James D Nickel on The Dance of Number (Part 2)

This is part 2 of yesterday's interview with James D Nickel, author of the upcoming book The Dance of Number. When I interviewed him four years ago I asked about his influences. He replied, "Authors who have influenced my worldview thinking are Abraham Kuyper, Cornelius Van Til, Francis Schaeffer, Vern Poythress, Albert M. Wolters, and Greg Bahnsen. In mathematics, the authors I really appreciate are Morris Kline, Stanley L. Jaki, Harold R. Jacobs, Carl Boyer, Eli Maor, Paul J. Nahin, Howard Eves, Calvin C. Clawson, Jerry P. King, Rózsa Péter, I. M. Gelfand, A. P. Kiselev, Edward Burger, Michael Starbird, and David Berlinski." This led me ask the following.

EN: Bertrand Russell, considered one of the great mathematical minds of the 20th century, was simultaneously a staunch atheist. Your first book, Mathematics: Is God Silent?, asserts that mathematics is inseparable from a belief in the triune God of creation. What are the problems that occur when mathematics gets separated from Christian faith?

Bertrand Russell

JDN: Bertrand Russell (1872-1970) was considered one of the great mathematical minds. He collaborated with another great mind, Alfred North Whitehead (1861-1947), to co-author the epochal three-volume Principia Mathematica (1910-1913), an attempt to ground mathematics in the certainty of logical analysis. It took the authors 362 pages to establish the proposition that 1 + 1 = 2. According to mathematicians Philip J. Davis (1927-) and Reuben Hersh (1923-), this extensive edifice is “an outstanding example of an unreadable masterpiece.”

The Austrian mathematician Kurt Gödel (1906-1978), by proving his incompleteness theorem in 1930, demolished Russell’s attempt to build an indubitable foundation for mathematics by showing that the soundness, acceptability, and completeness of any mathematical system, even the arithmetic of the counting numbers, cannot be established by logical principles.

Toward the end of his life, Russell evaluated his efforts:

I wanted certainty in the kind of way in which people want religious faith. I thought certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers expected me to accept, were full of fallacies, and that, if certainty were indeed discoverable in mathematics, it would be in a new field of mathematics, with more solid foundations than those that had hitherto been thought secure. But as the work proceeded, I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was no more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.(1)

Russell is an example of a very intelligent man who, beginning only with his mind, searched for ultimate answers for why mathematics works, for the ultimate ground of certainty, for the ultimate ground of rationality, a search that terminated in the abyss of despair. What Biblical Christianity offers to atheists like Russell is the revelation of the ultimate ground of rationality in the universe, the ultimate ground of certainty, the Creator and Sustainer of all things, the Living, Triune God and the revelation of that God in the person and work Jesus Christ (John 1:1-14; Colossians 1:15-17). When man does not ground his reasoning abilities in the wisdom revealed in this God (the fear of the Triune God is the beginning of wisdom), he will attempt to either justify or ground knowledge in some aspect of created reality: his mind or the physical world. Gödel’s proof demonstrated that man must submit to a transcendent ground for truth since logic can only go “so far.” The rationalistic goal of Russell is hubristic by its very nature.

The words of science historian and Roman Catholic theologian Stanley L. Jaki (1924-2009) call for mathematical and scientific humility, a trait that is the essence of the Christian faith:

For one thing, Gödel’s theorem casts light on the immense superiority of the human brain over such of its products as the most advanced forms of computers. Clearly, none of these machines can ever yield an answer comparable in its breadth and depth to Gödel’s theorem. For another, despair can grow only in a soil where a rigid rationalism has already killed off the seeds of intellectual humility. Such a soil cannot nurture the recognition that there is no escape from admitting that in mathematics and a fortiori in physics certainty is not the fruit of a “pure rationalistic” procedure alone.(2)

EN: When does your book come out and where can people find it? 

James D. Nickel

JDN: Targeted date: Middle to late summer of 2013, if there is no change in my work schedule. The hardcopy version with a solutions manual will be available for purchase on Amazon. My James Nickel author page at Amazon.com. My website biblicalchristianworldview.net will also provide a link to Amazon. Making an eBook of The Dance of Number is envisioned, but it will not be done this summer.

(1) Bertrand Russell, The Autobiography of Bertrand Russell (London: George Allen and Unwin, 1969). 3:220.
(2) Stanley L. Jaki, The Relevance of Physics (Edinburgh: Scottish Academic Press, [1966] 1992), pp. 129-130.