Beliefs by Nilsson

8/3/2019 Beliefs by Nilsson

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BELIEFS

WHAT THEY DO FOR US, HOW DO WE GET THEM,HOW TO EVALUATE THEM

(DRAFT)

Nils J. Nilsson

Stanford University

[email protected]

http://ai.stanford.edu/ ∼nilsson

July 20, 2011

Copyright c 2011 Nils J. Nilsson, All Rights ReservedJuly 20, 2011

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http://ai.stanford.edu/~nilsson






[Belief] . . . that upon which a man is prepared to act. – Alexander Bain,Psychologist 1

“Man’s most valuable trait is a judicious sense of what not to believe.”– Euripides

“We may not know very much, but we do know something, and whilewe must always be prepared to change our minds, we must act as best wecan in the light of what we do know.” – W. H. Auden 2

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Quotation taken from Louis Menand, The Metaphysical Club: A Story of Ideas in America , p. 225, New York: Farrar, Straus and Giroux, 2001.2 W. H. Auden, as quoted in “The Double Man,” by Adam Gopnik in The New

Yorker , p. 91, Sept. 23, 2002. Originally from W. H. Auden,“Effective Democracy,”Booksellers Quarterly , 1939, reprinted in The Complete Works of W.H. Auden: Prose,Volume II, 1939-1948 , E. Mendelson, ed., Princeton University Press, 2002.

iiCopyright c 2011 Nils J. Nilsson, All Rights Reserved

July 20, 2011



Preface

[[To Be Written]]


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ivCopyright c 2011 Nils J. Nilsson, All Rights Reserved

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Contents

1 Belief, Knowledge, and Models 3

2 What Do Beliefs Do For Us? 7

3 Where Do Beliefs Come From? 13

4 Evaluating Beliefs 21

5 In All Probability 31

6 Reality and Truth 39

7 The Scientic Method 45

8 Robot Beliefs 63


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Prologue

Belief , knowledge, truth , and reality . These words trigger debates not onlyamong philosophers but also among ordinary people. We have beliefs abouta lot of things. Do some of these beliefs comprise part of our knowledgeabout reality , whatever that might be? And are any of our beliefs true ? Ihave some beliefs about these very topics – here, in a nutshell, are some of them:

1. Our beliefs are arrayed along a continuum. Some we hold verystrongly, some less so. When we say we “know” something, we aresimply saying that we believe it extremely strongly. There is nodifference in kind between believing and knowing . Knowing isbelieving at the “most-certain” end of the continuum.

2. We live in a “real world,” not in a solipsistic dream world. Realityimpacts our senses, and our actions affect that same reality. Beyondthat, we can’t say what reality is, we can only do our best to describereality by constructing models of it. Our beliefs comprise a large partof those models.

3. When we say that something is “true” or a “fact,” we are saying thatwe know it – that is, we believe it extremely strongly. There isnothing more to say about “truth” than that. In particular, truthsand facts are not “out there” somewhere, independently of us andwaiting to be discovered. What is out there is reality, waiting to bedescribed as best we can.

4. We have individual beliefs of our very own, and many beliefs we sharewith others. The beliefs that are held by experts in a given subjectare worthy of special consideration.


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CONTENTS CONTENTS

5. To be an “accurate description of reality,” a belief must consistently

make predictions that are conrmed by observations. Not all of ourbeliefs meet this test, but we might hold them nevertheless for otherreasons.

This monograph is an elaboration of my ideas about beliefs, knowledge,truth, and reality. Among other things, I will be describing various ways toevaluate beliefs, including the scientic method.

2Copyright c 2011 Nils J. Nilsson, All Rights Reserved

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Chapter 1

Belief, Knowledge, and Models

Our beliefs constitute a large part of our knowledge of the world. Forexample, I believe I exist on a planet that we call Earth and that I share itwith billions of other people. I have beliefs about objects, such asautomobiles, airplanes, computers, and various tools, and (to variousdegrees of detail) how they all operate. I have beliefs about the twenty-rstcentury culture in which I live: about democracy and the rule of law, aboutthe Internet, and about science and the humanities, among other things. Ihave beliefs about many other people, including family, friends, associates,and even others yet unmet. In fact, to make an explicit list of all of mybeliefs would be impossible. Yet, all of these beliefs are there, somewhereand somehow represented in my brain, changing, growing, shrinking, andmostly ready for use when I need them.

If I were to try to list my beliefs, I would do so using English sentences,such as “the universe is around 14 billion years old,” “Salem is the capital of Oregon,” “John Jones usually does what he says he is going to do,” and soon. I can also state what I do not believe. For example, “I do not believe inextra-sensory perception.” And, I can state that I don’t have any idea aboutsomething. For example, “I don’t know how or why there was a Big Bang.”

We often refer to our beliefs as “theories.” We construct theories abouteveryday experience – both social and personal. Why are crime rates fallingin New York City? Why did Booth assassinate Lincoln? Why is my childfalling behind in school? Why is unemployment so high (or so low)?

Scientic theories are proposed and argued over by scientists. There are


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CHAPTER 1. BELIEF, KNOWLEDGE, AND MODELS

theories to account for fossils found in rocks, for the sun’s almost limitless

energy, for earthquakes and volcanoes, for the diversity of life forms, formental behavior, for the birth and death of stars, and for essentiallyeverything else we can perceive about the universe. Usually scientictheories are described by many sentences – replete with mathematics. Theyare written down in articles and books rather than existing as such in thebrains of scientists. When scientists say that they “believe” in quantummechanics, for example, they are assenting to what is contained in articlesand books about quantum mechanics.

Besides the literature of science, there are non-ction books such ashistories, political analyses, biographies, and narratives. These arepurported to be their authors’ beliefs about something, and you and Imight adopt some of these beliefs as our own. For example, one might saythat one believes Stephen Ambrose’s story about the Lewis and Clarkexpedition as told in his book Undaunted Courage . Even books of ctioncontain descriptions of the world that we might incorporate into our beliefs.

Cognitive scientists distinguish various kinds of knowledge. Knowledgerepresented by beliefs is called “declarative” because beliefs are stated asdeclarative sentences. No one really knows how beliefs are represented inour brains. The philosopher and cognitive scientist, Jerry Fodor, proposesthat they are represented as sentence-like forms in a “language of thought”he calls “mentalese.” Neuroscientists, psychologists, and philosopherscontinue to argue about whether there are any such sentence-likerepresentations in our brains at all. For our purposes we won’t worry abouthow beliefs are actually represented in the brain. Because we state themusing sentences, it seems reasonable to think of them as sentences.

Cognitive scientists also talk about another kind of knowledge, whichthey call “procedural.” It’s the kind that’s built right into our practicedactions, such as swinging a golf club or riding a bicycle. For tasks thatrequire real-time coordination between sensing and acting, proceduralknowledge is more effective than declarative knowledge would be. (Aftermemorizing some sentences about how to do a cartwheel, could you do

one?) Analogously, the knowledge that a computer system uses when itparks a car or lands a plane automatically is of this procedural sort. Mostlikely much of the knowledge that animals have about their world, such ashow to construct spider webs, how to migrate, how to chase prey, and so


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on, is procedural.

Procedural knowledge is important, but it is limited to those specicactions that contain it. The main reason that we humans are so much moreversatile than other animals is that a good deal of our knowledge about theworld is represented as sentences, which can be used to guide many differentactions. To use a rather mundane example, one’s belief that exercisepromotes good health can encourage one to swim, to cycle, or to jog.

Of equal importance to its utility in many different situations,declarative knowledge can be discussed and debated. Before we have totrust a belief by acting on it, we can analyze it and perhaps modify it –taking into account our own reasoning and the opinions and criticisms of

others. As the philosopher Karl Popper put it, “by criticizing our theorieswe can let our theories die in our stead.” 1

You might object when someone says that his or her beliefs constituteknowledge. Because your beliefs might differ, you might not call the beliefsof someone else “knowledge.” Nevertheless, all we know about the world iscontained in our beliefs, so I’ll continue to call our beliefs “knowledge” –inadequate and inaccurate as such knowledge might turn out to be.

We can think of our beliefs as components of our models of reality. Butthese models are only descriptions of reality, not the real thing. Even so,we often think of our models as reality itself. Because our models are all we

have to go on, they are a kind of “virtual reality” for us. As the biologistand writer Richard Dawkins wrote:

. . . we humans, we mammals, we animals, inhabit a virtualworld, constructed from elements that are, at successivelyhigher levels, useful for representing the real world. Of course,we feel as if we are rmly placed in the real world – which isexactly as it should be if our constrained virtual reality softwareis any good. It is very good, and the only time we notice it atall is on the rare occasions when it gets something wrong .2

Here’s one way to think about the virtual reality that we inhabit:1 Quotation from David Miller, (ed.), Popper Selections , p. 83, Princeton, NJ:

Princeton University Press, 1985.2 Richard Dawkins, Unweaving the Rainbow: Science, Delusion, and the Appetite for

Wonder , pp. 275-6, Boston: Houghton Mifflin, 1998.


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Imagine a pilot ying a giant jetliner through clouds. He can see nothing

outside the plane with his own eyes but must rely on the instrument paneldisplays, which inform him about the plane’s position, speed, andrelationship to the surrounding terrain. The plane is actually in the realworld, of course, but all the pilot knows about it is represented in thevirtual reality of the plane’s meters, displays, and force-feedbackmechanisms. Because this virtual reality is not reality itself, if the metersand displays present erroneous information, the plane might be in danger of stalling, running out of fuel, or even colliding with a mountain top.

We are all in a situation similar to that of the airplane pilot. What weknow about reality is contained in our models. Because we often base ouractions on them, we should constantly work to make them as accurate aspossible.


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Chapter 2

What Do Beliefs Do For Us?

Our beliefs serve us in several ways. Some help us predict the future andchoose actions, some help us understand a subject in more detail, someinspire creativity, some generate emotional responses, and some can beself-fullling.

First, let’s look at some of the ways people use beliefs to makepredictions and select actions. In medicine, for example, a physician useshis or her beliefs (learned in medical school, in journals, from clinicalstudies, and from on-the-job practice) to diagnose and predict the course of

a disease and to prescribe a therapy predicted to cure or mitigate it. Acorporate CEO uses his or her beliefs about business practices to predictthe likely results of new strategies, capital allocations, reorganizations, andother actions that might be taken. An attorney uses his or her beliefs abouttorts, about the client, and about the surrounding circumstances to devisea strategy for trying an injury case.

In everyday life, we all make belief-based predictions. For example, if we believe that John Jones keeps his appointments, we can condentlypredict that he will be there to meet us at the time and place he specied(which time and place, incidentally, are also represented as beliefs). Or, if we believe a radio traffic report that our usual route to work is congested,we can predict that we will be delayed unless we choose an alternative.

More consequently, our beliefs are the basis for many of our decisionsabout education, career choice, mate selection, child raising, health choices,family nances, friendships, ethics, voting, and many other aspects of our


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CHAPTER 2. WHAT DO BELIEFS DO FOR US?

personal lives. Actions evoked by these beliefs can have profound

consequences, both benecial and harmful. Consider, for example, thedifferent consequences of a parent’s belief in the value of a college educationand a suicide bomber’s belief that martyrdom will land him in paradise.We have the opportunity and, I think, the duty to scrutinize our beliefscarefully.

