy of ScienceSimple (abstract algebra)Universal setSet theoryNaive set theoryquasi-empiricism and mathematics Lakatos mathematical research programmes Cantor-Zermelo set theory philosophy of mathematics mathematical knowledgeMathematicsEpistemologydescription
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).
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2006-03-01 |