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For to say of what is that it is not, or of what is not that it is, is false. And to say of what is that it is, and of what is not that it is not, is true.
—Aristotle, Metaphysics TRUTH, n. An ingenious compound of desirability and appearance.
—Ambrose Bierce, The Devil’s Dictionary
TOPICS
• Objectivity and Truth
• Probability, Evidence, and Truth
• Self-Evidence
• Experiential Evidence
• Strategies for Evaluating Premises
This chapter provides an introduction to one of the central merits of arguments: the truth of premises.
In a way, the entire book is about truth, since it aims to offer guidance, by way of good reasoning, for anyone who wishes to know the truth. But the point of this chapter is more specific: it aims to provide detailed practical directions for thinking about whether premises are true.
Remember—it takes only one false premise to render any argument unsound.1 A false premise doesn’t guarantee that the conclusion is false, since anyone can concoct a bad argument for a true conclusion.
But if the unsound argument is the best reason you have for that conclusion, then it does guarantee that you have no good reason to accept the conclusion as true.
9.1 Objectivity and Truth
9.1.1 Two Laws of Truth
There are two venerable so-called laws of truth which serve us well for practical purposes. One of them,
1. There is one exception. Some arguments have “throwaway premises” that should not be included in the clarification because they make no logical contribution to the argument. If one of these is false, it is not in the clarification so it doesn’t make the argument unsound (so, excluding it is an application of the principle of charity). Suppose someone argues as follows: All men are mortal; Socrates is a man;
Socrates is fat; and thus Socrates is mortal. You would not include Socrates is fat in your clarification, so it doesn’t matter whether it is true or false.
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the law of noncontradiction, says that no statement is both true and false. It follows from this that truth is objective and absolute—there cannot be any statement, for example, that is true for you but false for me. Its flip side is the law of the excluded middle, which says that every statement is either true or false. It follows from this that there is no middle ground between the true and the false. Truth- values are evaluations—like true and false—that can be given of how well a statement fits with the world. (In the same way, moral values include evaluations—like good and evil—that can be given of, say, actions; and aesthetic values include evaluations—like beautiful and ugly—that can be given of, say, paintings). Another way of stating the law of the excluded middle is to say there are exactly two truth-values—namely, true and false—with nothing in the middle.
Why, then, is it so commonly asserted that truth is relative, that “what is true for you may be false for me”—a remark that seems to violate the law of noncontradiction? According to one poll, 62 percent of American adults believe that “there is no such thing as absolute truth.” The proportion rises to 74 percent for those ranging in age from 18 to 25.2
Should this be interpreted as flagrant disregard for the law of noncontradiction? Probably not. The survey response provides a good opportunity to apply the principle of charity; these apparent denials of absolute truth are often used as a convenient shorthand for a variety of other related and reasonable expressions, including these:
What you believe to be true I may believe to be false.
What works in your life may not work in mine.
The way you see things may not be the way I see things.
The evidence available to you may not be available to me.
What is reasonable for you may not be reasonable for me.
Neither one of us is in the position to decide the truth for everyone everywhere always.
These paraphrases not only are fully harmonious with the law of noncontradiction, but also are absolutely true.
As Aristotle says, a true statement is one that says of what is that it is and of what is not that it is not.
What is may appear to you to be different from the way it appears to me. And you may desire it to be different from the way I desire it to be. But this can’t make what is be two different ways at the same time; it can be only the way it is. When Ambrose Bierce writes satirically of “an ingenious compound of desirability and appearance” it is not really truth that he refers to (and he knows it) but what is often believed to be the truth.
Guideline. For practical purposes, assume that no statement is both true and false and that every statement is either true or false.
2. Poll conducted by the Barna Research Group. It does not say whether those polled believed it to be absolutely true that there is no absolute truth.
Two Practical Laws of Truth
1. Law of noncontradiction—no statement is both true and false.
2. Law of excluded middle—every statement is either true or false.
9.1.2 Ambiguity Rather than Relative Truth
Some statements appear to violate these laws even though, on closer inspection, they do not. Consider the following:
Today is July 9.
