God, Unifier of Mathematical Truths

Postmodern secularism assumes that modern-day advancements of mathematics and science have discredited truth claims of universal standards made apparent in the Bible or other religions. Surprisingly, however, former holders of such anti-theist positions have come to acknowledge the plausibility of the Biblical platform. Earlier this year, Professor Richard Dawkins, regarded widely as the spokesperson for atheism, admitted to uncertainty that there is no God. In fact, his remaining qualm with religion is what he sees as a lack of beauty. To him, putting a creator into the picture makes the story ugly. The “extraordinary beauty of the idea that life started from nothing” with no creator is, in his opinion, a very “staggering, elegant, beautiful thing.”1 In response, I will offer the Christian presuppositions that appease this desire for an explanation of the teleological elegance and coherence within the universe, which is clearly reflected in the field of mathematics. More than appease, I will present a rebuttal claim to argue for the necessity of a Biblical worldview in order to derive any sensible meaning from mathematics versus other worldviews that cannot give mathematics meaning.

It is peculiar enough that Christianity was once considered the more elegant worldview, and from this worldview came the rise of modern mathematics. Expanding onto the face of polytheistic Greek territories, Christianity’s monotheism provided sound rationalism standing in stark contrast to cultures whose gods had fickle wills and irrational temperaments. Three presuppositions determined a Christian’s interpretation of observed creation:

  1. Universal matter and order exist on the basis of being under the authority of one rational God that created it from nothing.2
  2. Man, in being given the communicable attributes of God as an image-bearer of him, is granted an understanding of the order and can grow in knowledge of it.3
  3. Man can, and is actually ordered to, subdue the earth and control it.4

From the many proof texts gleaned from the first chapter within the book of Genesis, the Abrahamic God can be seen specifying the order of planetary motion and biological life.5 Without the presumed control of God, the colloquial phrase “laws of nature” is misleading because the phrase implies the autonomy of nature. However, God never has to break any laws to ordain acts. God speaks, and so it is done: “He sends his word and melts [snow and ice]; he stirs up his breezes, and the waters flow.”6 God’s act of speaking makes apparent miracles in the Bible appear less like anomalies and more like the operation of the only law – God’s word. The fathers of modern mathematics used this knowledge about God to fuel their investigation into further understanding, most famously Copernicus, Kepler, Galileo, Pascal, and Newton. Copernicus claimed that the universe was “built for us by the Best and Most Orderly Workman of all,” while Newton believed that the discussion of God “does certainly belong to Natural Philosophy.”7,8 The New Testament confirms both the belonging and the holding together of creation by God; it even goes further to state his purpose in uniting the sum of creation’s parts to fully glorify God himself. Thus, acts of mathematical revelation to humans from the creator depict a beautiful plan for mere creatures to ultimately grasp the divinely ordained coherence present throughout the universe.

The next challenge is to understand the necessity for a Biblical worldview in applying mathematics logically. Let’s take the simple equation: 1 + 1 = 2. Contrary to popular opinion, this equation, 1 + 1 = 2, is not a worldview-neutral statement. One’s worldview on the source of truth ultimately determines one’s corresponding claims about mathematical logic. A non-Christian epistemology is left to explain the correctness of the equation 1 + 1 = 2 either a priori or a posteriori, that is, intuitively or experientially. First, an a priori answer that asserts 1 + 1 = 2 as a constant universal truth would require its removal from all experiential contingencies. Therefore, “1 lamp + 1 lamp” needs a separate qualification from “1 post + 1 post.” This subsequent diversity of definitions is unable to generate a consistent definition for 1 + 1. A more practical objection to the a priori worldview is its inability to reconcile the counterintuitive nature of some functions that exhibit pathological phenomena, e.g., everywhere-continuous, nowhere-differentiable functions. On the other hand, a posteriori knowledge of 1 + 1 = 2, possibly derived from seeing two cats or two buildings, can be invalidated as the orders of magnitude extend to 1 trillion + 1 trillion = 2 trillion, in which case it is highly unlikely that the human mind has ever perceived the tangible existence of 1 trillion of any entity. An adherent to the a posteriori worldview would argue that the latter equation was formulated under the knowledge of more minute generalizations; but yet again, that conglomerate of smaller generalizations then begs the question of which particular generalization to use. The decision to choose one generalization over another is based on some previous generalization, and so on goes the recursive question-asking until the a posteriori worldview-holder must come to admit that there is an element of intuition required in order for the human mind to grasp its knowledge of the nature of numeral relationships. Anti-theistic philosophies of mathematics are condemned to seesaw between a plurality and unity of truth without a solution for integrating both schools. The Bible is different. Man, explained before as being created in the image of God, already has some intuition of mathematical truth without needing to define it in its entirety, yet, through natural revelation, man can grow in understanding with each novel theorem. This solves both the problem within a strict a priori and a posteriori worldview.

