General Description of the Knowledge Problem

Francis Bacon, one of the luminaries of modern science, is thought to have said that “knowledge is power.” Since Bacon made that statement, it has become abundantly clear that humans have a very distinct and difficult “knowledge problem.” There is a fundamental defect in how we come to know anything, and while this is recognized as a problem, the depths of the problem are seldom appreciated and even less frequently discussed. At first glance such a statement may seem ridiculous. What is the problem in saying someone knows something? I know where I am and what I’m doing. I know the names and faces of my friends, family, and acquaintances. I know how to drive a car, how to cook (at least somewhat), and how to pay bills. In fact, just to navigate the tasks of daily life one has to “know” a great number of things.

The knowledge problem in its classic form is not a challenge to one’s knowledge of the things that one has observed or the techniques one has acquired. No one questions that you know that you have a car, that you know you’re married, or that you know you own a collection of Elvis Presley commemorative plates from the Franklin Mint that you inherited from your grandmother.Footnote ¹ However, the word “knowledge” takes on a very different character as soon as one goes beyond that which is directly observed or experienced. Substantial problems emerge the moment that knowledge claims are extended to things that have not yet been observed, either now or in the past or future. An additional and separate problem emerges once one claims knowledge regarding the relationships and associations between things. Over the past two millennia, as historians, sociologists, anthropologists, and philosophers have analyzed how claims to knowledge arise, develop, and collapse, there has been an expanding appreciation of just how limited our ability is to know.

Since ancient times humans have been on a quest for a higher form of knowledge that can make universal claims. Knowledge in its most ambitious form consists of fundamental truths about which we can be certain, about which we cannot be mistaken or wrong, of which we are sure. Facts and understanding of this kind can be forever considered true; we no longer need to worry about their validity, as these are things that must be so. We can put them in the “true folder” on our computer and forget about having to continue questioning them, they are certain. This is the meaning of knowledge in its extreme form, and it is with this form of knowledge that the knowledge problem is most pronounced.

For some people, it is both unacceptable and distasteful to admit that there is no certain knowledge; they hold particular ideas and convictions with absolute certainty, and there are many systems of belief constructed on such premises. For others, certain knowledge does not and need not exist, as it is not required to navigate the world and enjoy one’s life.Footnote ² From a pragmatic point of view, if an understanding works, then it is useful, even if in substance it only reflects some misunderstanding. In reading this book, I would ask those who believe in certain knowledge to have an open mind when we analyze the basis of its claims to certainty. I would likewise ask the pragmatist to consider that the problem of certain knowledge does not confine itself to ivory tower epistemology, but extends its tentacles into pragmatic knowledge, as we shall see. There are serious implications and ramifications associated with the view that if a theory works, then it is a useful theory regardless of its “truth.”

Predicting the Unobserved

The knowledge problem is most evident when we discuss our ability to predict that which has not yet been observed. Most people would say that they “know” the Sun will rise tomorrow. However, can we call this a certainty? It seems very likely, but it has also been predicted that the time will come (hopefully far in the future) when the Sun runs out of fuel, swells massively, and consumes the Earth. We don’t know if this prediction is true, but it is consistent with our best understanding and we cannot rule it out. It is also possible that the Earth will explode due to some internal process with its molten core, which we had not anticipated. A massive comet that our telescopes have not observed may crash into the Earth and destroy the planet. These examples seem a bit extreme, but consider the 230,000 people who died in the tsunami in Sumatra in 2004, which resulted from an undersea megathrust earthquake that had not been anticipated. The most reasonable prediction on that day was that it would be an average day, like so many days before it, not that a massive wave was going to destroy many thousands of lives; tragically, such was the case.Footnote ³

Another problem with the concept of knowledge is caused by the association of things. Humans are highly skilled at observing patterns of associations. Whenever there are dark clouds, sounds of thunder, and flashes of lightning, we consider it more likely to rain than if such things are not observed. The more people smoke cigarettes, the more likely they seem to suffer from breathing problems, heart attacks, strokes, and lung cancer. Children who get measles vaccines appear to have higher rates of autism. However, while we are very good at observing patterns and associations, we often see patterns that are not there. More important, if the patterns are there, we often assert causal relationships between things (e.g., more people who smoke have lung cancer, therefore smoking causes lung cancer). However, we do not observe causal relationships between things; we only observe sequences of events. Thus the knowledge problem finds its place here as well, as we cannot observe causality and can only speculate as to causal relationships.Footnote ⁴ Our speculation is not limited to passive observation of association; indeed, all manner of tests can be conducted to get closer to the causality question (as will be explored in later chapters); however, at the end of the day we are limited to reasoning to the existence of causal relationships, which we cannot ourselves directly observe.

