When should we say, "I know," and do so with complete assurance?

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"?

The criteria for drawing the line that divides the realm of certitude from the realm of doubt can be stated abstractly. The criteria are as follows. A judgment belongs in the realm of certitude when it is of the sort that 1) cannot b e 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. Such judgments are be yond doubt. (Whether any such judgments can be made is a question that remains to be addressed by us.)

In contrast, a judgment is subject to doubt if there is any possibility at all 1) of its being challenged in the light of additional or more accurate observations or 2) of its being criticized on the basis of more cogent or more comprehensive reasoning.

In the affairs of daily life, many of the judgments we make are beyond a reasonable doubt or are favored by a preponderance of the evidence. For all practical purposes, they are so highly probable that we act on them as if they were certain. . . But w e 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 "practical certainty" lies in the finality and incorrigibility of indubitable judgments.

In a wide variety of daily affairs, we frequently act on judgments that are not beyond a reasonable doubt, but are simply more probable than their opposites. In 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 realm of doubt is the realm of judgments that have a future.

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.

(Frequently, what these disciplines offer us is not knowledge but informed opinion.) The world of "knowledge" has the connotation of "truth." 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. (You cannot know something to be so if it isn't. You cannot know that 2+2=5. You can think it, or you can be of that opinion, but you cannot know it. In speaking this way we are using t he word "knowledge" in the strongest possible sense. It implies finality and incorrigibility, and these are the attributes of judgments in the realm of certitude.)

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 a re 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. It is subjective, and frequently nothing more than a matter of personal taste.

Is the realm of certitude a completely empty domain? 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 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.

The 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 state ment, "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 no nadjacent angles. Seeing at once that a triangle contains no nonadjacent angles, we see at once that no diagonals can be drawn in a triangle.

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 a certain characteristic.

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 di rectly, 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 actu ally perceiving.

(Moving on from this consideration of mere opinion and certitude, we want to now concern ourselves with those judgments located in the realm of doubt, for it is these judgments that have a future.)

(1)This material is taken largely from the 7th chapter of SIX GREAT IDEAS, by M. Adler