The Profound Limitations of Knowledge

Socrates is famous for having explained why he was such a wise man. “I am the wisest man alive, for I know one thing, and that is that I know nothing.” The belief that we know nothing is called radical skepticism. My goal for the book The Profound Limitations of Knowledge is to show that radical skepticism is correct—and to make each reader as wise as Socrates.

Knowledge seems to arise from five different sources that I call the five pillars. The first is awareness of certain bodily states, epitomized by Descartes’ famous “I think, therefore I am.” His ability to think proved to him that he was alive. Somewhat similarly, people know if they are experiencing pain. That is real knowledge—but such a tiny pillar that it can’t support a doll house. And the others are all hopelessly defective.

Immanuel Kant proposed a second pillar: innate knowledge. Kant argued that we are born knowing certain things. Religious faith is a third pillar. People of faith are told who created the world, when He did it (almost always a He, and in some religions, to the day), and what will happen when we die. Reason is a fourth pillar. Humans discern patterns and use logic to make deductions. The fifth pillar is sensory data. We experience the world through the five senses, then combine this with logic to advance from simple observations to complex inferences. The naïve view is that we observe, and then we know. Seeing is believing. Ha!

Innate Knowledge

Kant claimed that certain beliefs such as ‘Every event has a cause’ precede all experience. Even six-month old babies act as though they understand connections between causes and effects. But radical skeptics question the correctness of beliefs, not their origins. Newly hatched ducklings ‘know’ that the first moving object they see will be their mother, so they follow it. But when nasty biologists substitute objects like shiny balls or shoes, the ducklings follow those too. Their ‘knowledge’ is incorrect.

Religious Knowledge

Imagine a science fiction scenario in which extraterrestrial beings assemble the leaders of today’s more than 730 world religions. Eager to know which is correct, they allow each leader  to make his or her case. What evidence might the leaders give? “God told me this.” Or, “On Easter Sunday I bought a bushel of potatoes, and one of them was the spitting image of the Virgin Mary.” Would a Christian’s argument that the Son of God rose from the dead play better than the Hindu idea that each soul undergoes many reincarnations until united with the universal soul? Maybe the major religions would expect their large numbers of devotees to count in their favor; but large numbers do not constitute proof. Furthermore, no religion attracts a majority of the world’s people. ET would end up shaking her three heads in dismay.

If religious beliefs were based on meaningful evidence, religious preferences would be independent of time and place of upbringing. They are, of course, not. More Baptists live in Biloxi than Bombay, more Jews in Jerusalem than Jakarta, and more Muslims in Malaysia than Mississipi.


Many philosophers believe that the only path to certain knowledge is through reason. But reasoning abilities are greatly overrated (which presents me with a paradox, since my book attempts to persuade through reasoning). The skeptic philosopher Agrippa contended that all arguments claiming to establish anything with certainty inevitably commit at least one of three fallacies:

  1. Infinite regress. The claim that a statement is true needs evidence to support it. But the evidence must also be supported, and that evidence too, and on and on, ad infinitum.
  2. Uncertain assumptions. Foundationalists claim that some beliefs are self-evident, so can be used as starting points for complex arguments. For some foundationalists, mathematics and logic provide such basic beliefs: ‘2+2=4’; ‘If X is true, then X cannot be false’. Other foundationalists insist that basic beliefs come from direct sensory experience: ‘That cat is black’. But none of the candidates lead to the enormous number of complex, detailed beliefs that are part of everyone’s worldview.
  3. Circularity. Coherentists assert that statements can be considered provisionally true if they fit into a coherent system of beliefs. But coherentism is circular: A explains B, B explains C, and C explains A. Circular arguments are invalid. Furthermore, statements may cohere with many others, some of which are false. So it is possible to develop a belief system that is both coherent and entirely untrue.

If reason were so powerful, people would more often be persuaded to change their views. Yet throughout history, illustrious philosophers wrote lengthy reasoned arguments, and illustrious others rebutted them. Every year, brilliant lawyers present arguments to the U.S. Supreme Court. Every year the nine Justices, chosen in large part because of their exceptional powers of reasoning, listen attentively. But whenever the dust has settled on arguments concerning gun control, abortion, affirmative action and so forth, the votes of most judges have been highly predictable. Brilliant Antonin Scalia consistently drew one conclusion, brilliant Ruth Bader Ginsburg consistently the opposite. And brilliant Clarence Thomas was mute.

“So convenient a thing is it to be a rational creature, since it enables us to find or make a reason for everything one has a mind to” – Ben Franklin.

Jean Piaget showed that young children invariably think illogically in some situations. How can we be so arrogant as to assume that Twenty-First Century adult Homo sapiens has reached the pinnacle of logical thinking!