These problems are compounded when we are speculating about causal relationships between one thing and an additional entity that we cannot observe. If a person is found dead with a knife sticking out of his or her chest, an investigation is launched to identify the person (or persons) who murdered the victim; however, this action is based on an assumption that someone did murder the victim, and thus we are ascribing a cause to an unobserved source. When people have symptoms that resemble the flu, we ascribe the cause of their illness to a microscopic virus that we do not directly observe. Even the diagnostic test we employ to “confirm” influenza does not typically observe the microbe, but rather observes other effects of the microbe (e.g., antibodies in the patient). No human has ever observed a magnetic field directly; rather, the effects that we observe on magnetic metals cause us to evoke the concept of a magnetic field. In recent years, astrophysicists have postulated the existence of “dark matter” that makes up the majority of stuff in the universe and which causes the stars and planets to have their current locations and orbits, yet no one has directly observed dark matter. In these cases, the problem is not only that we are postulating a cause and effect relationship that we cannot observe between two entities, but that we also cannot directly observe one of the two entities posited in the causal relationship.

Certainly, things exist that we cannot directly observe. Denying this would be intellectually paralyzing, because we could only act on that which we could perceive. In such a case, I would have to assume that nothing existed behind walls that I could not see through. Our inability to observe things doesn’t mean they don’t exist, nor is it a problem to use theories that assume their existence if such theories help predict the natural world in a meaningful way. However, it is a problem in the context of knowledge of the unobserved entities and their associations. Evoking an unobservable entity that may explain observable things does not mean that the unobserved entity actually exists, any more than not perceiving it means it does not exist. We shall explore this more deeply in Chapter 2.

To fully explore the depth and manifestations of the knowledge problem, and how it really is a human problem, it is necessary to explore types of reasoning employed by humans, as the nature of human thinking leads to both the benefits and problems of human understanding. This is a separate topic from issues of human cognitive errors (e.g., the common sources of misperceptions or errors in reasoning); rather, it is an exploration of the limits of knowledge even in the context of correct perceptions and cognition.

Induction as a Basis for Thinking

Experience and the ability to learn from such experience convey fundamental advantages to any creature that can modify its behavior based on past events. This is why memory is so important. As we catalog our different observations throughout life, we gain wisdom that can give us profound advantages over those who are less experienced or completely inexperienced. If you had to subject yourself to a surgical procedure, would you prefer a surgeon who had successfully performed the same operation hundreds of times or a doctor who had never done the operation even once? The second or third time you travel through a foreign country, travel through an airport, or even go to a restaurant, you have abilities that you didn’t previously have. Basically, you “know the drill” – where the bathrooms are, what the different lines are for, what documents you need, and what the culture is like. Do you remember your first day of high school? For many of us it was a terrifying thing for a number of reasons, not the least of which was not knowing how to navigate an unfamiliar environment (forget for a moment that the madness of adolescence was clouding our feeble minds). However, as days and weeks went by, we became familiar with the place and the process, and were able to navigate a system and structure that we previously found confusing and intimidating.Footnote ⁵

Induction is a natural form of human thinking that is practiced routinely and often unknowingly, and is required for everyday navigation of the world. It is basically the use of experience to predict events that one has not yet encountered. I distinctly remember an argument I had with my daughter in our kitchen one Saturday morning. She was 7 years old at the time and quite displeased with whatever it was I was telling her. She folded her arms across her chest, scrunched her face in frustration, and blurted out, “You can’t predict the future!” My response was, “Of course I can. I predict that if I push this salt shaker off the counter, it will fall.” Which I proceeded to do. She responded, “That’s not what I meant. You can’t really predict the future.” She summarily dismissed my argument and stomped off in frustration. This incident illustrates a point that gives thinking animals with memories a profound advantage over other kinds of creatures. In fact, I had predicted the future and the prediction had held. It wasn’t a stunning or unexpected prediction, and it was in a very limited context, but the fact remains that I had predicted the outcome of an event that had not yet occurred, and my prediction was spot on correct. I foresaw that the salt shaker would fall, as every previous salt shaker I had ever dropped had fallen; I had induced the prediction.

In more general terms, induction can be described as predicting the quality or behavior of the unobserved based on the observed. When you are only concerned with what has already been observed, that’s not induction, it’s description. In other words, if one were to restrict statements of knowledge to that which has already been experienced, the observations speak for themselves. I might simply state that every salt shaker I have dropped from my hand has fallen. It would actually be safer to state that I perceived every salt shaker I remember dropping to have fallen. If one restricts statements to the already observed, then one can make very clear statements about the perceived properties, but no predictions about the future are being made. Again, this is not induction but observation and only leads to encyclopedic information about things and situations already encountered. In this case, knowledge is no longer power, or at the very least a far less useful power, to the extent that power is the ability to predict and control – the ability to promote or prevent something.

