# Infinity and the Mind

## Preface

This book discusses every kind of infinity: potential and actual, mathematical and physical, theological and mundane. Talking about infinity leads to many fascinating paradoxes. By closely examining these paradoxes we learn a great deal about the human mind, its powers, and its limitations.

The study of infinity is much more than a dry, academic game. The intellectual pursuit of the Absolute Infinite is, as Georg Cantor realized, a form of the soul's quest for God. Whether or not the goal is ever reached, an awareness of the process brings enlightenment.

Infinity and the Mind has been written with the average person in mind. Most of the main text should prove digestible, if chewed. By and large, the separate sections are complete in themselves, and the reader should feel free to skip about in the book.

At the end of each chapter there is a section with puzzles and paradoxes; answers are provided. For those who may wish to delve a bit deeper into set theory and logic, I have organized two mathematical excursions which are placed at the end of the book.

Infinity and the Mind was thought out and written over a period of some ten years. I started having ideas for it in that most Sixties of years, 1972. At that time I was writing a doctoral dissertation in set theory for Erik Ellentuck at Rutgers University and attending a logic seminar led by the eminent proof theorist Gaisi Takeuti at the Institute for Advanced Study in Princeton, New Jersey. The first time I met Takeuti I asked him what set theory was really about. "We are trying to get exact Description of thoughts of infinite mind," he said. And then he laughed, as if filled with happiness by this impossible task.

The same year I met Kurt Godel at the Institute for Advanced Study. No one in modern times has thought more logically than Godel, no one has proved theorems of greater mathematical complexity. Yet the man I met was a joyful, twinkling sage-not some obsessed fossil. What struck me most about Godel was his intellectual freedom-his ability to move back and forth between frankly mystical insights and utterly precise logical derivations. As I began to study the writings of Georg Cantor, the founder of set theory, I realized that Cantor shared this freedom. Logic and set theory are the tools for an exact metaphysics.

The writing of this book started with a paper I did for a logic colloquium at Oxford University in 1976 and began in earnest with a set of mimeographed lecture notes for an interdepartmental course I taught with my friend William J. Edgar at SUNY Geneseo in 1977. In 1978 I rewrote my notes and reproduced them by photo-offset for an experimental metamathematics course. Those notes make up the present Chapters One and Three and the more technical Excursion I.

I spent the years 1978-1980 at the Mathematics Institute of the University of Heidelberg, a guest of Gert Mijller and the Alexander von Humboldt Foundation. While there, I wrote Chapter Four with Excursion II for a course of lectures on the philosophy of mathematics. Chapters Two and Five have been written this winter at Randolph-Macon Woman's College.

Infinity and the Mind is a work of transmission. I dedicate it with love and respect to everyone in the channel.

R.v.B.R
Lynchburg, Virginia
June 19,1981