Outer Limits of Reason (65 page)

However, there is a property that most thinkers agree reason has: one cannot use reason to derive contradictions and false facts. Throughout this book these two pitfalls were studiously avoided. Whenever we assumed some idea and derived a contradiction, we knew immediately that the assumption was wrong. The universe simply does not permit contradictions. A property cannot be both true and false. Similarly, if we derived a fact that is false, we knew that some assumption or reasoning process was wrong. Our reasoning would be worthless if we derived false facts. The facts stand and bad reasoning must be avoided.
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Our quest for a definition of reason can now be focused. What reasoning processes will ensure that we do not reach a contradiction or derive a false fact? Can we characterize the types of processes that lead to such bad conclusions? Which reasoning processes avoid such dreadful results?

Rather than giving an exact characterization of the processes that avoid contradictions and falsehoods, let us make this our very definition of reason:
Reason is the set of processes or methodologies that do not lead to contradictions and falsehoods.
Any process that will not lead us to a contradiction or falsehood is legitimate reason. Any time we arrive at a contradiction or falsehood, we know we have stepped over the bounds of reason and are being irrational. We have defined reason by examining its boundaries. What exactly will ensure that we don't step over these boundaries is hard to determine, but when we get to a contradiction or a direct falsehood, we know that we went too far. While we cannot provide exact rules on what is reasonable, we can tell when a process is wrong. Although this might sound like a strange definition, it works.

Since we do not know what will and will not cause one to err, our definition of reason is somewhat time dependent. What was once considered reasonable, could, in the future, be shown to cause contradictions. In fact, throughout history, there have been many times that something was considered part of science and only later turned out to be false. Some prominent examples include the following:

• Ether was a substance that light waves were supposed to travel through. Scientists only realized in the early twentieth century that this substance could not be detected.

• Chemists of yore believed in a substance called phlogiston that evaporates when an object is burned. It took many years until chemists realized that there was no such substance.

• Phrenology, the belief that different human traits can be learned by looking at physical characteristics of skulls and brains, was considered good science well into the twentieth century.

• Humorism and spontaneous generation were once considered legitimate science.

In contrast, there are many times that some idea has been considered silly and as time progresses it becomes part of reason and science:

• In classical Greece, the universe was considered to have always existed. It is only relatively recently that science realized that the universe came into existence within some finite time.

• The germ theory of Louis Pasteur and Ignaz Semmelweis was ignored when it was introduced. Now their ideas are taught to preschoolers to induce them to wash their hands.

• Negative and imaginary numbers were considered strange curiosities when they were first introduced. It took centuries for people to realize they actually had meaning.

This list can be extended for pages and pages. The point I am making is that there are no exact rules to determine when some idea or process is part of reason or beyond its boundaries.
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One might protest that empirical evidence should always be used to determine the truth of an idea. While this might be true, it is not always so simple. For example, Copernicus and Galileo said the Earth moves around the stationary sun. Pope Urban VIII said that the sun travels around the stationary Earth. As you look around the seemingly stationary Earth it feels like the pope was right. We now know that the pope and his empirical evidence were wrong. Galileo had done experiments showing that since the Earth is moving at a constant speed, we cannot feel it. As he said, one must look at
all
the empirical evidence to see that although the Earth appears not to move, “Nevertheless it moves.”
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One problem with differentiating reason and nonreason is that our intuition sometimes fails us. Usually when something goes against our intuitions we deem it false. This is not always justified. For example, one of our most basic intuitions is that objects are in one place at one time. We learn this simple lesson as a young toddler. However, quantum mechanics with its shocking doctrine of superposition has shown us that this simple intuition is false. Another obvious intuition is that objects have fixed lengths and processes last set times. Relativity theory has shown us that this simple intuition is false. What other intuitions that we currently have will turn out to be false?

Since the limits of reason are not fixed, there are ideas whose status is still in limbo. There are many ideas in contemporary science that have neither been shown to be true nor false. Some examples are dark matter, dark energy, multiverses, string theory, the Higgs boson, and supersymmetry. All these ideas have many proponents and might be true, but we are not sure yet. Are they within the bounds of reason or not?

With this definition of reason in hand, we can perhaps answer some of the questions posed in
chapter 1
about the nature of reason.

Why is one assumption more reasonable than another? Many times in the book when dealing with limitations, we have encountered conflicting reasonable assumptions. For example, it is intuitive to assert that

(a) Proper subsets of a set have fewer elements than the original set.

However, in our chapter on infinity, we found that

(b) Some proper subsets are the same size as the original set.

Which of these assertions is the right one? As I showed in
chapter 4
, we can get into contradictions if we do not follow the dictates of set theory, which assert (b). Since we want to avoid contradictions in reasonable processes, (b) is accepted and (a) is ignored. As counterintuitive as it sounds, (b) is correct and (a) is incorrect. Bad intuitions are not feared. Only contradictions are feared.

Why is it reasonable to check your blood pressure and not check your horoscope? Very simple: it is a basic fact that a healthy life depends on having good blood pressure. In contrast, there is no reason to check your horoscope because its predictions have been shown to be different from observable facts. Hence paying attention to your horoscope is beyond the bounds of reason.

