Shall We Reason Together? Part 8: Virtual Certainty

by Kevin T. Bauder at http://www.sharperiron.org/2006/11/07/shall-we-reason-together-part-8-virtual-certainty/#more-865

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.}

Shall We Reason Together? Part Seven: Probability and the Limits of Logic

by Kevin T. Bauder

I have been arguing against a philosophical theory that denigrates reason by stating that inferences drawn from Scripture are always lower in authority than the straightforward declarations of Scripture. I have attempted to show that this theory is bad philosophy, bad exegesis, and bad theology. Necessary inferences drawn from Scripture are just as authoritative as the Scriptures themselves.

Now it is time to back up and to discuss certain conditions that necessarily limit the usefulness of logic when understanding the Scriptures. Within those limits, logic is necessary, useful, and in at least some instances, unerring. Outside of those limits, logic can become a tool with which we deceive ourselves and others. It is important for us to know where those limits are.

The first condition has to do with the distinction between deductive and inductive reasoning. In deductive logic, the conclusions arise necessarily from the premises. When a deductive syllogism is valid and the premises are true, the conclusion must without exception be true. 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.

For example, Scripture nowhere teaches the doctrine of the Trinity in so many words. What the Bible teaches in various places is that God is One; that the Father, Son, and Holy Spirit each are God; and that these three are somehow distinct from each other. When we reason deductively from these truths, we derive the doctrine of one God in three divine persons.

The same is true of the hypostatic union. The formula of Chalcedon is not found in the New Testament. Rather, the New Testament shows in one place that Jesus is truly God; in another place that He is truly Human; in yet another place that He is one person. It is by reasoning from these truths deductively that we define the two-natures-one-person dogma.

Neither the Trinity nor the hypostatic union is stated in so many words anywhere in the Bible. Nonetheless, for orthodox Christians these doctrines are as authoritative as any biblical statement. They are rightly regarded as fundamentals of the faith. One reason that they are so authoritative is that they are necessary inferences, conclusions that are unavoidable in the light of biblical revelation.

Most theological and ethical arguments, however, are inductive rather than deductive. They may even alternate between the two methods. In an inductive argument, we draw inferences that are not necessary. They are merely probable. Their degree of probability limits the extent to which we ought to press their authority.

In my opinion, the Bible teaches premillennialism, but not with deductive certainty. The premillennial theory is, at best, probable (I think quite probable, given the way that I view the evidence—but still only probable). Pretribulationism, while still probable (in my opinion), is less certain than premillennialism. The identity of the sons of God in Genesis 6 is only marginally probable—and on that point I am not even revealing my own view!

One must not confuse certainty with authority. God’s Word teaches exactly one view of the nature of the millennium, the timing of the rapture, and the identity of the sons. Whichever view is taught in Scripture is absolutely authoritative. Our problem, however, is that we are only relatively sure which view the Bible teaches.

What are the consequences of this uncertainty? When our conclusions are merely probable, we must hold ourselves ready to reexamine them in the light of new information or new perspectives. We should be conscious of (and willing to state) the conditions under which our minds could be changed. We should advocate our conclusions, but only with the force that their probability warrants. We should be willing to recognize the strength of the evidence that counts against our own conclusions. We should be fair with those who disagree with us—in fact, we should be able to state their position as well as they themselves do. We ought to exhibit charity toward those who disagree with us, displaying evenness in our responses. In short, we must manifest a spirit of genuine humility while advocating the conclusions that we believe are reasonable in light of the evidence.

Of course, most of these attitudes should characterize the work of the mind under all circumstances. Docility (teachability) is a virtue that we must never outgrow. Furthermore, the key difference between instruction and indoctrination is the willingness to tell the whole story, i.e., to expose ourselves and others to conclusions that we think are incorrect, and to appreciate the evidence that supports those conclusions—even at the risk of changing our minds.

Most of the ethical and theological conclusions that we draw from the Scriptures are inductive, and consequently they are probable in nature. We should recognize our lack of certainty about these inferences. Lacking certainty, we should hold our conclusions humbly. That does not imply, however, that we should become timid about drawing inductive inferences.