A lot of everyday reasoning (and most science) is inductive. Our senses reveal the immediate present, and we use reason to generalize about the future. But the generalizations require the assumption that the future will resemble the past. Bertrand Russell invoked a chicken, fed by a man every day of its life and eventually learning to expect its daily feedings, but in the end having its neck wrung by the same man. Russell added that although we believe that the sun will rise tomorrow, we are in no better position to judge than was the chicken. Russell and many other eminent philosophers concluded that there is no rational basis for induction.

Following are two examples of inductive reasoning in mathematics. The first leads to a true conclusion, the next to a false one.

  1. Consider the numbers 5, 15, 35, 45, 65, 95. Every number ends in 5 and is divisible by 5. An inductive inference is that every number that ends in 5 is divisible by 5. This inference is correct.
  2. Consider the numbers 7, 17, 37, 47, 67, 97. Every number ends in 7 and is a prime. An inductive inference is that every number that ends in 7 is a prime. The inference is false. For example, 27 is divisible by 3 and 9.

Here is a nonmathematical example in which an inductive inference may be incorrect: He is 50. He is articulate and healthy-looking. He drives a nice car. Therefore, at some point in his life he probably worked for a living. However, it’s possible that somewhere on earth lives a bright middle-aged Kuwaiti emir, or Rockefeller, or Bush, with hands never soiled by work, who drives a different luxury car every day.

David Hume destroyed the illusion that induction can be rationally justified, and Nelson Goodman put a stake through its dead heart. Goodman showed that a limitless diversity of inductive inferences can be drawn from any body of data. For example, since all emeralds ever observed have been green, the obvious inductive inference is that all emeralds are green. So Goodman coined a new word, ‘grue’, which refers to objects that are green before a certain future date and blue from that date on. Prior to that future date, all evidence supporting the induction ‘All emeralds are green’ equally supports ‘All emeralds are grue’.

So, inductive reasoning is imperfect. But deductive reasoning follows universal principles based on rules of logic, probability theory, and decision theory. Conclusions from such reasoning must be correct – with iron-clad certainty.

Or maybe not. William Alston observed that “anything that would count as showing that deduction is reliable would have to involve deductive inference and so would assume the reliability of deduction.” Complicating matters even further, logicians have proposed many principles of reasoning, several of which are incompatible with each other.

Moreover, even if two disputants each reason flawlessly, they might never come to agreement if they start from different premises. And premises come from observations which, as shown below, are unreliable. Consider a syllogism: All A is B. Some C is not B. Therefore, some C is not A. Whether or not you judge the reasoning valid, unless you know from observation what A, B, and C represent, you have not increased your knowledge of the world.

“All knowledge of reality starts from experience and ends in it. Propositions arrived at by purely logical means are completely empty as regards reality.” Albert Einstein

Sensory Data

Empiricists believe that everything we know comes through observations and inferences induced from them. Maybe, but almost all important observations are second- or third- or tenth- hand. Few people have walked on the moon or seen the chromosomes of a fruit fly, and nobody I know attended the signing of the Magna Carta. Furthermore, observations don’t help distinguish truth from illusion. Mental institutions are crammed with people who hear voices or speak with long-dead relatives. Just because people outside institutions are in the majority does not necessarily make their visions more credible.

Empiricists acknowledge the occurrence of hallucinations and sensory illusions; but they say that hallucinations are rare and illusions play a trivial role in daily life. They conclude that sensory data are generally accurate. Empiricists Gilbert Ryle and John Austin argued that our ability to detect illusions is evidence for the general trustworthiness of our senses. That is, from the fact that imperfections are infrequently detected, they made the dubious inferences that imperfections are rare and perceptions are typically accurate. Yet reliable estimation of the frequency of illusions and hallucinations is impossible. You may be experiencing one this very moment and not know it. Furthermore, even if our sensory systems were perfect, we’d still face two insurmountable obstacles to certainty. First, the fidelity of human memory is, to put it charitably, considerably less than high. Second, an infinite number of interpretations are compatible with any given perception. Maybe it’s churlish to point out yet another problem but, strictly speaking, empiricism is self-refuting – the claim that all knowledge is gained through the senses is a claim not gained through the senses.

We can never be certain or even mildly confident of the feelings or intentions of others. Polygraph expert Leonard Saxe said, “We couldn’t get through the day without being deceptive.” Daniel Ariely analyzed data sets from insurance claims, employment histories, and treatment records of doctors and dentists. He concluded that almost everybody lies. Our world of used-car salesmen, pyramid schemes, and politicians gives good reason for generalized suspicion. We are constantly fed inaccurate and misleading information. My book gives dozens of examples from personal, historic, journalistic, governmental, corporate, and scientific sources. Any form of information about anything may be incorrect because of unintentional error, misguided theory, or deliberate deception.

