Abstract
In this paper, we develop an alternative strategy, Platonized
Naturalism, for reconciling naturalism and Platonism and to account for our knowledge of mathematical objects and properties. A systematic (Principled) Platonism based on a comprehension principle that asserts the existence of a plenitude of abstract objects is not just consistent with, but required (on transcendental grounds) for naturalism. Such a comprehension principle is synthetic, and it is known a priori. Its
synthetic a priori character is grounded in the fact that it
is an essential part of the logic in which any scientific theory will
be formulated and so underlies (our understanding of) the
meaningfulness of any such theory (this is why it is required for
naturalism). Moreover, the comprehension principle satisfies
naturalist standards of reference, knowledge, and ontological
parsimony! As part of our argument, we identify mathematical objects
as abstract individuals in the domain governed by the comprehension
principle, and we show that our knowledge of mathematical truths is
linked to our knowledge of that principle.