There might be a process that is somewhat counterintuitive. We do not know if this process will lead us to correct predictions or to contradictions. Is this process reasonable? Perhaps yes and perhaps no. One thing we know for sure is that if a process leads to a false fact or a contradiction, then it is not reason. This gives a hierarchy of reasonable processes. At the very core is our fear of contradictions and false facts. That will be our final criterion for any reasonable process.

What should we believe in and what should we discard? Human beings are inherently gullible. People accept many ideas that are beyond reason. We want to believe our horoscope. We want to believe that by popping some pill we will lose weight without doing any exercise or curtailing our caloric intake. We want to believe that we will look as good as the model when we wear that outfit. But, alas, it is false. The human mind is susceptible to false ideas. When we step outside the bounds of reason, we need to be vigilant about what to accept as truth. By being cognizant of our gullibility, we are taking the first steps in our defense.
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As time progresses and we gain more experience with reason, science, and mathematics, we learn more about the boundaries of reason. We learn more about our faulty intuitions, and about processes that will make false predictions and contradictions. Thus the boundaries and definition of reason become more apparent.

10.3  Peering Beyond

After seeing the limitations of reason and defining it, we can wonder what is beyond reason. What methods can we use when reason fails us? How can we learn information that reason will not reveal to us? We should be cautious about overstepping the boundaries of reason. It is dangerous to use other methods outside of reason to understand the world around us or to build new technology. What was said at the beginning of
chapter 1
must be reiterated: reason is the only methodology that improves our well-being.

• Jonas Salk did not find a cure for polio using intuition. He used reason and the scientific method.

• Imagination was not used to get humans to the moon. Technology based on reason and science was employed.

• World hunger will not be solved using feelings of love and warmth. Rather, genetically modified crops and ammonium nitrate fertilizers will help feed the world.

Reason is necessary for all these achievements. Even though we have highlighted many limitations of reason, still we should be hesitant to go outside of reason.

What is beyond the bounds of reason? This book has discussed certain boundaries that we are not to exceed for fear of contradictions and falsehoods. But what happens if we peer beyond the boundaries like the searcher in the old wood engraving shown in
figure 10.1
?
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What are we missing by staying within the bounds of reason? What is out there?

Let me include a caveat about the many spatial metaphors in this book. The phrase “outer limits” is used as if it is a place. The word
beyond
is used as if there is a geographic boundary with two sides. We have “boundaries” that we are not permitted to “step over.” Are we “peering” into a place? Such spatial phrases can lead to error. There are no places and there are no walls. By visualizing a wall, we may incorrectly assume that it is equally legitimate to investigate both sides of the wall. This is simply not so. As beautiful as the woodcut in figure 10.1 is, it is not real. Do not mistake the metaphor for reality.
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Nevertheless, the question of what is beyond reason does have a certain legitimacy. Reason is a methodology of learning and applying information. This book has shown that there are limitations on our ability to gather and use such information. However, the information exists. Some examples of such hidden information include the following:

• There is a shortest route for the Traveling Salesman Problem. We will not be able to acquire this knowledge, but it does exist.

• Chaos theory has shown us that we will never be able to predict the future of a chaotic system. Nevertheless, a future for the system does exist.

• We might not be able to determine whether a computer program will eventually halt, but the program will halt or go on for eternity.

• Although, by definition, we cannot prove that Gödel's sentence is true, nevertheless it is true.

In all these cases, the information exists
¹⁶
and is “really out there” but we have no way of knowing what that information is. What other methods are there for obtaining such information? We have the right to speculate.
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Although it is nice to speculate, unfortunately I do not think it is possible to say anything intelligent on this topic. Our definition of reason is an approach that avoids contradictions or false facts. Anything intelligible about the information beyond such boundaries must be a guess and hence there is nothing intelligent we can really say. We might be able to guess the information or receive the information in some other way. Someone might give us the information and we might simply accept it as true. Such methods of obtaining information are not within the purview of this book and, as with anything outside the bounds of reason, we have to accept the fact that contradictions and falsehoods might be before us. There might be much information out there but without the right tools for ascertaining that information, we are forced into silence.

Imagine being given a metal box and told that it is impossible to learn the contents of the box. You can try to drill it, burn it, x-ray it, shake it, break it, and so on, but you will never be successful at opening it or knowing its contents. It is true that in the box there might be an expensive jewel or useless sand. The box could also contain a piece of paper with the number 42 on it. We must also entertain the possibility that there is nothing inside the metal box. It could simply be an empty box. We will never know. This is similar to the point I am making. We are given the bounds of reason and are told we cannot go beyond those bounds without getting into the world of contradictions or inaccuracies. There might be some type of knowledge or information outside the bounds of reason that we cannot come to know. Nevertheless, as with the box, we must realize that we will simply never know. We might feel or intuit some information. We might have wishes about what is beyond the boundary. But we must tread with great trepidation for fear of the specter of contradictions and falsehoods.