The Epistemic Statuses: Certainty, Probability, Possibility, and Arbitrariness

§3.3

In evaluating arguments, it is necessary to determine the epistemic status of each premise—where it falls along the scale running from ignorance to knowledge.

In some unusual cases we might be able to specify this to such a fine degree of resolution that we can assign a number to it, and different scales have been devised for assigning such numbers. In most cases, however, this is not possible, and we distinguish epistemic statuses more coarsely using terms like “unfounded”, “possible”, “probable”, and “certain”. In order to get clearer on epistemic status, we will need to discuss each of these terms.

Let’s start with certainty. We’ve been using this word a lot in the last few paragraphs, in a way that makes it seem to be nearly synonymous with “knowledge”. Understanding the relation between these two concepts will help us to understand epistemic status better. To be certain of a proposition is to regard it as knowledge, as opposed to regarding it as doubtful. When you are certain of something you act on it and draw inferences from it confidently, whereas when you are uncertain you are more tentative, always keeping in mind the possibility that the proposition is false and planning for that contingency. In this sense, people are sometimes certain of things unreasonably. The fervent racist discussed above, for example, might not hesitate to act on his belief. However, when we speak of certainty as an epistemic status, we are referring not to the way a person actually does regard the proposition but to the way it is reasonable for him to regard it. We might call this rational certainty or objective certainty (as opposed to subjective certainty). In any case, this is how I am going to use the word “certain” going forward.

There are some disputes among epistemologists about the relationship between certainty and knowledge. However, the following is comparatively uncontroversial: the beliefs that a person is entitled to classify as knowledge and those that he is entitled to classify as certain are the same. The difference between classifying them as certain and classifying them as knowledge is that, in classifying them as certain, he is contrasting them specifically with beliefs that have a lower epistemic status and is focusing on the fact that he is in a position to act on these beliefs and to draw inferences on these beliefs without hesitation.

In thinking about the different epistemic statuses, it is often helpful to consider how they come up in the criminal justice process, when police officers, judges, and juries often need to weigh evidence, and to specify how sure they are of various propositions. The concept of “certainty” is central to criminal trials, where the jury is instructed to return a guilty verdict only if they are certain that the defendant is guilty—only, to use a familiar phrase, if his guilt has been established “beyond a reasonable doubt.” In general, we can think of certainty as the state we are in with respect to a proposition when there is no reasonable doubt about it. Thus, the proposition that Bob was on the quad is not certain because there is a reasonable doubt about it: you didn’t get a good enough look at the person in question to eliminate the possibility that it was someone else who vaguely resembled Bob. Whereas, if you had seen Bob clearly and heard and recognized his voice, these doubts would have been assuaged, and you could be certain that Bob was on the quad.

Of course, there are still doubts that someone might raise here, based on such farfetched scenarios as Bob impersonators, holograms, or hallucinogens; but most of us, in most contexts, would consider such doubts unreasonable, and certainly they would be ruled out as unreasonable in court (unless there was some specific evidence for them in a certain situation). As you might imagine, there is room for argument about what sorts of doubts are reasonable in what contexts and about when we have certainty. Indeed, some philosophers think that there is very little about which we can be genuinely certain—that there is very little that we really know—while others think that we know a great deal. We will have occasion to discuss this debate later. For now, let’s put this issue aside and proceed on the assumption that we can be certain of such things as that the people we see in front of us are really there. This is an assumption that we all do make in our daily lives.

If a proposition fails to be certain, it may still be probable. A proposition is probable if the evidence is strong enough that it is more likely to be true than not, so that it is reasonable to assume it provisionally, while still making allowances for the possibility that it is false. For example, suppose that on your way to class you and one of your classmates, who you don’t know well, both stopped at an ATM to make a withdrawal and you happened to see his receipt and notice that the balance was $602.47. Half an hour later, during the class, it would be probable that this was still his balance. Since you have been with him in the intervening time, you would know that he hasn’t made any further withdrawals or deposits or used a debit card. But you could not be certain of the balance, since you do not know whether anyone else has access to the account, or whether any previous transactions posted to the account during this period; and you know that these sorts of events regularly happen with bank accounts. Still, because thirty minutes is so short a time, the odds are against any of these things having happened in this period, so it is more likely than not that the balance has remained the same.

I discussed earlier how juries are instructed to convict in criminal cases only when they are certain that the defendant is guilty. In civil cases (that is, lawsuits) there is a less rigorous standard and only probability is required. In legal terms, a jury should find for the plaintiff and order the defendant to pay damages if “the preponderance of the evidence” favors the plaintiff’s case. This means: if the plaintiff’s case is more likely to be true than false, given all the evidence presented.