We tend to choose those actions whose predicted consequences we likeand to avoid those actions whose predicted consequences we dislike. Afterseveral instances of these kinds of deliberate belief-based choices, theactions chosen become more habitual and automatic. We take themwithout needing to consult the beliefs that gave rise to them. This sort of habit-forming process is an instance of declarative knowledge becomingembedded in procedures. In fact, many of our daily actions are automatic,taken without thought. We drive our automobiles, run errands, and evenengage in conversations largely on “auto-pilot.” Someone says something tous, and we frequently react without thinking. Some psychologists claimthat it is only when these automatic actions result in a surprise, that weregain “consciousness.”

Even so, our beliefs themselves are called into play in many importantlife situations. That’s because we don’t have appropriate automaticreactions for everything. To ensure that we end up in situations we likeinstead of those we dislike, we need beliefs that make accurate predictions.The most important measure of the quality of a belief is the accuracy of itspredictions.

Beliefs are also used to explain observations and other beliefs. Forexample, long experience evokes the belief that in the earth’s temperatezones, it is generally colder during some parts of the year, the parts we callwinter, than it is during the other parts, called summer. This belief explainsprevious observations, makes predictions about subsequent observations,and prompts us to take preparatory actions. However, it turns out that weare constitutionally unable to leave it at that – we seek and must havedeeper explanations. Why is it colder in winter than in summer? A rst

attempt at an explanation might be that the sun is lower in the sky duringthe winter than it is during the summer. Thus, the earth’s temperate zonesreceive less heat in winter than they do in summer and that explains whywinter is colder than summer. But why this odd behavior of the sun?


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Primitive peoples probably had their explanations. Perhaps one of their

gods arranged it to be so. Modern knowledge has a more satisfactoryexplanation: the tilt of the earth’s axis results in a change of the angle of the mid-day sun relative to places on earth as the earth traverses its orbit.Why does the earth’s axis tilt? Scientists have explanations for that also.Each level of belief gives us additional understanding . Beliefs gaincredibility if they are explained by other beliefs having high credibility.

We sometimes think of an explanatory belief as describing the cause of that which is explained. Thus, we might say that the tilt of the earth’s axiscauses it to be colder in winter than in summer. In addition to our evolvedability to have beliefs in the rst place, we probably also have evolved acompelling need to seek explanations or causes for the things we believe.Science is all about inventing explanations or causes for things we observe.So is mythology for that matter. The main difference between the two isthat science is concerned with subjecting its explanations to rigoroustesting and analysis, whereas mythology is not.

Scientic beliefs usually involve a deep hierarchy of beliefs. Each belief in the hierarchy is an explanation for the beliefs immediately above it andfollows from the explanation below it. For example, the belief that theearth and its sister planets travel around the sun in elliptical orbits can beexplained by Newton’s laws of motion and gravity. Gravity, in turn, can beexplained by Einstein’s notion of curved space-time. Scientists are stillseeking a deeper explanation for gravity, one that is consistent withquantum mechanics. Some physicists think they have found such anexplanation in string theory.

Explanations frequently cross scientic disciplines. For example,complex biological processes can be explained by chemical reactions, whichin turn are grounded in physics. The process of explaining scientictheories by more detailed theories is often called “reductionism.” Becausethat word is sometimes misunderstood to imply that something is lost inthe explanation, I prefer the term “explanationism.”

Besides helping us to make useful predictions and to achieve greaterdepths of understanding, some beliefs can evoke profound emotional andcreative responses. Religious and aesthetic beliefs continue to inspire greatart, music, literature, and poetry and move us with awe and wonder. So doscientic beliefs, many of which overwhelm the imagination. The Big Bang


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gave rise to billions and billions of galaxies which are now moving farther

and farther apart at unimaginable speeds and distances. The processes of selective survival of organisms coded by DNA (itself a wonder), togetherwith random changes and shuffling in DNA, produced all the innitelyvaried and amazing life forms on earth. Perhaps blind to the possibilitiesfor scientic knowledge to inspire awe, Keats, in his poem Lamia ,complained that Newton’s scientic experiments with the prism haddestroyed the poetry of the rainbow. But an understanding of how sunlightand water droplets actually create a rainbow can, as Richard Dawkinsobserved, inspire its own poetry. The physicist Richard Feynman,commenting on the beauty of science, once said “It only adds. I don’tunderstand how it subtracts.”

Some beliefs just make us feel good, and that’s one reason people holdthem. That rationale for belief is called credo consolans (I believe becauseit is comforting). Some believe in life after death. Some believe that theyhave personal angels who look after them. Many believe there is a God whodirects their lives. Such beliefs, in my opinion, are fairy tales, but fairytales can be quite seductive, as the following song lyrics explain:

truth is hard and tough as nails,that’s why we need fairy tales.I’m all through with logical conclusions,

why should I deny myself illusions?1

The economist Robin Hanson has an interesting analogy about beliefs.He says that the beliefs people hold are like the clothes they wear. 2 Peoplewear clothes for a variety of reasons – for the strictly utilitarian reason tokeep warm, of course. But they also choose clothes because they arefashionable, because they feel good, or because they are the clothes thatthey just happen to have. It’s the same with beliefs, although I think weshould think more carefully about our beliefs than we do about our clothes.In particular, we shouldn’t necessarily accept beliefs just because they makeus feel good. Likewise, we shouldn’t necessarily reject ones that make usfeel bad.

1 From the lyrics of “Munchhausen” by Friedrich Hollaender.[English lyrics by Jeremy Lawrence from a translation by Alan Lareau; from the printedmatter of the London CD “Ute Lemper, Berlin Cabaret Songs” (452 849-2).]

2 Robin Hanson, private communication, 1999.


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In summary, we use beliefs to predict, to explain, to create, to inspire,

and to feel good. They are an important part of what makes us human.But, where do we get these beliefs? That’s the subject of the next chapter.


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Chapter 3

Where Do Beliefs Come From?

Have you ever asked yourself, “Where did I get that belief?” or “Why do Ibelieve that?” Sometimes we can give answers to such questions. “I saw itwith my own eyes.” “I learned it in school.” “I read it in the Wall Street Journal .” “I heard it on TV.” “My parents told me.” “I found it on theInternet.” Sometimes we aren’t sure and have to say something like “I don’tknow; it just seems right to me.”

Interestingly, the anthropologist David Fleck describes a languagespoken in Amazonian Peru and Brazil that requires “speakers to precisely

and explicitly code their source of information every time they report apast event.” 1 For example, Fleck writes, one cannot simply say in thatlanguage “A non-Indian passed by” and leave it at that. Instead, thegrammar required for stating such reports forces one to say something like“A non-Indian passed by, according to my father, who heard about it frommy grandfather, who in turn heard about it from Tumi.”

Even though our own language does not require us to be explicit aboutthe sources of our beliefs, they all do have sources. We aren’t born withthem. We get beliefs in two main ways: rst from all of our senses,especially seeing, hearing, and reading, and second by inventingexplanations for what we sense. As small children, we infer the existence of objects and construct beliefs about them to explain our earliest sensations.As adults, we continue to pile beliefs upon beliefs to explain all the new

1 David W. Fleck, Evidentiality and Double Tense in Matses , pp. 589-614, Language ,Vol. 83, No. 3, 2007.


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CHAPTER 3. WHERE DO BELIEFS COME FROM?

things we observe including what we hear and read.

Regardless of what Plato might have thought, there is no way that ourminds have direct access to “eternal truths.” Our senses, especially visionand hearing, are our only portals to reality. However, indispensable as theyare, our senses can also mislead us. Vision provides a good example.“Seeing is believing.” But not always. Errors can arise because what wethink we see is inuenced by what we already believe. We often “see” whatwe expect to see, and don’t see what we don’t anticipate. In a famous 1949experiment, for example, the psychologists Jerome Bruner and Leo Postmanpresented quick glimpses of pictures of trick playing cards to a group of subjects. Quite often the subjects said that a black three of hearts, forexample, was either a normal three of spades (misperceiving the heart for aspade) or a normal three of hearts (misperceiving the black color for red).Their expectations about playing cards interfered with accurate perception.As another example, eyewitness reports at crime scenes, althoughimportant in court proceedings, are nevertheless notoriously unreliable,being inuenced, as they are, by misperceptions and mis-remembrances.

Visual perception attempts to extract three-dimensional informationfrom the two-dimensional images gathered by each one of our eyes. Thatcan only be done if our models of the world, our expectations, supply themissing information. Usually, the process works amazingly well, but thereare many well-known visual illusions caused by inappropriate expectations.Here’s an interesting example:


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Are the two tables really different? They appear to be because we interpretthem as tables in three dimensions. But what about the two-dimensional gures representing the table tops? If you actually measure them on thepage, you will see that one is just a rotated version of the other. Ourpropensity to see the picture as a representation of a three-dimensionalscene overwhelms any attempt to perceive the gures in two dimensions.Compelling expectations can cause perceptual errors. 2

Even reliable perception doesn’t always give us a good description of reality because things are not always what they appear to be. The earthappears at – except for the bumps of hills and valleys – as early humansthought it to be. And the sun appears to move through the sky. In thesecases, and in many others, a model other than the one directly constructedby our sensory apparatus is needed. One of the Beatles’ songs gives an apt

2 In the animation by Michael Bach (athttp://www.michaelbach.de/ot/sze shepardTables/index.html. ) you can watch while thetable-top is rotated between the two positions. The illusion was called“turning-the-tables” by its inventor, the psychologist Roger Shepard.


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http://www.michaelbach.de/ot/sze_shepardTables/index.html

http://www.michaelbach.de/ot/sze_shepardTables/index.html




example:3

. . . the fool on the hill,Sees the sun going down,And the eyes in his head,See the world spinning ’round.

These days, most of what we sense is mediated by language. Our eyessee written texts of all kinds – books, newspapers, articles, scientic papers,and Web pages. Our ears hear what people say to us – people talkingdirectly to us, such as parents, friends, teachers, salespeople, clerks, and so

on. We also hear people talking on the radio and television. Combinedvideo and audio media such as movies, television, and the Internet oodboth our eyes and ears and the brain behind them.

Processing all of this visual and aural linguistic information adds to andotherwise affects our beliefs. As children, we often believe what people tellus and what we read in books. As adults, we gradually learn that what wehear and read informs us only about what others believe or want us tobelieve. We then have to decide whether we should believe these thingsourselves or not.

There are people who believe we have ways of getting information about

reality other than through the usual sensory channels of seeing, hearing,and so on. The idea that there are extra-sensory ways of perceiving“truths” is actually quite common. And, every age has had mystics whoclaimed to hear voices revealing eternal truths. It’s not unusual for peopleto say something like “I know in my heart that it’s true.” It’s as if aninternal “truth bell” rings loudly for some beliefs – when it rings, its ownerexperiences an intense feeling that that belief must be true.

