The Early Hilbert’s Ontology of Mathematics

Hilbert’s views on the ontology of mathematics changed significantly between 1891 and 1904. Although his contributions to the foundations of mathematics in the years 1899-1904 paved the way for his later program of formalism, in the ontology of mathematics he was then still far from methodological nominalism associated with his mature formalism. Paradoxically, Hilbert’s original position in the ontology of mathematics (from 1891) was that of conceptualism combinedwith constructivism. These two views were the philosophical basis for Brouwer’s intuitionist attacks on Hilbert’s account of the foundations of mathematics in the 1920s