Chastened Realism: Mathematics as a Model for Theology

Abstract

INTRODUCTION

Mathematics and theology represent the only two disciplines that attempt a systematic treatment of infinity. Historically in mathematics, only the potential infinity was recognized as being meaningful until Gregory Cantor developed his transfinite arithmetic in the late 1800s. Mathematics and theology have other characteristics in common, including an historical claim of certainty, a rationalist tradition which is not limited to empirical observation, and claims of realism. This paper will explore these similarities between mathematics and theology and, in particular, the issue of realism.

REALISM IN MATHEMATICS

Plato saw mathematics, especially geometry, as the key to “eternal knowledge” and more real than what our senses could experience. “The knowledge at which geometry aims is knowledge of the eternal, and not of the perishing and transient.” [Plato, The Republic, Book VII]

The systematic form for this was established in Euclid’s Elements. What could be clearer or more certain than a few self-evident axioms upon which literally hundreds of theorems could be proven by the use of deductive logic alone? This was knowledge more sure than anything the senses could tell us. It was insight into reality, our best way of knowing. This model of secure knowledge influenced science, philosophy and religion for nearly two thousand years as can be seen in the writings of Aristotle, Augustine and Aquinas.

With the rise of the empirical sciences, the role of mathematics as the language of science continued its status as the “queen of the sciences.” The major figures in the early development of modern science, including Copernicus, Galileo, Newton and Kepler, were not just finding mathematical laws to describe physical reality; they were, to their thinking, discovering the very mind of God.

This status of realism in mathematics suffered numerous blows especially during the nineteenth century with the development of non-Euclidean geometry and the “foundations crisis” during the later part of the century and the early twentieth century.

Under the leadership of mathematician David Hilbert, a formalist philosophy was developed which claimed no status of realism for mathematics.

STRUCTURAL REALISM

More recently, structural realism has emerged in the philosophy of mathematics as a new approach to justify objectivity in mathematics. Patterns or relationships are critical to understanding the nature of mathematical knowledge. Thus the philosophers who argue for or against mathematical realism by looking at numbers or points as objects are raising inappropriate comparisons to the material objects which are the subject matter of the natural sciences. We do not find the reality of mathematics in the objects, such as points, lines, or numbers, but in the structures that are described and in the relationships that exist.

Structural realism, building on this mathematical philosophy, will be described as a model for understanding the nature of realism in theology.

Biography

P. Douglas Kindschi is currently the University Professor of Mathematics and Philosophy at Grand Valley State University in Grand Rapids, Michigan, where he previously served for over 20 years as the Dean of Science and Mathematics. His interest in science and religion goes back to his graduate studies at the University of Chicago Divinity School and his leading a campus ministry science-religion program while completing his PhD in mathematics at the University of Wisconsin. At Grand Valley State University, he developed the course Science, Mathematics, and Religion: Ways of Knowing, which received a Templeton Course Award. He founded and has led for the past nine years a faculty discussion reading group in science and religion. He currently directs a new Local Society Initiative program which brings together individuals from nine colleges, universities, and organization in an interdisciplinary, inter-institutional, and interfaith dialogue for the greater Grand Rapids area.