A ficitionalist approach to the ontology of mathematics

Gustavo E. Romero.

Serie: Trabajos publicados del IAR ; no. 1904

Resumen: Mathematics is defined as the study and development of conceptual interpreted formal systems that are closed by deduction. These systems are not merely syntactic in the manner of logistic systems. They are interpreted, but their reference class is constituted by conceptual artifacts. Mathematical constructs are human-made creations that exist solely within the context of a specific formal system. Consequently, mathematics is devoid of any ontological import. The referents of mathematics cannot exist independently of the human mind. The theory is consistent with any general materialist worldview.