Shall We Reason Together? Part Nine: The Problem of Premises

All cats are dogs.
All dogs are quadrupeds.
Therefore, all cats are quadrupeds.

We merely have to glance at the above syllogism to know that something is wrong—but what? It is formally valid. The conclusion is actually true. When we examine the minor premise, however, we discover that this premise is false. The argument is unsound, and consequently its conclusion does not compel us. Though the conclusion happens to be true, it is true “by accident.” In other words, its truth has nothing to do with the argument itself.

No argument, however valid, can be sound unless it reasons from true premises. No conclusion, however necessary, can be compelling if it has been inferred from premises that are false or even questionable. In other words, the usefulness of a logical inference is always limited by the truth-value of its premises. Even when logic is functioning flawlessly, a false premise will always yield a worthless conclusion.

The problem is that logic, in and of itself, is never adequate to establish the truth of the premises. Logical arguments always begin with something that is “given,” and where nothing is given, no conclusions can be drawn. Without some prior assumption or information, even the most rational beings would have nothing to reason about. C. S. Lewis pictures this situation famously in his allegory, The Pilgrim’s Regress. [Incidentally, this is one of the books that every collegian ought to read.] In that allegory, the protagonist is rescued from the Spirit of the Age (pictured as a giant) by Reason, who is depicted as a sun-bright woman on a black horse. She slays the Spirit of the Age by pointing out the self stultifying nature of his arguments. When the protagonist begs her for positive direction, however, she replies, “I can tell you only what you know. I can bring things out of the dark part of your mind into the light part of it.” Reason by itself cannot carry one forward. Lewis’s metaphor for this limitation is that “Reason is a virgin.”

Where do premises come from? Sometimes they are sheer assumptions or even fabrications. Sometimes they are given by tradition, custom, “common knowledge,” experience, or expert authority. Often they rely upon inductive observations. Wherever they come from, however, premises must be true before deductions drawn from them can be trusted.

At first glance, it might appear that this limitation would not affect conclusions drawn by valid arguments from Scripture. Since the Bible is inerrant, everything that the Bible affirms is true. Therefore, any conclusion necessarily arising from biblical affirmations must be true, right?

Right—but only as long as the premises really are biblical affirmations. We must be sure that what we assert as a premise is really what the Bible affirms. Very often, it is not.

I have pointed out more than once that we read the Bible inductively. All of our understanding of Scripture arises from the analytical and inductive work of the mind as we read. Since inductions never yield epistemological certainty, all of our biblical understanding occurs at the level of probability. Sometimes the degree of probability is so high as to approach certainty asymptotically, but it remains probability. Sometimes the degree of probability is lower—much lower. Sometimes our assertions about what the Bible says are actually improbable, and sometimes they are even implausible.

Reasoning from Scripture involves a process of alternating between inductions and deductions. This process is sometimes called abduction or retroduction. In order to draw deductive conclusions, we must first have premises, and those premises are usually supplied inductively. As a rule, we are not in a position to draw necessary inferences from biblical premises until we have drawn more-or-less probable inferences about what the Bible actually says.

This method is not a problem as long as we recognize its limitations. Given true premises, a valid deduction will yield true conclusions. When an element of uncertainty is introduced into the premises, however, the certainty of the conclusion has to suffer. To the degree that premises are less certain, any inference (however necessary) will also be less certain. If a premise contains error, then the conclusion cannot be trusted. As with computers, so with arguments: Garbage In, Garbage Out.

Generally, our problem is not so much that we are too confident in the validity of our inferences as that we overrate the probability of our premises. We rely upon terms that we have not carefully defined. We leap to hasty generalizations. We overvalue some premises because of emotional involvement or vested interest. We allow ourselves to be persuaded by the popularity of a premise, mistaking wide acceptance for self-evidence. We become enamored with a premise because of the authority or likeability of some person who advances it—or else we permit our dislike of our opponents to color our evaluation of the assertions that might count against our beliefs. We fail to see the flaws in faulty analogies. We take perverse delight in premises that appear to overthrow established opinions. We confuse cause with effect, or we identify events as causes when they are merely precursors. We judge a counter-premise guilty and dismiss it prematurely because of its associations. We allow ourselves to be distracted by matters that have nothing to do with the premise at all. We base arguments upon unexamined assumptions, sometimes because we don’t know how to conduct the examination, and sometimes because we are simply too lazy or too proud to go through the trouble. In all these ways (and more!) we end up thinking that our premises are more certain than they actually are.

We still have to read the Bible, and we still have to understand it. The assertions of the Bible are sufficiently clear that a decent reader can grasp its core affirmations without special intellectual equipment. In other words, Scripture is perspicuous. Some biblical teachings, however, are less clear. We ought to be careful, not only in the way that we affirm our understanding of the less certain teachings, but also in the way that we reason from them.