Adler: The Realm of Doubt

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Artwork: Shadow of Doubt, by Greg Staples

Adler: The Realm of Doubt

My students occasionally ask me epistemological questions, such as: "How do we know that we know what we know?" "What level of certainty do we need in order to believe something?" "What is the difference between knowledge and opinion?" and the like. 

The clearest and most enlightening statement I have read about questions like this is from Mortimer J. Adler, in The Six Great Ideas (1981), pp. 45-55. Here is the relevant excerpt, without commentary.

The Realm of Doubt – Mortimer J. Adler  - from Six Great Ideas (1981), chapter 7, pp.44-55 

When should we say, “I know,” and do so with complete assurance? When, after expressing a judgment, are we warranted in adding, “This is something that I know beyond the shadow of a doubt”?
When instead, with something less than complete assurance and yet not without some basis for our judgment, should we say, “I believe,” “I think,” “I have the opinion that ...” or use such phrases as “in my judgment” or “in my opinion”? When, after expressing a judgment, should we add the comment: “This is something I have reason to believe is true”?
The criteria for drawing the line that divides the realm of certitude from the realm of doubt can be stated abstractly. As so stated, the criteria are not difficult to understand. Difficulties only arise when we try to apply these criteria to particular cases in an attempt to decide which of our judgments belong in the realm of certitude and which in the realm of doubt.
The criteria are as follows. A judgment belongs in the realm of certitude when it is of the sort that (1) cannot be challenged by the consideration of new evidence that results from additional or improved observations, nor (2) can it be criticized by improved reasoning or the detection of inadequacies or errors in the reasoning we have done. Beyond challenge or criticism, such judgments are indubitable, or beyond doubt.
In contrast, a judgment is subject to doubt if there is any possibility at all (1) of its being challenged in light of additional or more accurate observations or (2) of its being criticized on the basis of more cogent or more comprehensive reasoning.
Let me illustrate this by reference once again to judicial proof in a jury trial of issues of fact. In criminal prosecutions, the degree of proof required is defined as being “beyond a reasonable doubt.” But this does not take the verdict rendered by the jury out of the realm of doubt.
What the jury is asking to bring in is a verdict that they have no reason to doubt – no rational basis for doubting – in the light of all the evidence offered and the arguments presented by opposing counsel.
It always remains possible that new evidence may be forthcoming and, if that occurs, the case may be reopened and a new trial may result in a different verdict. It also remains possible for the verdict to be appealed to a higher court on the grounds of procedural errors that affected the weighing of the evidence in the deliberations of the jury.
The original verdict may have been beyond a reasonable doubt at the time it was made, but it is not indubitable – not beyond all doubt or beyond the shadow of a doubt – precisely because it can be challenged by new evidence or set aside by an appeal that calls attention to procedural errors that may have invalidated the jury’s deliberations – the reasoning they did in weighing and interpreting the evidence presented.
In civil litigation, the degree of proof required is defined as being “by a preponderance of the evidence.” Here the jury’s verdict claims no more than that the answer it gives to a question of fact has greater probability than the opposite answer. As the jurors have interpreted and weighed the evidence, they have found that it tends to favor one answer rather than another. Here, as in a criminal prosecution, additional evidence or better thinking on the jury’s part might result in a different verdict. The balance might shift in the opposite direction.
In the affairs of daily life, many of the judgments we make are, like jury verdicts, beyond a reasonable doubt or are favored by a preponderance of the evidence. For all practical purposes, we regard judgments of the first sort as being so highly probable that we act on them as if they were certain. We need not hesitate to act on them even though new evidence may be discovered. In the light of all the evidence we have before us and the thinking we have done, we have no reason at present to doubt the truth of such judgments. But we should always remember that that does not make them indubitable; that does not give them the kind of certitude that removes them from the realm of doubt.
The essential difference between genuine certitude and the substitute for it that is often called “moral certainty” or “practical certainty” lies in the finality and incorrigibility of indubitable judgments. Even when we act on a highly probable judgment as if it were a certainty for all practical purposes, it remains a judgment that is subject to correction, to challenge, and to criticism. It is one about which we may in the future think it reasonable to change our minds.
In a wide variety of daily affairs – in the conduct of family life, in the care of our bodies and in all matters of health and disease, in our business or professional careers, in our financial dealings, especially in making investments, in our political discussions, especially with regard to foreign policy and internal relations – we frequently act on judgments that are not beyond a reasonable doubt, but are simply more probable than their opposites. In the light of the evidence available at the time and in the light of the best thinking we have done so far, we regard them as more likely to be true.
The critical caution we must exercise is contained in the words “at the time” and “so far.” These words remind us that the future always holds the possibility of additional evidence and better thinking, either of which may shift the weight of probability in the opposite direction.
The realm of doubt is the realm of judgments that have a future, for better or for worse. This is not so in the case of judgments that have the finality and incorrigibility of certitude.