Some individuals are reluctant to reach a conclusion unless they can hold it with certainty. In the absence of overwhelming evidence, they defer judgment indefinitely. Such timidity is as great an error as arrogance. God would not speak to an issue if He did not intend to communicate something to us, and He would not communicate if He did not expect us to understand. We must try to reach some conclusion, even when Scripture is not as clear as we would like.

Furthermore, as long as we advance them humbly, we do not need to be afraid to advocate such conclusions. Indeed, we must: the truth is authoritative, even if we grasp it only imperfectly. God’s sovereignty obligates us to believe and to practice what we believe God has said, and Christian charity obligates us to seek to convince our brethren of whatever we think is true. The same is true of our brethren, and we should not take offense when we find them seeking to convince us of what they believe to be true. Rather, we should be grateful for such a demonstration of their brotherly love.

Necessary inferences drawn from biblical premises are just as authoritative as the text of Scripture itself. A necessary inference is one that is drawn through valid arguments from true premises. Conclusions drawn inductively rather than deductively are probable rather than necessary. Probable inferences should generally be advanced with greater caution. They should be advocated only as strongly as the probability that they are true.

This rule of thumb prompts a question. Are there any instances in which inductive inferences could and should be advocated as strongly as deductive ones? This is an important question, and it concerns some of the core of the Christian faith. Therefore, I want to take a brief detour to answer it. Afterwards, I shall address the second condition that limits the usefulness of logic as a tool for drawing conclusions from Scripture.

PERSEVERANCE.

George Herbert)

My God, the poor expressions of my Love
Which warm these lines, and serve them up to thee
Are so, as for the present, I did move
Or rather as thou movedst me.
But what shall issue, whither these my words
Shall help another, but my judgment be;
As a burst fouling-piece doth save the birds
But kill the man, is seal’d with thee.
For who can tell, though thou hast died to win
And wed my soul in glorious paradise;
Whether my many crimes and use of sin
May yet forbid the banes and bliss.
Only my soul hangs on thy promises
With face and hands clinging unto thy breast,
Clinging and crying, crying without cease
Thou art my rock, thou art my rest.—————-
^{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. In The Nick of Time is also archived here}

Shall We Reason Together? Part Six: Reason and “Reason”

by Kevin T. Bauder

Whatever Scripture affirms is absolutely authoritative. Many of the biblical affirmations imply other affirmations. The question is, how authoritative are the affirmations that Scripture implies?

Some people suggest that only the bald statements of Scripture exert truly divine authority, and that all inferences drawn from Scripture, however necessary they may be, come with a lower level of authority or with no authority at all. These people would argue that we must not insist upon such inferences as matters of belief and practice.

I have been arguing to the contrary. I believe that it is wrong to limit the authority of any necessary implication of Scripture. Rather, the necessary inferences that we draw from the Bible should be accepted with all the authority of the Bible itself. They are part of what God has revealed in His Word.

In reading the Bible, however, we find that the writers of Scripture are sometimes highly critical of human reasoning. This creates a problem for someone who holds my view: how can reasoned conclusions be as authoritative as Scripture itself when Scripture sometimes seems to take a dark view of reason?

The problem is not simply mine. It is one that is present within the pages of Scripture itself. As we have seen, the writer to the Hebrews thought that his readers should have reasoned to certain conclusions from brief statements in the Old Testament. Those conclusions should have been absolutely authoritative for them. Their failure to reach those conclusions was a token, not merely of intellectual limitation, but of spiritual immaturity. Likewise, Jesus thought that the Sadducees should have recognized certain implications about the resurrection from a verse in the Old Testament. Jesus did not treat these conclusions as a separate thing from knowing Scripture. Instead, He accused the Sadducees of not knowing Scripture, and the accusation was grounded in their failure to draw the necessary inferences from the text.

Both Jesus and the writer to the Hebrews thought that people should recognize the authority of inferences drawn from the text of Scripture. For Jesus, drawing a correct inference is tantamount to knowing Scripture itself. In Hebrews 5, drawing sound inferences is an indispensable aspect of spiritual maturity. Given this high view of necessary inferences, how could Scripture elsewhere speak so disparagingly of Reason?

