SEPTEMBER 2009 • MATH HORIZONS • WWW.MAA.ORG/MATHHORIZONS 1 God? A Mathematician Challenges the Proofs Reviewed by Samuel Otten Michigan State University I t is the job of mathematicians to think carefully about definitions, to be aware of underlying assumptions, to construct and analyze arguments, and to ultimately uncover truths. For these reasons it seems appropriate that mathematicians have stepped forward to join the discussion regarding the existence (or nonexistence) of God. Reasoning and rationality—central characteristics of mathematics—are precisely the things that distinguish us as humans, and it is only natural that we should use them when contemplat- ing questions that we consider most important to humanity. With his new book Irreligion, mathe- matician John Allen Paulos has entered the swirling debate regarding the role of religion in society and of science in religion. Paulos is by no means the first to make an intellectual case for atheism (Paulos himself calls attention to the work of people like Sam Harris and Christopher Hitchens) but he does offer something unique and personal: a mathematical perspective leading to the conclusion that arguments for God’s existence “don’t add up.” Making his position eminently clear, Paulos defines the term irreligion as “topics, arguments, and questions that spring from an incredulity, not only about religion, but also about others’ credulity.” He asserts that “the first step in untangling religious absurdities” is to examine the definition of God. Paulos clarifies that the arguments addressed in Irreligion are essentially geared toward the familiar monotheistic God— a personal creator with a wise and powerful hand in daily events. This becomes vitally important later in the book. For instance, in the chapter on the Argument from Redefinition, Paulos admits that a sufficient watering down of the concept of God assures God’s existence, albeit in a “very strained Pickwickian sense.” Similarly, the Argument from First Cause, even if it did hold, would only prove the existence of a God who is the cause of the universe; none of the benevolent or moral characteristics ascribed to such a God would necessarily follow. Clarity of definition comes into play elsewhere in the book. While address- ing the Argument from Interventions, Paulos unpacks the term “miracle.” If a miracle is a highly unlikely event, then miracles happen every day. Many people, however, use the term to refer to an act of God. They then claim that the existence of miracles (even under the first definition) proves God’s existence. Paulos points out this conflation of concepts and, concerning the divine interpretation of miracles, asks, “Why do so many in the media and elsewhere refer to the rescuing of a few children after an earthquake or a tsunami as a miracle when they attribute the death of perhaps hundreds of equally innocent children in the same disaster to a geophysical fault line? It would seem either both are the result of divine intervention or both are a consequence of the earth’s plates shifting.” Another mathematical skill on display in Irreligion is the detection of latent assumptions. For example, take the Argument from First Cause: 1. Everything has a cause. 2. Nothing is its own cause. 3. Causal chains can’t go on forever. 4. So there has to be a first cause, namely, God. Paulos points out several problems with this argument, starting with the “gaping hole” in assumption 1. When considered with assumption 4, we see that assumption 1 should actually read “Either everything has a cause or there’s something that doesn’t.” Paulos continues, “If everything has a cause, then God does too, and there is no first cause. And if something doesn’t have a cause, it may as well be the physical world as God.” Two other common flaws with arguments for the existence of God that Paulos engages are logical fallacies and errant notions of probability. From a logical standpoint, he quickly uncovers circular reasoning within the Argument from the Anthropic Principle and the Argument from Prophecy. There is also a chapter concerning the logic of self-reference and recursion, which contains familiar but nonetheless interesting thoughts from Bertrand Russell. (See Russell’s 1957 book, Why I Am Not a Christian, for another mathematician’s take on religion.) Irreligion: A Mathematician Explains Why the Arguments for God Just Don’t Add Up, by John Allen Paulos, Hill and Wang, ISBN: 978-0-8090-5919-5 E Book Reviews