If we turn now from judgments that we make in the practical affairs of daily life to the conclusions of historical research, to the findings, hypotheses, and theories of the investigative sciences, and even to certain branches of mathematics, the same criteria function to place in the realm of doubt a fairly large portion of what these learned disciplines offer us as knowledge. This assessment may appear shocking to those who, distinguishing between knowledge on the one hand and opinion or belief on the other hand, regard history, science, and mathematics as branches of organized knowledge, not as collections of mere opinions or beliefs.
The word “knowledge” for them has the connotation of truth; in fact, it is inseparable from it. There cannot be false knowledge, as there can be false opinions and beliefs. The phrase “true knowledge” is redundant; the phrase “false knowledge” is self-contradictory.
However, those who hold this view acknowledge that there is progress in these disciplines. They as well as everyone else speak of the advancement of learning in all these fields. They attribute it to new discoveries, improved observations, the development of sounder hypotheses, the substitution of more comprehensive theories for less comprehensive ones, more elaborate and more precise analysis or interpretation of the data at hand, and rectified or more rigorous reasoning. Less adequate formulations are replaced by better ones – better because they are thought more likely to be true, or nearer to the truth being sought and, therefore, better approximations of it.
In short, all these branches of organized knowledge have a future, a future they would not have if the present found them in possession of judgments about what is true or false that had finality and incorrigibility. To whatever extent history, science, and mathematics have a future, to that same extent these bodies of “knowledge” belong in the realm of doubt, not in the realm of certitude.
I put the word “knowledge in quotation marks because the word has two meanings, not one. The same holds for the word “opinion.” The recognition of the two senses in which we use these words will overcome the shock initially experienced by those who recoiled from locating history, science, and mathematics in the realm of doubt, because they are accustomed to regarding them as branches of knowledge, not as collections of opinions or beliefs.
Let us first consider the meaning of the word “knowledge” that has already been mentioned. It is the sense in which knowledge cannot be false and, therefore, has the infallibility, finality, and incorrigibility that are attributes of judgments in the realm of certitude. Let us call this the strong sense of the term.
At the opposite extreme from knowledge in this strong sense is opinion in the weak sense of that term. When we use the word “opinion” in this sense, we refer to judgments on our part that are no more than personal predilections or prejudices. We have no basis for them, either empirical or rational. We cannot support them by appeal to carefully accumulated evidence or by appeal to reasoning that gives them credibility. We do not, in short, have sufficient reason for claiming that they are more likely to be true than are their opposites.
We prefer the opinions to which we are attached on emotional, not rational, grounds. Our attachment to them is arbitrary and voluntary – an act of will on our part, whatever its causes may be. Since we may just as capriciously adopt the opposite view, unfounded opinions of this sort fall to the lowest level of the realm of doubt.
In between these two extremes lie judgments that can be called knowledge in the weak sense of that term and opinion in the strong sense of that term. Here we have judgments that are neither arbitrary or voluntary, judgments we have rational grounds for adopting, judgments the probability of which we can appraise in the light of all the evidence available at the moment and in the light of the best thinking we can do – the best analysis and interpretation we can make of that evidence, again at the moment.
At the moment! The future holds in store the possibility of additional or improved evidence and amplified or rectified reasoning. That fact, as we have seen, places such judgments in the realm of doubt. They have the aspect of opinion because they may turn out to be false rather than true, but they also have the aspect of knowledge because, at the moment, we have no reason to doubt them. They are beyond reasonable doubt, but not beyond the shadow of a doubt, from which they cannot escape because they have a future.

