In Realistic Rationalism, Jerrold 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. He develops a rationalist and non-naturalist account of philosophical knowledge and argues that it is preferable to contemporary naturalist and empiricist accounts.
About the Author
Jerrold J. Katz is Distinguished Professor of Philosophy and Linguistics at the Graduate Center of the City University of New York.
"Engaging and provocative."
—A.W. Moore, Times Literary Supplement
“This book is certainly going to count as one of the most important contributions to the philosophy of mathematics of the last decades.”
—Paolo Mancosu, Assistant Professor of Philosophy, University of California, Berkeley
“Many philosophers of mathematics have assumed that the metaphysical position, call it ‘full-blooded Platonism,’ is incompatible with the various sorts of ‘naturalisms’ that most of us are committed to. Here is a brave book illustrating that very claim: readers will find it (among other things) a full-scale assault on naturalism, a complex metaphysics of abstract, concrete, and composite objects, and a rationalist epistemology based on rich notions of Reason and intuition. Perhaps the strongest arguments available for such a position may be found here.”
—Jody Azzouni, Department of Philosophy, Tufts University
“What is philosophy? The dominant view is that philosophy, where it is not the unravelling of linguistic confusions, is an inseparable part of empirical inquiry. Katz sharply challenges this. In clear and relaxed prose he advocates an earlier view: philosophy is the study of reality at the most general level through rational reflection. But he does not simply return to the position of a former age. Drawing on a mastery of twentieth-century analytic philosophy, Katz takes us one whole cycle higher up the helix of metaphilosophy, reconstructing our understanding of the relations between science and philosophy in the process.”
—Marcus Giaquinto, Department of Philosophy, University College London
“In the waning of the twentieth-century the tension between the dominance of philosophical naturalism and the intrinsic recalcitrance of mathematics to such a philosophy is coming to a head. Professor Katz’s new book furnishes the beleaguered mathematical realist with some powerful weapons in the form of detailed and novel arguments designed, for a change, to put the universal naturalist on the defensive. In particular, one finds here a breath of fresh air with regard to the problematics of realism made prominent by Benacerraf’s influential writings on the philosophy of mathematics, a rare attempt to combine a highly articulate realistic ontology with a substantial rationalistic epistemology for all of the formal sciences.”
—Palle Yourgrau, Department of Philosophy, Brandeis University
“Katz supplies a dazzling array of often fresh, sometimes daring, always vivid and cogent arguments that will become part of the armament of anyone down the road who seeks to develop a defensible nonreductive theory of abstract objects.”
—Robert Tragesser, Class of ’43 Professor in the History and Philosophy of Science and Mathematics, Connecticut College