Are Non-Christians Unable to "Account for" Their Counting?

Presuppositionalists are often fond of quoting a statement commonly attributed to Cornelius Van Til, to the effect that

Unbelievers can count, but they cannot account for counting. (Paraphrased by Chris Bolt in his blog entry titled An Objection That Does Not Count; see also, among others, Greg Bahnsen, Van Til’s Apologetic: Readings & Analysis, p. 407)

Similarly, in his essay Counting, Infinity, and the Foundation of Knowledge, James D. Nickel concludes:

In other words, the unbeliever can count without being able to account for counting. Unbelievers can count but they cannot offer a philosophy that accounts for their practice of counting. Only the believer, redeemed by grace through Christ and in subjection to God’s written word, can truly account for the ability to count.

What I have observed as a habit among presuppositionalists who recite this viewpoint, is twofold:

a) They provide no argument to support it, and

b) They do not explain how they as Christians “account for counting” beyond merely asserting that the existence of their god is somehow a necessary precondition for this ability.

In the case of the first deficiency, note that the claim that non-Christians “cannot account for counting” is a categorically negative claim, and the burden of proving such claims is notoriously difficult to meet. Just how would one go about proving such a claim? How does the believer know that there is not some non-Christian out there who can “account for counting”? The reply “Van Til says so” certainly would not be very compelling, unless of course one were confessionally sympathetic to viewing non-Christians in a negative light. But this amounts to an attitude, not a proof. At any rate, typically the farthest that a presuppositionalist usually goes in making good on such self-serving denouncements of non-Christians, is to quote bible verses, a move which suggests that apologists have nothing better than to beg the question when it comes to supporting their assertions about non-Christians.

In his article (cited above), James D. Nickel does make a fainthearted stab at trying to provide some kind of rationale for supposing that counting presupposes the Christian god. For instance, he states:

At the very beginning of mathematical foundations, with simple counting numbers, we are introduced to a concept that transcends and perplexes human comprehension. We can conceive of the concept of infinity (through the counting numbers) only because we are made in the image of the infinite, eternal, and personal God of the Scripture.

Apparently Nickel seems to think that, since the number series is “infinite,” this means that we can only conceive of the number series (qua an infinite series) “because we are made in the image of the infinite, eternal, and personal God of the Scripture.” How precisely this is supposed to follow, is not explained.

But even Nickel points out a significant difference between the Christian god and the number series. Having just affirmed that the Christian god is eternal, Nickel explains this as follows:

By eternal, we mean “without beginning or end.” God is not subject to time.

So, according to Christianity, the Christian god is “without beginning or end.”

By contrast, however, the number series already represents a departure from the superlative characteristics attributed by Christianity to its god:

We see that in the set of natural numbers there is a dim reflection of the nature of this transcendent God. Although this set has a beginning (the number 1), it has no end.

While the Christian god is allegedly “without beginning or end,” the number series does have a beginning. It starts at a specific point, while the Christian god, as Christianity imagines it, has no starting point. Thus the number series “is a dim reflection of the nature” of the Christian god. So quickly its incorruptible brightness loses its sheen.

It is interesting to note, however, that Christianity claims that its god is “infinite.” Nickel explains:

By infinite, we mean “without limitation.” God is not subject to any limitations. He is without boundary limitations.

In other words, Christianity affirms the existence of an actual infinite. Believers, then, could not know when their god’s being stops and when another being (say, some thing it is said to have created) begins. It is “without boundary limitations,” so the believer has nothing to go on to distinguish the Christian god from anything else.

Of course, Objectivists are right in dismissing the claim that such a being exists from this very ascribed attribute, since Objectivism recognizes the fact that the actual is always finite. The axiom of identity tells us this: to exist is to be something specific, finite. If something exists, it is itself, nothing less, nothing more. If the Christian god existed, it would be just one among a gazillion other entities.

But believers are anxious to resist any such conception, so they inflate their god with puffed up imagery, and lofty descriptors to suit.

What’s even more perplexing is the fact that it never seems to occur to apologists like Nickel that the concept ‘infinity’ essentially refers nothing more than to one’s ability to continue extending a series indefinitely. It is true that the number series has no terminus; it is “infinite” in the sense that one can always continue to add more units to whichever specific number he has identified. As Ayn Rand poignantly notes:

An arithmetical sequence extends into infinity, without implying that infinity actually exists; such extension means only that whatever number of units does exist, it is to be included in the same sequence. (Introduction to Objectivist Epistemology, p. 18; emphasis added.)