A proposition that is not probable may still qualify as possible. To call a proposition “possible” in the relevant sense is to say that there is some reason to believe it, and that it is therefore reasonable to regard it as something that “might be” true and to take it into consideration in our thinking. Thus, in the example from above concerning Bob, it is at least possible that he was on the quad at 8:00am (even if it turns out that it is not probable). He might have been there.

Perhaps you’re thinking that “anything is possible” and that you would be in a position to say that Bob “might have been on the quad” even if you hadn’t had the experience of seeing someone who you thought you recognized as him there. There is a sense of the word “possible” in which you could say that it was possible that Bob was on the quad, even if you hadn’t had the experience, but there is another sense of the word in which this would be false. And it is this sense—let’s call it epistemic possibility that is relevant for our present purposes.

To see this, imagine calling the police to tell them of the possibility that Bob was on the quad at 8:00am, three minutes before the robbery in Manhattan. They would ask you why you thought it was possible, and they would not react favorably if you responded that “anything’s possible”. They would have quite a different response, however, if you told them about your experience of thinking you recognized him. (Indeed, this report could prove quite useful to them. If Bob has been claiming that he was on the quad at that time, your report could make this alibi considerably more credible.)

There are other contexts in which we can see the idea of epistemic possibility at work in the law. We are all familiar with the idea of a “suspect”—that is, of a person whom the police think might have committed a certain crime, and whom they set to work investigating. There may be a number of suspects for a given crime but notice that the police don’t regard everyone as a suspect, nor do they consider everyone who had the opportunity and ability to commit it a suspect, unless there are only a few such people. (Recall the case discussed earlier, in which the fact that Natalie was one of the several million people who had access to the garden in which Carl was killed didn’t give us any reason to suspect that Natalie was the murderer.) In general, the police need some specific reason to suspect someone of a crime, and likewise we need some specific reason to suspect a proposition of being true—that is, to classify it as “possible”.

Epistemically possible propositions are to be contrasted with unfounded ones. A proposition is unfounded when there is no reason to believe it. This is the status of things that you make up out of thin air—for example, that there are monsters under your bed, that your roommate committed a murder five years ago, or that his second cousin once lived in Manhattan. Some of these propositions are more far-fetched than others—there are no such things as monsters, and very few people commit murders, but many people live in Manhattan. However, all these propositions have in common that you have no reason to think they are true, or even to consider them, and the proper course of action is to dismiss them out of hand.

Because we have no reason to believe them, unfounded premises can offer no support whatsoever to any conclusions that we might infer from them. Thus, arbitrariness is the lowest epistemic status.

In some cases, we not only have no reason to believe that a proposition is true, we actually have reason to believe that it is false. This happens when the proposition contradicts something that we know (or have reason to believe) to be true. For example, if you knew that that your roommate only had one second cousin and that she spent her whole life in Wyoming, you would know that the proposition that she lives in Manhattan was false—or, to put it more simply, you would know that she did not live in Manhattan. (By the same token, if it were probable that she had spent her whole life in Wyoming, it would be probable that she didn’t live in Manhattan.) In certain respects, propositions that are certainly or probably false can be thought of as having an even lower status than that of unfounded propositions. However, as far as their value as premises is concerned, an unfounded premise is no better than one that is certainly false: neither gives us any reason at all to believe any conclusion.

Thus, we can think of the continuum of epistemic statuses as running from arbitrariness to certainty, with the “possible” and “probable” denoting ranges in between. Of course, among the propositions which are possible, some will be nearer to being probable than others, and, within the probable propositions, some will be nearer than others to being certain. To capture this, we often use the words “probable” and “certain” in a comparative (rather than absolute) sense and say that one proposition is “more probable” or “more certain” than another. This should not be taken to imply that either proposition is probable or certain. For example, when two propositions are merely possible, one may nevertheless be more probable than the other. A proposition is probable in the absolute (rather than comparative) sense when it is more probable that it is true than that it is false—or, as we put it earlier when the preponderance of the evidence favors it. And a proposition is certain (in the absolute rather than the comparative sense), when it is no longer epistemically possible that it is false (that is, when it has been established beyond a reasonable doubt.)

We often assert propositions tentatively, indicating that they are probable rather than certain, by qualifying them with adverb “probably” (for example, “Bob was probably on the quad”), and we usually assert possibilities by saying that they “may” or “might be” the case (“Bob may have been on the quad”).

Additionally, the fact that a conclusion can be inferred from false premises does not give us any reason to believe that the conclusion is also false. In fact, you can take any true proposition and make up arguments that infer it from false premises. Here’s an example:

Since the premises are false this argument doesn’t give us any reason to believe that pigs are mammals, but it certainly doesn’t show that they’re not mammals!

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