Knowledge and Opinion

by Mortimer J. Adler, Ph.D.


All men, Aristotle said, by nature desire to know. It may not be true that, born with that native propensity, all persons in fact continue to nourish it. But certainly there are but few who do not regard knowledge as desirable, as a good to be prized, and a good without limit — the more, the better.

It is generally understood that those who have knowledge about anything are in the possession of the truth about it. Individuals may at times be incorrect in their claim that they do have knowledge, but if they do, then they have some hold on the truth. The phrase “false knowledge” is a contradiction in terms; “true knowledge” is manifestly redundant.

That being understood, the line that divides knowledge from opinion should also be clear. There is nothing self contradictory in the phrase “true opinion”, or redundant in the phrase “false opinion”. Opinions can be true or false, as knowledge cannot be. When individuals claim to have knowledge about something that turns out not to be knowledge at all because it is false, what they mistook for knowledge was only opinion.

Closely connected with this distinction between knowledge and opinion are two other distinctions. One is the distinction between the things about which we can have certitude — beyond any shadow of a doubt — and things about which some doubt remains. We may be persuaded by them beyond a reasonable doubt, but that does not take them entirely out of the realm of doubt. Some doubt lingers.

The other distinction is that between the corrigible and mutable and the incorrigible and immutable. When we have certitude about anything, we have a hold on truth that is both incorrigible and immutable. When anything remains in doubt, to even the slightest degree, it is both mutable and corrigible. We should recognize that we may change our minds about it and correct whatever was wrong.

By these criteria for distinguishing between knowledge and opinion, how much knowledge do any of us have? Most of us would admit that we have precious little. Most of us are aware that in the history of science even the most revered formulations have been subject to change and correction. Yet at the same time most of us would be reluctant to say that the great generalizations or conclusions of science, those now regnant, are nothing but mere opinions. The word “opinion,” especially when it is qualified by the word “mere,” carries such a derogatory connotation that we feel, quite properly, that to call science opinion rather than knowledge is inadmissible.

The only way out of this difficulty that I know is one that I proposed in an earlier book (Six Great Ideas) that contained a series of chapters on the idea of truth. I repeat it here in order to lay the ground for discussing two modern philosophical mistakes about the character and limits of human knowledge.

The solution, it seems to me, lies in recognizing the sense in which the word “knowledge” signifies something that is quite distinct from anything that can be called an opinion, and the sense in which a certain type of opinion can also quite properly be called knowledge. That would leave another type of opinion, quite distinct from knowledge, which should properly be called mere opinion.

When the criteria for calling anything knowledge are such exacting criteria as the certitude, incorrigibility, and immutability of the truth that is known, then the few things that are knowledge stand far apart from everything that might be called opinion.

Examples of knowledge in this extreme sense of the term are a small number of self-evident truths. A self-evident truth is one that states something the opposite of which it is impossible to think. It can also be called a necessary truth because its opposite is impossible.

That a finite whole is greater than any of its component parts and that each part of a finite whole is less than the whole are self-evident, necessary truths. We cannot think the opposite. The terms “part” and “whole” are indefinable. We cannot say what a part is without using the notion of whole, or what a whole is without using the notion of part, and so we cannot define either part or whole by itself. Nevertheless, we do so understand what parts and wholes are in relation to one another, that we cannot understand a part being greater than a whole or a whole less than a part.

Sometimes definitions enter into our grasp of self-evident truths. We define a triangle as a three-sided plane figure. We define a diagonal as a line drawn between nonadjacent angles in a regular plane polygon. We know that, being three-sided, a triangle has no nonadjacent angles. Therefore, we know with certitude that it is necessarily true that there can be no diagonals in triangles, as there can be in squares, pentagons, and the like.

Whether they know it or not, those who say that we have precious little knowledge that has such certitude may not realize that the little knowledge we have of this kind consists of a handful of self-evident or necessary truths like those just noted.

Is everything else opinion, then? Yes and no; yes, if we insist upon the criteria of certitude, incorrigibility, and immutability of the truth known; no, if we relax those criteria and recognize that there are opinions we can affirm on the basis of evidence and reasons that have sufficient probative force to justify our claiming at the time that the opinion affirmed is true.

I stress “at the time” because, since we have given up the criteria of incorrigibility and immutability, we must be prepared to have the opinion we now claim to be true on the basis of the evidence and reasons now available turn out to be false in the future, or in need of correction or alteration at some future time when new evidence and other reasons come into play.

