Shall We Reason Together? Part 8: Virtual Certainty

Here is a thought experiment. Imagine that you are given access to a banking machine, and told that you may withdraw in one transaction up to 500,000 dollars. You are also permitted to make subsequent withdrawals, but no withdrawal can amount to more than half of the previous withdrawal. How many withdrawals will you have to make before you have a million dollars?

The answer is that you will never reach a million—quite. Enough withdrawals, however, will bring you to within a penny of a million. If it were possible to split a penny, you could get within half-a-cent, then a quarter‐cent, and so forth. Given an infinite number of withdrawals, you could arrive at an amount that was so close to the million that no human could measure the difference. You would never get to the full million dollars, but the difference would be infinitesimal. You could approach the million asymptotically.

I have argued that necessary inferences (conclusions) drawn from Scripture are just as authoritative as the direct statements of the Bible. Necessary inferences are those that are drawn deductively through valid syllogisms. Since these inferences are drawn from true premises (what else could Scriptural premises be?), they are necessarily true, and consequently, they are necessarily authoritative.

Inferences that are reached inductively are not necessary, but merely probable. I have suggested that such inferences should be pressed no more vigorously than their probability warrants. Generally, this means that they need to be held and advocated with greater caution than necessary inferences.

Probability, however, comes in degrees. As the degree of probability increases, uncertainty over the soundness of an inference has to decrease correspondingly. At the upper end of the scale, probability may become so strong as to constitute virtual certainty.

In the thought experiment, you could never quite get to a million dollars—but you could get so close to it that no human could tell the difference. You approached a million asymptotically. In the same way, the probability for the truth of a conclusion may be so strong that it approaches certainty asymptotically.

What I now wish to suggest is that some inductive conclusions are so probable that they must be treated as virtually certain. Such inferences, even though drawn inductively, are just as authoritative for belief and practice as necessary inferences. When the degree of probability is high enough, even inductive inferences drawn from Scripture must stand with all the authority of Scripture itself. I suggest that this must be the case for at least two reasons.

The first reason is that all knowledge of biblical propositions, and therefore of biblical truth, is already inductive in nature. Reading is an irrefragably inductive exercise. The only way to understand a single sentence (either in the Bible or out of it) is to read it inductively. All exegetes know this: interpretation at every level is an application of inductive reasoning. Every semantic and semiotic component of writing is identified and correlated inductively. There is no such thing as a straightforward, uninterpreted morpheme, lexeme, phrase, clause, sentence, paragraph, or discourse. Everything is interpreted, and interpretation is always an exercise in inductive logic.

To put it bluntly, if inductions can never be authoritative, then Scripture is never authoritative, for all knowledge of Scripture is inductive. We do not know any brute facts, not even in the text of Scripture. We examine the statements of Scripture and draw conclusions about what God has said. In some cases, our conclusions are less probable, while in others they are virtually certain. In every instance, however, our understanding of Scripture arises through inductive reasoning. That is the first reason that we must treat at least some inductive inferences as authoritative.

The second reason is that almost all biblical doctrines must be assembled inductively. With very few exceptions, even the fundamentals are put together inductively from biblical assertions. Because doctrines are logical constructs, it is not uncommon to encounter biblical evidence that, taken at face value, does not neatly fit. In such cases, the doctrine must be modified or the evidence must be explained.

Consider the question of Christ’s deity. Anyone who has ever argued with a Jehovah’s Witness knows, first, that some biblical passages can be construed to contradict the suggestion that Jesus is God, and, second, that there are ways of explaining away the texts that refer to the deity of Christ. When we weigh the evidence, however, we discover that the verses that are used to refute Jesus’ divinity (John 17:3, e.g.) actually do help us understand it when they are taken in context and their implications are grasped. We also find that the Arian explanations of verses like John 1:1 and Titus 2:13 are generally supported by bad handling of the grammar in the original languages. We conclude that the probability of Jesus’ divinity is very high. We have no trouble insisting that the deity of Christ is right at the center of the Christian faith, even though we discover and support that doctrine inductively. We even require people to confess it in our churches and institutions.

Does the Bible teach the deity of Christ? Of course it does! Yet we both grasp and defend this doctrine inductively. The evidence is not without some ambiguity, but the degree of probability is so strong that no thoughtful person would contradict it. Furthermore, the stakes are so high that no sensible person would risk ignoring it.

Therefore, in at least some cases, conclusions drawn through inductive reasoning are so probably true and so authoritative as to be virtually indistinguishable from those drawn through deductive reasoning. In both instances, these inferences are just as authoritative as the statements of Scripture itself—which, as a matter of fact, must also be interpreted through inductive reasoning before their authority can be applied.

ERRATUM The following statement appeared in the last In the Nick of Time.

“Inferences that are drawn by strict induction (a valid syllogism) from biblical propositions (true premises) are always true and must be just as authoritative as the Scriptures themselves.”

The word “induction” should be replaced by “deduction.” We apologize for the confusion, and temper our claim of having achieved personal perfection. Our thanks to Mr. Jesse Van Der Molen for catching this error.

Church Lock and Key.

George Herbert (1633)

I Know it is my sinne, which locks thine eares,
And bindes thy hands,
Out-crying my requests, drowning my tears;
Or else the chilnesse of my faint demands.

But as cold hands are angrie with the fire,
And mend it still;
So I do lay the want of my desire,
Not on my sinnes, or coldnesse, but thy will.

Yet heare, O God, onely for his blouds sake
Which pleads for me:
For though sinnes plead too, yet like stones they make
His blouds sweet current much more loud to be.
–––––-
^{This essay is by Kevin T. Bauder, president of Central Baptist Theological Seminary. Not every one of the professors, students, or alumni of Central Seminary necessarily agrees with every opinion that it expresses.}