Nor do observations tell us anything about underlying reality. Friedrich Nietzsche wrote that we can get no closer to reality than our own sense experience and have no way of evaluating its correspondence with the real world. Kant distinguished between noumena and phenomena. He called external reality the noumena. But we perceive only phenomena – the appearances – since all our knowledge is filtered through our mental faculties.


Our ancestors lived in a world of unpredictable famines, floods, plagues, and saber-toothed tigers. To explain such events, the more imaginative among them constructed rich cosmologies of gods, demons, and other supernatural forces. A few primitive scientists noticed that some phenomena recur in predictable intervals. They measured, experimented, and theorized. Their intellectual descendants made science the preferred method for advancing knowledge. The scientific method is the most powerful ever developed for studying the properties of the world. Science is empiricism in its most sophisticated form. Shakespeare, Dostoevsky, Freud, and others may have probed deeper into the human condition, but science has dramatically changed how people live. Yet there are reasons to be wary about scientific studies. Both inadvertent errors and outright fraud are common, perpetrated by both mediocre and eminent scientists.

Many philosophers claim that the scientific approach is irredeemably flawed. Consider two syllogisms:

  1. Theory T predicts that, under carefully specified conditions, outcome O will occur. I arrange for these conditions, and O occurs. Therefore, I have proven theory T.
  2. Theory T predicts that, under carefully specified conditions, outcome O will occur. I arrange for the conditions, but fail to obtain the predicted outcome. Therefore, I have disproved T.

The second syllogism is valid (at least, according to the party line—I question the validity in the chapter on reasoning). If the premises are true, the conclusion must also be true. The first syllogism is invalid. Counterexamples are easy to imagine. For example, a prediction from the hypothesis that unicorns run around at night in Golden Gate Park is that animal droppings will be found in the park. But finding animal droppings would not  prove the existence of unicorns. Yet this invalid syllogism form is the basis of much of both scientific and everyday reasoning.


If I’ve done my writing job well, readers will accept that nothing is certain, not even death or taxes, and nothing can be ruled out with certainty. Still, they are likely to resist any suggestion that the world is substantially different from what they think it is. They may grudgingly acknowledge the possibility that elves and mermaids exist and chickens understand quantum physics, but they will consider the possibilities miniscule.

However, without certainties to rest on, probabilities cannot be meaningfully assessed. We assess probability by using assumptions that themselves have only a probability of being true. For instance, in calculating the probability of getting two sixes on a roll of dice, we assume that (a) the dice are fair; (b) the roll is fair; (c) the numbers that come up on the two dice are independent of each other; (d) the probability of two independent events occurring simultaneously is the product of their independent probabilities. If any of the assumptions are wrong, so is the final probability.

What is the probability that your next door neighbor or close friend – who you’ve had over for dinner, who has baby-sat your children, who was maid of honor/best man at your wedding – is a serial killer? Al Qaeda terrorist? Participant in a witness protection program? Of the other gender from what you believe? CIA spy? Polygamist? Embezzler? You may say “Zero”, but people just like you have been stunned to find out otherwise. The best spies do not look like Sean Connery in his prime, bench press five hundred pounds, and drink double martinis, shaken, not stirred.


The skeptical argument can be put even more strongly: everything we think we know is probably false, since the assumptions upon which our beliefs are based are selected from an infinite pool of alternatives.

The nearest star to our sun is about twenty-four trillion miles away. Our Milky Way galaxy has hundreds of billions of stars, some of them thousands of times larger than the sun. A computer simulation estimated five hundred billion galaxies. The prestigious scientific journal Nature published a study suggesting that there are about three hundred sextillion (3 x 1023) stars in the universe. The speed of light is a little over 186,000 miles per second, so light can travel from the Earth to the Moon in about 1.3 seconds. Yet a beam of light would take about twenty-seven billion years to travel from one end to the other of the known universe. Some people may conceive of a universe infinite in size and duration or with equal ease imagine a universe with boundaries. Both strike me as wildly improbable, yet I can’t even conceive of a third alternative. With that in mind, the leap from our infinitesimally tiny part of the universe to claims about eternal and universal laws seems preposterous.

So, we are left with three possibilities, and the last two require a profound overhaul of worldview. Acceptance of either would leave no guidelines for behaving one way rather than another, as the world would then be completely unpredictable. I grant the implication.

Possibility 1. My reasoning is flawed. One or more errors invalidate the conclusions.

Philosopher G.E. Moore argued against radical skepticism. He wrote that, if a seemingly sound argument leads to an implausible conclusion, the argument may not be sound after all. There is probably an error in either the premises or the argument form. So, readers should evaluate every step leading to my outrageous conclusions. My PhD is not in philosophy, and my knowledge of the literature is limited, so there may be some important omissions. But I’m convinced that there are no serious errors of reasoning.

Possibility 2. Radical skepticism is correct. We cannot know anything, apart from the fact that radical skepticism is correct.

Possibility 3. We must give up on reasoning as a path to the truth.

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