Even some scientists claim to have inner feelings about the truth of something or other. The physicist, Roger Penrose, thinks that somehumans have a built-in ability to perceive mathematical truths directly. Hebelieves that mathematical quantities, like π , or numbers like 0, 1, and soon exist out in the world and are there to be perceived by those capable of doing so. Many mathematicians say they have a powerful feeling thatcertain propositions just must be true. And, there are physicists who say

3 Paul McCartney, The Fool on the Hill , (Lyrics), 1967.


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that certain theories are “too beautiful not to be true.” Perhaps to be a

good mathematician or physicist, the impact of ideas must be so intensethat it’s as if these ideas were actually out there, waiting to be discovered.However, rather than coming to us through extra-sensory means, I thinkthat those beliefs that we “know in our hearts are true” are actually mentalconstructions composed of parts of already existing ideas strung togetherby our creative and reasoning processes.

Most of our beliefs are mental constructions – invented to explain whatwe and others sense. Scientists, peering at the world around them withsensory augmentations such as telescopes, microscopes, MRI machines,x-ray detectors, atom smashers and ultrasound machines, invent newobjects, such as quasars, bacteria, and quarks, to describe what they see.And they invent new theories to describe the properties of these objects. Asthe physicists, Robert Lindsay and Henry Margenau, put it:

. . . the physicist constructs [my emphasis] what he terms thephysical world, a concept which arises from a peculiarcombination of certain observed facts and the reasoningprovoked by their perception. 4

Belief construction is not conned to scientists – we all do it. Everydayexperiences provide material out of which we construct beliefs. Forexample, if someone happens to observe that event A is followed event B ,he or she is likely to adopt the belief that A causes B . Beginning even inearly childhood, we form and test beliefs about the physical world fromthese kinds of observations. Dropping an egg causes it to break open. Doesthat always happen? If so, we have a new belief about eggs. Beingespecially sensitive to temporal sequences of events was probablyprogrammed into us through evolution. The ow of events provides cluesfor beliefs about how we can predict and affect that ow.

Of course, the proximity of events in time can also be due to randomchance – a coincidence. Such coincidences are the source of many

superstitions. For example, if a baseball pitcher observes that he wore hiscap a certain way while having a good run of strike-outs, he might think it4 Robert Bruce Lindsay and Henry Margenau, Foundations of Physics , p. 1,

Woodbridge, CN: Ox Bow Press, 1981. (My thanks to Sidney Liebes for pointing outthis quotation.)


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to be a cause of his success and insist on wearing it that way even through

a run of bad pitches. Superstitions are surprisingly robust.Explanatory beliefs and theories are constructed from existing beliefs

and theories. Early humans constructed models for that part of reality thatthey saw, heard, and felt. Then, as now, explanations can only beconstructed from the materials at hand – that is, from whatever beliefs,theories, and concepts that happen to be around. We can see now that thematerials primitive peoples had available were quite limited, but theyconstructed explanations anyway – many in the form of myths and fancifulstories.

People have a wired-in need and ability to construct – and re-construct

– models for describing their world. People are extraordinarily creative atconstructing theories. Ideas such as astrology, extra-sensory perception,guardian angels, communication with the dead, auras, reincarnation, thelost continent of Atlantis, alien abduction, and “energy” ow in the bodyare quite imaginative if not very believable to the twenty-rst centuryscientic mind. Equally imaginative, and perhaps more believable, arecurrent theories in physics and biology, such as string theory, the top quark,general relativity, protein folding, and epigenetics. All of these display thefruits of fertile brains attempting to create explanations.

What accounts for our brains being able to come up with such ideas?

The British neurobiologist, Charles Sherrington, said it was the action of the human cerebral cortex “a sparkling eld of rhythmic ashing pointswith trains of traveling sparks hurrying hither and thither . . . an enchantedloom where millions of ashing shuttles weave a dissolving pattern, alwaysa meaningful pattern though never an abiding one; a shifting harmony of subpatterns.” 5 Neuroscientists are gradually providing a deeper scienticmeaning for Sherrington’s poetic description of how the ring of corticalneurons produces “meaningful patterns” of thought.

What about logical reasoning? Is it a useful tool for theoryconstruction? Perhaps, but I don’t believe that the use of logic aloneprovides new information about reality; it just rearranges what is alreadyin our models – expressing things in a more useful form. The subject of geometry provides an example. It was thought by early geometers andphilosophers that by thinking alone one could establish geometric facts

5 Charles Sherrington, Man on his Nature , Cambridge University Press, 1942.


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about the world. But all such thinking did was to derive consequences

implicit in the axioms of Euclidean geometry. But astronomicalobservations, not logic, were needed before modern physics could come upwith axioms that describe the universe more accurately than did those of Euclid.

In the next chapter, I’ll describe some methods for evaluating beliefs,whether they come to us from our senses, from others, or from our inventiveimaginations.


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Chapter 4

Evaluating Beliefs

We hold some of our beliefs more strongly than others. If asked whether webelieve such and such, we might answer by saying things like “Yes,denitely, it’s a fact” or “It’s quite likely to be so,” or “It’s possible,” or“It’s doubtful,” or “I don’t know,” or “Not at all.” These are some of theways of describing degrees of belief. No one knows how our brains actuallyrepresent belief strengths. Perhaps we store some of them as sentences suchas “I doubt that vitamin C can cure a cold.” Or, maybe our brainsassociate something like numbers with beliefs to indicate their strengths.But regardless of what is going on in our brains, we are able to state howcredible a belief is. And, we are able to change the credibility of a belief byconsidering evidence for and against it.

Beliefs with the very highest possible degree of credibility are called“facts.” For example, “At the present time, I live in Oregon.” That belief of mine is a fact. “George Washington was the rst president of the UnitedStates,” and that belief of mine is also a fact. It would be unnecessary tokeep open the possibility that the strengths of those kinds of beliefs mightchange. On the other hand, just because someone claims that such andsuch is a fact, doesn’t mean that I would necessarily agree with him.Furthermore, his belief might even change someday if confronted by newevidence. After all, Columbus once believed that it was a fact that he haddiscovered a new route to the Indies. While he himself might never havechanged that belief, we don’t claim it to be a fact anymore.

How do we decide to say of some beliefs that they are “facts,” and of


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CHAPTER 4. EVALUATING BELIEFS

others that they are only likely? There are several ways that people use to

decide about the strengths of beliefs. Any method for evaluating beliefs isfaced with a trade-off. If our criteria for belief acceptance are too strict, weare likely to exclude some useful beliefs. Missing out on useful beliefs is theprice we pay for extreme skepticism. On the other hand, if we want to besure that we do not exclude useful beliefs, we are likely to accept manyquestionable, even useless or harmful ones as well. Accepting bad beliefs isthe price we pay for extreme credulity.

Scientists usually operate toward the skeptical end of this spectrum,whereas other people differ widely in their willingness to accept beliefs.Some people are quite credulous, willing to believe almost anything,especially if the belief sounds fascinating or just makes them feel good.Others are very skeptical, with a “show me, I’m from Missouri” attitude.Whether credulous or skeptical, some judge a belief on whether or not it“feels right.” The sense of feeling right might be caused by certain brainprocesses, which while perhaps unconscious, might nevertheless be takingaccount of many other related beliefs with high credibilities. Theseprocesses are probably the basis of what we call “intuition.” But becausemissing out on useful beliefs or accepting bad ones can have life-alteringconsequences, we should back up our intuitions about beliefs with moredisciplined critical thinking.

As young children we usually believe quite strongly what our parentsand teachers tell us. After all, the beliefs passed down by one’s parentsmight well have had survival value. But parents, along with everyone else,might believe a lot of nonsense. As young children, we haven’t yet beenexposed to a wide range of alternative beliefs. Such exposure, along withcritical thinking, is necessary before we can jettison some of the beliefs of our parents and elders. Doing so often takes an act of conscious will.

What are the elements of critical thinking? Suppose we are consideringsome proposition as a possible belief – perhaps one we read or heard about.How would we evaluate it? To illustrate, let’s consider, for example, theproposition that the earth is warming. Because a warming earth would

have a great effect on our future, it’s important to think critically about itspossibility.

The rst step in critical thinking is to seek the opinions of experts. Arethere experts who believe that the earth is warming, and do they know


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enough about the subject of global warming for us to trust their

judgement? Do these experts agree with each other? On some subjects,there are no experts – or if there are, they might disagree. For example, noone really yet knows what causes schizophrenia. But global warming isdifferent. In a summary of the ndings of a report by the IntergovernmentalPanel on Climate Change (IPCC), whose members included the mosthighly respected experts on the subject, its chairman, Dr. RajendraPachauri, wrote that “warming of the climate system is unequivocal . . . ” 1

That’s good enough for me. I agree with the philosopher BertrandRussell who wrote, “ . . . the opinion of experts, when it is unanimous, mustbe accepted by non-experts as more likely to be right than the oppositeopinion.” 2

The next steps of critical thinking are to consider the consequences of and the explanations for a belief. In rendering their opinion about globalwarming, the IPCC analyzed in great detail its consequences andexplanations. Let’s consider the consequences of global warming rst. Inhis summary, Dr. Pachauri mentioned some of them, namely, “increases inglobal average air and ocean temperature, widespread melting of snow andice, and rising global average sea level . . . ” What about thoseconsequences? Are they themselves credible? A NASA documentsummarizes the evidence for them. 3 (One can also look at the IPCC reportitself for more detailed discussion.4)

1. “All three major global surface temperature reconstructions showthat Earth has warmed since 1880. Most of this warming hasoccurred since the 1970s, with the 20 warmest years having occurredsince 1981 and with all 10 of the warmest years occurring in the past12 years. . . . The oceans have absorbed much of this increased heat,with the top 700 meters (about 2,300 feet) of ocean showing warming

1 Statement by Dr. Rajendra Pachauri, Chairman of the Intergovernmental Panel onClimate Change at the Opening of the UNFCCC meeting (COP16), 29 November 2010,Cancun, Mexico. Available online from

http://www.ipcc.ch/news and events/press information.shtml.2 Bertrand Russell, “On the Value of Scepticism,” from The Will to Doubt , New York:Philosophical Library, 1958.

3 “Global Climate Change: NASA’s Eyes on Earth,”http://climate.nasa.gov/evidence/.

4 http://www.ipcc.ch/publications and data/publications ipcc fourth assessment report synthesis report.htm


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http://www.ipcc.ch/news_and_events/press_information.shtml

http://climate.nasa.gov/evidence/

http://www.ipcc.ch/publications_and_data/publications_ipcc_fourth_assessment_report_synthesis_report.htm

http://www.ipcc.ch/publications_and_data/publications_ipcc_fourth_assessment_report_synthesis_report.htm

http://climate.nasa.gov/evidence/

http://www.ipcc.ch/news_and_events/press_information.shtml




of 0.302 degrees Fahrenheit since 1969.”

2. “Data from NASA’s Gravity Recovery and Climate Experiment showGreenland lost 150 to 250 cubic kilometers (36 to 60 cubic miles) of ice per year between 2002 and 2006, while Antarctica lost about 152cubic kilometers (36 cubic miles) of ice between 2002 and 2005.. . . Glaciers are retreating almost everywhere around the world –including in the Alps, Himalayas, Andes, Rockies, Alaska and Africa.”

3. “Both the extent and thickness of Arctic sea ice has declined rapidlyover the last several decades.”

4. “Global sea level rose about 17 centimeters (6.7 inches) in the lastcentury. The rate in the last decade, however, is nearly double that of the last century.”