Readers who have followed the argument so far may begin to wonder whether the realm of certitude is a completely empty domain. If not, what sort of judgment can we expect to find there?
The answer I am about to give applies not only to judgments we make in the course of our daily lives, judgments ordinarily made by persons of common sense, even the judgments such persons may come to make when their common sense is enlightened by philosophical reflection. It also applies to judgments in the field of mathematics and in some, if not all, of the empirical sciences.
Truths called self-evident provide the most obvious examples of knowledge in the strong sense of that term. They are called self-evident because our affirmation of them does not depend on evidence marshaled in support of them nor upon reasoning designed to show that they are conclusions validly reached by inference. We recognize their truth immediately or directly from our understanding of what they assert. We are convinced – convinced, not persuaded – of their truth because we find it impossible to think the opposite of what they assert. We are in no sense free to think the opposite.
Self-evident truths are not tautologies, trifling and uninstructive, such as the statement “All triangles have three sides.” A triangle being defined as a three-sided figure, we learn nothing from that statement. Contrast it with the statement, “No triangle has any diagonals,” which is both self-evident and instructive, not a tautology.
The self-evidence of the truth of the latter statement derives immediately from our understanding of the definition of a triangle as a three-sided figure and from our understanding of the definition of a diagonal as a straight line drawn between two nonadjacent angles. Seeing at once that a triangle contains no nonadjacent angles, we see at once that no diagonals can be drawn in a triangle.
Our understanding of diagonals also enables us to see at once that the number of diagonals that can be drawn in a plane figure that is a regular polygon having n sides (where n stands for any whole number) is the number of sides multiplied by three less than that number, the product being then divided by two.
Sometimes, as in the case of “No triangle has any diagonals,” the self-evidence of the truth derives from our understanding of definitions. Sometimes, it derives from our understanding of the terms that are not only undefined but are also indefinable, such as “part” and “whole.”
Since we cannot understand what a part is without reference to a whole, or understand what a whole is without reference to parts, we cannot define parts and wholes. Nevertheless, our understanding of parts and wholes makes it impossible for us to think that, in the case of a physical body, its parts are greater than the whole. That the whole body is always greater than any of its parts is not only true, but self-evident.
Equally self-evident is the truth that nothing can both exist and not exist at the same time; or that, at a given time, it can both have and not have certain characteristics. Our understanding of what it means for anything to act on another or be acted upon gives us another self-evident truth. Only that which actually exists can act upon another and that other can be acted upon only if it also actually exists. A merely possible shower of rain cannot drench anyone; nor can I be protected from the rain by merely a possible umbrella.
How about the prime example of self-evident truth proposed in the Declaration of Independence – that all men are created equal? Clearly, it is not self-evident as stated if the word “created” is understood to mean created by God, for the existence of God and God’s act of creation require the support of reasoning – reasoning that can be challenged. Suppose, however, that the proposition had been “All men are by nature equal.” On what understanding of the terms involved might that statement be regarded as self-evidently true?
First of all, we do understand “equal” to mean “neither more nor less.” If, then, we understand “all men by nature” to mean “all human beings” or “all members of the same species,” it becomes self-evidently true for us that all are equal, which is to say that no human being is more or less human than any other.
All persons have, in some degree, whatever properties belong to all members of the species Homo sapiens. The inequality of one individual with another lies in the degree to which this or that specific property is possessed, but not in the degree of humanity that is common to all.
I have dwelled at some length on this example not only because we will have to return to it in later chapters dealing with the idea of equality, but also because the proposition about the equality of all human beings may have to be defended against those who advance the opposite view – Aristotle, for example, who maintains that some human beings are by nature born to be free, and some are by nature born to be slaves; or the male chauvinists over centuries past, and even in the present, who believe that females are inferior human beings.
I think the truth of the proposition about human equality can be defended against all these errors, but a self-evident truth should need no defense whatsoever. Hence the proposition, though true, may not be a good example of self-evident truth.


Another whole class of truths for which certitude may be claimed consists of those called evident, rather than self-evident. I do not, as Descartes thought, have to infer my existence from the fact that I am aware of myself thinking. I perceive it directly, just as I perceive directly the existence of all the physical objects that surround me. If there is any doubt at all about the truth of such judgments, it is the merest shadow of doubt about whether I am suffering a hallucination rather than actually perceiving.
When I am perceiving, not hallucinating, there can be no doubt that the objects I am perceiving actually exist. Such judgments have a semblance of certitude that falls short of complete certitude only to the extent that a shadow of a doubt remains concerning the normality of my perceptual processes.
Whether my perceptual objects exist when I am not perceiving them is another question, to which I think the true answer is that they do, but its truth is neither self-evident nor evident. Reasoning and argument are required to defend its truth. If we go beyond judgments about the present existence of objects that we are at the moment perceiving to judgments about their existence at other times and placements, or to judgments about their characteristics or attributes, we pass from the realm of certitude to that of doubt. Though we less frequently misperceive than we misremember, our perceptions as well as our memories give rise to judgments that are often in error or otherwise at fault.
Judgments that articulate what we perceive or remember take the form of statements about particulars – this one thing or that, one event rather than another. We are also prone to generalize on the basis of our perceptual experience. In fact, the judgments we are most likely to be insistent about are generalizations from experience. Many of these are unguarded and turn out to be unwarranted because we have said “all” when we should have said “some.” Even scientific generalizations sometimes overstate the case. The history of science contains many examples of generalizations that have been falsified by the discovery of one or more negative instances.
The falsification that I have just referred to provides us with one or more example of judgments that belong in the sphere of certitude. When the discovery of a single black swan falsifies the generalization that all swans are white, our judgment that that generalization is false is knowledge in the strong sense of the term – final, infallible, incorrigible. Nothing that might possibly ever happen in the future could reverse the judgment and make it true rather than false that all swans are white.
The number of self-evident truths is very small. The number of falsified generalizations, both those made by scientists and those made by laymen, is considerable; and the number of perceptual judgments about the evident truth of which we have certitude is very large. But it is not the number that matters when we compare the realm of certitude with the realm of doubt. What matters is that only judgments in the realm of doubt have a future, a future in which the effort we expend in the pursuit of truth may bring us closer to it.