Induction’s immense power comes precisely from its ability to predict the future – that which has not yet occurred or been observed. However, this power comes with a tremendous vulnerability. The successful prediction of the falling salt shaker depended, as does all induction over time, on patterns in the future resembling patterns in the past. I have dropped a great many things in my life and almost all of them have fallen; indeed, every salt shaker I have ever dropped has fallen. So, it is easy to induce that when you drop things that are not otherwise supported, they fall. (The exception would be things that are less dense than air, e.g., helium balloons.) Yet just because things have behaved one way in the past does not necessarily mean they will continue to do so in the future – this assumption is the Achilles’ heel of induction.

At first, this problem with induction seems a very commonsense sort of thing that doesn’t set off any alarms. Everyone knows that things change, that things don’t generally stay the same forever, and that there are times when past experience no longer applies. However, the gravity of this problem may be highly underestimated. A classic example of this problem with induction was put forth by Bertrand Russell, who described a chicken raised by a farmer. Every day of the chicken’s life the farmer came out and fed the chicken. We’ll assume that the chicken couldn’t talk to the other chickens or to anyone else for that matter, and therefore the chicken’s specific life constituted the entirety of its information. Hence, from the chicken’s point of view, on every day that had ever existed, the farmer approached the chicken and gave it food. It would be a very reasonable induction for the chicken to predict that on the following day the farmer would once again give it food. Regrettably, when the next morning arrives, the farmer wrings the chicken’s neck, plucks its feathers, and cooks it for supper – a tragic failure of induction to be sure – at least for the chicken.Footnote ⁶ The example of the chicken is highly applicable to human behavior. I have not yet died in a car accident; thus, I do not predict that I will die in a car accident today, and I feel comfortable driving – a mistake made by the more than 3,000 humans who die in car accidents each day worldwide. The assumption that the future will resemble the past is a highly useful assumption, but it is by no means certain. In some cases, it is almost inevitably false.

A practical example of falsely assuming that the future will resemble the past can be found with the advent of antibiotics. When penicillin was first used therapeutically in humans, it was observed that the administration of penicillin in patients infected with gonorrhea was uniformly efficacious in killing off the bacteria. One might be tempted to conclude a general principle – that penicillin kills gonorrhea. In fact, this became an accepted practical truth, and penicillin was listed by the medical community as the definitive treatment for gonorrhea. However, given the selective pressure of widespread penicillin use, some strains of gonorrhea acquired resistance to penicillin through evolutionary processes. Thus, whereas essentially 100% of gonorrhea was observed to be sensitive to penicillin in the past, such is not the case at the current time, a clear example of the fallibility of induction in being able to predict the future.

The problem of predicting future events by induction can be expanded to include the assumption that relevant modifiers of future situations will also resemble the past. In other words, the assumption that all things are equal – that one is always comparing apples to apples. I have a vivid recollection of the first time I gave my daughter a helium balloon (she was 9 months old at the time). When I handed it to her, she was extremely upset that the balloon “fell up” instead of falling down. It was an unpredicted event, because up to that point in her life 100% of everything she dropped had fallen down. Thus, it would have been very reasonable for her to predict that the balloon, like every other object, would in fact fall down. Induction failed in this case because the generalized rule did not happen to extend to this particular situation (i.e., helium balloons are not the same as other dropped objects). This problem with induction was not that the future didn’t resemble the past, but rather that situational changes in the future didn’t line up with the past. If I were to hold a salt shaker in my hand and then let it go while I was a passenger in the international space station, I would likely observe a very different result than in my kitchen on Earth. However, in the case of both the helium balloon and the space station, the future exactly resembled the past – as far as we know, helium balloons have thus far always floated in the atmosphere of Earth and salt shakers have always floated in outer space; the failure of my prediction was that I didn’t understand how other circumstances and modifiers had changed.

The problem of background circumstances is ubiquitous and takes place in everyday interactions. We all know how frustrating it is to receive unsolicited advice from strangers that doesn’t seem to apply to our situations. Most of us have seen a child having a meltdown in a public place and the parents (or other responsible adults) struggling to calm the child. For those of us who have been that struggling parent, it seems that onlookers have a variety of responses: sympathy, relief that it is not their problem, annoyance at being disturbed, and disapproval of the child, the parents, or both. In many cases the onlookers are critical of how the parents are handling the situation and, in some cases, can’t resist giving “helpful” advice.

