Realistic Rationalism

by Jerrold J. Katz

In Realistic Rationalism, Jerrold J. Katz develops a new philosophical position integrating realism and rationalism. Realism here means that the objects of study in mathematics and other formal sciences are abstract; rationalism means that our knowledge of them is not empirical. Katz uses this position to meet the principal challenges to realism. In exposing the flaws in criticisms of the antirealists, he shows that realists can explain knowledge of abstract objects without supposing we have causal contact with them, that numbers are determinate objects, and that the standard counterexamples to the abstract/concrete distinction have no force. Generalizing the account of knowledge used to meet the challenges to realism, he develops a rationalist and non-naturalist account of philosophical knowledge and argues that it is preferable to contemporary naturalist and empiricist accounts.

The book illuminates a wide range of philosophical issues, including the nature of necessity, the distinction between the formal and natural sciences, empiricist holism, the structure of ontology, and philosophical skepticism. Philosophers will use this fresh treatment of realism and rationalism as a starting point for new directions in their own research.

Genres: Philosophy, Realistic Fiction

252 pages, Paperback

First published December 8, 1997

Reviews

[Pedro Rosario-Barbosa · Rating 5 out of 5]

This book is a gem for me. The renowned philosopher Jerrold J. Katz builds a case for mathematical realism, i.e. the statement that abstract mathematical objects actually exist as objects of reason (or understanding). What I like about this book is that it is one of the very few attempts made by realists to provide a satisfactory account on both the ontology of mathematical entities as well as their epistemology. The latter has been historically a real challenge for mathematical realists (particularly platonists). What draws my attention to this work, beside its excellence dealing with the subject is how much it assumes a structuralist platonistic view, that mathematical entities can be grasped on the basis of a particular abstract structure on experiential basis. That abstraction is itself the referent of mathematical entities themselves. His portrayal of how this is done, is not too far from Edmund Husserl's categorial intuition and abstraction.

Another thing that I love about the book is that it challenges antirrealists' positions, and explains why they are not viable. This book is one of those works that challenge the naturalistic presuppositions of W. V. O. Quine, and the Quine-Putnam Thesis: that there is fundamentally no difference in kind between abstractions like mathematical objects, and the objects of sensible experience. Katz shows that this is false, that mathematical truths can only be known a priori, and can never be refuted a posteriori.

[Arthur Drury · Rating 5 out of 5]

Jerrold Katz was a virtuoso. Right or wrong, it's a pleasure to watch him work. This book is worth it for the discussions of the history of philosophy alone.