A metaphysical foundation for mathematical philosophy

Although mathematical philosophy is flourishing today, it remains subject to criticism, especially from non-analytical philosophers. The main concern that even if formal tools serve clarify reasoning, they themselves contribute nothing new or relevant philosophy. We defend against such concerns here by appealing its metaphysical foundations. Our thesis can be founded on the phenomenological theory of ideas as developed Roman Ingarden. From this platonist perspective, “unreasonable effectiveness mathematics in philosophy”—to adapt Wigner’s phrase—is analogous explanations science. As success-criteria for philosophy, we propose should correct, responsive, illuminating, promising, relevant, and adequate.