The problem with such advice is that every child is different, every parent is different, every child–parent dynamic is different, and there are all manner of specific modifiers that may affect a given situation (i.e., the child’s pet might have died, the child might be on the autism spectrum, or the family may have different cultural norms or be facing some unusual stress, etc.). In most cases the person giving the advice has limited experience with a small number of children and yet feels comfortable generalizing his or her advice to this child, and maybe to all children. Of course, there are some generalities to human behavior, and certain advice may very well apply, but for obvious reasons, it may not. This is most acutely felt when one’s parents offer advice (often unsolicited and typically obnoxious) about how their grandchildren are being raised, because their advice is no longer applicable (and in some cases no longer legal), coming from a generation when corporal punishment was not only allowed but encouraged, when car seats had not been invented, and when there was no problem with chain smoking in the nursery. Likewise, conversely, it is easy for children to criticize their parents’ past behavior when held up to current norms, which were not in existence when the behavior in question was taking place. In all these cases generalizations about what “should be done” are being drawn that may not be valid, because the specifics upon which the generalizations are based may not apply to the situation in question. This represents a fundamental weakness in all experience-based predictions, or, in other words, a fundamental problem with induction – the situational specifics from which the experience was derived are different in the new instance.

Problems of induction are not restricted to generalizations and predictions about the future, but also extend to knowledge claims about unobserved entities in the present time. A classic example would be a naturalist who had observed a great many swans and noted that all of them were white. How confident can one be in the generalization that all swans are white, not only all swans of the future, but all other swans currently in existence that one has not observed? How many swans would you have to observe in order for the principle to be true that all swans are white? Would half of all swans be enough? How about nine-tenths? Regretfully, epistemologists have more or less reached the consensus that in order to be sure one must examine every swan. No matter how many white swans a biologist observes, all that has to happen is for one black swan to be seen. The moment that occurs, the conclusion “all swans are white” is rejected, regardless of the vast quantity of white swans that have been previously observed. In other words, the only way to eliminate this problem with induction is to limit one’s statements to that which has already been observed, which as described earlier is no solution at all, because by doing this one is no longer inducing but describing. We are no longer generating knowledge of the unobserved based on principles derived from the observed, and thus the problem of induction has not been remedied. (On a somewhat comic note, arrival of Europeans in Australia resulted in the discovery of black swans,Footnote ⁷ thus demonstrating the point logicians had been making for some time.)

There have been a number of elegant defenses of induction, but at the end of the day they all appear to fail to solve the fundamental problems described previously. One such defense would be to state that all swans are white, and should one ever find a nonwhite bird that otherwise appeared to be a swan, then it would no longer be defined as a swan. This essentially makes the hypothesis nondisprovable through self-definition.Footnote ⁸ Another common defense of induction is that while it is not perfect, it has worked pretty well thus far, and hence can be assumed to continue working pretty well into the future. However, this is simply justifying induction with induction. In other words, it’s not a problem with induction that things that worked in the past may not work in the future, because induction has worked many times in the past and will thus work in the future. This is equivalent to saying that I know the information I get from the Internet is true because of an article I read on the Internet saying all things on the Internet are true, or that I know the Bible is true because the Bible tells me so. A detailed cataloging of the different defenses of induction is well outside the scope of this book, but excellent discussions of this issue are available to the interested reader.Footnote ⁹

No defense of induction has yet solved the problems I have described, but this isn’t meant to imply that induction has not been an incredibly useful tool or that humans shouldn’t continue to use induction. It is simply to illustrate that one cannot arrive at certain kinds of knowledge using induction. David Hume, who gave the most famous description of why induction is flawed, went so far as to say that not only are inductive predictions not certain, they are not logically supported at all.Footnote ¹⁰ In other words, it’s not just that there is no certain basis to predict the Sun will rise tomorrow, but that there is no logical reason for this prediction whatsoever. Hume also expressed a certain gratitude that human behavior did not depend upon logical certainty and absolute predictions, as nothing would ever have been accomplished had we waited for such predictions before acting. Humans cannot help but induce in all aspects of life, as it is one of the fundamental ways by which we navigate the world. A person who has complete amnesia, or who cannot form new memories and is thus deprived of the ability to induce due to lack of conscious memory and experience, is at a tremendous disadvantage in the world. Induction has thus far been superior to random guessing or untargeted trial and error; however, as stated previously, it is not a path to certain knowledge about unobserved things, and it can be (and will be) tragically wrong at times.

