Metaphysical explanation and the philosophy of mathematics: Reflections on Jerrold Katz's Realistic Rationalism (Q2765251)

This is a critical review essay on J. \textit{Katz}'s ``Realistic rationalism'' [Cambridge, Mass., MIT Press (1998; Zbl 0996.00006)]. Katz provides a realist account of metaphysics and epistemology of the formal sciences mathematics, logic, and linguistic. According to the author Katz's theory ``provides a useful case study for realist metaphysics in general'' (p.\ 155). However, the author aims at going considerably beyond Katz's theory in exploring ``the scope, limits, and possibility of metaphysical explanation in the philosophy of mathematics'' (p.\ 156).NEWLINENEWLINENEWLINEIn Katz's ontology considerable methodological weight is placed on intuition regarded as pretheoretic. Intuition has to be codified and systematized by the theory (p.\ 159).NEWLINENEWLINENEWLINEAs a ``militant realist'' (p.\ 165) Katz rejects behaviorism, psychologism and empiricism. A realist like Katz supports the intuition that abstract entities have existence, but neither spatial nor temporal location (p.\ 168). Katz draws, however, a very special pictures of antirealism. According to him, it consists in the repudiation of abstracts objects. Every existent entity is a concrete object which is spatiotemporally located (ibid.). This kind of antirealism is close to materialism (all existent is part of a causally interrelated spatiotemporal realm) and naturalism (all discursive practices are constrained by the epistemic and ontological norms of natural sciences).NEWLINENEWLINENEWLINEKatz opts for an a priori approach to mathematics going beyond \textit{Kant}'s, as he calls it, `mentalistic' approach.NEWLINENEWLINENEWLINEKatz's theory is applied to discuss some arguments relevant for the ontology of mathematics such as the indeterminacy arguments of \textit{Quine} and \textit{Benacerraf}, and structuralism.