We should be prepared to say that such corrigible, mutable opinions are knowledge — knowledge of truths that have a future in which they may undergo correction or alteration and even rejection. As against opinions that deserve the status of knowledge in this sense of the term, there remain what must be called mere opinions because they are asserted without any basis at all in evidence or reason.

Our personal prejudices are such mere opinions. We assert them stoutly and often stubbornly, even though we cannot point to a single piece of evidence in support of them or offer a single reason for claiming that they are true. This is also true of some of the beliefs we harbor and cherish.

Sometimes we use the word “belief” to signify that we have some measure of doubt about the opinion we claim to be true on the basis of evidence and reasons. In that case, it is not incorrect to say of one and the same thing that we know it (because we have sufficient grounds for affirming it to be true) and that we also believe it (because the grounds we have still leave us with some trace of doubt about its truth).

However, at other times, we use the word “belief” to signify total lack of evidence or reasons for asserting an opinion. What we believe goes beyond all available evidence and reasons at the time. Then we should never say that we know, but only that we believe the mere opinion that we are holding on to.

The only time when it is totally inappropriate to use the word “belief” is in the case of self-evident or necessary truths. We know that the whole is greater than any of its parts. To say that we believe it is an egregious misunderstanding of the truth being affirmed. The same thing applies to many, but not all, mathematical truths. We know, we do not believe, that two plus two equals four.

Not only personal prejudices but all matters of personal taste, liking one thing and disliking another, fall in the realm of mere opinion. In such matters of taste or personal preference, we may have our own reasons for liking this and disliking that, but those reasons carry no weight with others whose likes and dislikes, or preferences, are contrary to our own.

The extension of the word “knowledge” to cover all corrigible and mutable opinions that can be asserted on the basis of evidence and reasons available at a given time covers more than opinions that can be affirmed beyond a reasonable doubt, if not beyond the shadow of a doubt. It includes opinions that have a preponderance of evidence or reasons in their favor as against opinions supported by weaker evidence or reasons.

In general it can be said that knowing is not like eating. When we eat something, we take it into our bodies, digest it, assimilate it. It becomes part of us. It no longer remains what it was before it was eaten. But with one striking exception, our knowing something in no way affects or alters the thing we know. We may take it into our minds in some way, but doing that leaves it exactly the same as it was be fore we knew it. The one exception occurs in the case of quantum mechanics, where the instruments we use to investigate the phenomena to be observed and measured do affect the phenomena as we observe and measure them.

What I have just said about the difference between knowing and eating requires me to call attention to an other special use, or misuse, of the word “knowing.” It involves the distinction between two acts of the mind to which I called attention in a previous essay.

The first act of the mind is simple apprehension. Some object is apprehended, be it a perceptual object, an object of memory or imagination, or an object of conceptual thought. Strictly speaking, with one exception, we should not use the word “knowledge” for such apprehensions. Except for perceptual apprehensions, which cannot be separated from perceptual judgments, all other apprehensions are totally devoid of any judgment about the object apprehended — whether or not it does exist, whether or not its character in fact is identical with its character as apprehended.

Devoid of such judgments, an apprehension is not knowledge because there is nothing true or false about it. True and false enter the picture only with the act of judging, and only then do we go beyond apprehension to what, strictly speaking, can be called knowledge.

There is a sense in which knowing is like eating. The edible, before it is eaten, exists quite independently of the eater and is whatever it is regardless of how it is transformed by being eaten. So, too, the knowable exists quite independently of the knower and is whatever it is whether it is known or not, and however it is known.

The word that most of us use to signify the independent character of the knowable is the word “reality.” If there were no reality, nothing the existence and character of which is independent of the knowing mind, there would be nothing knowable. Reality is that which exists whether we think about it or not, and has the character that it has no matter how we think about it.

The reality that is the knowable may or may not be physical. It may or may not consist solely of things perceptible to our senses. But whatever its character, its existence must be public, not private. It must be knowable by two or more persons. Nothing that is knowable by one person alone can have the status of knowledge. Whatever can be genuinely known by any one person must be capable of being known by others.

Let this suffice as background for the discussion to follow. I will be using the word “knowledge” to cover the necessary and self-evident truths we know with certitude and also the opinions we are able to assert on the basis of sufficient evidence and reasons to outweigh any contrary opinions. I will be using it to cover things about which we can say both that we know them and also that we believe them, because some measure of doubt remains about them. I will be using it always for judgments that are either true or false, but never for apprehensions that are neither true nor false. And I will use the phrase “mere opinion” for whatever is deemed by anyone not to be knowledge in any of the foregoing senses.

