## God: One and Infinite

by Dr. Daniel Kiteck, Indiana Wesleyan University

The following is from a talk given by Dr. Kiteck at the ACMS Conference this past May. It is with his gracious permission that I am sharing it here.

Abstract

The ontology of mathematical objects has been of interest for millennia. I focus on the ontology of the number one in relationship to the ontology of God.

1. Introduction

Let ONE represent “the essence of what ‘the number one’ is.” I focus on the cardinal nature of the number one as opposed to its ordinal nature. The primary question is “What is ONE?” First, consider:

“There is no physical entity that is the number 1. If there were, 1 would be in a place of honor in some great museum of science, and past it would file a steady stream of mathematicians gazing at 1 in wonder and awe.” [Fraleigh and Beauregard, Introduction]

Why would mathematicians be in wonder over the number one?

2. ONE in Mathematics

ONE is foundational to counting, which is foundational to much of mathematics. This is nicely shown by Doron Zeilberger in his Fundamental Theorem of Enumeration: [Gowers et al., 2010, p. 550]

With some philosophical hand waving (which I admit deserves more attention, but that will be suppressed for now), ONE can be seen as foundational to much of the mathematical spaces that mathematicians work within. Just starting with ONE, we immediately have a unit {1}. From this we can imagine the existence of the unit and the non-existence of the unit: {0, 1}. But, imagining ONE twice, ONE three times, and so on brings us to N. Bringing in the concept of symmetry of an anti-ONE, an anti-ONE twice, etc., gives us Z. But then considering the set of all integers over non-zero integers, Q, and the set of all Dedekind cuts, R, (recalling that each Dedekind cut is an infinite set of rational numbers), we quickly imagine ordered pairs, triples, etc. to then have R 2 , R 3 , etc. So ONE is important to mathematics. But, is ONE important to Jesus?

3. ONE in Theology

3.1 Mark 12

In Mark chapter 12, someone asks Jesus “Of all the commandments, which is the most important?” Jesus famously responds with loving God and loving neighbor. But, the first part of Jesus’ response in verse 29 is

“The most important one,” answered Jesus, “is this: ‘Hear, O Israel The Lord our God, the Lord is one.’ ”

Jesus is quoting one of the most important pieces of scripture for the Jews, from Deuteronomy 6:4. My understanding is that this is commonly not seen as God being numerically one, so differing from ONE, but I still see it as reasonable to ask about how “One God” is related to ONE. But, first, where else in the Bible is it common to use the word “one?”

3.2 More than One?

In Genesis 2 we have two (husband and wife) becoming “one flesh.” But then in Ephesians 5 Paul informs us that this is a mystery actually referring to Christ and the Church. In traditional Christian Theology we have God as trinity [1] : “Three in One.” How are these connected to ONE?

4 The Ontology of ONE

4.1 Trinity

Does the concept of the trinity lead us to ONE and THREE as eternal concepts? Or does it lead us to conclude that we must leave the relationship between God and numbers a mystery? [2]

4.2 One God

Was there one God before God created the number one? I like asking this question to my students. Here are some responses attempting to honor God’s sovereignty: ONE is…

• part of a “continuous creation,” so distinct from God [Howell and Bradley, 2001, p.71]
• uncreated, so part of the nature of God in a mysterious way [Boyer and Huddell III, Spring 2015]
• not “real” in a Platonic sense [Bradley and Howell, 2011, p. 230-235]
• …wait!…Is “one” the same in “one God” and “number one?” [Ibid.]

Let’s explore this last question.

4.3 Necessity

Is ONE necessary in any universe God may create? I claim “yes” since one universe would be recognized by God.

But what if God had chosen not to create anything? Is ONE necessary then? [3] Perhaps another way to put it is: Must God’s eternal unique existence correspond to ONE? In light of the trinity, I am not confident in making a claim either way. And, in fact, in light of the oneness of Christ and the church, there seems to be some things concerning ONE that may be beyond our understanding. Or perhaps ONE should be seen as a rather distinct idea from many other ideas that are represented by the word “one.”

5 Conclusion

ONE is important to mathematics. “One God” is important to Jesus, but we must be careful with how this relates to ONE, especially in light of the trinity and the sovereignty of God. May our questions concerning ONE, and with mathematics in general, increase our wonder of the ultimate one, God.

I give a special thanks to my wife Karen for helping me sort my thoughts.

Bibliography

Steven D. Boyer and Walter B. Huddell III. Mathematical knowledge and divine mystery: Augustine and his contemporary challengers. Christian Scholar’s Review, XLIV(3):207–235, Spring 2015.

W James Bradley and Russell W Howell. Mathematics through the eyes of faith. HarperCollins Publishers, 2011.

J Fraleigh and R Beauregard. Linear algebra. 1990.

Timothy Gowers, June Barrow-Green, and Imre Leader. The Princeton companion to mathematics. Princeton University Press, 2010.

Russell W Howell and W James Bradley. Mathematics in a postmodern age: A Christian perspective. Wm. B. Eerdmans Publishing Co., 2001.

References

[1] I thank William Lindsey for pointing out the importance of including the trinity in this presentation

[2] I thank Kevin Vander Meulen for this question.

[3] A conversation with Jim Bradley sparked this question. Thank you Jim Bradley for the opportunity!