The IPCC’s conclusions that global warming is indeed happening isbased partly on the fact that these predictions have been conrmed.Additional support for their conclusions is given by the fact that there arecredible explanations for global warming. An explanation for a propositionis any statement (or set of statements) that might be considered its cause.A credible explanation for a belief helps to make the belief itself morecredible. Here are some possible explanatory causes for global warming:

1. Increased heat radiation from the sun.

2. Increased retention of heat by the earth’s atmosphere.

Are either of these explanations credible? According to experts, the sun’sradiance does go through various periodic cycles, but the magnitudes of these cycles are too small to cause the observed increases in temperature.So we can eliminate that explanation.

What about increased retention of heat by the earth’s atmosphere? It

happens that heat retention has its own explanation, namely increasedconcentrations of carbon dioxide, CO 2 , a “greenhouse gas.” Scientists haveestablished that carbon dioxide, together with other gases, allows heat fromthe sun to penetrate the atmosphere but prevents it from escaping backinto space – much like glass traps heat inside a greenhouse. If the levels of


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carbon dioxide are indeed increasing, that increase would help explain (and

thus help to conrm) that the atmosphere is retaining heat, which helps toexplain (and thus helps to conrm) global warming. Indeed, atmosphericCO2 has been increasing over the past 150 years, and this increase isroughly correlated with the increase in average global temperature.

All the propositions in this global-warming example can be assembledin a network of beliefs. Such a network is illustrated in the following gure:


25




GlobalWarming

Air & OceanTemperature

Increasing Snow & Ice

Melting Sea Levels Rising

Increase in CO 2

Consequences

Explanations Atmospheric HeatRetention

Observations


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Each belief in the network can be thought of as a consequence of the beliefs

below it and an explanation for the beliefs above it. The credibility of eachbelief in the network inuences the credibilities of the others. Credibleconsequences of and explanations for a belief add “points,” as it were, tothe strength of that belief.

Interestingly, our global warming network can be extended in bothdirections. For example, one expected consequence of rising temperatures isearlier spring-time budding of deciduous trees in temperate zones. Indeed,this phenomenon has been observed. And one explanation for theincreasing levels of CO2 is the increased burning of fossil fuels, which hasbeen occurring since the industrial revolution. Factories, automobiles,heating and cooling systems, and electric power generation facilities releasesufficient CO2 to account for its increased concentration in the atmosphere.This explanation has led to the IPCC’s conclusion that global warming islargely “anthropogenic,” meaning caused by people.

People who argue against global warming attempt to weaken thecredibilities of the various pieces of evidence in its favor. For example, theytry to argue that the atmospheric and ocean temperature readings andreconstructions are faulty. And, to argue against a belief that globalwarming is anthropogenic, some people have claimed that the observedincrease in CO 2 is being caused by volcanic eruptions, not by the burning of fossil fuels. Offering a credible alternative explanation for a belief canweaken a competitive explanation. This strategy of argument is called“explaining away.” It is used quite often in the back-and-forth of debatesabout beliefs. But volcanic eruptions fail to explain away fossil fuel burningas the explanation for increased CO 2 concentrations. Scientists haveestablished that “ . . . the anthropogenic CO 2 emission rate is more than ahundred times greater than the global volcanic CO 2 emission rate.” 5

All of these elements of critical thinking, namely testing predictions,creating explanations, and explaining away are mental activities thatpeople, even children, naturally use all the time. For example, a childnipped by an over-eager pet dog might form the explanatory theory that

“all dogs bite.” The adventurous child might discard that theory afterpetting another dog without experiencing the predicted bite. To employ

5 “Volcanic Gases and Climate Change Overview,” USGS Volcano Hazards Program,http://volcanoes.usgs.gov/hazards/gas/climate.php.


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http://volcanoes.usgs.gov/hazards/gas/climate.php

http://volcanoes.usgs.gov/hazards/gas/climate.php




these processes in a disciplined manor though, takes more deliberate effort

than most people usually exert.Professional people, however, are quite rigorous when they use these

styles of reasoning. For example, when physicians attempt to diagnose thecause of a patient’s presenting symptoms, they look for diseases known tocause those symptoms. For example, if the presenting symptoms are feverand headache, a physician might suspect that the patient has a case of theu. If it were the u, additional common symptoms would be muscle achesand chills. Finding those symptoms in the patient would strengthen adiagnosis of u. But these same symptoms might also indicate some varietyof pneumonia. A physician would then check for pneumonia symptoms bylistening to the chest and, perhaps, ordering chest x-rays. Failing to ndany pneumonia symptoms would let the physician rule out that disease.

Scientists also use these very processes, in the specic and exactingways of science, to evaluate theories. Checking to see if the predictedconsequences of a theory are conrmed is an important part of all science.Conrmations of the predictions of a theory by several independentexperiments or observations combine to increase condence in the theory.And, failure of repeated experiments to conrm a prediction made by atheory would overturn that theory (or at least weaken belief in it). Theexplaining-away strategy is commonly used by scientists when they rejectone theory in favor of another. For example, the theory of evolution, itself convincingly supported by several independent strands of evidence, is fullyadequate to account for the astounding complexity of all life forms on earth(including us). It thus explains away creation myths, such as “intelligentdesign.” These reasoning strategies are important aspects of what is calledthe “scientic method,” a subject which I will describe in more detail in asubsequent chapter.

If we were to examine the relationships among all of our beliefscarefully, an impossible task in practice but one that is interesting to thinkabout, we would see that some of them should make others more credibleand some less. They would even compete among themselves with

conicting inuences. We can imagine all of the beliefs in our large networkof beliefs “ghting it out” to agree nally on the strength of each belief inthe network. When they do nally agree, we say that the beliefs cohere.Checking for coherence in belief networks containing millions upon millions


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of related beliefs would be impossible. All we can hope to do, when

thinking critically, is to ensure that a relatively small, circumscribed set of our beliefs is locally coherent. As one discusses one’s beliefs and comparesthem with those of others, the boundaries of local regions graduallyexpand, allowing more global checks on coherence. That’s the principaladvantage of discussion and criticism of one’s beliefs. One should neverback away from it! As the philosopher Karl Popper has written:

There is only one element of rationality in our attempts to knowthe world: it is the critical examination of our theories. Thesetheories themselves are guesswork. We do not know, we onlyguess. If you ask me, “How do you know?” my reply would be,“I don’t; I only propose a guess. If you are interested in myproblem, I shall be most happy if you criticize my guess, and if you offer counterproposals, I in turn will try to criticize them.” 6

On many things, our minds are made up. But they can only stay madeup if we never challenge them with new experiences, new information, anddiscussions with knowledgeable people who might hold opposite beliefs.These challenges present occasions for employing the elements of criticalthinking described in this chapter. They are: seeking the opinions of experts, considering the consequences of and the explanations for beliefs,and eliminating suspect explanations that can be explained away by morecredible alternative ones. Changing one’s mind is difficult, but it isnecessary if one wants to have an ever-more-useful description of reality.

6 From Popper Selections , David Miller (ed.), p. 30, Princeton, NJ: PrincetonUniversity Press, 1985.


29





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Chapter 5

In All Probability

Many of our beliefs fall somewhere between the two extremes of denitelyfalse and denitely true. Their position on that scale is indicated by what Ihave called a “strength.” To represent these strengths, we could usephrases, such as “almost certainly not,” “unlikely,” “possible,” “somewhatlikely,” “likely,” “very likely,” or “virtually certain.” Or, we could usenumbers between 0 (standing for denitely false) and 1 (standing fordenitely true), such as 0.7 or 0.9. It’s relatively easy to convert phrasesabout strength into numbers. For example, we might translate “virtuallycertain,” into 0.99 and “likely” into 0.7.

Using numbers to represent strengths reminds us of the probabilitynumbers used by statisticians and others in dealing with uncertainty.Health scientists use probabilities when assessing the likelihoods of variousdiagnoses and the efficacies of treatments. Insurance underwriters useprobabilities to take into account the likelihoods of losses and other eventsin order to establish premium rates. And, of course, we are all familiar witha weather forecaster saying the probability of rain tomorrow is 70%. Moststatisticians claim that probability theory is the only mathematicallyrigorous way to deal with uncertainty. Let’s take their advice and useprobabilities to represent the strengths of beliefs. Probability theory isespecially useful for updating the strengths of beliefs based on evidence. Inthis chapter, I’ll summarize some basic facts about probabilities andindicate how probability theory can be used to update belief strengths.

Probability values are always numbers between 0 and 1. (Sometimes


31



CHAPTER 5. IN ALL PROBABILITY

they are expressed as percentages between 0% and 100%.) When we are

completely certain that a proposition is true, it has a probability of 1.When we are completely certain that a proposition is false, it has aprobability of 0. If we are uncertain about a proposition, its probabilitywould lie somewhere between 0 and 1.

The probability values of some propositions are constrained by those of others. For example, suppose one believes that there are only three peoplewho might actually have written The Merchant of Venice , namelyShakespeare, Jonson, or Marlowe. Further, suppose that one, and only one,of them must have written it. These three cases are said to be “mutuallyexclusive and exhaustive.” The probabilities of mutually exclusive andexhaustive propositions must sum to 1. So, if one is certain thatShakespeare wrote the play, then one must also be certain that neitherJonson nor Marlowe did. Of course, one could be uncertain, and believethat Shakespeare wrote it with probability 0.85, that Jonson did withprobability 0.05, and that Marlowe did with probability 0.1.

Sometimes probabilities are expressed as “odds.” If the odds on a belief are 4 to 1 in favor, then the probability of that belief is 0.8 or 80%, and theprobability of its opposite is 0.2 or 20%. The odds are obtained by dividing80 by 20. In sports events, such as football, the odds are sometimesestimated by experts who review past team performances and otherpossibly relevant factors such as weather and player injuries. All of thisinformation is combined into a judgment they make about the odds.

Quoting the odds of a belief prepares us to place a bet on that belief.Looked at in this way, a belief is a bet that future observations will resultin winning the bet. Beliefs are bets on the future. 1 When we buy a share ina company, we believe that its price will rise and are making a bet on thatbelief. When an insurance company accepts a premium from you against are loss on your house, it believes that your house won’t burn and ismaking a bet on that belief. When we travel on an airplane, we believe(and bet with our life) that the plane will not crash.

There are two major ways to assign probabilities to beliefs. The most1 The author Louis Menand wrote, “[The pragmatists] Holmes, James, Peirce, and

Dewey . . . said repeatedly [that beliefs] are just bets on the future.” Louis Menand, TheMetaphysical Club: A Story of Ideas in America , p. 440, New York: Farrar, Straus andGiroux, 2001.


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obvious method involves collecting statistics about a large number of cases.

Suppose, for example, that during the last 100 years, it rained four times inPasadena on New Years Day. Then the probability of rain in Pasadena onNew Years Day next year could be guessed to be about 4/100 or 0.04. Thisversion of assigning probabilities to events is called the frequency method .It’s commonly used in many situations for which it’s possible to collect alot of data. For example, in 2006 the National Transportation Safety Boardestimated that there are only 1.7 deaths per hundred million miles for travelby air. We use data like that to decide that it’s safe to travel on airplanes.