The authors of the two philosophical mistakes with which we are here concerned are David Hume and Immanuel Kant. The influence that, historically, Hume had upon Kant, conceded by Kant to have prompted the philosophical edifice he constructed in order to avoid the conclusions reached by Hume (which he thought untenable, even disastrous), throws some light on the relation of the two mistakes.

Looked at one way, the two mistakes represent opposite extremes. Looked at another way, they represent opposite faces of the same error. The error in both cases has to do with the role that sense-experience plays with regard to the origin and limits of knowledge. The two mistakes are opposed to one another by reason of the fact that they take opposite stands with regard to the certitude, immutability, and incorrigibility that does or does not belong to knowledge.

Hume’s mistake had its roots or origin in earlier mistakes, and especially the mistakes made by John Locke with regard to the senses and the intellect and with regard to ideas as objects we directly apprehend. On the other hand, Kant’s mistake had its origin in the mistake made by Hume. He might have avoided his own mistake by pointing out that the conclusions Hume reached, which he found so repugnant, were based on false premises.

Had he rejected those premises, that by itself would have sufficed to avoid Hume’s conclusions. But he did not do so. Instead, he invented and erected a subtle and intricate philosophical structure in an effort to reach and support conclusions the very opposite of Hume’s, and just as incorrect.

Let us begin with David Hume and then go on to Immanuel Kant. The place to begin is with the conclusion that Hume reached in the very closing pages of his Enquiry Concerning Human Understanding.

It is here that Hume proposes to adopt what he calls “a more mitigated skepticism” than the extreme form that denies that we can have any knowledge at all — that there is anything either true or false. Accordingly, he concedes that we do have knowledge of two sorts.

One is the kind of knowledge to be found in mathematics. He refers to this as “abstract science” because it involves no assertions or judgments about matters of fact or real existence. It deals only with the relation between our own ideas — our ideas of quantity and number. Here it is possible to have demonstration and a measure of certitude. But, he goes on to say, “all attempts to extend this more perfect species of knowledge beyond these bounds are mere sophistry and illusion.”

Our definitions of certain terms give us some propositions or judgments that also have a measure of certitude. Thus if we define injustice as a violation of property, then we can be certain that where there is no property, there can be no injustice. But this is just a matter of definition. Injustice can be defined differently, and so it is not intrinsically impossible to think that there can be injustice where there is no property.

Hume then tells us that, apart from mathematics, “all other enquiries of men regard only matters of fact and existence; and these are evidently incapable of demonstration.” The opposite of any judgment that something exists or that it is such and such is always possible. Judgments about matters of fact and real existence can be supported by evidence and reasons. When they are, they constitute knowledge, not mere opinion; but they are always knowledge that lacks certitude and falls within the sphere of doubt — the sphere of the corrigible and the mutable.

Such knowledge depends upon our sense-experience. “It is only experience,” Hume writes, “which teaches us the nature and bounds of cause and effect, and enables us to infer the existence of one object from that of another.” According to these criteria, Hume admits into the sphere of empirical knowledge (as contrasted with abstract science) such things as history, geography, and astronomy, and also the sciences “which treat of general facts…politics, natural philosophy, physics, chemistry, etc.” This brings him to his thundering conclusion in the last paragraph of the Enquiry:

When we run over our libraries, persuaded of these principles, what havoc must we make? If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matters of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.

The line that divides what deserves to be honored and respected as genuine knowledge from what should be dismissed as mere opinion (or worse, as sophistry and illusion) is determined by two criteria. (1) It is knowledge and can be called science if it deals solely with abstractions and involves no judgments about matters of fact or real existence. Here we have mathematics and, together with it, the science of logic. (2) It is knowledge, if it deals with particular facts, as history and geography do, or with general facts, as physics and chemistry do.

In both cases, it is knowledge only to the extent that it is based upon experimental reasoning, involving empirical investigations of the kind that occur in laboratories and observatories, or methodical investigations of the kind conducted by historians and geographers.

What did Hume exclude from the realm of knowledge? Even though he refers to what he calls “natural philosophy,” which in his century was identical with what we have come to call physical science, his intention was to reject as sophistry and illusion, or at least as mere opinion, what in antiquity and in the Middle Ages was traditional philosophy, including here a philosophy of nature, or physics that is not experimental and does not rely on empirical investigations, as well as metaphysics and philosophical theology.

