1st Edition

Do Numbers Exist? A Debate about Abstract Objects

    In Do Numbers Exist? Peter van Inwagen and William Lane Craig take opposite sides on whether there are abstract objects, such as numbers and properties. Craig argues that there are no abstract objects, whereas Van Inwagen argues that there are. Their exchange explores various arguments about the existence and nature of abstract objects. They focus especially on whether our ordinary and scientific thought and talk commit us to abstract objects, surveying the options available to us and the objections each faces. The debate covers central problems and methods in metaphysics, and also delves into theological questions raised by abstract objects.

    Key Features:

    • Showcases the presentation and defense of two points of view on the existence of abstract objects, from two of the world’s leading philosophers
    • Presents definitions in an easily accessible form
    • Provides frequent summaries of previously covered material
    • Includes a glossary of all specialized vocabulary

    Foreword by Mark Balaguer

    Opening statements

    1. Opening Statement
    Peter van Inwagen

    2. Opening Statement
    William Lane Craig

    First Round of Replies

    3. Reply to William Lane Craig’s Opening Statement
    Peter van Inwagen

    4. Reply to Peter van Inwagen’s Opening Statement
    William Lane Craig

    Second Round of Replies

    5. Response to William Lane Craig’s Reply
    Peter van Inwagen

    6. Response to Peter van Inwagen’s Reply
    William Lane Craig


    Peter van Inwagen is the John Cardinal O’Hara Professor of Philosophy Emeritus at the University of Notre Dame. He is the author of two seminal works, An Essay on Free Will (1983), and Material Beings (1990), both of which are still in print.

    William Lane Craig is Professor of Philosophy at Talbot School of Theology and at Houston Christian University. He has authored or edited over 40 books, including The Kalām Cosmological Argument; God, Time, and Eternity; and God and Abstract Objects, as well as over 200 articles in professional publications of philosophy and theology.