Rejecting Populations Based on Single Instances

The experience of life is distinct and particular to each of us. Forget for a moment that even when faced with the same experience, we may each perceive it differently; clearly, we each encounter a particular set of conditions and life events, and we each have a different interface with the world. While we may also incorporate the information of others through communication, we still have direct access to only a very small slice of the pie that is our world. Most of what is in existence (the universe) is simply not accessible to us, and we know little of even that to which we do have access. What percentage of people do you actually know in your hometown, on your street, or in your workplace? For the nearly 50% of Americans who live in large cities, it is likely that you know very few of the people in your general proximity and very little about them. Certainly, none of us has met a significant percentage of the approximately 7 billion people on Earth, seen a significant amount of the 197 million square miles of the Earth, encountered a significant number of the animals on Earth, etc. Yet, in order to use the power of induction to help us navigate the world, it is necessary that we make generalizations of some kind. Basing such generalizations on the small amount of data we have seems like a better guess than basing it on no data at all.

While we may be stuck doing our best to navigate the world with what we have, it is nevertheless a big problem to reject factual claims made about populations by using minuscule sample sizes. Nevertheless, this seems to be an enduring human trait. One reads that, on average, smoking increases the risk of getting lung cancer. This is a population-based argument. A group of smokers will have a rate of lung cancer that is 23 times more likely (for males) and 13 more likely (for females) than for similar populations who do not smoke.Footnote ¹¹ However, this situation is often offered as the answer to the question: Does smoking cause lung cancer? When faced with such a statement, it is common to hear, “Well, you may say that smoking causes lung cancer, but my grandfather smoked four packs of unfiltered cigarettes for 35 years, and he never got lung cancer.” This may have been the case for the grandfather, and that’s a great thing for him, but it is irrelevant to the claim that smoking, on average, increases the risk of lung cancer. The claim was not that smoking causes lung cancer (i.e., if a person smokes, then he or she will get lung cancer) in the same way that removing someone’s head causes death.Footnote ¹² By definition, if smoking increases rates of lung cancer to anything less than 100%, then the population-based argument can be true even though some people will smoke their whole lives and never get lung cancer.Footnote ¹³

Positive assertions of generalizations are no less based on minuscule data sets than are the rejections of assertions. One might go to two different restaurants and have a wonderful dining experience at one of them and a horrible dining experience at the other. Based on this experience, one rates the first restaurant as good and the second restaurant as horrible. However, the first restaurant may have gotten the wrong shipment of food that day, receiving excellent ingredients instead of the bargain basement, outdated food they normally buy to save money. In contrast, the second restaurant may have had both cooks and half their servers call in sick that day. The statements we tend to make are not that one particular meal was good at one place and poor at the other. Rather, we conclude one restaurant is good and the other bad, a generalized statement.

During the 2016 American presidential election, much regrettable rhetoric was passed around regarding whether or not individuals of the Muslim faith, or even of Middle Eastern background (regardless of faith), should be allowed into the country, or whether they should even be eligible to run for president if already citizens based on the assertion that people of the Muslim faith tend to be terrorists. As tragic as terrorist events have been in the Western world (and I use the Western world merely as a basis of comparison, not meaning to imply terrorism is any less tragic anywhere else), the perpetrators of these acts represent a very small number of individuals out of a world population of 1.6 billion Muslims (22% of all living humans on Earth). Surely, one cannot draw a meaningful generalization about 1.6 billion people based on the actions of a handful of individuals. If one were to look at Muslim-related terrorism in the United States, fewer than 20 individuals in recent years have engaged in terrorist acts out of 1.8 million Muslims in the country. This in no way rejects the observation that terrorist acts can be carried out by people of this group or that some extreme variation of ideology may drive the actions of these few individuals. However, this is a very small quantity of evidence to justify broader generalizations about Muslims. If anything, we can conclude that 99.9% of Muslims in the United States are not terrorists, the very opposite of what the rhetoric was suggesting. Moreover, this situation is a prime example of the availability heuristic (heuristics will be discussed in Chapter 4) combined with the base rate fallacy. When someone perpetrates a terrorist act, the media tells us the characteristics of that person. However, the media seldom (if ever) tells us the number of people with the same characteristics who don’t carry out such acts.

This tendency to draw generalized knowledge from scant data may be the best we can do as individuals, as performing population-based studies is not a typical activity of humans; even if we were so inclined to engage in systematic study, most of us have neither the resources nor the ability to do so. However, the fact that individuals are doing the best they can doesn’t mean their best is necessarily doing it well. Moreover, even when we do have access to the population data (e.g. with Muslims and terrorism), we are prone to ignore it. As will be discussed in more detail later in the book, it can be argued that the study of science has focused on (and analyzed) only a very few scientists and drawn general conclusions based on them. Moreover, by focusing on the scientists who have made the most progress (or at least are the most famous), those who study science bias themselves to the extreme of the population, potentially hobbling any ability to capture what scientists do in general (or as a group).