This view of knowledge and opinion comes down to us in the nineteenth and twentieth centuries in the form of a doctrine that has been variously called positivism or scientism. The word “positivism” derives its meaning from the fact that the experimental or investigative sciences, and other bodies of knowledge, such as history, that rely upon investigation and research, came to be called positive sciences.

Positivism, then, is the view that the only genuine knowledge of reality or of the world of observable phenomena (i.e., matters of fact and existence) is to be found in the positive sciences. Mathematics and logic are also genuine knowledge, but they are not knowledge of the world of observable phenomena, or of matters of fact and real existence. The twentieth-century form of scientism or positivism thus came to be called “logical positivism.”

Here we have one facet of the mistake about knowledge and opinion, the other facet of which is to be found in Immanuel Kant’s Critique of Pure Reason. The latter is by far the more serious and the more far-reaching in its consequences.

Kant tells us that David Hume awakened him from his dogmatic slumbers. His prior dogmatism, as well as Hume’s skepticism, which Kant also found repugnant, was replaced by the critical philosophy that he developed. It is also sometimes called a transcendental philosophy because of its transcendence with regard to experience.

In order to understand this, it is necessary, first, to pay attention to two distinctions that are operative in Kant’s thinking. One is the distinction between the a priori and the a posteriori. The other is the distinction between the analytic and the synthetic.

The a priori, according to Kant, includes whatever is in the mind prior to any sense-experience and also whatever judgments it can make that are not based upon sense experience. The a posteriori is, of course, the opposite in both respects.

The analytic consists of judgments the truth of which depends entirely upon definitions. Thus, if lead is defined as a nonconducting metal, then the judgment that lead does not conduct electricity is an analytically true judgment. So, too, if man is defined as a rational animal, the judgment that men have reason is analytically true. In each example, the term that is predicated of the subject being considered (“does not conduct electricity” and “have reason”) is already contained within the definition of the subject being considered (“lead” and “men”).

Clearly, such analytical judgments can be, in fact must be, a priori. Their truth depends solely upon a definition of terms, not upon sense-experience. Hume would have regarded such analytical judgments as truths that deal with the relation of our own ideas, not with matters of fact and existence. John Locke, before him, regarded them as mere verbal tautologies; in his words, judgments that are “trifling and uninstructive.” Locke, in my judgment, is correct in dismissing them as unworthy of serious consideration.

Earlier in this essay, I explained the character of self-evident truths, truths that have certitude and incorrigibility because it is impossible for us to think their opposites. Such a truth as a finite whole is greater than any of its parts is not analytical in Kant’s sense: its focal terms — whole and part — are indefinable. Nor is it a priori in Kant’s sense: its truth depends upon our understanding of the terms whole and part, an understanding that is derived from a single experience, such as tearing a piece of paper into pieces, thus dividing a whole into parts.

Philosophers since Kant have misconceived what an earlier tradition in philosophy had understood to be self-evident truths or axioms. They have mistakenly accepted Kant’s restriction of such truths to verbal tautologies, to trifling and uninstructive statements.

But this is not the worst of Kant’s mistakes. Much worse is his view about synthetic judgments a priori. A synthetic judgment is not trifling or uninstructive. It does not depend upon an arbitrary definition of terms. It is the kind of judgment that Hume regarded as a truth about matters of fact or real existence. In every such case, the opposite of what is asserted is possible — thinkable, conceivable. But for Hume, the very fact that a judgment is synthetic involves its dependence on experience of one sort or another. It cannot, therefore, be a priori — independent of sense experience.

To maintain that there are synthetic judgments a priori, as Kant does, is, perhaps, the single most revolutionary step that he took to overcome the conclusions reached by Hume that he found repugnant. What was his driving purpose in doing so? It was to establish Euclidean geometry and traditional arithmetic as sciences that not only have certitude, but also contain truths that are applicable to the world of our experience. It was also to give the same status to Newtonian physics.

To do this, Kant endowed the human mind with transcendental forms of sense-apprehension or intuition (the forms of space and time), and also with the transcendental categories of the understanding. These are not to be confused with Descartes’ “innate ideas.” The mind brings these transcendental forms and categories to experience, thereby constituting the shape and character of the experience we have.

