Jody Azzouni - Deflating Existential Consequence: A Case for Nominalism

Azzouni, Jody Professor of Philosophy, Tufts University

Deflating Existential Consequence

A Case for Nominalism

Print ISBN 0195159888, 2004
doi:10.1093/0195159888.001.0001

Abstract: What in our theoretical pronouncements commits us to objects? The Quinean standard for ontological commitment involves (nearly enough) commitments when we utter "there is" or "there are" statements without hope of eliminating these by paraphrase. Coupled with the indispensability of the truth of applied mathematical doctrine, the result is that the ontologically hard-nosed scientist is a Platonisthaplessly commited to abstracta. In this book Azzouni offers a way around the Quinean straitjacket: ontological commitment turns on how theories are (nearly enough) nailed to the world. The specifics of how theories are applied indicates which among the posits of a theory are mere mathematical garb and which are genuine connections to items out there. In the first part of the book Azzouni undercuts the arguments, both actual and possible, in support of Quine's criterion. An alternative criterion for what existsontological independenceis offered, one in sturdy accord with ordinary folk views on the matter. In the second part of the book, a beginning is made of bringing this alternative to bear upon scientific theories with a rich mathematical component. Along the way, old philosophical issues about absolute space and time versus relative space and time, the status of mathematical posits, such as spatial and temporal points, and so on, are illuminated.
Keywords: application of mathematics,criterion for what exists,existence,indispensability,ontological commitment,ontological independence,physics,Platonism,Quine,truth

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My thanks to Jeff McConnell for urging me to take pages 49-51 of my 2000b and rework them. (He claimed the argument that appears there is too condensed to be understood. He's probably rightespecially since the result turned out longer than I expected: chapters 1 and 2.) I'm also grateful to him for a number of useful suggestions regarding this material, and also for helpful suggestions that led to substantial improvements in chapter 3. My thanks to Sarah McGrath for her comments on the introduction and chapters 1 and 2, as well. My gratitude to John T. Roberts for some pointed remarks that helped sharpen an argument in chapter 2. My thanks to Mike Resnik for some off-the-cuff (but nevertheless devastating) objections to (an earlier version of) chapter 3; I hope all is well now. I'm grateful for comments from the audiences at the University of Leeds (October 17, 2001), California State University, Fresno (March 5, 2002), and the University of North Carolina at Chapel Hill (April 5, 2002), where I presented some of chapters 1 and 2; my thanks to the audience at the University of Sheffield (October 12, 2001), where I presented material from chapter 3; I'm grateful to the audience at the UCI Workshop in the Philosophy of Applied Mathematics on March 8, 2002, where I presented some of the material from chapters 8 and 9. My gratitude to my Mathematical Realism class at Tufts University in the spring of 2001, where we studied (a quite early version of) part I. And finally, my thanks to one of the anonymous reviewers at Oxford University Press for helpful comments, and to a second reviewer for helping me to see that my work (and my way of putting things) sometimes gets a rise out of people.

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