Why Probability-Based Thinking Doesn’t Help with Induction

A common approach to the problem of induction, which is often invoked in response to the previously stated concerns, is to state induced knowledge claims in probabilistic terms. This applies both to making statements about unobserved entities in the present and also across time. For example, if one had observed 99 ravens and all were black, then one might induce the statement that “all ravens are black.” However, if the 100th raven observed was not black, we wouldn’t throw up our hands in frustration at having no knowledge of ravens. Rather, one would simply modify the knowledge claim by saying that “99% of observed ravens are black.” This maneuver is simply restating the data to modify a principle about all ravens. This can then be used to predict unobserved events from a probabilistic point of view; you can’t tell what color the next raven you encounter will be, but you can say that 99% of the time it will be black and 1% of the time it will be nonblack – not with absolute certainty regarding the next raven, but with predictive power regarding a whole population and the relative likelihood of what color the next raven will be. A probabilistic point of view can’t predict an individual event, but there is no reason it can’t make predictions about populations with great accuracy.

Although probability statements may bring comfort to some people, they fail to help much with the knowledge problem itself and with the issue of induction. The reason probability determinations do not help with the knowledge problem is that even if the probability statement is true with a capital “T”, it cannot provide the ability to predict next events with certainty. While a probability statement can tell you the odds that the next raven will be black, the next raven can only be either black or nonblack.Footnote ¹⁴ Being able to state the likelihood that the next raven will be black is a type of prediction. Nevertheless, even if one has absolute knowledge of a population, it does not speak to specific cases, and thus one still cannot predict particular events. When most people talk to their doctor they don’t want to know what their probability of getting cancer is; they want to know whether or not they themselves will get cancer.

Another problem with probability statements is that, much like simple induction itself, one can never rule out things changing in the future. After observing another 100 ravens, the 99% probability determination may change again, and in fact will change, unless 99 of the next ravens are black and one is nonblack. Thus, while the 99% probability determination may be better than random guessing, it is not knowledge about which we cannot be wrong. Let us retreat even further from our desire for absolute knowledge and stipulate that the more ravens we observe, the better and better our probability determination will become.Footnote ¹⁵ This seems a justifiable statement (often called the law of large numbers). This is just another way of saying that the closer we get to having observed every raven, the closer we get to knowing the color that all ravens are.Footnote ¹⁶ This view and approach would be acceptable and would lead to certain knowledge (albeit probabilistic) if one could make the assumption that things are distributed around the universe in a uniform fashion. However, any clustering of any kind, either at a specific time or over time, destroys this principle, and there is no justification to support uniformity in the universe; indeed, there are ample data to the contrary. Let us back off even further and stipulate that we have made an absolutely correct probability assessment of the universe and that distribution of variability is not a problem. There is still no way of assessing whether the existing probability distributions in the universe will hold into the future, which brings us back full circle to the main problem of induction in the first place.

Deduction as a Basis for Thinking

Deduction is a separate means of generating understanding and knowledge claims that suffers none of the problems of induction. This does not mean it doesn’t have its own problem and limits, but at the very least they are different then the problems of induction. Aristotle’s writings provide the earliest known Western codification of deduction, which he demonstrated in the form of syllogistic constructs. Aristotle defines a syllogism as “a discourse in which certain things having been supposed, [and] something different from the things supposed results of necessity because these things are so.” This statement, although almost circular in its appearance, defines the traditional basis for deduction. A syllogism has premises (statements of fact) and a conclusion that appears to be “different” from either premise alone. For example, consider the following two premises.

These two statements are presented as matters of fact known to the thinker. Based on these two premises, one can reach the following conclusion:

Although no direct information is explicitly stated in any one premise regarding the color of bears at the North Pole, deduction based on the combined content of the premises leads to the conclusion regarding the color of bears at the North Pole. Hence, new understanding has been deduced by analyzing and combining the premises.

A more general form of the previous syllogism, but of the same construct, is as follows:

The tremendous strength of deductive reasoning is that if the premises are correct and the logic is valid, then the conclusions are certain to be true – not likely to be true, not probable, but incapable of being incorrect. This sounds an awful lot like the type of knowledge we’re seeking when we talk about true knowledge. If correct premises and valid deduction lead to certain conclusions, then this sounds promising indeed. Of course, there are many fallacies in deductive reasoning, and, like any weapon of logic, if it is not wielded correctly the result can be incorrect conclusions, even from true premises.