My name is David Carl Wilson.
A train station is one mile from here.
Chocolate ice cream tastes bad.
When I express these words here and now the statements are true. But when you express them at a different place and time, the statements are probably false. Does this mean they are both true and false or, perhaps, that they are neither?
No. In each case there are two different statements, one true, the other false. We are tempted to think otherwise only because the statements can be referentially ambiguous (to make use of terminology from Chapter 5). When I say today on July 9, it refers to July 9—thus, it can be disambiguated with the true statement Today, July 9, is July 9. But when you say it on November 18, it refers to November 18, and would be properly disambiguated by the false statement Today, November 18, is July 9. My name is David Carl Wilson and A train station is one mile from here are similar. The referents of my and here would change with a change of speaker and location; when disambiguated, it would become clear that the statement with a different referent is a different statement.
Chocolate ice cream tastes bad is a trickier case. When I say it now it is true, but I probably mean to allow that it could be false when you say it or even when I say it next month. (If I mean instead that it tastes bad always and for everyone—and that you’re just mistaken if you think it tastes good—then I may have a strange view, but there is no apparent lack of objectivity to explain away.) But the statement includes no expression that changes its referent when expressed by a different person or at a different time or in a different place. This is because such an expression is implicit; what I am really saying is Chocolate ice cream tastes bad to me now, which can be made even clearer as Chocolate ice cream tastes bad to David Carl Wilson on July 9. So when you say it, or when I say it next month, it really is a different statement with potentially a different truth-value. The same thing is usually true of any other sentence including a subjective verb such as tastes, looks, smells, feels, or sounds.
Guideline. If it looks as though the truth-value of a statement will be different depending on who
expresses it, it is usually because the statement is referentially ambiguous. Look for the ambiguous term, which may be implicit, and eliminate the ambiguity before evaluating its truth.
EXERCISES Chapter 9, set (a)
Paraphrase each statement to eliminate the appearance that its truth is relative. (You do not need to make the statement true; simply eliminate any possibility of referential ambiguity.)
Sample exercise. My state is one of the biggest in America.
Sample answer. California is one of the biggest states in America.
1. Harleys are the best-sounding bikes on the road.
2. My brother is shorter than I am.
3. Last year our country enjoyed a boom in the stock market.
4. The home team is enjoying a winning season.
9.1.3 Some Cases in Which You Can’t Decide
I have described the two laws of truth as “useful for practical purposes”—not as necessary, inviolate, and unbending. This is because language is not always law-abiding. The ordinary folks who constantly use language in new and serviceable ways seldom get a note from their logician first. The result is that there are some interesting and puzzling cases in which it is at least conceivable that a statement is both true and false, or that it is neither true nor false. And in each case, there is not any simple and uncontroversial way of settling the matter (though in none of these cases is there any worry about whether truth is objective).
• Robert is bald. (Imagine that Robert is exactly in the border area between bald and not bald.)
• Hans is a Kraut. (Imagine that it is true that Hans is German, but false that Hans is deserving of disparagement on that count.)
• This sentence is false. (Just think about it!)
• Hercules cleaned the Augean stables. (It isn’t clearly true, since Hercules didn’t even exist, but it also seems mistaken to say it is false, since it is certainly truer than, say, Hercules cleaned the Augean stables using power tools.)
Sometimes there is a well-defined fictional world that a character such as Hercules inhabits; in those cases, the best strategy is to evaluate premises like Hercules cleaned the Augean stables according to whether they are true or false in their fictional world. Otherwise, in the fairly unusual instances when statements like these four appear as premises, it is best to evaluate them as can’t decide, with an explanation.
Generally, as we will see, when you evaluate a premise as can’t decide it will be because the evidence you have is more or less evenly balanced; if you were able to collect more evidence, you would be able eventually to settle the question. But it is at least conceivable in these four cases that the reason for evaluating a premise as can’t decide is that there is no fact of the matter—perhaps the statement is neither true nor false, or both true and false, and thus there is no choice to be made regardless of how much evidence you go on to collect. (On this option, indeterminate could actually be a third truth-value, between truth and falsity.) Fortunately, given our practical aims in this text, we don’t need to decide why we can’t decide in these sorts of cases.