When there isn’t sufficient data to use the frequency method, one canstill make an informed guess. For example, in 1999, a U.S. GeologicalSurvey report 2 estimated the probability of one or more large earthquakesin the San Francisco Bay Region in the next 30 years to be 0.70. Guesseslike these, based on expert judgement, are called subjective probabilities.For most of the beliefs about which we are somewhat uncertain, and forwhich there is inadequate data, about the best we can do is makesubjective probability estimates.

Rather than rely on one’s own judgement to make a probabilityestimate, one can use the combined judgements of a pool of people. Onefamiliar example of exploiting this kind of “crowd wisdom” is a parimutuelsystem for calculating the probabilities that particular horses will win arace. Using that system, several people place bets using initial probabilitiesprovided by an expert. The results of all of these bets are usedcontinuously, as they are made, to update the probabilities. In athree-horse race, for example, if there is a total of $3,000 so far bet onSilky, $4,000 bet on Stewball, and $3,000 bet on Scramble (all to win), thenthe probabilities of winning will be 0.3 each for Silky and Scramble, and 0.4for Stewball. These probabilities are then used to calculate the payoffs of winning: 7 to 3 each for Silky and for Scramble, and 6 to 4 for Stewball.

Another method of pooling judgements to arrive at subjectiveprobabilities is based on markets. People buy and sell contracts in a futuresmarket about beliefs, and the prices of the contracts are used to estimate

probabilities. For example, people might buy contracts on which team, A2 USGS Working Group on California Earthquake Probabilities, “Earthquake

Probabilities in the San Francisco Bay Region: 2000 to 2030 – A Summary of Findings,”available online at http://geopubs.wr.usgs.gov/open-le/of99-517/# Toc464419657.


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http://geopubs.wr.usgs.gov/open-file/of99-517/#$_$Toc464419657

http://geopubs.wr.usgs.gov/open-file/of99-517/#$_$Toc464419657




or B , say, will win a World Cup soccer match. Initially, a market maker

and a contract purchaser have to agree on a price for the contract. Supposethe agreed upon price is $0.75 for a contract on team A . That is, thecontract purchaser pays $0.75 for a one-dollar contract on team A . Then, if team A wins, the holder of the contract is paid one dollar by the marketmaker. If team A doesn’t win, the contract is worthless. Anytime beforethe game, people can buy and sell contracts to each other, and the price of the latest contract can be published for all to see – just like in a futuresmarket. In this way, a price is established that reects all of theinformation possessed by all of the people participating. This price willchange over time as people take into account the latest information. If atsome time the price for a one-dollar contract on team A is $0.80, forexample, the subjective probability that team A will win can be taken atthat time to be 0.8, and the odds in favor of team A would be 4 to 1.

Even when the outcome might be far in the future, or there is nodenite outcome, one can still use markets to establish probabilities.Market prices would uctuate as new information comes in, and holders of contracts could always sell them to people who think they can make aprot by buying a contract now and selling it to someone else at a higherprice later. And, someone who thinks the price will drop can sell short.

When experts participate in these markets, the probabilities oughteventually to be based on the opinions of the experts. As long as there areenough experts around who judge the probabilities to be different fromthose so far established by the market and who have condence in theiropinions, they can bid heavily with a view to making a large prot at theexpense of the more ill-informed participants. Their bidding will work tobring the probabilities more in accord with expert opinion.

These kinds of markets aren’t just theoretical ideas. There actually aresuch markets. One, used primarily for teaching and research, is the IowaElectronic Markets (IEM). Others are the Foresight Exchange (FX) and theHollywood Stock Exchange (HSX). 3 Traders in these markets can “invest”in the outcomes of a wide variety of unresolved outcomes. For example, at

FX, one can bet on whether a power plant will sell energy produced bynuclear fusion by 31 December 2045. (The probability of that is now

3 Their Web sites are, respectively: http://www.biz.uiowa.edu/iem,http://www.ideosphere.com/fx-bin/ListClaims, and http://www.hsx.com


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http://www.biz.uiowa.edu/iem

http://www.ideosphere.com/fx-bin/ListClaims

http://www.hsx.com/

http://www.hsx.com/

http://www.ideosphere.com/fx-bin/ListClaims

http://www.biz.uiowa.edu/iem




around 70%.) At HSX, one can bet on who will win Oscar, Emmy, and

Grammy awards. Prices in the latter market are said to correlate well withactual award outcome frequencies.

Although he probably didn’t anticipate these sorts of markets, JusticeOliver Wendell Holmes, Jr. once wrote “ . . . the best test of truth is thepower of the thought to get itself accepted in the competition of the market. . . ”4 I include this quote not because I endorse the idea that the bestbeliefs are those held by a majority of people. The crowd is often misled,especially the not-sufficiently-informed crowd. On the other hand, I dothink that the beliefs of experts are worth adopting as one’s own – so longas one continues to monitor possible shifts in expert opinion.

Recall that in Chapter Four I displayed some of the beliefs about globalwarming in a network. (See the diagram following page 25). Belief networks have been used to represent and reason about knowledge in manydifferent subject areas, including medicine, genomics, meteorology, andengineering. In some applications the networks are very large, oftencontaining several hundreds or thousands of propositions.

I have already mentioned that the credibility of each belief in a networkinuences the credibilities of others. Now, by using probability numbers torepresent credibilities numerically, we can use probability theory tocompute how belief probabilities inuence each other. The mathematical

computations are rather complex, so I won’t go into them here. Instead, I’lluse the global-warming network, repeated below, to illustrate the mainideas.

4 See Abrams v. United States , 250 U.S. 616,630 (1919).


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GlobalWarming

Air & OceanTemperature

Increasing Snow & Ice

Melting Sea Levels Rising

Increase in CO 2

Consequences

Explanations Atmospheric HeatRetention

Observations


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Suppose rst that increased levels of CO 2 in the atmosphere are

actually observed and measured. Meteorologists can use those observations,together with known models about how atmospheric CO 2 causes heatretention, to estimate the probability that the atmosphere is retaining moreheat. In turn, because atmospheric heat retention is a cause of globalwarming, meteorologists can calculate the probability that the earth is,indeed, warming. This kind of reasoning, proceeding upward in thenetwork, is called causality reasoning , based as it is on causal models of physical processes.

Next, going to the top of the network, suppose that sea levels are infact rising as indicated by actual measurements. Can we work our waydownward in the network to calculate how these observations affect theprobability of global warming? We could use a causal model of how globalwarming affects the probability of rising sea levels. But that’s reasoning inthe opposite direction from what is desired here. What we want is theprobability of global warming given that sea levels are rising. Reversing thedirection of “probability ow” can be done by using a rule invented by anEnglish clergyman, the Reverend Thomas Bayes, in the mid-1700’s. Whathas come to be known as “Bayes’ Rule” is used to reason “downward” fromeffects to causes in belief networks. That style of reasoning is calledevidential reasoning – reasoning from evidence to possible causes. It iswhat physicians do, albeit informally, when they use observed symptoms to

infer probabilities of underlying causes of those symptoms.Additionally, if we next learn that the temperatures of the air and

ocean are rising, we can use another bout of evidential reasoning to increasefurther the probability that the earth is warming. Evidential reasoning canaccumulate. Two or more pieces of independent evidence give extra supportfor a belief. To continue this example of how probabilities of propositionschange based on evidence (or lack thereof), suppose at this stage that nomeasurements have yet been made about melting snow and ice. But,because that is a consequence of global warming (itself now estimated to berather probable), we can use causality reasoning to estimate the probability

of observing melting snow and ice. If we were to look and fail to observemelting snow and ice (contrary to what was predicted), that failure would,by evidential reasoning, reduce the probability of global warming. In factthough, as mentioned in a previous chapter, snow and ice are actuallyobserved to be melting, so the probability of global warming is increased


37




rather than suffering a decrease.

In Chapter Four, I mentioned another type of reasoning, namelyexplaining away. If, for example, another highly probable cause could befound for global warming, such as an increase in heat energy coming fromthe sun, that cause would, by itself, reduce the probability that theunderlying cause for global warming is atmospheric heat retention.Actually, no such alternative cause has yet been found to be very probable,so heat retention is not explained away. The actual numerical calculationsused to assign probabilities to propositions in belief networks are verycomplex, but the necessary computations can be performed by computerseven for rather large networks.

In their everyday reasoning activities, people frequently use informalversions of causality, evidential, and explaining away methods. However, itis easy to be misled by failing to appreciate some of the subtleties of probabilistic reasoning. For example, suppose someone tells you that acertain stock-market analyst, say Mr. Smith, accurately predicted that thestock market would crash in October of 1987. Before adopting the belief that Smith has unusually accurate prediction abilities and relying on hisfuture forecasts, one would need to consider how he had done in the past,and to realize that of the various stock market predictions by the manyhundreds (perhaps thousands) of analysts it is likely that at least one of them (this time it was Smith) would have been right about October, 1987.If you have enough forecasters, someone among them is bound to have beenright about the past. Would Mr. Smith be right the next time? Well,maybe, if there really were some basis on which accurate predictions couldbe made. But, otherwise, success is just a chance event. As they say ininvestment circles “past performance is no guarantee of future results.”


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Chapter 6

Reality and Truth

There are several philosophical schools with different ideas about realityand truth. For example, one version of a doctrine called realism holds “thatthe objects, properties and relations the world contains exist independentlyof our thoughts about them or our perceptions of them.” 1 People whoadopt this point of view are called realists . I am not a realist because Ithink objects, properties and relations are concepts that we have invented,not “things” that actually exist in the world. Other “isms” in philosophyare more in accord with my ideas. For example, empiricism is the doctrinethat all knowledge ultimately comes from experience. Fallibilism is thedoctrine that absolute certainty is impossible and that all knowledge issubject to revision by further observation. One version of instrumentalism(the version I like) is the doctrine that knowledge should be judged by itsability to make accurate predictions, both those made in the past and thoseyet to be made.

To claim that objects, properties, and relations actually exist in theworld independently of our own thoughts about them is to confuse ourdescription of reality with reality itself. I do believe that reality exists(independently of our own thoughts and perceptions about it) and that theimpact of this reality on our senses causes us to invent objects, properties,and relations to describe these impacts. Objects, properties, and relations

1 Drew Khlentzos, “Semantic Challenges to Realism,” The Stanford Encyclopedia of Philosophy (Winter 2004 Edition) , Edward N. Zalta (ed.), URL =http://plato.stanford.edu/archives/win2004/entries/realism-sem-challenge/.


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CHAPTER 6. REALITY AND TRUTH

exist in our models of reality –not in reality itself. Using our model-building

apparatus and informed by our perceptions, we can only say things about reality. We can never say what it is. And, what we say about it is alwayssubject to revision.

Several thinkers agree with this point of view, expressing it in variousways:

“Objects” do not exist independently of conceptual schemes.We cut up the world into objects when we introduce one oranother scheme of description. – Hilary Putnam, Philospher 2

There was no way to hook up ideas with things . . . because ideas– mental representations – do not refer to things; they refer toother mental representations. – Louis Menand, Author,referring to thoughts of philosopher C. S. Peirce 3

There is no quantum world. There is only an abstract physicaldescription. It is wrong to think that the task of physics is tond out how nature is. Physics concerns what we can say aboutnature ... – Niels Bohr, Physicist 4

Even some theologians around the time of Galileo acknowledged thatthere was a difference between reality itself and mere descriptions of reality.For example, they thought that the geo-centric, Ptolemaic universe was“real,” while acknowledging that the helio-centric system of Galileo mightbe a useful description for calculating predictions needed for navigation. Tome, both are just descriptions, the latter more useful than the former.