According to Kant, the mind is not (as John Locke rightly insisted it was in his refutation of Cartesian innate ideas) a tabula rasa — a total blank — until it acquires ideas initially from sense-experience. Locke rightly subscribed to the mediaeval maxim that there is nothing in the mind that does not somehow derive from sense-experience. It was this maxim that Kant rejected.

The transcendental forms of sense-apprehension and the transcendental categories of the understanding are inherent in the mind and constitute its structure prior to any sense-experience. The common experience that all of us share has the character it does have because it has been given that character by the transcendental structure of the human mind. It has been formed and constituted by it. This elaborate machinery invented by Kant enabled him to think that he had succeeded in establishing and explaining the certitude and incorrigibility of Euclidean geometry, simple arithmetic, and Newtonian physics. Three historic events suffice to show how illusory was the view that he had succeeded in doing that.

The discovery and development of the non-Euclidean geometries and of modern number theory should suffice to show how utterly factitious was Kant’s invention of the transcendental forms of space and time as controlling our sense-apprehensions and giving certitude and reality to Euclidean geometry and simple arithmetic.

Similarly, the replacement of Newtonian physics by modern relativistic physics, the addition of probabilistic or statistical laws to causal laws, the development of elementary particle physics and of quantum mechanics, should also suffice to show how utterly factitious was Kant’s invention of the transcendental categories of the understanding to give Newtonian physics certitude and incorrigibility.

How anyone in the twentieth century can take Kant’s transcendental philosophy seriously is baffling, even though it may always remain admirable in certain respects as an extraordinarily elaborate and ingenious intellectual invention.

So much for the illusory character of what Kant claimed for his transcendental philosophy as an attempt to give mathematics and natural science a certitude and incorrigibility that they do not possess. What about the critical character that Kant claimed for his philosophy — critical in the sense that it would save us from the dogmatism of traditional metaphysics, especially its cosmology and natural theology?

Kant argues for the exclusion of traditional metaphysics from the realm of genuine knowledge on the grounds that it must employ concepts derived from experience to make assertions that go beyond experience — the experience that is constituted by the a priori structure of the human mind. Where Hume dismissed traditional metaphysics as sophistry or illusion, Kant dismissed it as trans-empirical.

However, all the ideas used in metaphysics are not empirical concepts. The idea of God, for example, and the idea of the cosmos as a whole are not concepts derived from sense-experience. They are instead theoretical constructs. There is, therefore, nothing invalid about employing such an idea even if it goes beyond all the sense-experience available to us. Let me add here that, unlike an empirical concept, a theoretical construct does not and cannot have any perceived particular instances.

What I have just said about such metaphysical concepts as God and the cosmos as a whole applies equally to some of the most important ideas in twentieth-century theoretical physics, such ideas as the idea of quark, of certain elementary particles, such as mesons, or of black holes. All of these are theoretical constructs, not empirical concepts.

Kant had no awareness of the distinction between empirical concepts and theoretical constructs. His reasons for dismissing traditional metaphysics as devoid of the validity appropriate to genuine knowledge would apply equally to much of twentieth-century physics. Here, once more, we have grounds for not taking much stock in Kant’s claims for the critical character of his philosophy.

Finally, we come to what is, perhaps, the most serious mistake that modern philosophy inherited from Kant — the mistake of substituting idealism for realism. Even though Locke and his successor Hume made the mistake of thinking that the ideas in our minds are the only objects we directly apprehend, they somehow (albeit not without contradicting themselves) regarded us as having knowledge of a reality that is independent of our minds. Not so with Kant.

The valid knowledge that we have is always and only knowledge of a world we experience. But precisely because it is a world as experienced by us, it is not, according to Kant, a world independent of our minds. It is not independent, as we have already seen, because experience is constituted by the transcendental or a priori structure of our minds — its forms of intuition or apprehension and its categories of understanding. Not being independent of our minds, it can hardly be regarded as reality, for the essential characteristic of the real is independence of the human mind.

For Kant the only things that are independent of the human mind are, in his words, “Dinge an sich” — things in themselves that are intrinsically unknowable. This is tantamount to saying that the real is the unknowable, and the knowable is ideal in the sense that it is invested with the ideas that our minds bring to it to make it what it is.

The positivism or scientism that has its roots in Hume’s philosophical mistakes, and the idealism and critical constraints that have their roots in Kant’s philosophical mistakes, generate many embarrassing consequences that have plagued modern thought since their day. In almost every case, the trouble has consisted in the fact that later thinkers tried to avoid the consequences without correcting the errors or mistakes that generated them.

