ABSTRACT
Balaguer's project is to develop a philosophical justification for platonism and anti-platonism. Balaguer's defense of platonism's external body of truths through an emphasis on their internal consistency provides a transition to the other form of mathematical absolutism, namely, formalism. Hilary Putnam clarifies this point in a discussion of object and modal descriptions of mathematics. While the Platonist sees no need to justify mathematical pursuits or explain their relevance, as the realness of math is evident, formalists argue that in shifting from Platonism to formalism, mathematics does not become devoid of meaning. David Hilbert’s formalism grew out of a dislike for other projects that attempted to shore up the foundations of mathematics. Hilbert was disturbed by Russell and Whitehead’s logicism. He was equally troubled by the philosophical movement of intuitionism, particularly the work of Luitjens Brouwer.
