Yesterday I wrote that in order to advance a religiously informed public philosophy, it was useful to clarify what was meant by a religious belief . In the comments section Barry Addington notedthat the mission of First Things is not to advance a religiously informed public philosophy “if the ‘religious’ in ‘religiously informed’ is defined as broadly” as I had defined it and that “it should be clear that whatever the word “religious” means, in practice FT gives a voice to only a fraction of religiously informed authors (and rightly so).”
This is certainly true. The purpose of clarifying our terms was meant only to clear the decks and provide a justification for a religiously-informed approach. As Roy Clouser says, religious neutrality is a myth. Everyone brings their religious beliefs to the public square. (We at FT —and many of our readers—are just more explicit and less apologetic about it.
Once we agree that everyone has religious beliefs (which requires understanding what is meant by the phrase) it is easier to show how those beliefs undergird all of our other beliefs. The most important ramifications are likely for culture and politics. But to provide an a fortiori justification for my claim, I’ll try to show how religious beliefs shape a most unlikely area: mathematics.
This will likely sound odd (if not downright absurd) since beliefs about math and science are presumed to be completely separate from religion. The reason for this is that most views shaped by these areas have a minimal pragmatic affect on how we actually live our lives. Both my neighbor and I, for example, may get sunburned even if we different scientific beliefs about the sun. The fact that I think it 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 sun?”) that our religious beliefs come into play. (Note: To avoid confusion let me reiterate that what I’m claiming is that the beliefs come into play only on these deeper levels of explanation , which admittedly most people never think about.)
For example, even the concept that 1 + 1 = 2, 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 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, according to Clouser, is whatever is just there . 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, but they all agree 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 Judeo-Christian view on math, science, and everything else must ultimately differ—at the most primary level—from theories predicated on other religious beliefs.
If such beliefs can shape our view of mathematics, how much more will they shape such areas as anthropology, political science, or sociology? By acknowledging the fact that our most basic premises differ based on what discern is ultimately real and non-reducible, we are better able to understand why our conclusions these areas can differ so radically from those who hold different religious presuppositions.