Apart from epistemological problems, the anti-theist will struggle to find a solution to the metaphysical “Problem of Universals,” that is, the problem of defining abstract entities, such as numbers, as existing independently yet falling under a unity, here, within a system of arithmetic. This is not simply a problem with semantics: 1 + 1 = 2 holds meaning not as a fact learned by rote but as a truth that has value when given application, bringing back the example of adding lamps and posts. This single equation that evokes a plurality of experiences presents a plurality and unity of truth that must be reconciled to employ mathematics satisfactorily. To bring this problem to a macro level, observe the diversity of the universe embedded within a semblance of structure. Throughout this paper, what has been assumed is that mathematical order naturally expresses itself into physical order, meeting the above pluralistic and unifying requirements. Secular researchers have not entirely dismissed this fascinating link between mathematical and physical order. Princeton professor and Nobel laureate Eugene Wigner delivered a lecture titled, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” Wigner found himself disconcerted by the bizarre grounds on which mathematics and physical entities coalesce into a mysterious thread of truths – “The first point is that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it. … It is not at all natural that ‘laws of nature’ exist, much less that man is able to discover them.”9

On the other hand, the Bible offers a rational framework for the compatibility. In the first chapter of the book of John, the apostle writes: “In the beginning was the Word, and the Word was with God, and the Word was God. He was in the beginning with God. All things were made through him, and without him was not any thing made that was made.”10 These verses present the mystery of one God as multiple persons. The Word, that is, Christ, was with God the Father before the creation of all things. Christ is also God and is the one from which and through which all things are created. God is preeminent in all of creation, and mathematical truths fall under this category, as does all order in creation – physical matter and antimatter – that subsequently assents thereto. Here highlights the wisdom and rationality and harmony of God, displaying these qualities within himself through the indispensable doctrine of the ontological Trinity: three persons as one God. The “Problem of Universals” is hence solved quite elegantly and beautifully. A plurality and unity exists in God, the source of definitive truth, and he thus reflects his attributes to enable a plurality and unity of truth to exist in his creation.

References:

  1. Bingham, John. Richard Dawkins: I can’t be sure God does not exist. News Report: Interview. Chatham, Kent, United Kingdom: The Telegraph, 2012.
    2 Genesis 1:1; 1 Corinthians 14:33.
    3 Genesis 1:26-27.
    4 Genesis 1:28.
    5 Genesis 1:11 and 1:14-15.
    6 Psalm 147:18 ESV.
    7 Copernicus, Nicolaus. On the Revolutions of the Heavenly Spheres. Chicago: Brittanica, 1952. Great Books of the Western World. 508.
    8 Newton, Isaac. Philosophiae Naturalis Principia Mathematica. PenguinO PS, 1686. 442.
    9 Wigner, Eugene P. “The unreasonable effectiveness of mathematics in the natural sciences.” Communications on Pure and Applied Mathematics (May 11 1960): 13(1):1-14. Richard Courant Lecture in Mathematical Sciences delivered at New York University. 2-5.
    10 John 1:1 – 3 ESV.

Willis is in the School of Engineering and Applied Sciences studying Electrical Engineering (C’2012 BSE, C’2013 MSE).

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