On a Distinction Between Pure and Applied Mathematics

The thesis of the paper is that is essential for mathematics, when it is pure mathematics, to be free from any kind of ontological commitments, and more, that mathematics is a science that should be possible without ontological commitments. Applied mathematics, on the contrary, is descriptive, and therefore includes ontology.  The final thesis of the article is that set theory, as applied mathematics, cannot provide a foundation for pure mathematics.