Naturalized Platonism vs. Platonized Naturalism


Bernard Linsky and Edward N. Zalta


Journal of Philosophy, XCII/10 (October 1995): 525-555.


Naturalism is the realist ontology that admits only those objects required by the explanations of the natural sciences. But both mathematical objects and properties are needed to explain scientific theories and scientific laws. To account for our knowledge of properties and mathematical objects, some naturalist philosophers have introduced these entities into the causal order, arguing that truths about them are empirical, discovered a posteriori, and subject to revision. This Naturalized Platonism has certain intrinsic problems.

In this paper, we develop an alternative strategy, Platonized Naturalism, 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.

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