PREFACE

Ignorance, so we are told, is bliss. But that is very questionable. Were it so, the human condition would be far happier than it actually is. Yet if ignorance is not the key to happiness, is it perhaps the key to wisdom? Some have thought so. In Plato's dialogical Apology, the Delphic oracle held Socrates to be the wisest of men because he realized that he knew nothing.¹ But perhaps the oracle was misquoted. Perhaps it actually praised Socrates not for claiming to know nothing but for not claiming to know what he actually did not.

There are many different types of ignorance, prominently including that of the stupidity of one who cannot learn and that of the foolishness of one who will not learn. Neither of these is at issue here. For our present concern is specifically with the sort of unavoidable ignorance that besets man notwithstanding his best efforts and intentions.

The present book is a synthesis that brings together the results of various earlier investigations to give a coherent overall picture of the ramifications and implications of human ignorance. For the limits of our own knowledge represent a theme to which I have given much attention over the years, and this book is a work of synthesis. It seeks to weave together the ideas developed in various special investigations into a comprehensive tapestry that affords a systematic picture of the overall situation.

Not withstanding its emphasis on the extent of our ignorance, this book is certainly no foray in scepticism. Quite the reverse! For to argue that knowledge has its limits is to hold that it has its domain as well. The sceptic has it that no secure knowledge of fact is available. And this is absurd—although this volume is not the place to set out the reason why.² The really problematic issue is one the sceptic simply avoids with his all-out denial of knowledge—namely, that of setting out the burden between what is knowable and what is not, exploring its placement and examining its rationale.

Issues of the limits of knowledge and the limits of science have preoccupied me for many years, and the present book provides a convenient occasion for bringing the various threats of these discussions together in a synoptic and systematic examination of ignorance, thus returning to some of the themes that my medieval namesake Nicholas of Cusa addressed in his classic, On Learned Ignorance. As this learned author emphasized, discussions about ignorance need not—should not—themselves betray ignorance.

Ignorance prevails insofar as there are actual facts that one does not know, significant questions that one cannot cogently answer. It is a matter of defeat in regard to knowledge and is, next to outright error, the most serious form of cognitive deficiency there is. There is no alchemy by which we can transmute mere ignorance into knowledge—or indeed even into probabilities. (If we do not know what word was written on a card, we can not even be sure that a word was written there.)

That which perhaps more than anything else betokens the importance of ignorance is that there is so much of it about. Realizing the limited extent of one's knowledge is the beginning of wisdom. Indeed, Diogenes Laertius tells us that Socrates mentioned that the only thing he knew for a fact was the reality of his own ignorance.³

Ignorance exists because man is a being of limited intelligence and power. We humans are finite beings—small potatoes in nature's grand scheme of things. And as beings of limited capacity, we cannot manage to wrap our minds adequately around the world's vast manifold of complex and complexly interrelated realities. Accordingly, there is nothing incidental or fortuitous about our ignorance—it is something deep-rooted in the nature of things.

But just how does this ignorance manifest itself and how far does it extend? And what are its implications for the human condition in general and our own prospects for happiness and well-being in particular? These are the key issues to which the present deliberations will be addressed. For, perhaps surprisingly, ignorance is itself a fertile topic of knowledge.

I find that in my recent work I am caught up in a dilemma. For my overall effort seeks to articulate a systematic position, and by nature a system involves interconnections and overlaps through pervasive interlinkages. This feature inevitably contains repetitions and redundancies in exposition among various expository books. For the interests of self-sufficiency in one branch calls for overlapping redundancy with another. From the angle of the average reader, this poses no problem. After all, it would be inappropriate hubris to suppose that the reader of one book knows the relevant material already expounded in another. But the reviewer, ideally an expert in the field who knows the general lay of the land, may well chafe at re-exposure to something familiar and find such redundancies objectionable. I see no help for this and will accept such reviewer complaints with stoic resignation. The book, after all, is being written for its readers rather than its critics.

I am grateful to Estelle Burris for her competent work in preparing this material for print.

1

The Reach of Ignorance

WHAT IGNORANCE IS ALL ABOUT

Cognitive ignorance is the lack of knowledge of fact. Error is a matter of commission. With error we have the facts wrong. Ignorance, by contrast, is a matter of omission: with ignorance we do not have the facts, period. By and large, error is thus worse than ignorance. As Thomas Jefferson wrote: Ignorance is preferable to error; and he is less removed from the truth who believes nothing, than he who believes what is wrong.¹ In a way this is true enough. Ignorance leaves us without guidance, error sends us off in the wrong direction. And frequently we are better off staying put.

However, the reality of it is that ignorance (error of omission) often leads to outright error (errors of commission). Of course, ignorance is not an all-or-nothing matter; it is only too often a thing of aspects and facets. "Given me a five-letter word for visitor beginning with G," asks the crossword-puzzle solver. Granted, he does not know the word. But he has narrowed things down quite a bit.

The clearest index of ignorance is the inability to answer meaningful questions in a way that manages to convince people—ourselves included. For if a question is indeed authentically meaningful, then it will have an answer, and if we are unable to resolve that question then we are through this very fact ignorant of what the answer is. The inability to identify the answer convincingly is the clearest possible indication that we do not know it.

Often we do not simply respond to ignorance by leaving a mere blank. We have a natural and perfectly reasonable inclination to fill in those gaps in the easiest, most natural, and sometimes even most attractive way. Who has not overtaken some stranger on the road and been disappointed by the visage on which Reality decided? Who has not been startled by the actual deeds that filled the gap left open by a political candidate's vacuous campaign? Jumping to conclusions over a chasm of ignorance is a natural human tendency from which few of us are exempt.