Let’s look at the following example:

The conclusion in this case is not a correct result of the premises. The reason is that while the second premise limited where polar bears can live (i.e., at the North Pole), this does not rule out that additional bears (nonpolar bears) also live at the North Pole. Hence, bears at the North Pole may consist of some polar bears and some brown bears. This possibility does not necessarily make the statement false, as it doesn’t guarantee that brown bears will be at the North Pole; however, it doesn’t rule it out and thus allows for the possibility that the conclusion is incorrect. In other words, the conclusion is not necessarily true and is thus a fallacy that doesn’t lead to certain knowledge.

Like induction, deduction is a common tool of human reasoning, without which we wouldn’t navigate the world as well as we do. While Aristotle may have first named and characterized deduction, it is not something that Aristotle invented. Rather, he described a process that, like induction, is a normal part of everyday human thinking. Deductive thought in humans can be found in children as young as preschoolers.Footnote ¹⁷ This is not to say that humans are perfect deducers; indeed, a whole body of studies has shown that we tend to deduce incorrectly, especially in certain circumstances.Footnote ¹⁸

The correct application of formal logic is a highly complex and well-developed field, much of which is difficult to learn and certainly not intuitive. Nevertheless, like induction, deduction is a normal part of human thinking that we deploy as part of our navigation of the world. However, errors in deduction are also a normal human trait. Moreover, when we make such errors, we often feel as though we have reasoned our way to a correct conclusion, even though we have actually failed to do so. It is for this reason that logicians have invented specific ways to express logical statements, have defined different types of logic and the rules by which they work, and have made tremendous progress in such thinking. Indeed, much of mathematics can be described as a deductive language.

While very powerful, deduction does not solve the knowledge problem. The first thing to note, which is a fundamental limit to deductive reasoning, is that it doesn’t generate information about the unobserved; rather, it only reveals complexities that are already contained within the premises, but which may not be intuitively obvious until the deductive reasoning is fully carried out. In other words, no new information has been generated that wasn’t already contained within the premises; nevertheless, without the syllogism, the fullest meaning of the stated facts could not be demonstrated and may not be appreciated. This seems to be a real limitation to deduction, as without the ability to make any predictions about the unobserved, our ability to predict or control is limited. However, this limitation can be overcome if the premises are universal, thus allowing the deduction of universal conclusions. In other words, consider premises that include the type of language of “every A is a B” or “no A is a B.” Based upon such universal premises, one can deduce knowledge statements that apply to every instance of A, even instances that have not been experienced. Thus, one is deducing knowledge of the unobserved. This is one reason why deductivist thinkers tend to prefer premises of a universal type (e.g., all As are Bs), for without such universal premises the conclusions are not universal. If the conclusions are not universal, then one cannot make statements (with certainty) about unobserved things. If one has not achieved certainty of unobserved things, then one has not gained true knowledge (at least as we have defined it), and the knowledge problem remains unsolved.

If deduction can generate true knowledge so long as it uses premises of a universal nature, then where is the problem? The problem is in being able to determine a justifiable premise of a universal nature. For centuries, a number of notable philosophers have believed that humans have some inherent ability to recognize natural truths. However, in recent times, neurology’s and cognitive psychology’s understanding of human perception and thinking has advanced to the point that we now appreciate that humans can be pretty terrible at perceiving the world right in front of them, let alone coming up with universal statements of truth (this is explored in detail in later sections). If there is a single error in a premise upon which a deduced system of knowledge is built, then the whole system may come crumbling to the ground. If the premises are not certain, then the knowledge is not certain, no matter how good the reasoning. If there is no reliable source for certain premises, then deductive thinking cannot solve the knowledge problem.

Some of our greatest institutions have solved the premise problem by simply stating that a given premise is true. For example, the U.S. Declaration of Independence states: “We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty, and the pursuit of Happiness.” In other words, these truths are self-evident because we say so (so there!), and we will now build a system of beliefs based in part on this premise.Footnote ¹⁹ If the truths really were self-evident, then this might be okay, but what justification is there for such an assertion other than the authors stating that they hold them to be self-evident? – in other words, their opinion, and what is the justification that their opinions are correct? In the same fashion, many religions are based on an irrefutable premise that a given god or gods exist. Likewise, many systems of belief, even without a formal deity, state the presence of a force, or energy, or structure in the universe. Such premises of gods or forces are certainly not without evidence; indeed, evidence of the divine can be obtained through an experience of god, through observable consequences that would come about in the event that there was a god, or even through revelation. One can feel universal sources through a spiritual experience or perceive the effects of such forces in the world.

