There are other profound questions of human existence children may ask that I would like to bring to your attention. Seventh grade Sarah will ask, “You know…like…where did language and like all that come from?”
Of course, we won’t drop the ball and answer that language is the evolved grunts and growls of evolved primates that help us survive in our environments. Language is the gift of God to Man given to communicate among ourselves and most importantly given for us to have a true knowledge of Him. Therefore, a Christian teacher can appropriately start off the school year telling Sarah and the rest of the students that learning how to express oneself well is a spiritual exercise.
From a biblical standpoint, communication has great dignity. The pertinent Trinitarian consideration in this: even as the Persons of the Trinity have spoken to each other from eternity and from the beginning to us through intelligible utterances, so are we.
It pleased God to reveal His Word to us through a Book with different genres, with poetry, prose, narrative, with all kinds of literary devices to communicate a knowledge of Himself and His works. Respect for language, for the only adequate vehicle for intelligible thought, is to be oriented to a reverence for God since language comes from Him. With this in mind, we guide and encourage our students to learn the parts of speech, to learn proper grammar, to learn the mechanics of language, to read between the lines, to express intellectual creativity and to do all this to display God’s magnificence, to each others edification, and for the advancement of His kingdom.
Now, this doesn’t mean that all our students without exception will become Christian Studs Terkels or Maya Angelous because of our thoughtful efforts. Some will use their academic competencies in the area of Language for downright rebellious, anger-driven, anti-Christian purposes and be successful and influential at it. When that turns out to be the case, we shouldn’t lose heart, but should humbly submit before God’s sovereign will knowing that “Surely the wrath of man shall praise [God].”5
Our confidence is placed in God alone because His wise, holy, and sovereign purposes can’t be thwarted. He is in control. It doesn’t even mean that our students will always write a clear message to put on the refrigerator for that matter. But it does mean that they have been given a basis to appreciate the true worth of their students. It is a worth only Christianity invest in their education.
Whatever the outcome, teachers have said that this along with other areas of study belongs to King Jesus and we have resolved to do nothing less than to fight for His crown rights here and across the curriculum one day at a time, one lesson at a time, one photocopy at a time.
What about mathematics? Surely, mathematics can’t be Christian, can it? Math is neutral, isn't it?
Consider the nature of mathematics for a moment. Take it slow. Bring your presuppositions forward. Your Christian presuppositions. Ready? What follows isn’t a demonstrative proof. I can’t even hope to get too deep. God hasn’t given me the ability to. Perhaps He has given you the knowledge to dig deeper. If so, share your thoughts with me and others for His glory!
I want to share a line of thought that highlights the applicability of God’s Word to the sphere of knowledge we call math.
Rambunctious, fourth grade Johnny is learning his multiplication tables. He will ask his teacher, “Yo, Mrs V., like where does math and numbers and all that come from anyways?”6 Johnny has unwittingly asked his instructor a question concerning a profound problem of human existence.
How should we explain or account for mathematical truth?
If we go to the local bookstore for answers, we’ll encounter two general answers that flow from an approach that is antagonistic towards Christianity. One answer to the problem of where math comes from is that math is the function of brains. This type of book is usually thick because it depends on research, experiments, and theories about consciousness from which inferences are drawn to show that math is literally all in our head. Let’s call this the materialist math answer. The other answer to the problem of where math comes from is that math just is. This type of book is usually thin because it rejects most research and experiments as irrelevant and instead is more analytic about theories and about defining its terms, but fails to ground mathematics on anything transcendent. Let’s call this the mere metaphysical math answer. The former answer is presumptuously wrong while the latter is humbly mistaken. Both approach the dilemma posed by math from non-Christian presuppositions.
Any way you look at it, math is shared reality. After all, Christians and non-Christians alike deposit and withdraw funds from their bank accounts. The difference is, as Reformed apologist Cornelius Van Til wryly stated, that while “Non-believers can count, they cannot account for counting” and the Christian worldview alone provides a rational ground for the properties that everyone attributes, knowingly or unknowingly, to mathematical truth.
Christian teachers can deal with the materialist math answer in two ways. First, we must reject the basic materialist contention that mathematical thinking must be construed as activity in brains instead of the universal, non-physical activity in non-physical minds. Second, we may reveal the major embarrassment in such a materialist math answer. The materialist math answer will grant that mathematical truth is mental, but will define the term mind to mean our brains. Toes wiggle, tongues taste, glands secrete, and brains think mathematics. Any kind of thinking, is reduced to chemical or physiological activity in our literal heads.
Right away, though, the question arises as to how they can justify calling, chemical, physical, or neurological activity either true or false. In redefining mind to mean brain, materialists have denied themselves any possibility of valid argumentation to justify an acceptance of their position. Why? Because physical motions in our heads cannot produce the rationality of a valid argument.
We all agree that mathematical truth is mental, but only propositions (which are non-material) can be the objects of knowledge in minds (which are also non-material). Physiological activity in a brain is just a bodily change. No matter how much we observe and experiment with the brain, we cannot derive propositions to construct an argument from it that warrants our acceptance of the materialist math answer. Materialists, in redefining mind to mean brain, have done Christians a favor in demolishing their own position.