In this short essay, it is impossible to deal with the shortcomings, embarrassments, and additional errors in nineteenth- and twentieth-century thought. I will confine myself to a brief treatment of knowledge and opinion that corrects and avoids the philosophical mistakes made by Hume and Kant.

Let us return to the focal point of this discussion — the distinction between knowledge and mere opinion. On the one hand, we have self-evident truths that have certitude and incorrigibility; and we also have truths that are still subject to doubt but that are supported by evidence and reasons to a degree that puts them beyond reasonable doubt or at least gives them predominance over contrary views. All else is mere opinion — with no claim to being knowledge or having any hold on truth.

There is no question that the findings and conclusions of historical research are knowledge in this sense; no question that the findings and conclusions of the experimental or empirical sciences, both natural and social, are knowledge in this sense.

As contrasted with such knowledge, which is knowledge of reality or, as Hume would say, knowledge of matters of fact and real existence, mathematics and logic are also knowledge, but not of reality. They are not experimental or empirical knowledge. They do not depend upon investigative research for their findings and conclusions.

The question that remains to be answered is the one that, in my judgment, Hume and Kant answered erroneously, an answer that has persisted in various forms down to our own day. Where does speculative or theoretical philosophy (by which I mean philosophical physics, metaphysics, and philosophical theology) stand in this picture? Is it mere opinion or is it genuine knowledge, knowledge that, like the empirical sciences, is knowledge of reality?

According to Sir Karl Popper, one of the most eminent philosophers of science in our time, the line of demarcation between knowledge and mere opinion is determined by one criterion: falsifiability by empirical evidence, by observed phenomena. An opinion, a view, a theory, that cannot be thus falsified is not knowledge, but mere opinion, neither true nor false in any objective sense of those terms. Drawing this line of demarcation, Popper places the experimental and empirical sciences on one side of the line, and theoretical philosophy (covering what I have indicated above) on the other side of the line.

Though it is couched in somewhat different terms, Popper thus repeats the conclusion Hume reached in his Enquiry. The reasons for reaching the opposite conclusion are as follows.

In the first place, what has been overlooked is the distinction between common and special experience. The empirical evidence to which science and history appeal is evidence that consists in observed data produced by methodical investigation, using all the devices and instrumentation of the laboratory and the observatory. Such observed data are no part of the experience of ordinary individuals who do not engage in scientific or historical investigation.

In sharp contrast to such special experience, available only to those who engage in investigation, there is the everyday, ordinary experience that all of us have during the waking hours of our life. This experience comes to us simply by our being awake and having our senses acted on. We make no effort to get it; we are not seeking to answer questions by means of it, we employ no methods to refine it; we use no instruments of observation to obtain it. Within the range of such experience there lies a core that constitutes the common experience of mankind — experience that is the same for all human beings at all times and places.

With this distinction in mind, between special and common experience, between experience resulting from investigation efforts and experience enjoyed without such efforts, we can distinguish between bodies of knowledge that, while depending on experience as well as upon reflective thought, rely on different types of experience.

Mathematics is a case in point. Mathematical research is carried on mainly by reflective and analytical thought, but it also relies on some experience — the common experience that all human beings have. Mathematicians do not engage in empirical investigation. They need no special data of observation. Mathematics can be called an armchair science, and yet some experience — the common experience of mankind — lies behind the reflective and analytical thought in which the mathematician engages.

Speculative or theoretical philosophy, like mathematics, is a body of knowledge that can be produced in an arm chair or at a desk. The only experience that the philosopher needs for the development of his theories or the support of his conclusions is the common experience of mankind. Reflecting on such experience and proceeding by means of rational analysis and argument, the philosopher reaches conclusions in a manner that resembles the procedure of the mathematician, not that of the empirical scientist. However, we must not fail to note one important difference, a difference that aligns the theoretical philosopher with the empirical scientist rather than with the mathematician. Unlike mathematics, but like empirical science, theoretical philosophy claims to be knowledge of reality.

In the light of what has just been said, we can divide the sphere of knowledge into (1) bodies of knowledge that are methodically investigative and (2) bodies of knowledge that are noninvestigative and that employ only common, not special, experience. To the first group belong history, geography, and all the empirical sciences, both natural and social. To the second group belong mathematics, logic, and theoretical philosophy.