The answer is that “Reason” (in quotation marks, with a capital “r”) is not the same thing as reason. In the latter instance, reason is a synonym for logic, whether deductive or inductive. In the first, “Reason” denotes something like plausibility. In this sense, when people say that an idea is reasonable, they mean that it seems credible or likely to them. I suggest that what the Scriptures disparage is not reason (the drawing of sound inferences from the text,) but rather the wrong use of “Reason.”

In a statement that allows no exceptions, Paul writes that humans, having rejected God, became empty in their reasonings and stupid (literally “ununderstanding”) in their hearts (Rom. 1:20-21). He grounds this observation in the fact that all creation points to the True and Living God. When people reject God, they must still explain what they see in creation. All their attempts, however, are skewed. Due to their prior moral commitments, natural humans invariably draw the wrong conclusions concerning the Creator.

Such people cannot reason correctly. Sound reason requires us to reason in valid syllogisms from true premises. Depraved humans, however, always begin with untrue premises. Only meaningless conclusions can be drawn from false assumptions. By definition, natural human reasoning about God is unsound—even when the arguments are formally valid.

That is precisely why natural humans cannot know the things of the Spirit of God (1 Cor. 2:14). They rely upon false assumptions, and therefore they do not welcome divine truth. Given their pre-commitments, God’s revelation seems absolutely ludicrous to them. They invent alternative explanations that fit their own perceptions of what is plausible.

In fact, they construct elaborate intellectual systems in order to explain away the God of the Bible. These systems are the “strongholds” that Paul condemns in 2 Corinthians 10:3-6. Paul made it his business to dismantle such strongholds by casting down the false reasoning (reasoning based upon false assumptions) and bringing every thought-system into captivity to the obedience of Christ. He did this, not by using carnal weapons such as coercion, but by using spiritual weapons, namely, by challenging the false assumptions and invalid arguments upon which the unsound reasoning was based. Actually, 2 Corinthians is filled with examples of that activity.

Invalid arguments are like bad plumbing. Even if they are connected to true premises, the water never gets to the tap. Valid arguments that rely upon false premises are like good plumbing that has been hooked up to foul water. However functional the plumbing itself may be, nothing drinkable will come out of the tap.

Natural humans invariably reason from first premises that are false. Sometimes they also reason in ways that are not valid. They do both of these things in order to protect themselves from the full knowledge of God that is breaking in all around them. They use “Reason”—bad “Reason”—as an engine against the Almighty. This is the depraved “Reason” that Scripture condemns.

Not once does the Bible ever rebuke the drawing of valid inferences from true premises. In fact, the Bible overtly requires God’s people to draw valid inferences from its own statements. Clearly, this is not the “Reason” that God condemns. It is a part of spiritual maturity, and, indeed, an aspect of knowing Scripture itself. As Jesus intimates, we do not know the Scriptures unless we know what the Scriptures imply.

There is such a thing as bad reason. The solution for bad reason, however, is never simply to abandon rationality. The solution for bad reason is always good reason. We must replace bad arguments with better arguments.

More than that, we must be humble enough to acknowledge that some truths could never be discovered by any amount of argument. Without revelation, reason is always inadequate. One aspect of reasoning well is to know the limitations of reason itself. Perhaps we had better turn our attention to some of those limitations.

Conscience.

George Herbert (1633)

Peace, prattler, do not lour:
Not a fair look but thou dost call it foul;
Not a sweet dish but thou dost call it sour;
Music to thee doth howl.
By list’ning to thy chatting fears,
I have both lost mine eyes and ears.

Prattler, no more, I say:
My thoughts must work, but like a noiseless sphere.
Harmonious peace must rock them all the day:
No room for prattlers there.
If thou persistest, I will tell thee
That I have physic to expel thee.

And the receipt shall be
My Saviour’s blood: whenever at His board
I do but taste it, straight it cleanseth me,
and leaves thee not a word;
No, not a tooth or nail to scratch,
and at my actions carp, or catch.

Yet if thou talkest still,
Besides my physic, know there’s some for thee:
Some wood and nails to make a staff or bill
For those who trouble me:
The bloody cross of my dear Lord
Is both my physic and my sword.

—————-
This essay is by Kevin T. Bauder, president of Central Baptist Theological Seminary. Not every one of Central’s professors, students, or alumni necessarily agrees with every opinion that it expresses. In The Nick of Time is also archived here.

Discuss this article.