Guideline. The rare statements that appear to violate the two laws of truth, yet do not merely suffer from a referential ambiguity, should be evaluated as can’t decide, with an explanation.
9.2 Probability, Evidence, and Truth
What makes a statement true is the way the world is; and it is always possible for me to make a mistake about the way the world is. This is because the world is one thing, while my judgment about the world is something else—and as the ancient proverb says, there is many a slip ‘twixt the cup and the lip. Many things can go wrong in that gap between the world and my judgment about it, no matter how tiny the gap might be. I may have poor evidence. I may be subject to wishful thinking. I may be inattentive. I may be fooled. Thus, it is ordinarily better to avoid evaluating premises with the unmodified adjectives true and false and to prefer expressions such as probably true and probably false (or even, in the strongest cases, certainly true and certainly false, assuming that by this we mean extremes in probability).
9.2.1 Probability as a Measure of Evidence
But what exactly is meant here by probably? There are at least three different and legitimate notions of probability. The one that we are most concerned with in this text is epistemic probability. which is the likelihood that a statement is true, given the total evidence available to you—that is, given all of your background beliefs and experiences. (Epistemic means having to do with knowledge.) This is the notion of probability that should be used in your evaluation of premises. To say in your evaluation that a premise is probably true is just to say that you have fairly good evidence for its truth.
Unlike truth, epistemic probability always comes in degrees. It ranges along a continuum that can be expressed either colloquially (ranging from certainly true to certainly false) or quantitatively (ranging from 1 to 0, respectively). Here are some examples:
Degrees of Epistemic Probability
Colloquial Quantitative
Certainly true Probability of about .99 or 1
Probably true Probability of about .75
Can’t decide Probability of about .5
Probably false Probability of about .25
Certainly false Probability of about .01 or 0
Although it can sometimes be useful to express these probabilities quantitatively, doing so is likely to convey a false sense of precision. I might be able to tell the difference between beliefs with epistemic probabilities of .6 and .9 (that is, those that are somewhat probable and those that are very probable), but I doubt that I could discriminate between a .84 and a .85 belief. So I will rely chiefly on the less precise—but less misleading—colloquial expressions.
Epistemic probability, again unlike truth, has a very definite relative component. It is relative to you.
It is your evidence—your background beliefs and experiences—that determine whether a statement is epistemically probable for you. There is widespread agreement about epistemic probabilities among many people regarding many statements. This is because we share such a wide range of background beliefs and experiences. Anyone with a rudimentary understanding of U.S. geography, for example, would assign a very high epistemic probability to this statement:
Alaska is larger than Rhode Island.
But consider this statement:
Minnesota is larger than Oregon.
I would have to say that I can’t decide (or that it has an epistemic probability of about .5). My meager evidence does not point clearly in either direction. But there are others (the current governors of the two states, for example, or those who are interested enough to Google it) who have evidence for its truth or falsity which is every bit as strong as the evidence most of us share regarding the statement about Alaska and Rhode Island. For them, it is either almost certainly true or almost certainly false (that is, it has an epistemic probability either close to 1 or close to 0).
It is important to add that epistemic probability has an objective component as well. Given the evidence that you have, there is nothing relative about how probable it makes the premise. There is a fact of the matter about how probable it is—regardless of whether you assess its probability correctly or not. In this way, epistemic probability is like the strike zone in baseball. A pitched ball is in the strike zone if it is over home plate and between the knees and arms of the batter. The strike zone is relative to the batter because a shorter batter or a batter who crouches will have a smaller strike zone. But it also has an objective component. Given the size and stance of the individual batter, there is an objective fact about whether the ball is in the zone—regardless of whether the batter assesses it correctly or not.
Guideline. Evaluate premises according to their epistemic probability —that is, according to how strong your evidence is for their truth or falsity—using expressions such as probably true and probably false.
EXERCISES Chapter 9, set (b)
Provide two statements to which most people would assign the following measure of epistemic probability.