If the division is made in terms of whether the body of knowledge claims to have a hold on truth about reality, then theoretical philosophy, even though it is noninvestigative in method, belongs with history, geography, and the empirical sciences.

Each of these disciplines, according to its distinctive character, has a method peculiarly its own and, according to the limitations of that method, can answer only certain questions, not others. The kind of questions that the philosopher or the mathematician can answer without any empirical investigation whatsoever cannot be answered by the empirical scientist, and, conversely, the kind of questions that the scientist can answer by his methods of investigation cannot be answered by the philosopher or the mathematician.

The line of demarcation between all these bodies of knowledge and mere opinion involves criteria other than the one proposed by Popper. Falsifiability by experience — whether it be the observed data of scientific investigation or the substance of common experience — is certainly one criterion by which we separate genuine knowledge from mere opinion. But it is not the only one.

Another is refutability by rational argument. The only irrefutable truths we possess are the very few self-evident propositions that have certitude, finality, incorrigibility. Since our knowledge of reality, whether scientific or philosophical, does not consist exclusively of self-evident truths nor does it consist of conclusions demonstrated to be true by deduction from premises that are self-evidently true, scientific and philosophical theories or conclusions must be refutable in three ways.

One way is falsification by experience, which produces evidence contrary to the evidence that has been employed to support the opinion that claims to be true and to have the status of knowledge. A second way is by rational argument, which advances reasons that correct and replace the reasons advanced to support the opinion that claims to be true and have the status of knowledge. The third way is a combination of the first and the second — new and better evidence, together with new and better reasons for holding a view contrary to the one that has been refuted.

Opinions that cannot be refuted in one or another of these three ways are not knowledge, but mere opinion. Were this not so, this essay would be fraudulent in its claim to point out philosophical mistakes and to correct them by offering evidence and reasons to expose their errors. Nor could we replace them with views that are true or more nearly true.

If philosophy were mere opinion there would be no philosophical mistakes, erroneous views, false doctrines. There would be no way of substituting views or doctrines more nearly true because they employed insights and appealed to distinctions that for one reason or another were not in the possession of those who made the mistakes.

The foregoing analysis has not been exhaustive. It does not include bodies of knowledge that result from scholarly re search in fields such as philology, the comparative study of religion, or the fine arts. If these bodies of knowledge rely upon methodical investigation they belong with the empirical sciences, not philosophy. The other question to be decided is whether or not they are knowledge of reality.

Reference to religious belief or faith has also been omitted. It claims to be knowledge and would lose all its efficacy if it were reduced to mere opinion. But the grounds on which it makes such a claim are so utterly different from the criteria we have employed to divide genuine knowledge from mere opinion that it is impossible within the brief scope of this discussion to put religious faith or belief into the picture we now have before us.

On the basis of the common experience that all of us possess, we have commonsense knowledge about matters of fact and real existence, knowledge that is neither scientific nor philosophical. There is, however, a relation between such commonsense knowledge and theoretical philosophy that does not exist between it and empirical science.

Theoretical philosophy is an analytical and reflective refinement of what we know by common sense in the light of common experience. Our commonsense knowledge is deepened, illuminated, and elaborated by philosophical thought. There is little if any sound philosophy that conflicts with our commonsense knowledge, for both are based on the common human experience out of which they emerge.

That is why I have reiterated again and again that philosophy, unlike the investigative sciences, historical research, or mathematics, is everybody’s business. All the latter are fields that tend toward greater and greater specialization and become the province of a wide variety of specialist experts. Philosophy alone, because of its intimate connection with the commonsense knowledge of the ordinary individual, remains unspecialized — the province of the generalist, the business of everybody.

The importance of refuting the errors made by Hume and Kant, errors that are widely prevalent in the twentieth century, is that the relegation of theoretical philosophy to the realm of mere opinion amounts to a cultural disaster in an age that is so dominated by increasing specialization in all other fields of learning. If philosophical speculation is not respected in its claim to have a hold upon the truth about reality, our culture will cease to have generalists.

Knowledge is not the highest of the intellectual goods. Of higher value is understanding and, beyond that, wisdom. These are goods that, to whatever extent they can be achieved, become ours through philosophical thought, not scientific knowledge. Philosophy makes it’s contribution not only as a body of knowledge, but also because it is through philosophical thought that we are able to understand everything else that we know. We are justified in hoping that from such understanding, with maturity of judgment and wide experience, some measure of wisdom will ultimately be attained.