Outer Limits of Reason (66 page)

 

One should not be too burdened by the bounds of reason and rationality. There is no cause to be despondent because we are unable to see beyond the bounds outlined in this book.
We human beings already live beyond reason
. The world humans inhabit is not the cold, heartless world of reason, logic, mathematics, and science. Our minds do not live in a world of stones, carbon-based life forms, and molecules following habitual laws of physics. Rather, we all have feelings and emotions that are not dictated by reason and logic. We have a sense of beauty, wonder, ethics, and values that are beyond reason and defy rational explanation. We appreciate beautiful art and music for no logical reason. While contemplating a mountain range, we are full of awe and wonder. We try to avoid performing deeds that are wrong even though they might be beneficial to us. The time we spend with our loved ones is treasured even though there is no logical necessity for it. We feel pain when we are distant from our loved ones. Our decisions are not made on the basis of logic and reason. Instead we use aesthetics, practical experience, moral inclinations, gut impulses, emotions, intuitions, and feelings. In this sense, every one of us already transcends the bounds of reason.

To some extent, the explanation for why human beings have such a hard time getting along with each other is that we all have desires and values that are beyond objective logic and reason. If we were all strictly logical like a computer or
Star Trek
's Spock, we would all be on the same page and never argue with each other. This diversity of will makes life interesting. The cacophony of various human desires gives color to our relationships with other people. It also gives us the feeling that everyone
else
is crazy and irrational. Of course, everyone else has similar feelings about us. We all have irrational desires and wills that control us in ways that are different from others.

Not only do we have this nonreasonable part of our psyche, but this irrational component is our most important component. It is what gets us out of bed in the morning. It is our motivation and our will. There is no logical reason to do anything. Reason and logic tell us what is and in some cases they can tell us what will be. These tools can be used to help us get what we want. But they do not tell us what to want or what ought to be. Only will and desire tell us that.
¹⁸
Unless love, desire, music, and art exist, our world has no meaning. Real life has importance only when it includes ethics, values, and beauty. Will and desire are fundamental, while reason is a tool for that will and desire. Reason is a powerful—but nevertheless limited—tool.

Further Reading

Many interesting philosophy books discuss related topics—for example, Eddington 1958, Fogelin 2003, Priest 2003, and Rescher 1999, 2009. There is also a nice BBC documentary that covers some of our topics called
Dangerous Knowledge
(
http://www.dailymotion.com/video/xdoe8u_dangerous-knowledge-1-5_shortfilms
).

Notes

Preface

1
. Popper 2002, 38.

Chapter 1

1
. From the preface to Kant 1969. The original is
Die menschliche Vernunft hat das besondere Schicksal in einer Gattung ihrer Erkenntnisse: daß sie durch Fragen belästigt wird, die sie nicht abweisen kann; denn sie sind ihr durch die Natur der Vernunft selbst aufgegeben, die sie aber auch nicht beantworten kann; denn sie übersteigen alles Vermögen der menschlichen Vernunft
.

2
. It is not clear if Einstein ever actually said this. However, Horgan (1996, 83) quotes a similar statement by John Archibald Wheeler: “As the island of our knowledge grows, so does the shore of our ignorance.” Friedrich Nietzsche uses the same metaphor in
The Birth of Tragedy
(2000, 97): “But Science, spurred by its powerful illusion, speeds irresistibly toward its limits where its optimism, concealed in the essence of logic, suffers shipwreck. For the periphery of the circle of science has an infinite number of points; and while there is no telling how this circle could ever be surveyed completely, noble and gifted men nevertheless reach, e'er half their time, and inevitably, such boundary points on the periphery from which one gazes into what defies illumination.”

3
. This statement needs a little justification. One must distinguish between craft or technique, which does build on itself, in contrast to art and creativity, which do not build on themselves. In fact, creativity demands that the art be
different
from previous generations. It would be hard to claim that literature progresses when it can be argued that the greatest literature was written centuries ago by writers like Dante and Shakespeare. The Holocaust, genocides, and the wars of the twentieth century are counterexamples to any claims of an improvement with regard to human morality.

4
. This chessboard-and-dominoes puzzle was cribbed from Gardner 1994, where it is called the “Mutilated Chessboard.” The puzzle is, however, much older.

5
. From Quine 1966, 3.

6
. I am not equating human thought and human language. The latter is far more organized, coherent, and codified than the former. Whereas human thought does not have to be intelligible to any mind other than the thinker—in fact, it usually is not—human language is an attempt at making human thought understandable to other human minds. This is true for spoken language and even more so for written language. For the written word, even more codification and organization are required. A great piece of writing will be codified and clear enough for many other minds to appreciate. In contrast, literary theorists describe written language that “descends” to the level of human thought as “stream of consciousness.” Examples of such literary works are James Joyce's
Finnegans Wake
and T. S. Eliot's
The Love Song of J. Alfred Prufrock
. Most people find these works unreadable. The relationship between human thought and language was dealt with by the Russian psychologist Lev Vygotsky in his book
Thought and Language
and in the later works of Wittgenstein. Nevertheless, both thought and language are prone to contradictions.

7
. Einstein 1936.

Chapter 2

1
.
Wovon man nicht sprechen kann, darüber muß man schweigen.

2
. Alas, I was unable to ascertain if Yogi Berra actually said this.

