Redeeming Mathematics: A God-Centered Approach.
Challenged by Kuyper's declaration that faith affects all of life, Poythress begins his book with a keen interest in exploring how faith applies to mathematics. There are other books on the subject, but in this short book, Vern Poythress adds his own view to the mix. He introduces some of the theological and philosophical work of the Reformed theologian John M. Frame, for example, The Doctrine of the Knowledge of God, and he acknowledges the influence of the Reformed philosopher Dirk Vollenhoven. He challenges the notion that mathematics is merely secular; instead, to cite one argument, arithmetic laws are "in essence personal" and imply a lawgiver. Poythress observes that the rules and order of mathematics demonstrate the biblical principle that God upholds the world. He attributes mathematics to God's law, a divine command, for the universe. Poythress tries to develop a philosophical position that steers away from both Christian Platonism and Christian empiricism.
While available in hardcover, Redeeming Mathematics is one of 20 free ebooks that Poythress has written. The list includes Chance and the Sovereignty of God, Logic, Redeeming Science, Redeeming Sociology, and Symphonic Theology. Many of his books share a variation of the subtitle "A God-Centered Approach" with the book under review. In this mathematics edition, Poythress leans heavily on his other work, such as Redeeming Science. In fact, some paragraphs are borrowed verbatim, and some of these words also appeared in his 2003 article "Why Scientists Must Believe in God: Divine Attributes of Scientific Law." In other places he encourages the reader to consult his other works to get the full details of his argument. In the end, I would have preferred that the book were self-contained and did not lean so much on his other works. His brief supplemental chapter on other resources could have been more robust and included, for example, brief commentary on the edited books by Bradley and Howell, Mathematics in a Postmodern Age: A Christian Perspective and Mathematics through the Eyes of Faith, or Byl's The Divine Challenge: On Matter, Mind, Math and Meaning, which are listed in the bibliography.
This book is not specifically written as an apologetic argument; rather, it is meant to help Christians consider Kuyper's clarion call in the context of mathematics. In a world that views mathematics as purely secular, Poythress aims to recover "a robust doctrine of God's involvement in daily caring for his world." Poythress leans heavily on the Reformed Christian apologist Cornelius Van Til, often via the work of John Frame. In particular, he draws on the concept of the Trinity to bolster his ontology of mathematics and he uses Van Til's analogical approach with an oft-repeated refrain that we are "thinking God's thoughts after him."
In chapter 1, Poythress ties arithmetic statements such as 2 + 2 = 4 to some attributes of God, such as being immutable, omnipresent, and omnipotent. He develops the idea that arithmetical rules are part of the Law of God for creation, part of God's Word. He then describes the personal character of Law, the goodness of Law, the beauty of Law, the righteousness of Law, and the Trinitarian nature of Law, declaring that arithmetic participates in all these attributes. Through these, Poythress recognizes a nonsecular approach to mathematics. He observes that "people working with mathematics rely on God's Word in order to carry out their work" and exposes the nonbiblical notion that God acts in creation, but only in supernatural ways via miracles. After all, as noted in Psalm 104, God "causes the grass to grow." Poythress notes that laws reflect God's character, but in my mind, he takes the analogy too far. Instead of simply saying that mathematics captures part of God's regular working in the world, he equates the laws directly with part of his character.
In chapter 2, Poythress briefly addresses the philosophical problem of the one and the many, tying it to one's understanding of mathematics. He uses the concept of the Trinity to make sense of the unity and diversity of the created world, describing how the expression of unity and diversity in number concepts reflects God's character.
In chapter 3, he describes the limitations of a materialist worldview to answer the philosophical problem of the one and the many. He argues that materialism does not adequately explain the origins of mathematics. In chapter 4, Poythress reflects on the nature of numbers. He attributes mathematical equations to God's speech, associating them with the divine characteristics of omnipresence, eternality, and omnipotence. In this chapter, he develops an analogical tie to the Trinity using Frame's three perspectives: normative, situational, and existential. He develops these perspectives to further connect arithmetic with God's character.
In chapter 5, Poythress describes Frame's square diagram for understanding transcendence and immanence in Christian perspective. He connects the square to different interpretations of arithmetic statements such as 2 + 2 = 4. In chapter 6, Poythress covers the concepts of necessity and contingency with respect to God and mathematics, elaborating on the relevance of Frame's square for transcendence and immanence. He notes that numbers exist eternally, "not as Platonic abstractions, but as an aspect of God's knowledge." In a later chapter, he argues, based on the character of God, that numbers could be no different in any alternate universe.
In chapters 7-10, Poythress explores addition, the idea of succession, and multiplication. He develops curious links to the Tabernacle, the Trinity, and breeding animals. For example, Poythress argues that since God uses numbers to describe proportions for the earthly temple, this illustrates that numbers derive from God, instead of allowing for the fact that God may be communicating a broader principle using human-accessible terms. In chapters 11 and 12, he links symmetries and sets to the character of God. In chapters 13-16, Poythress links fractions, irrationals, and imaginary numbers to God via his three perspectives. In chapters 17-19, he touches on infinity, geometry, and higher mathematics before ending with a very brief conclusion. In the appendices, Poythress helpfully describes other philosophies of mathematics as well as other Christian approaches to the philosophy of mathematics. He describes Christian Platonism as well as a Christianized empiricism, giving critiques from his perspective.
There are a few places where Poythress could have taken more care in his writing. Some chapters start with stunted introductory paragraphs that deserve to be developed. He makes a speculative conjecture about the etymological roots of the word "irrational," tying it to later decimal representations instead of to the ambiguity of the Greek word for ratio within the context of the Greek worldview. He incorrectly states that imaginary numbers were introduced historically to be solutions to equations, rather than a means to a real solution. When reflecting on unexpected applications of imaginary numbers, he provides the unsatisfactory statements that "God in his wisdom made it so," and that such numbers "are known by God," making them "real." Finally, on occasion in an argument, he has inserted the word "clearly" unnecessarily. For example, he brushes off a common inference as "clearly invalid" (p. 20); the adverb is either redundant or dismissive.
But these issues are minor and perhaps picky concerns. The bigger concern is with the overall argument itself. While I appreciate his anti-reductionist approach, allowing for the complexity and diversity of the created world, I do not find the analogical approach particularly convincing. In my opinion, it is applied too literally. And his oft-repeated refrain of thinking God's thoughts muddles the distinction between God's character and the specific way God upholds the creation, not to mention the particular ways that humans observe God's handiwork. In the end, despite his intention, I find it hard to distinguish his position significantly from a Christianized Platonist approach. Nevertheless, Poythress provides food for thought for those exploring the relationship of faith and mathematics.
Reviewed by Kevin N. Vander Meulen, Professor of Mathematics, Redeemer University College, Ancaster, ON L9K 1J4.
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|Author:||Vander, Kevin N.|
|Publication:||Perspectives on Science and Christian Faith|
|Article Type:||Book review|
|Date:||Mar 1, 2017|
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