To reduce any mathematical truth as elementary as 2 x 2 = 4 to physical motions in the brain erects other insurmountable problems: (1) No one person can have the same mathematical thought twice since any thought we have is a “fleeting event…distinct from every other” due to its physiological nature (2) No two persons can share the same mathematical thought at all because the juices that flow in one brain are different that the juices that flow in another brain (3) As a consequence of reducing mathematical truth in such a materialist fashion, “memory and communication would both be impossible” since no one could repeat the same thought twice nor could one receive another’s identical thought.
We may end our rejection of the materialist math answer by revealing its major embarrassment. Since Christians would clearly have to be committed to a view of mathematical truth that transcends the material world and the materialist would object, we can simply reply that based on his own terms, “his denial [of our position] must be conceived to exist in his own mind only; and since it has not registered in any other mind, it does not occur to us to refute it”.7
What, then, can we tell Johnny about Math? We can tell him and the rest of the class that mathematical truth exists universally, it exists mentally and not materially, and that our minds are judged by math. In the classroom, teachers only declare whether students have reasoned their way through a problem correctly or not. We don’t manufacture its truth. We aren’t the basis of mathematics. Students sometimes even catch our mistakes at the board and let us know that we haven’t reasoned our way through a problem either. I hate when that happens!
Some years ago, the lives of Enron and Arthur Anderson employees were being affected by omnipresent and unwavering mathematical truth. (Sadly, one of those people, embracing despair, committed suicide because he wanted to avoid being held accountable for his part in mathematical dishonesty).
It is also apparent that mathematical truths defy matter and space because such truths can be present in more than one place. We can also say that mathematical truths defy time because such truths never began nor will ever end. 2 x 2 = 4 was true before any of us was conceived and will be true after we’re long gone.
This is just for starters.
Because of the difficulties of the materialist math answer, some offer the mere metaphysical math answer. This answer recognizes certain mathematical properties and the inadequate account for them by materialists. Proponents of the mere metaphysical math answer rightly define the term mind to mean something non-physical so as to preserve a consistent basis for memory and communication (remember that one form of communication is sharing a valid argument). These folks stand in awe of the order, beauty, and universality of math and like to talk of the mystery of it all. I tend to think that these proponents don’t have any children because if they did, they might offer a more satisfying answer than one that simply concludes that mathematics is just out there.
Why is mathematics “out there”?
Of course, math neither begins nor ends. Of course, math defies matter, space, and time, but why?
Given the qualities of mathematical truth already mentioned, what else does mathematical truth imply? We can also say that math is unchanging. We can also say that math is superior to any one of our minds and to all human minds. Proponents of the mere metaphysical math answer engage in pedantic analytic discussions of terms and definitions, but are hard pressed to account for mathematics’ immutability or superiority to the human mind. They rightly humble themselves in light of their finiteness. They wrongly humble themselves before mathematics.
They offer no basis for why math is just out there, but they do admit that the foundation for math cannot be something limited or temporary. The foundations of math have to resemble the properties of math. Rejecting the Bible as God’s Word from the start, proponents of the mere metaphysical math answer offer a solution incompatible with allegiance to the all-encompassing Lordship of Christ. Although the Christian parent or Christian teacher might think so, the Lord of heaven and earth doesn't consider mathematical truth neutral territory.
As I see it, our Lord looks upon mathematics and declares, “This is Mine!”
Christians can account for mathematics on the basis of the biblical triune depiction of God. If truth exists, including mathematical truth, its basis is God whose attributes are reflected in the properties of math. Is mathematical truth unchanging? God is unchanging. Is mathematical truth eternal? Only because God is. Does mathematical truth defy matter, space, time? So does God because He is Spirit. Is mathematical truth an object of thought in non-physical minds and yet superior to human minds? Well, God’s mind is omniscient knowing all truths. Do we stand in judgment of mathematical truth? Not any more than we stand in judgment of God.
Math is not just out there as a mysterious curiosity of the universe. Math pervades all of our lives because God pervades all of our lives. A Christian’s reflection upon math positions him to stand in awe not of it, but of the tri-personal God of the Scriptures (see Ps. 139: 17-18). Since mathematical truth manifests certain properties consonant with the attributes of God as revealed in His Word of Truth the basis and ground for mathematical truth is that God Himself is Truth (Deut. 32:4, John 14:6 John 16:13—a Trinitarian emphasis on God as truth).
We can lead students through these considerations and they will respond with examples of mathematical truths thought by God on their own. I’ve experienced it during my years as a teacher.
The upshot of these Christian mathematical musings is when any of us learn math, we also get to know something of God’s nature because mathematical truths are the eternal thoughts of God. Others may not believe so, but Christians have a basis for thinking so. Gordon H. Clark maintains, “insofar as man knows anything [as truth, mathematical or otherwise] he is in contact with God’s mind. Since further, God’s mind is God [based on His attribute of simplicity], we may legitimately [though figuratively]…say, we have a vision of God.”8
To be continued...
Take up and listen to Episodes 1 & 2 of Urban Puritano
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