| Abstract [eng] |
This paper provides an analysis of the traditional problems of Mathematical Platonism and Mathematical Conventionalism. In light of these problems, the superiority of E. N. Zalta’s and J. Warren’s theories against their traditional counterparts is considered. While examining the additional problems Zalta’s and Warren’s theories face, this paper analyzes the required fundamental assumptions for the successful theories of Mathematical Platonism and Mathematical Conventionalism. It is also stated that Warren’s theory is superior to Zalta’s, because of how it answers the traditional problems of Mathematical Conventionalism. In addition, Warren’s theory proves that Conventionalism can also satisfy platonistic views on the existence of abstract mathematical entities and the necessity of mathematical truths. Furthermore, it is demonstrated that Zalta’s theory compromises Mathematical Platonism by showing that the answer to the epistemological Benacerraf-Field problem requires to reject the traditional concept of mind-independence of abstract entities. |
