[Note: This is the sixth article in an occasional series on apologetics and worldview analysis.]
Over the past few decades evangelicals have expressed a renewed interest in the concept of vocation. No longer is it uncommon to hear call to "think Christianly" about our work or, for academics, their fields of study. Some people (like me) go a step further and claim that we're merely fooling ourselves if we believe that we can approach our vocations at the deepest levels of engagement with a sense of religious neutrality. "Thinking Christianly" about our work is not something we add on as an afterthought; it radically changes the nature of our work.
Not surprisingly, this view is often met with skepticism. Even those who agree with my general point do not see, for example, how there could be a particularly Christian view to subjects like mathematics.
While I certainly understand their hesitation, I do in fact believe there is a Christian view of mathematics. Indeed, I believe that there is a distinctly Christian view of everything.
The reason this idea seems so foreign (if not downright absurd) is that most of our theories about the world have only a minimal pragmatic affect on how we actually live our lives. Both my neighbor and I, for example, may get sunburned even if we hold radically different beliefs about the sun. The fact that I think the sun is a ball of nuclear plasma while he believes that it is pulled across the sky in a chariot driven by the Greek god Helios doesn't change the fact that we both have to use sunscreen. It is only when we move beneath the surface concepts ("The sun is hot.") to deeper levels of explanation ("What is the essential nature of entities like the sun?") that our religious beliefs come into play.
Even the concept that 1 + 1 = 2 -- a formula which almost all people agree with on a surface level -- has different meanings based on what theories are proposed as answers. These theories, claims philosopher Roy Clouser, show that going more deeply into the concept of 1 + 1 = 2 reveals important differences in the ways it is understood, and that these differences are due to the divinity beliefs they presuppose.
But before we can see why this is true, let's review the claims made in my previous article about what constitutes a religious belief.
A belief is a religious belief, says Clouser, provided that (1) It is a belief in something(s) or other as divine, or (2) It is a belief concerning how humans come to stand in relation to the divine. The divine, in this definition, is whatever is "just there." He contends that self-existence is the defining characteristic of divinity, so that the control of theories by a belief about what is self-existent is the same as control by a divinity belief and thus amounts to religious control of all theories.
Whether we refer to it as being self-existent, uncaused, radically independent, etc., it is the point beyond which nothing else can be reduced. Unless we posit an infinite regress of dependent existences, we must ultimately arrive at an entity that fits the criteria for the divine.
Different traditions, religions, and belief systems may disagree about what or who has divine status, or whether such an ontological concept should be considered a "religious belief." But what they all agree upon is that something has such a status. A theist, for instance, will say that the divine is God while a materialist will claim that matter is what fills the category of divine. Therefore, if we examine our concepts in enough detail, we discover that at a deeper level we're not agreeing on what the object is that we're talking about. Our explanations and theories about things will vary depending on what is presupposed as the ultimate explainer. And the ultimate explainer can only be the reality that has divine status.
Returning to our example, we find that the meaning of 1 + 1 = 2 is dependent on how we answer certain questions, such as: What do "1" or "2" or "+" or "=" stand for? What are those things? Are they abstract or must they have a physical existence? And how do we know that 1 + 1 = 2 is true? How do we attain that knowledge?
Let's look at the answers proposed by four philosophers throughout history:
Leibnitz's view -- When Gottfried Wilhelm Leibniz, an inventor of the calculus, was asked by one of his students, "Why is one and one always two, and how do we know this?" Leibnitz replied, "One and one equals two is an eternal, immutable truth that would be so whether or not there were things to count or people to count them." Numbers, numerical relationships, and mathematical laws (such as the law of addition) exist in this abstract realm and are independent of any physical existence. In Leibnitz's view, numbers are real things that exist in a dimension outside of the physical realm and would exist even if no human existed to recognize them.
Russell's view -- Bertrand Russell took a position diametrically opposed to Leibnitz. Russell believed it was absurd to think that there is another dimension with all the numbers in it and claimed that math was essentially nothing more than a short cut way of writing logic. In Russell's view, logical classes and logical laws -- rather than numbers and numerical relationships -- are the real things that exist in a dimension outside of the physical realm.
Mill's view -- John Stuart Mill took a third position that denied the extra-dimensional existence of numbers and logic. Mill believed that all that we can know to exist are our own sensations -- what we can see, taste, hear, and smell. And while we may take for granted that the objects we see, taste, hear, and smell exist independently of us, we cannot know even this. Mill claims that 1 and 2 and + stand for sensations, not abstract numbers or logical classes. Because they are merely sensations, 1 + 1 has the potential to equal 5, 345, or even 1,596. Such outcomes may be unlikely but, according to Mill, they are not impossible.
Dewey's view -- The American philosopher John Dewey took another radical position, implying that the signs 1 + 1 = 2 do not really stand for anything but are merely useful tools that we invent to do certain types of work. Asking whether 1 + 1 = 2 is true would be as nonsensical as asking if a hammer is true. Tools are neither true nor false; they simply do some jobs and not others. What exists is the physical world and humans (biological entities) that are capable of inventing and using such mathematical tools.
For each of these four philosophers what was considered to be divine ("just there") had a significant impact on how they answered the questions about the nature of the simple equation. For Leibnitz it was mathematical abstractions; for Russell it was logic; for Mill is was sensations; and for Dewey it was the physical/biological world. On the surface we might be able to claim that all four men understood the equation in the same way. But as we moved deeper we found their religious beliefs radically altered the conceptual understanding of 1 + 1 = 2.
What all of the explanations have in common, what all non-theistic views share, is a tendency to produce theories that are reductionist -- the theory claims to have found the part of the world that everything else is either identical with or depends on. This is why the Christian view on math, science, and everything else must ultimately differ from theories predicated on other religious beliefs. We may appear to agree on the surface, but dig a little deeper and we find that what we believe about God changes everything.
Other Posts in This Series: