One day in 1894, when he was only 22 and in his final year at Cambridge, Bertrand Russell went out to buy tobacco and had a surprising flash of insight. It was one of those privileged moments that comes to philosophers and mathematicians, especially when they are young. Strolling along Trinity Lane, he tossed his packet of tobacco high into the air and exclaimed, “Great Scott! The ontological argument is sound.” Even in turn-of-the-century Cambridge, a place with more than its share of dotty philosophers, Russell’s exclamation must have sounded eccentric. The “Principia Mathematica,” the great work which he would co-author with Alfred North Whitehead, still lay 16 years in the future, but by that time Russell had changed his mind. He now thought the argument unsound and yet the moment when its truth seemed to burst upon him remained in his memory until old age. This may have something to do with the nature of the ontological argument. It, too, was born, more than 800 years earlier, out of just such a moment of illumination.

In “The Proof of God: The Debate That Shaped Modern Belief” (Atlas, 217 pages, $20), Larry Witham describes how the medieval theologian Anselm of Bec — better known as St. Anselm of Canterbury (1033-1109) — first hit upon his unusual argument, and how it has intrigued, and divided, philosophers from his own time to the present. The argument has enjoyed a surprisingly stubborn life and it continues to puzzle. By using it as a touchstone, Mr. Witham is able to provide brisk but cogent accounts of philosophers as diverse as Aquinas and Kant (who rejected it), Duns Scotus and Descartes (who accepted it), and, finally, Wittgenstein (who dismissed its very premises).

Anselm’s reasoning seems simple. Suppose I say, “God does not exist.” When I use the word “God,” I must have some notion of what the word “God” means. But God is by definition the greatest of beings, so great in fact that nothing greater than him can be conceived. If such a being existed only in my mind, he wouldn’t be the greatest of beings. Something else, which exists outside my mind, would automatically be greater since actual being is superior to mere mental being. Thus, if I say, “God does not exist,” I contradict myself. The notion of God, the word “God” itself, irresistibly denotes the existence of “something than which nothing greater can be thought,” as Anselm put it. The very fact that I can conceive of God proves that he exists.

This is an ingenious argument, but it seems a bit slick; we sense a fallacy without quite being able to nail it. A logician by training, Anselm wanted to devise a proof for God’s existence that would compel assent because it depended not on external evidence, such as the order of things in nature, but on the operation of the mind itself. (Ontology is the study of being, of existence as such; the proof is “ontological” because it establishes God’s existence on the basis of our very understanding of the notion.) The insight came to Anselm in the year 1078 in the monastery of Bec in Normandy. As his faithful biographer and companion Eadmer reports, “one night during matins the grace of God illumined his heart, the whole matter became clear to his mind, and a great joy and exultation filled his inmost being.” When Anselm published his argument in his “Proslogion,” the second of his three great theological works, Gaunilo, a monk at a neighboring monastery, objected. Just because I can think of something doesn’t mean that it exists, he argued: I can think of the “Blessed Isles,” but they exist only in my mind. Humans, Gaunilo insisted, can speak only of “finite things.” God is beyond our subtlest reasonings.

Anselm didn’t develop his proof because he doubted God’s existence. His motto was “faith seeking understanding.” Belief did not depend on reason, but reason could clarify belief and strengthen it. As Mr. Witham shows, however, Anselm’s argument touches on any number of slippery issues central to philosophy. Are words simply convenient signs or do they correspond to the essences of things? Are abstract concepts, such as justice or existence, merely names, little more than useful fictions that enable us to bandy categories, or do they exist in themselves as ideal templates of reality? If philosophy is only a “language game,” as some modern thinkers hold, is it pointless to speak of “existence,” let alone to try to prove the existence of God?

Mr. Witham’s book could have been dry but he enlivens every page. He accomplishes this not only by showing the subtle dynamism of Anselm’s thought, but by embedding him, and his successors, firmly in their times. Anselm himself comes through as a man of hard-won serenity in an age of upheaval. He weathered the Norman invasion only to find himself caught between king and pope in the long-drawn-out investiture conflict. A logician to the core, he could scribble on a margin, “Listen! I think I hear the distant rumble of a contradiction,” but he could also speak movingly of the “terror” he experienced when he examined his own heart. When he addressed his reader, in the “Proslogion,” as “Insignificant man!” he was addressing himself. He saw himself as the least of creatures. Perhaps only that awareness, sharpened by reason, could open his mind to the largest thought of all.

eormsby@nysun.com