Anthony F. Peressini

The subject with which Mark Colyvan's book deals is timely indeed. While discussions of mathematical ontology have been a mainstay in philosophy of mathematics for the last century (at least), for the last thirty years or so this discussion has begun with (and often not left) the Quine/Putnam indispensability argument. Though the argument is widely cited, to my knowledge this is the first book-length project exclusively dedicated to articulating and defending the Quine/Putnam indispensability argument for mathematical platonism. In the first section below, I shall run through a summary of the book (following its chapter layout) with a few critical remarks. In the second section I shall raise a few critical issues organized topically.

I argue that a broad conception of behavior makes considerable headway toward an account of psychological explanation that preserves the intuitive correctness of belief/desire psychological explanations and whose explanatory utility is not undercut by neurophysiological explanations. The rough idea behind a broad conception of behavior is that the basic units of behavior, which constitute the primary explananda of psychology, are themselves essentially goal-directed. As such, behavior supervenes on more than the physical properties of the bodily motions which comprise it; it supervenes also on the historical/teleological properties that give it its goal

Much of the current thought concerning mathematical ontology and epistemology follows Quine and Putnam in looking to the indispensable application of mathematics in science. A standard assumption of the indispensability approach is some version of confirmational holism, i.e., that only "sufficiently large" sets of beliefs "face the tribunal of experience." In this paper I develop and defend a distinction between a pure mathematical theory and a mathematized scientific theory in which it is applied. This distinction allows for the possibility that pure mathematical theories are systematically insulated from such confirmation in virtue of their being distinct from the "sufficiently large" blocks of scientific theory that are empirically confirmed.