We have invented all kinds of objects to populate our models of reality,including many that are part of our scientic vocabulary, such as atoms,quarks, ribosomes, and DNA. Each helps us describe reality so that we canmake more accurate and detailed predictions. Some of our descriptionscannot be related easily to common, everyday experiences. In quantum

2 Hilary Putnam, Reason, Truth, and History , p. 52, Cambridge: CambridgeUniversity Press, 1981.

3 Louis Menand, The Metaphysical Club: A Story of Ideas in America , p. 363, NewYork: Farrar, Straus and Giroux, 2001.

4 As quoted in The philosophy of Niels Bohr , by Aage Petersen, in the Bulletin of theAtomic Scientists , Vol. 19, No. 7, September 1963.


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mechanics for example, weird phenomena such as “superposition” and

“entanglement” have no satisfying, intuitive explanations – yet they aredescribed mathematically in ways that make consistently conrmedlaboratory predictions and may even be used someday in super-fastcomputers. There are physicists who claim not to be bothered by this lackof a mental picture; they belong to what some call the“shut-up-and-calculate” school. So long as the model makes goodpredictions, who cares?

Philosphers’ views about reality affect their views about truth. Forexample, some claim that a true statement is one that “corresponds” withreality, that is, with the way things “actually are.” That denition soundsseductively simple and obvious. However, I think the phrase “the waythings actually are” is meaningless. Let’s see why by examining how thecorrespondence theory is supposed to work. The sentence “coal is black” istrue, according to the correspondence theory of truth, if coal (that object inthe world referred to by the word “coal”) actually is black (that property in

the world referred to by the word “black”). What could be more obvious?Indeed! But the problem is that what we think of as coal (that alleged

object in the world) and blackness (that alleged property in the world) arewords that describe concepts that we invent to help us carve up anddescribe reality. Those words and the concepts they describe are just as


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much a part of language as are the words “coal” and “black” in the sentence

“coal is black.” As a slang expression would have it, “reality doesn’t knowfrom coal” – it just is. We only end up chasing ourselves around in alinguistic circle when we try to decide how things “actually are.”

Other philosophers, recognizing some of the difficulties of thecorrespondence theory of truth, attempt to dene truth using the idea of “coherence.” In one version of the coherence theory of truth, each memberof a set of beliefs can be considered true if, taken together, there are nocontradictions among them, that is, if they are internally consistent. So, forexample, the statements “all swans are white,” and “Pollux is a blackswan,” do not cohere – they cannot both be true. But the statements “allswans are white,” and “Castor is a white swan,” do cohere – they couldeach be true. Short of having a way to evaluate the credibility of a set of statements in light of evidence, about all we can do is check to see if theyare consistent. Someone confronted with a logical inconsistency among hisor her beliefs should, at least, seek to adjust them to eliminate theinconsistency. The coherence theory of truth recalls Richard Rorty’sstatement, “ . . . only a sentence can be relevant to the truth of anothersentence . . . ”5

When members of a set of related beliefs have probability valuesassociated with them, a version of coherence generalized to this caseinvolves checking to see if these probability values together satisfy the lawsof probability theory. Propagating probabilities in a belief network basedon new evidence makes all of the probabilities mutually coherent. Then, if any of them have a probability value very close to 1.0, the associated beliefscan be labeled true.

One of the consequences of my view about truth and reality is thatthere are no “absolute truths” that are “out there” in some sense. When aperson says that such-and-such is absolutely true, I conclude that theybelieve “such-and-such” very, very strongly and that they don’t think theywill ever, ever change their minds about it. “Absolute truth” is just a labelwe apply to beliefs that are held very, very strongly. Some people have

claimed that to say there are no absolute truths is self-contradictorybecause that statement itself is an absolute truth. But, I am not subject to

5 Richard Rorty, “Being that can be understood is language,” Richard Rorty on H.-G.Gadamer, London Review of Books, Vol. 22, No. 6, 16 March 2000.


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that contradiction because I don’t claim that my belief that there are no

absolute truths is an absolute truth. It’s just one of my beliefs.What about mathematical and logical truths? Isn’t it true (even

absolutely true in some sense) that 2 + 2 = 4? Why quibble with that? Yes,there are mathematical and logical truths, but they depend on a specializeddenition of truth used in mathematics and logic. There, truth has to doessentially with different ways of saying the same thing. For example, it is amathematical truth that at least two of the sides of an isosceles triangle areequal. That fact is inherent in the denition of an isosceles triangle, namelythat at least two of its angles are equal, plus some of the standardassumptions about plane geometry. Saying that the two sides of an isoscelestriangle are equal doesn’t say anything new beyond what was alreadyimplied by the denition and these assumptions. As a less mathematicalexample, if I already attach the label true to the belief “curing a cold takesseven days,” I can also attach the label true to the belief “curing a coldtakes a week.” Nothing new there.

In responding to someone telling us that such-and-such is true, wemight say “that’s right,” “that’s accurate,” or “that’s correct,” indicatingthat we also believe that such-and-such is true. Or we might say “that’swrong” if we don’t believe it. There are lots of synonyms and antonyms forthe word “true.” In any case, upon learning about a belief of anotherperson we have gained a new belief ourselves – a meta-belief , which is abelief about a belief. Our belief that John believes (strongly, say) that theearth is becoming warmer, for example, is such a meta-belief. Would we sayin this example that John “knows” that the earth is becoming warmer?Well, that’s really up to us and how we want to use the word “know.” If webelieve strongly that the world is becoming warmer , then we might wellsay that, in addition to our knowing it, so does John. However, someonewho doesn’t believe that the world is becoming warmer might not want tosay that John “knows” it because, he would reason, how could someoneknow something that’s not true. All such a person would be willing to sayis that John believes it. Usage of these words is entirely up to the person

using them.Not only is each of us able to use whatever words we choose in

describing our own beliefs and the beliefs of others, we are also able tobelieve what we want and with what strengths. We all our able to, and do,


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make our own different models of reality. The result is that some people are

led to say such things as “that may be true for you, but it isn’t true forme.” Quite so! Such statements are related to a philosophical positioncalled “relativism,” which Richard Rorty has dened as “. . . the view thatevery belief on a certain topic, or perhaps about any topic, is as good asevery other.” 6 Although everyone does have his or her own beliefs, Icertainly don’t believe (and would deny) that the beliefs of everyone areequally good.

How are we to judge, then, whether some beliefs are better than others?The answer is that we judge beliefs by comparing whatever predictions theymight make with careful observations and by seeking credible explanationsfor them. The most disciplined way to make these judgements is part of thescientic method, which brings us to the subject of the next chapter.

6 Richard Rorty, “Pragmatism, Relativism, and Irrationalism,” Presidential Address,Proceedings and Addresses of the American Philosphical Association , Vol. 53, No. 6,August, 1980. (Article Stable URL: http://www.jstor.org/stable/3131427.


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Chapter 7

The Scientic Method

The set of practices scientists use to tease out descriptions of reality hascome to be called “the scientic method.” As I have already mentioned, thescientic method is a highly disciplined, but still rather informal,application of the elements of critical thinking that many of us use quitenaturally. In fact, Albert Einstein once said “The whole of science isnothing more than a renement of everyday thinking.” 1 These renementsconsist mainly of careful observations followed by creating and testingexplanations for these observations. People as far back as the Babyloniansand ancient Greeks used many of these strategies in their attempts to learnabout the natural world.

Near the beginning of the 11th century, al-Haytham, an Islamic scholarwho lived in Basra and Cairo, wrote The Book of Optics, which included atheory of vision and a theory of light. According to one authority “. . . Ibnal-Haytham was the pioneer of the modern scientic method. With hisbook he changed the meaning of the term optics and establishedexperiments as the norm of proof in the eld. His investigations are basednot on abstract theories, but on experimental evidences, and hisexperiments were systematic and repeatable.” 2 In particular, al-Haythamcombined observations, experiments and rational arguments to support a

1 Albert Einstein, “Physics and Reality,” 1936, reprinted in Ideas and Opinions , p.290, New York: Crown Publishing Company, 1954.

2 Rosanna Gorini, “Al-Haytham the Man of Experience, First Steps in the Science of Vision”, Journal of the International Society for the History of Islamic Medicine , 2(4),53-55, 2003. Available online at http://www.ishim.net/ishimj/4/10.pdf.


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CHAPTER 7. THE SCIENTIFIC METHOD

theory of vision in which rays of light come from the objects seen rather

than from the eyes that see them.Notable European contributors to the development of the scientic

method include Robert Grosseteste (c. 1175-1253), Roger Bacon (c.1214-1294), Galileo (1564-1642), Francis Bacon (1561-1626), and ReneDescartes (1596-1650) – all preceding one of the greatest scientists of alltime, Isaac Newton (1643-1727).

Today, the scientic method is employed throughout the world, havingcreated an explosion of knowledge during the last few centuries. To be sure,the ways the method is applied in the laboratories of chemists, in the eldwork of geologists, in the observatories of astronomers, and at the desks of

theorists are slightly different, but the spirit is the same: observe, explain,and test. In this chapter, I’ll rst describe what I think scientic knowledgeitself is all about and then turn to the essential processes of science – itsmethod.

Scientic knowledge consists of many facts, theories, and other beliefsdescribing the universe – from its billions of immense galaxies to its smallestsub-atomic particles. In between, there are stars and planets, life forms andtheir constituent components, chemical compounds, and atoms. In additionto these “things” (I remind the reader that I believe we invent and namethings as a way to describe reality), there are the various processes (also

our inventions) that these things undergo. These include the Big Bang thatstarted it all, the births and deaths of stars, the movements of continents,the changes in climate and weather, the beginnings and evolution of life,the migrations of peoples, the development of language, the workings of thecell, the shuffling of DNA, and the behavior of electrons, to name just a fewof the thousands of processes scientists identify and study. It takes manytheories to describe the world scientically, and so far no single one doesthe entire job. Instead, scientic knowledge consists of many, manytheories, at many levels of detail, scattered around the world in books, journal articles, computer databases, and peoples’ heads.

Some scientic knowledge can be called “textbook knowledge” –sufficiently regarded by the experts that it is taught to generations of newscientists. Much of quantum mechanics, for example, is now textbookknowledge. Some scientic knowledge, on the other hand, is “frontierknowledge,” recently minted and still in need of testing. Ideas about the


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possible genetic causes of some diseases are examples of frontier knowledge.

Whether in textbooks or at the frontier, all scientic knowledge is subjectto change. New experiments with new observational equipment mightrequire replacing existing knowledge with new. Yet, regardless of itstentative status, today’s scientic knowledge constitutes the bestdescriptions of reality presently available.

Scientists distinguish between two main types of scientic knowledge,“facts” and “theories.” Facts usually refer to the specic results of carefulobservations or experiments. For example, a scientist might say that it’s a fact that a 10-kilogram object dropped from a height of 10 meters reacheda velocity of 14 meters per second when it hit the ground. But he mightalso mention Galileo’s theory that two heavy objects of different massesdropped simultaneously from the same height would reach the ground atthe same time.