3
. Some analysis shows that Epimenides' declaration is not really a paradox. For one thing, we are subtly assuming that every sentence that a liar utters is a lie. This is false. A liar is someone who lied at least once. We have all lied at least once in our lifetime and hence we are all liars. Furthermore, there is something wrong with the logic in deriving a contradiction. Assume for a moment that Epimenides is telling the truth. This would imply that he is a liar and that the sentence is false. But a false sentence is not a contradiction. In contrast, assume that Epimenides' sentence is false. That means that not all Cretans are liars and that a Cretan exists who is not a liar. Such a pious truth-teller can be anyone on the island. (What if Epimenides were the only person on the entire island?) If this truth-teller were Epimenides, then he is telling the truth and the sentence is true. That would be a contradiction. However, the truth-teller need not be Epimenides and could be someone else on the island. So there would be no contradiction if we simply accept that Epimenides was stating a falsehood. There is one last interesting idea to point out. We have determined that Epimenides' statement cannot be true and must be false. From this we logically conclude that someone on the island must be a truth-teller. This demonstrates the power of language and logic: from the fact that Epimenides made his statement, we conclude a fact about someone else's piety. Despite these problems with Epimenides paradox we will see that there are other similar linguistic paradoxes that are bona fide, red-blooded paradoxes. It turns out that the classic example of a paradox is not really a paradox at all. How paradoxical!

4
. The feminist response to this little quandary is that the barber's wife shaves the barber. This is just one of the many arduous tasks that she has had to perform over the centuries without getting any credit. She has pulled mankind from the abyss of contradiction!

5
. We will meet this paradox again in 
section 4.4
.

6
. Hardy 1999, 12.

7
. Michael Barr pointed out to me that 1729 is the first number only if you restrict it to positive whole numbers. If you permit negative whole numbers, then 91 = 6
³
+ (−5)
³
= 4
³
+ 3
³
.

8
. We will meet vague terms again in 
section 3.3
.

9
. Richard's paradox will be much better understood after reading 
section 4.3
.

Chapter 3

1
. Similarly, the USS
Constitution
has been docked in the port of Boston for almost 200 years. The USS
Intrepid
is docked in the port of New York City.

2
. Aristotle posits that there are four main “causes” of objects: the material cause (what it is made of), the formal cause (its shape), the efficient cause (who/what made it), and the final cause (its purpose). Each of these causes somehow accounts for what the object is. In this paragraph, I showed how we can make changes to all four “causes” of the ship of Theseus. Nevertheless, despite these changes, many people would consider the ship unchanged.

3
. However, we can perform the same analysis with atoms. Is a carbon atom still a carbon atom if it loses one of its electrons? How about if it loses a neutron? What if it forms a chemical bond with another atom? Even atoms do not exist as atoms.

4
. I am invoking Occam's razor as a criticism of (extreme) Platonism.

5
. What Kant called
ding an sich
or thing-in-itself.

6
. It is beyond the purview of this book to discuss Eastern philosophy. However, some of these ideas figure prominently in classical Indian and Chinese philosophy. It might be said that one of the primary purposes of meditation and “nullification of the self” is the ability to see beyond the classifications of objects. Without classifications and names, there are no distinctions between concepts or objects. Reality then takes the form of the oneness and unity that is so central to the mystical traditions.

7
. This is actually one of the simplest theorems to prove and worthy of taking a minute to actually demonstrate it. Let us say we do not know what the sum is and call it
x
:

x
= 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + . . .

Again, we do not know what
x
is but, by naming it, we can manipulate it. Consider 1/2
x
. By the distributive property of arithmetic we know that

1/2 (
a
+
b
+
c
) = 1/2
a
+ 1/2
b
+ 1/2
c
.

This is not only true for three numbers but for infinitely many numbers. And so we have that

1/2
x
= (1/2) 1/2 + (1/2) 1/4 + (1/2) 1/8 + (1/2) 1/16 + . . .

         = 1/4 + 1/8 + 1/16 + 1/32 + . . . .

Subtracting 1/2
x
from
x
gives us

x
– 1/2
x
= 1/2
x

or

x
– 1/2
x
= (1/2 + 1/4 + 1/8 + 1/16 + . . .) – (1/4 + 1/8 + 1/16 + 1/32 + . . .) = 1/2.

This gives us

1/2
x
= 1/2

or
x = 1.
And we are done.

8
. We will meet and explain some of these concepts in 
section 7.2
.

9
. Aristotle wrote: “Besides, a view which asserts atomic bodies must needs come into conflict with the mathematical sciences, in addition to invalidating many common opinions and apparent data and sense perception” (
De Caelo
, 303a21).

10
. If we assume the world is discrete, the mathematics needed to build rockets and bridges is far more complicated than calculus. Perhaps calculus is simply an easy approximation of the true mathematics that has to be done to concretely model the discrete world in which we live.

11
.
Chapter 7
discusses them in greater depth.

12
. We are all time travelers: we constantly travel
forward
in time.

13
. It should be noted that if I had been able to go back to something similar to the Continental Congress, this would only be confusing to me. For my part, I know that I was not there at the original Congress, and now I will be there. However, to everyone else, given that I changed history by being there, it will not be strange.

14
. This was a theme in the 1985 movie
Back to the Future
.

15
. Rucker 1982, 168.

16
. Even
pornography
is a vague term. As Supreme Court Justice Potter Stewart has said, he cannot define pornography “but I know it when I see it.”

17
. One usually says that two animals belong to the same species if they can mate with each other. However, there is a major problem with this definition: animal A might be able to breed with animal B, making them the same species. At the same time, animal B might be able to breed with animal C, rendering them of the same species. However, animal A might not be able to breed with animal C, making them different species. This lack of transitivity of identity for species is similar to other problems we saw with the problem of identity in 
section 3.1
.

18
. This explains why this section is in this chapter, not in the chapter on linguistic paradoxes (
chapter 2
).

19
. Our old friend Zeno also has a version of this paradox. Some even find sorites-type arguments in the Bible (see Genesis 18:23–33).