Sample exercise. Certainly false.
Sample answer. Two and two are five.
The United States has 100 states.
1. Certainly true.
2. Probably true.
3. Can’t decide.
4. Probably false.
5. Certainly false.
9.2.2 Probability as a Measure of Confidence
There is a second notion of probability, one that is not necessarily connected to evidence. Suppose you say, “I’m probably going to win the lottery, even though I realize that everything points against it.” You are acknowledging that the evidence is bad and thus that the epistemic probability of your winning is low. In this case, to say that you will probably win is to say merely that you have confidence you will win. You are not describing the strength of your evidence but the strength of your confidence, that is, the strength of your belief.
This is sometimes termed subjective probability and may be roughly defined as the amount of confidence you have that a given statement is true. Like epistemic probability, it is a matter of degrees and can also be expressed in colloquial terms ranging from certainly true to certainly false or in quantitative terms ranging from 1 to 0. But, unlike epistemic probability, it is relative to you; there is no fact over and above your level of confidence.
If we are intellectually honest—if our aim is to know the truth regarding the questions we care about—then we will endeavor to match subjective probability to epistemic probability. That is to say, we will aim to have the amount of confidence in a statement’s truth that is warranted by the total available evidence. When we succeed, our evaluations of probability will at the same time indicate both epistemic and subjective probability. This frequently does not happen. Even when my evidence for a belief remains the same from today to tomorrow, my mood about it may change. In Chapter 1 much was said about
cases in which we adopt and support beliefs with little regard for the evidence—sometimes because of our innocent misuse of shortcuts in reasoning, sometimes because of bad motives. The problem in those cases can now be stated in another way—as the problem of mismatch between the subjective and epistemic probabilities.
The importance of matching subjective with epistemic probability, however, should not tempt you to make certain mistakes. Note, for example, that if I find that my confidence outstrips my apparent evidence—if, for example, I have a hunch that you are a decent human being despite my inability to say exactly why—this is not necessarily an indicator of bad reasoning or dishonesty on my part. It may mean there is some good reason submerged within my total evidence that I have not yet been able to put my finger on—I sense a reason is there, but it isn’t vivid enough for my thinking to have quickly turned it up. Hunches can go in either direction, however—they may be caused by still-subconscious evidence, or they may be caused by wishful thinking. There is no formula for telling the difference; continued cultivation of the intellectual virtues is the only way to get better at doing so.
Another mistake to avoid is the assumption that I must act with tentativeness if my belief is tentative—that is, if my belief is only slightly probable (whether epistemically or subjectively). Consider the statement My child is at the bottom of the pool. If both my evidence and my confidence are only slightly greater than .5 that this is true, it surely does not follow that I should be tentative as I dive in to rescue what may be my child. In short, when it comes to beliefs about the way the world is, confidence about how the belief translates into action must be distinguished from confidence in the belief itself.3
Guideline. Aim to match your subjective and epistemic probabilities —that is, to have the amount of confidence that is warranted by the evidence.
EXERCISES Chapter 9, set (c)
For each of these statements, describe a way in which your own epistemic and subjective probabilities might differ.
Sample exercise. The Yankees will win the World Series this year.
Sample answer. The epistemic probability might be in the area of “somewhat probable that this is
3. Some theorists have tried to make subjective probability more scientific—to move it from the vague and hidden realm of inner moods to the measurable realm of external behavior—by spelling it out in terms of betting behavior. Consider these two statements: Sitting Pretty will win the third race. Harvest Moon will win the third race. The subjective probability of the first statement would be higher than the second if and only if I were willing either to bet more money or to take longer odds on Sitting Pretty. The same principle would apply to any belief (say, It is wrong to tell a lie). This approach ultimately does not completely work, for there are many reasons that my betting behavior might not reflect my actual confidence level. For example, if I strongly believed it was wrong to bet, then I would probably not bet any money on the statement It is wrong to bet, even though it would have a high subjective probability! But is does nicely illustrate how it is that our subjective probability has much more influence on behavior than does epistemic probability—and, thus, the importance of matching them.