Theories are constructs meant to explain facts and to predict theresults of observations, or to explain in more detail already existingtheories. In all cases, acceptable theories must be consistent with the factsthey are meant to explain and must be capable of predicting the results of new observations. If these new predictions, when tested by carefulexperiments, are satised, the theory gains credibility. So, besides coveringexisting facts, a scientic theory must also extend its reach beyond thosefacts to predict how new observations might turn out.

Scientic theories must satisfy other requirements also. For one, theyhave to be testable, and it has to be the case that they might fail the test.That is, all scientic theories must be falsiable. So, even though a scientistmight hope that her theory will be consistent with the results of futureexperiments designed to test it, it must at least be conceivable that itwouldn’t be. Even though scientic theories must be falsiable, saying thatsomething is a theory (instead of a fact) does not necessarily cast doubt onit. Most textbook theories, for example, are highly credible – so crediblethat we label them “true” just like we label facts “true.” Even so, we wouldnever assign 100% probability to a theory, because then (according to a

technical result in probability theory) it could never be weakened –whatever the evidence. In science, we are always willing to entertain theidea that a theory might be overturned.

To understand the importance of falsiability, think of the game


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“twenty-questions.” You ask a series of yes-no questions trying to pin down

what object someone is thinking about. You try to ask a question whoseanswer would provide you the most information. You never ask a questionthat can only be answered “yes” because it wouldn’t give you anyinformation at all about what the object might be. Any questions producedby non-falsiable theories can produce only “yes” answers (never “no”answers), and therefore such theories make no claims at all about whatreality might be like. They aren’t of any interest scientically because thetask of science is to say something about reality.

The most common kinds of unfalsiable theories are those with aninexhaustible supply of free parameters – “knobs” on the theory that canbe adjusted as needed to be consistent with any new data. For example,theories about extra-sensory perception (ESP) are especially prone to the“too-many-knobs” problem. ESP experimenters who devise tests forwhether people can “read” a remote person’s thoughts can usually think of excuses for never producing a “no” answer. Any one of a potentiallylimitless number of parameters about the “state” of either the subject or of the remote person can be used to explain away a failure. One of them washaving a “bad day.” Or one of them was “trying too hard.” Or, maybe itwas the experimenter’s fault. He was “too skeptical,” and his “negativeaura” interfered with the effect. Other free parameters may pertain to thekind of message that was supposed to be sent from sender to receiver. If an

ESP experiment doesn’t work, an ESP advocate might say that the subjectmatter was not “of the right type.” Because there could be an innitenumber of such excuses for failure, there is no possibility whatsoever of getting an answer that an ESP theorist would accept as “no.” Such aninnitely expandable theory could never be inconsistent with anyexperimental test, so the theory doesn’t really say anything about reality.

People have a lot of beliefs that are not falsiable, and therefore suchbeliefs cannot be considered to be scientic. Some people even base actionson non-scientic beliefs. These actions might have consequences that areharmless, good, or bad for the people concerned (and for others too). Most

theories about immortality – that is, life after death – cannot be tested, sothey are not scientic theories even though many people might believethem. Personally, I wouldn’t recommend basing actions on them.

The philosopher Karl Popper claimed that science advances mainly by


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falsifying old theories and replacing them with new ones that are immune

to the particular failures of the old ones. The new ones must be falsiablealso, but with different tests. No scientic theory can be immune fromeventual falsication.

A desirable feature of scientic theories is that they be consistent witheach other. However, many of today’s theories, even textbook ones, are not.For example, Newton’s gravitational theory, quantum mechanics, andEinstein’s general theory of relativity are inconsistent with each other. Buteach is useful in its limited setting. Newton’s theory describes the force of gravity between objects of rather large sizes and distances, quantummechanics describes phenomena at the sub-atomic level, and Einstein’stheory describes phenomena around really massive objects, like stars, andphenomena near the speed of light. Scientists and engineers use Newton’stheory for calculating spacecraft trajectories and the orbits of planets, theyuse quantum mechanics for calculating the behavior of sub-atomic particles,and they use Einstein’s theory for calculating how a massive star refractslight from a more distant star.

Physicists are still looking for a single theory – a “theory of everything”– that would unify electromagnetism, the strong and weak nuclear forces,quantum mechanics and gravity. One candidate, string theory, proposesthat all of the elementary particles – electrons, quarks, and so on – are tiny,tiny strings, vibrating in ten dimensions. 3 Six of these dimensions are rolledup into such small formats that we – so far – experience only the other fourdimensions of space-time. Who knows? Lots of people are out thereinventing theories. For the moment we must be satised with specializedtheories having different domains of applicability within which each makesaccurate and useful predictions. One just has to be careful to use thetheories appropriate to their settings – ones in which their inconsistencieswith other theories aren’t evident.

Scientic knowledge is produced by a highly interdependent socialmedley of observations, theorizing, experimental tests, and yet moretheorizing and tests – all occurring in a maelstrom of criticism and debate.

If one looks at the history of science, the whole process seems more like theopportunistic communal solving of several jigsaw puzzles, with many

3 Brian Greene, The Elegant Universe: Superstrings, Hidden Dimensions, and theQuest for the Ultimate Theory , New York: Norton, 1999.


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participants and vocal kibitzers, than it does a well-ordered, systematic

effort to describe the natural world. One shouldn’t, therefore, understandthe phrase “the scientic method” to be anything like a simplecrank-turning process for producing scientic knowledge. Scientists arehuman beings with the usual prejudices, egos, fears of failure, hopes forsuccess, and all the other hindrances to objectivity. Nevertheless, sciencehas given us, over the centuries, descriptions of reality sufficiently attunedto its workings that we are able to cure and prevent many diseases, sendspacecraft beyond our solar system, build nano-devices, provide standardsof living way beyond those of the richest ancient kings, and (sadly) producethermo-nuclear explosions. So, even though some have said that science ismerely “one particular way of knowing, no better than any others,” it hasproduced results that none of the others, whatever they might be, can comeclose to matching.

Not only is the scientic method used to test theories that describepresent reality, but it can also be used to test theories about past reality.There are theories about the birth of the universe in a “Big Bang,” forexample. One consequence of that cosmological theory is that stars andgalaxies should all be receding from the earth (and from each other), andthat consequence is consistent with modern astronomical observations. Wecan’t do any staged experiments involving a repeat of the “Big Bang,” sopassive observations must suffice. Much of science, such as geology and

paleo-anthropology, is concerned with past events. So, of course, is thesubject of human history. We can evaluate theories about these past eventsby making predictions about what the theory claims we might nd bysubsequent “digging.” (Some people call the predictions made from theoriesabout past events “postdictions.”)

How science actually progresses is what books and articles on thehistory of science are all about. For example, one fascinating part of thathistory is how our ideas about the nature of electromagnetic wavesgradually developed over the last few centuries – progressing from earlystudies of the properties of light all the way up through quantum

mechanics. An abbreviated description of part of that history will give aavor of how scientic knowledge evolves, building as it does on chancediscoveries and previous theories.

After Isaac Newton’s work with optics in the mid-1600’s, people


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experimented with prisms to refract light into its constituent colors, which

were projected as bands on a screen. In 1800, William Herschel, a Britishastronomer, observed that “something” was making a thermometer hotterwhen it was placed near the “un-illuminated” part of the screen next to theband of red light. Herschel theorized that there must be some “invisible”light coming through the prism impinging on the band below red (latercalled infrared). A year later, the German physicist Johann Wilhelm Ritter,thought that perhaps an opposite, or cooling, effect might occur justbeyond the band of violet light. One of his experiments found somethingelse, namely that “something” just beyond the violet band darkened papersoaked with silver chloride. Here was yet more invisible light, later calledultraviolet. Experiments showed that both types of these newly discoveredlight “rays” traveled in straight lines, exactly like visible light.

In another “territory” of science in the late 1700’s and early 1800’s,people such as Benjamin Franklin and Alessandro Volta were observingelectrical activity of various sorts and constructing theories about it.Electricity’s twin, magnetism, was known from ancient times. A connectionbetween these two previously separate phenomena was rst observed byHans Christian Ørsted (a Danish physicist and chemist) in 1820. He waspreparing materials for a lecture when he accidentally noticed that acompass needle moved when he switched a nearby current on and off.Immediately thereafter, Andre-Marie Ampere (a French physicist and

mathematician) developed a mathematical theory to represent the magneticforces between current-carrying conductors. Thus, the idea of “electromagnetism” was born.

In the 1830’s, the English chemist and physicist Michael Faradaydeveloped the concept of an “electro-magnetic force eld.” Building on thatidea, in the 1860’s James Clerk Maxwell, a Scottish physicist andmathematician, produced a mathematical theory of these elds and theirpropagation as waves. He showed that one consequence of the equationsconstituting his theory was that the speed of electromagnetic waves wasapproximately the same as the already-measured speed of light. This

coincidence led him to claim that light itself was also an electromagneticwave.4

4 Maxwell, James Clerk (1865). “A dynamical theory of the electromagnetic eld,”Philosophical Transactions of the Royal Society of London 155: 459512, 1865.


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Soon after Maxwell’s work, various physicists and engineers, primarily

in Germany, were experimenting with partially evacuated glass enclosurescalled Crookes tubes. When the cathode and anode elements in such a tubewere connected to an electrical source, a bluish uorescent glow appearedto project to the end of the tube. Specially designed experiments revealedthat the glow at the end of the tube surrounded a sharp-edged shadow castby the tube’s anode. In 1869, Johann Hittorf concluded that somethingmust be traveling in straight lines from the cathode [toward the anode] tocast the shadow, and in 1876, Eugen Goldstein proved that [these“somethings”] came from the cathode, and named them cathode rays(Kathodenstrahlen ).” 5 There was debate at the time about whether theserays were tiny particles or electromagnetic radiation. In 1896, the Englishphysicist, J. J. Thompson and others, showed that they consisted of previously unknown negatively charged particles – now called electrons –and that they had a mass approximately equal to about a thousandth of the mass of the hydrogen atom. Therefore, the Crookes tube cathode rays,being particles, were not themselves electromagnetic waves.

However, in the mid 1890’s the German physicist Wilhelm R¨ ontgenshowed that when these particles struck the anode or glass enclosure of aCrookes tube, they produced yet a new kind of radiation that could travelthrough various materials outside of the tube. He called them “x-rays” toindicate that they were an unknown type of radiation. In one of his

experiments, he used them to photograph his wife’s hand – the rst x-ray of a human body part. Later experiments showed that the paths of x-rayswere bent in crystals in the same way that the paths of light were bent ingratings, providing evidence that x-rays were another kind of electromagnetic radiation.

Meanwhile, people were curious about the space-permeating medium,the so-called luminiferous aether, that was thought to be required for thepropagation of electromagnetic waves. Was it like the air through whichsound waves propagated? The speed of the earth around the sun hadalready been measured, but what about the speed of the earth through this

aether? Equivalently, what was the speed of the aether “wind” as itbrushed by the earth? Two American scientists, Albert Michelson andEdward Morley, conceived an experiment to measure the speed of this

5 http://en.wikipedia.org/wiki/Crookes tube .


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wind. It involved measuring the difference in the speed of light traveling in

two different directions relative to the motion of the earth. Theirexperiments, performed in 1887, showed no difference beyond possiblemeasurement error. Two important conclusions followed from their results:rst, the speed of light, denoted by c , was constant regardless of itsdirection relative to the earth, and second, the imagined aether wind hadno speed at all. So, if there was no wind, there was not any such aether.

