Selected contexts in the philosophy of mathematics
Marian Ambrozy
DOI: 10.18355/XL.2024.17.03.04
Abstract
The present paper attempts to answer the question of whether it is reasonable to distinguish mathematical objects ontologically. It aims to demonstrate that mathematical objects can be divided into mathematical objects existing on their own and mathematical objects constructed by human beings. The present research also seeks to answer the questions raised by the philosopher Maco in his communication in response to my previous research. The paper presents the view that the ontological status of Lie groups and Lie algebras differs according to whether they are complex Lie groups and Lie algebras, respectively. Other questions were addressed on the status of Hilbert spaces, whether the set of natural numbers and the set of hyperreal numbers are independent. The present attempt to answer these questions does not, in my opinion, depart from the Wittgensteinian approach to mathematics, which is what I am trying to prove.
Key words: ontological status, mathematical object, Wittgenstein's philosophy of mathematics, Lie groups
Pages: 39-49
Full Text