One might then argue that there is no knowledge problem for philosophies that invoke self-evident premises or for religions that consider the experience of a god or revelation of the divine as sources of unequivocal truth. However, as will be explored in detail later, it should be noted that such systems do not typically deduce an entire system of belief, at least not in any formal sense of deduction, from the premises that are stated, and thus it is a kind of an apple and orange situation. Moreover, while feeling or perceiving something can be a compelling force in persuading an individual that the thing exists, perceptions and feelings are highly prone to error and misinterpretation, and thus do not provide a justification of knowledge that stands up to analytic thinking. This is not to say that such justification is not sufficient for theology or spiritual systems of belief, but it is clear that such justification is fallible. How many religions have existed in human history, many of which believed with certainty that they were the one true way? For this to be true, all of them, except one, must be wrong, and it is not clear that any of them need be right. Thus, theological revelation appears to be able to get things wrong. Hence, while religions typically state things in certain terms, and may lead to certain belief, they do not lead to certain knowledge. The making of claims with certainty and explanations of everything will be explored later as one of the criteria by which one can demarcate some categories of nonscience from science.

If we stipulate that humans have no access to fundamental premises, or first conditions, through either revelation or innate knowledge of such premises, then how is one to use deduction? If the premises are not certain to be true, then no matter how valid the deductive reasoning, the results are not certain to be true, which undermines the whole deductive program for generating knowledge. One might point to Euclid, who stated certain premises and was then able to deduce a complex geometry that was very useful in describing the natural world. Likewise, Sir Isaac Newton stated certain premises (laws of motion) from which he deduced a system of mechanics that could describe and predict motions of the planets with great accuracy and how forces worked on bodies in general. Isn’t the amazing predictive capacity of these systems a validation of the correctness of their premises? Regrettably, as we shall explore later, such is not the case. Of note, given modern theories of special relativity and the curved nature of time-space, both Newton’s and Euclid’s systems are considered to be profound intellectual achievements of great theoretical and practical value, but ultimately, these systems are not entirely correct due to the premises being not entirely correct.

At the end of the day, there is no clear way around the major problem of deductive knowledge. In order to have any ability to predict unobserved nature, deduction must make statements that are universal. Due to the problems of induction, universal statements based on experience cannot be justified, and no other source of universal premises seems supportable.

Although both induction and deduction have the problems described, in real life, one nevertheless uses induction and deduction (or at least reasoning that resembles deduction) together to navigate the world. Induction provides the justification for premises based on experience (albeit an imperfect justification). Deductive reasoning helps reason forward from the induced premises to generate all manner of new understanding of association within the induced premises. Hence the combination of induction and deduction certainly leads to new ideas that would have come from neither alone, but fails to solve the problems of either. In aggregate, the knowledge problem is solved by neither induction, deduction, nor a combination of the two.

The Utility of Uncertain Conclusions: Is the Knowledge Problem Really a Problem?

It seems that a solution to the knowledge problem is not likely to be forthcoming. However, how much of an impediment is this? It brings us to the question: What makes useful knowledge, and does useful knowledge have to be universally certain to be meaningful? Many thinkers have adopted a pragmatist school of thought that has placed value on scientific theories if the theories work in the real world. If a theory predicts the natural world, then it is a useful theory, regardless of whether or not it is ultimately true. Knowledge may be flawed, to be sure, and it may not result in any kind of absolute, objective truth. However, it is hard to ignore the explosion in science and technology that has transformed the world over the last four centuries. Most of this transformation was carried out using theories that were not only uncertain (as all scientific theories are) but which are now believed to have been disproven. While “wrong” they were nevertheless very useful theories. Whether or not the progress of science and technology is good, bad, or amoral, the fact remains that generation of imperfect, uncertain, and ultimately flawed understanding has had a very real effect on the lives of untold millions. Despite missteps and errors, the scientific process on the whole has been fruitful. Given the problems of induction, we cannot assume science will continue to work with any certainty, but it does not appear to have stopped working yet; it appears as though uncertain theories, albeit imperfect, can be pretty useful.

Of immense importance is the understanding that induction and deduction are tools in the toolbox of thinking, but that these are not in and of themselves methods of modern research. To be sure, there are modern inductivists (e.g., botanists in the rainforest cataloging new species of plants or those sequencing every bit of DNA they can get their hands on to generate encyclopedic databases) and modern deductivists (e.g., theoretical mathematicians). However, the important message here is the recognition that induction and deduction are parts of normal human thinking. While they are employed by scientists, they are also employed by basically everyone else. Thus, the weaknesses of induction and deduction are weaknesses of science and nonscience alike. Because they are ubiquitous, the simple use of induction, deduction, or both in combination cannot be a criterion to distinguish science from nonscience. Yet, while common to both science and nonscience, induction and deduction are nevertheless integral and essential to the scientific method, and therefore are essential trees to be understood as we continue to develop, in upcoming chapters, a view of the forest that will help distinguish science from nonscience.