Holistic Realism: A Response to Katz On Holism and Intuition

Abstract

In his book, Realistic Rationalism (henceforth RR), and his article, “Mathematics and Metaphilosophy”(henceforth MM), Jerrold Katz develops and defends a philosophy of mathematics that is realist in ontology and rationalist in epistemology. On his view, mathematics contains a body of necessary truths about certain abstract entities that are known a priori though the exercise of reason. Katz believes that his epistemology answers the familiar challenge, so well articulated by Paul Benacerraf, to mathematical realists that they explain how beings like us can acquire knowledge about causally inert, nonspatial, nontemporal, mathematical objects. Katz thinks the key to responding successfully to this challenge is to develop a “no contact epistemology,” that is, one that posits no physical process connecting us to mathematical objects. By basing his account of mathematical knowledge upon reason and intuition, Katz believes that he has avoided mysticism, such as that associated with Plato’s epistemology of recollection, and has given a deeper account than, say, Frege’s view that we grasp or apprehend abstract objects or Godel’s brief comparison of mathematical intuition with ordinary sense perception. Katz thinks that the only other no contact epistemology worthy of consideration is W. V. Quine’s confirmational holism. But he argues that this falls prey to his own Revisability Paradox and is inconsistent (RR, 72–4; MM, 375).