There are as many sorts of ignorance as there are sorts of things to be ignorant about. And so even as knowledge knows no bounds, so does ignorance. The price of ignorance in general is incapacity. The person who does not know where to find food cannot eat. The person who does not know the combination cannot open the lock. The person who does not know how to start the engine cannot drive the car. Even as knowledge is power, so ignorance is impotence. This is a key motivator for hoarding information and keeping secrets.

It is even difficult to obtain a taxonomy of ignorance. For the realm of ignorance is every bit as vast, complex, and many faceted as that of knowledge itself. Whatever someone can know, they can also be ignorant about—arguably exempting a handful of Cartesian exceptions, such as the fact that knowers are pretty much bound ex officio to realize that they themselves exist and can think.

Ignorance encompasses a vast and varied terrain. All sorts of information is simply not available. Many aspects of reality vanish without a trace—the array of yesterday's clouds, for example. And much about the thought life of others is inscrutable to us, unless they tell us—and do so honestly. (What was on Napoleon's mind on the long journey to St. Helena?) But while such things are difficult—perhaps even impossible—to find out about them is not in principle unknowable. (We could have photographed yesterday's clouds—though we didn't. Napoleon could have pounded out his mind into a journal—thought he didn't.) Nobody knows the day on which the last of the Neanderthals died or what Caesar had for breakfast on that fateful Ides of March. But it is in theory possible that the requisite information should come to light—there is nothing inherently unattainable about it. The issue of contingent ignorance—of what people are too lazy or too incompetent to find out about—does not hold much interest for cognitive theory. What matters from the theoretical point of view are those aspects of ignorance that betoken inherent limits to human knowledge.

The ignorance of people can only be compared in this, that, or the other respect. To amalgamate ignorance overall would involve comparing apples and oranges. There is no way to measure ignorance. Perhaps information can be measured textually by comparing the space that needs to be dedicated to its storage—the size of library holdings or the computer bits involved. But ignorance is immeasurable: we cannot know the lineaments of the unknown.

If we adopt the distinction between substantive knowledge about the factual matters of some domain and metaknowledge about our knowledge itself, then it is going to transpire that even in domains where (as per the sceptic's contention) substantive knowledge is not to be had. Nevertheless, the prospect of metaknowledge remains open and indeed is bound to be nonempty in view of what is, by hypothesis, the fact of our knowing substantive knowledge to be unavailable. And so, to acknowledge pervasive ignorance is not to endorse scepticism. After all, to claim to know that there is nothing that one knows is a paradox. On the other hand, the claim that there are some things that we do not know affords us as secure a piece of knowledge as there is.

It is important to heed the distinction between facts that nobody does actually know and facts that nobody can possibly know—between merely unknown facts and inherently unknowable ones.² Of some things we are (and must remain) ignorant because of the world's contingent arrangements. Of others our ignorance lies in conceptual structure of the situation with regard to the item at issue. The really interesting issue, accordingly, relates not to that which is not known to some or even to all of us. The examples one can offer of the former are too many, and of the latter too few. Instead, the really interesting question relates to that which cannot be known at all. From the theoretical point of view, this represents the most interesting form of ignorance.

One of the most obvious sources of ignorance is the sheer volume of available factual information. There is so much out there to be known that any given individual cannot ever begin to make more than an insignificant fraction of it. The vastness of any given person's ignorance is unfathomable. Isaac Newton wrote of himself as a boy standing on the seashore…whilst the great ocean of truth lay all underscored before me. This holds in spades for the rest of us. And, ironically, the more one learns, the more vast one's scope of ignorance is destined to become.

But are there actually any unknowable truths—cases in which there indeed are actual facts of the matter of such a sort that no one can possibly get to know them?

IGNORANCE ABOUT OUR OWN IGNORANCE IS FUNDAMENTAL

The very idea of cognitive limits has a paradoxical air. It suggests that we claim knowledge about something outside knowledge. But (to hark back to Hegel), with respect to the realm of knowledge, we are not in a position to draw a line between what lies inside and what lies outside—seeing that, ex hypothesi, we have no cognitive access to the latter. One cannot contemplate the relative extent of knowledge or ignorance about reality except by basing it on some picture of reality that is already in hand—that is, unless one is prepared to take at face value the deliverances of existing knowledge.

Now one key consideration here is that while one can know indefinitely that one is ignorant of something—that there are facts one does not know—one cannot know specifically what it is that one is ignorant of—that is, what the facts at issue are. One of the most critical yet problematic areas of inquiry relates to knowledge regarding our own cognitive shortcomings. It is next to impossible to get a clear fix on our own ignorance, because in order to know that there is a certain fact that we do not know, we would have to know the item at issue to be a fact, and just this is, by hypothesis, something we do not know. Being a fact I do not know is a noninstantiable predicate as far as I am concerned. (You, of course, could proceed to instantiate it.) But "being a fact that nobody knows is flat out noninstantiable—so that we here have a typical vagrant predicate.

Actually, if there is always a fact which a given individual does not know then there will be a fact that nobody knows. For if F1 is a fact that X1 does not know, and F2 is a fact that X2 does not know, then there will be a fact, namely F1-and-F2, which neither X1 nor X2 manages to know. And this cognitive route to unknown facts will extend across the entire landscape of existing individuals. There will, accordingly, have to be unknowns—facts that are not known to anyone at