Understood in this manner, the notion that the number series is “infinite” is rationally sensible, conceptually viable, and in no way implies the existence of a supernatural conscious being which is an “actual infinite.” Indeed, that apologists like Nickel seem to think that the infinity of the number series (which, as I have pointed out, is merely a potential, not an actual) is somehow a reflective indicator of the Christian god, only confirms that the Christian god is in fact merely imaginary. Indeed, we can imagine extending the number series beyond any finite number indefinitely, forever, without implying that anyone will ever undertake such a task.

In the case of the second deficiency which commonly accompanies the presuppositionalist recitation of the claim that non-Christians “cannot account for counting,” namely the failure to provide a specifically Christian “account for counting,” this is to be expected. Exactly how does Christianity “account for counting”? What you can count on here will not be a detailed explanation, but an appeal to superficial, even faulty associations, just as we saw in Nickel’s attempt to link the potential to extend the number series indefinitely to the “infinity” which Christians attribute to their god. And we saw how far that went.

What is lost in the presuppositionalist handling of the entire topic, however, is the inescapable fact that counting is a conceptual activity. But presuppositionalists do not offer a conceptual understanding of numbers and of counting in their “account for counting.” Instead, they want to point to an imaginary character from a storybook as the substance of their “account for counting.”

As an Objectivist, I “account for” counting objectively, specifically by first recognizing that numbers are a type of concept, and thus deferring to the objective theory of concepts. Human minds are certainly capable of counting. Also, Ayn Rand, in developing the objective theory of concepts (Introduction to Objectivist Epistemology), identified the fact that concept-formation is intimately related to measurement (pp. 5-18), noting that measurement as an epistemological process begins at the perceptual level of consciousness (pp. 14-15), and specifically provides an account of concepts of numbers and the process of counting in terms of the objective theory of concepts (pp. 63-64). So contrary to what Chris Bolt claims, my counting is not inconsistent with my worldview's fundamentals (since the conceptual activity of counting rests firmly on and is wholly consistent with the primacy of existence), I am in no way "borrowing" from the Christian worldview (which affirms the existence of invisible magic beings, miracles, knowledge through faith, the notion of "sensus divinitatus," a "Great Commission," the view that human beings are essentially "depraved," the belief that morality is sacrificial in nature, etc.) when I count things. Moreover, not only is there no need to point to some “supernatural” being or other figment of one’s imagination to “account for” counting, presuppositionalists – in claiming that non-Christians “cannot account for counting” – fail to interact with the Objectivist "account for counting" to which I have alluded here.

This is especially curious given the fact that some presuppositionalists do in fact acknowledge the conceptual nature of counting. For instance, Greg Bahnsen describes counting as follows:

Counting involves an abstract concept of law, universals, or order – which contradicts the unbeliever’s view of the universe as a random or chance realm of material particulars. (Van Til’s Apologetic: Readings & Analysis, p. 42n.18)

Notice how Bahnsen seeks to validate the claim that non-Christians “cannot account for counting” by assuming that, by virtue of being non-Christians, they necessarily assume the view that the universe is “a random or chance realm of material particulars.” Bahnsen continues, saying:

By rejecting God’s word, the unbeliever would not in principle be able to count and measure things. (Ibid.)

Here Bahnsen is clearly operating on a false dichotomy: either believe that the Christian god is real, or be committed to the view that the universe is “a random or chance realm of material particulars.” I explore this commonly assumed fallacy and expose its flaws in my blog The Concept of “Chance”: Right and Wrong Uses. But will presuppositionalists allow themselves to learn from this?

Of course, if a person has little or no understanding of how the human mind forms concepts, if he ignores the fact that numbers are a type of concept, and adheres to a worldview which blurs the distinction between the real and the imaginary (as Christianity does), then perhaps he might think that there’s something fundamentally supernatural involved in the process counting things. The process of counting is mysterious to him, so he assumes it is mysterious to everyone else, and uses this platform of ignorance as an opportunity to reinforce a confessional investment. In this sense, he would be essentially operating on an inference from ignorance: he does not understand what is happening in his mind when he counts things, so he figures that some invisible magic being is ultimately responsible for this phenomenon.

Now I have pointed out before that, as a worldview, Christianity suffers from a fatal deficiency just by lacking a theory of concepts (see for instance here and here). You can comb the Psalms, peruse the books of the prophets, or analyze the Pauline epistles, but you’ll find no theory of concepts proposed to guide its readers in understanding the process by which the human mind forms concepts and integrates them into larger cognitive structures. Christianity has no theory of concepts, so it cannot provide a conceptual “account for counting.” Thus it leaves believers completely in the dark on just how the human mind enumerates anything.

by Dawson Bethrick