Of course, Michelson and Morley were disappointed with their negativeresult. They were never quite convinced of the non-existence of the aetherand looked for aws or errors in their experimental setup. (That’s one wayscientists, being human and committed to their ideas, can deal with failedexperiments.) Michelson also thought that perhaps the earth “dragged” theaether along with it; that would explain away the zero wind speed.Gradually though, amidst much scientic discussion and with the negativeresults of additional experiments by Michelson and Morley and others, thetheory about the existence of the aether had to be abandoned. Apparently,electromagnetic waves could travel through empty space without a medium.

The Dutch physicist, Hendrik Lorentz, was one of those who developeda theory for why the speed of light was constant regardless of direction. Heproposed that moving bodies contract in the direction of motion. Any“ruler” used to measure the speeds of two light beams would contractprecisely enough to yield equal speed values. In 1905, motivated byMaxwell’s theory of electromagnetism, Albert Einstein incorporated thiscontraction idea into his special theory of relativity. That theory predictedmuch more than length contraction. It predicted that mass and energy areequivalent ( E = mc 2) and that clocks run more slowly in the direction of motion. All of these predictions have been conrmed by subsequentexperiments (and by atomic and thermo-nuclear explosions). Thecontraction effects are negligible at ordinary speeds but become dramatic atspeeds approaching the speed of light.

Theories about electromagnetic waves get even more interesting in theearly years of the twentieth century. In 1905, using Max Planck’s earlier

hypothesis that energy levels can only be changed by discrete amounts or“quanta,” Albert Einstein proposed that light (indeed, all electromagneticradiation) consists of individual particles, later called “photons.” Theenergy of these photons is proportional to the frequency of the radiation.


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Einstein’s photon theory was a major step in what came to be called

“quantum mechanics.”So what is the “real nature” of light – waves or particles? Well, it

depends on what we try to do with light. Because models are constructions,people can only build them out of the mental materials at hand. The ideaof a particle and the idea of a wave are both concepts that are grounded inthe everyday physical experiences of people. Attempts to explain whathappens when a beam of light passes through a narrow slit and producesbright and dim patterns on a screen naturally bring to mind how the crestsand troughs of intersecting waves at the seashore strengthen and canceleach other. Attempts to explain how light exerts pressure to move a tinymetal surface naturally bring to mind a stream of particles impacting thesurface. So far, we have no everyday experiences for building a single,consistent, intuitively understandable theory of light.

However, thanks to further developments in quantum mechanics byNiels Bohr and many others, both the particle-like and the wave-likebehaviors of light can be explained by a single mathematical description.Quantum mechanics has given us the rst example of the need to describereality with difficult to understand mathematics instead of easily graspedintuitive models. Because intuitive models are so much more satisfying andcompelling than ones built from mathematics alone, both the wave andparticle models survive, and are useful, even though they are inconsistent.One just has to be careful to use the one appropriate to the circumstances.

Even though quantum mechanics is beyond the comprehension of mostof us, its predictions have been veried experimentally, and it is vital to thedevelopment of much of modern technology. Examples include lasers,computer chips, electron microscopes and magnetic resonance imaging. Inthe future, we may even have quantum computers for performing certaintasks much, much faster than even our fastest current computers.

The entire process of lling in the jigsaw puzzles that led us fromoptical prisms to quantum mechanics was accompanied by the publicationof peer-reviewed scientic papers, by attempts to repeat experiments, andby the criticisms of other scientists. Trustworthy scientic knowledgedepends on these very important community efforts. Communityparticipation begins with the peer-reviewed publication of a scientic resultin an appropriate journal. Other scientists who are able to read and


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understand this result can then offer criticisms and, in the case of a new

experimental result, can attempt to repeat the experiment.Debate and criticism are extremely important to ensure objectivity in

science. As the historians Joyce Appleby, Lynn Hunt, and Margaret Jacobput it:

. . . [objectivity] does not simply reside within each individual,but rather is achieved by criticism, contention, and exchange.Without the social process of science – cumulative, contested,and hence at moments ideological – there is no science as it hascome to be known since the seventeenth century. Criticism

fosters objectivity and thereby enhances reasoned inquiry.Objectivity is not a stance arrived at by sheer willpower, nor isit the way most people, most of the time, make their dailyinquiries. Instead it is the result of the clash of social interests,ideologies, and social conventions within the framework of object-oriented and disciplined knowledge-seeking. 6

Scientists have a number of weapons when they debate a result ortheory. People who argue against a theory might claim that the experimentsupporting the theory was awed or that its results are erroneous. Forexample, people pointed out aws in the cold-fusion experiments performedby Pons and Fleischman, and aws are often found in experimentspurporting to support ESP. To guard against aws, it’s important thatcritical experiments be done very carefully and repeated by independent investigators – scientists who have a different emotional stake in theoutcome of their experiments. If aws cannot be found, opponents of atheory might be able to suggest a more credible alternative theory thatbetter explains the experimental results. Or, they can claim that newexperimental results are inconsistent with the theory.

People who argue for a theory can cite either the positive results of repeated experiments or of other conrmed new predictions. Or they canmention an agreed-upon underlying theory that supports the theory inquestion. To counter objections to a theory, its proponents might cite

6 Joyce Appleby, Lynn Hunt, and Margaret Jacob, Telling the Truth About History , p.195, New York: W. W. Norton & Co., 1994.


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evidence against any competing theories. In case an experiment fails to

conrm a theory, its proponents might try to explain away these negativeresults, as Michelson and Morley tried to do. In the history of scienticdebate, which is often raucous but always necessary, it is easy to nd all of these kinds of arguments.

There are some additional factors that affect the credibility of a theoryand that provide rationale for debate and criticism. Among these areparsimony, explanatory power, and boldness. Usually the simplest theoryconsistent with all of the data is afforded higher credibility than morecomplex theories. This preference is called the principle of parsimony andis sometimes called the Occam’s razor principle. William of Occam was a14th century logician and Franciscan friar who is alleged to have saidsomething like “Entities should not be multiplied unnecessarily.” The“razor” is used to shave away the unnecessary entities of the more complextheory. Sometimes the principle is quoted in one of its original Latin forms,such as Pluralitas non est ponenda sine neccesitate .

To some extent, simplicity is in the eye of the beholder and depends onthe language being used to describe theories, but there are some usefulmeasures. One such is the number of entities required by the theory. Forexample, in the Ptolemaic theory, which was the dominant theory in theEuropean Middle Ages, the sun, moon, and planets revolved around axed, central earth in circles. The radii of these circles were entitiesrequired by the theory. But to make the theory consistent withastronomical observations, the planets had to do little dances in smallcircles superimposed on their large circular orbits. These small circles werecalled epicycles, additional entities needed to preserve the earth-centrictheory. The helio-centric theory, which began with Copernicus and waslater modied by Kepler to be consistent with data gathered by TychoBrahe, had the planets all going around the sun in elliptical orbits. Eachorbit could be described by just two entities, namely the spatial locations of the two foci. The not-yet-dead Ptolemaic theory could be – and was –adjusted so that it also matched Brahe’s data. The adjustment consisted of

adding epicycles to the epicycles – yet more entities. Though they wereboth consistent with the data, the Keplerian theory, with its fewer entities,was the more parsimonious and therefore prevailed.

Even though there is no reason to believe that reality itself is simple


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(and thus might best be described by simple theories), there is a valid

technical reason to prefer simpler theories. It’s because each of the entitiesin a theory is like a knob that can be adjusted as needed to make a theoryconsistent with the experimental data. The more knobs there are totwiddle, the more different specic theories there are to select from. Andthe more theories there are to select from, the more likely it is that you willselect one that won’t be very good at making new predictions – eventhough it does happen to t the data at hand. All that the extra knobs cando is capture idiosyncrasies in the data you happened to have gatheredrather than any underlying regularities of reality. Statisticians, for example,have long known that a simple model that ts the data is more likely thana complex model to make good predictions.” 7

The explanatory power of a theory contributes to its credibility.Theories that explain independent observations in several separate subjectareas are said to have great explanatory power. For example, in addition tosea levels rising, air and ocean temperatures rising, and glaciers melting,there are many more independent sources of evidence supporting the theoryof climate change. Seasonal migrations of animals are happening earlier inspring and later in autumn, plants are owering earlier and going dormantlater, and extreme weather phenomena (such as hurricanes and oods) arebecoming more prevalent.

I could cite several other examples of theories with great explanatorypower. Plate tectonics is strongly supported by observations in a number of disparate elds including geology, biology, paleontology, seismology,geography, volcanology, and geophysics. Evolution explains a whole sweepof observations about living things – their diversity, relatedness, andbehaviors, and even such minutia as why some of them have vestigialorgans and appendages.

Besides explaining observations, some theories have high explanatorypower because they provide more detailed explanations of other theories.For example, Isaac Newton proposed theories of motion and gravity fromwhich he was able to derive mathematically the elliptical orbits of planets

rst proposed by Kepler. Because Kepler’s theory was already wellaccepted, Newton’s explanations for it became highly credible also.

7 Technical underpinnings for this claim involve what statisticians call “thebias-variance tradeoff.”


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If theories in different areas can be regarded as special cases of a more

general theory, then the more general theory has – in the words of EdwardO. Wilson – the property of consilience . Consilient theories cover broadareas and thus are accorded high credibility. For example, Newton’s theoryof gravitation linked heaven and earth – explaining not only earth-boundfalling bodies but planetary orbits as well. Newton seems to have been therst to propose that the laws governing earth-bound objects also governedobjects everywhere else – they were universal . And Maxwell’selectrodynamics linked electricity, magnetism, radio waves and light waves– subsuming earlier theories of Ampere, Gauss, and Faraday.

Theories that make surprising, bold, and testable predictions –predictions that differ substantially from what our other theories andcommonsense might have told us – are especially favored. The philosopherKarl Popper dened a bold theory as “one that takes a great risk of beingfalse – if matters could be otherwise, and seem at the time to beotherwise.” 8 If these surprising predictions stand up to experiments, thetheories are given higher rank than theories that make only veryconservative predictions. However scientists insist that unusually boldtheories must pass unusually rigorous tests. Because bold theories run a“great risk of being false,” it’s not surprising that they often fail. It is onlywhen they don’t fail harsh tests that one accords them high priority.

Einstein’s theories of special and general relativity are examples of boldtheories that made surprising predictions that have been conrmed bycareful experiments. Two particularly important predictions of generalrelativity are that a gravitational body, such as the earth, would warp spaceand time around it and that its rotation would pull space and time alongwith it. An extremely expensive and long-lasting experiment called GravityProbe B, conrmed both of these predictions by monitoring the orientationsof ultra-sensitive space-borne gyroscopes relative to a distant guide star. 9

Another example of a bold theory is the theory of cold fusion by StanleyPons and Martin Fleischmann. The theory was certainly bold because itchallenged well-established nuclear theory and made surprising predictions

that could be experimentally tested. But, so far, it has failed all of its tests.8 Quotation from Popper Selections , David Miller (ed.), pp. 119, Princeton, NJ:

Princeton University Press, 1985.9 See http://www.nasa.gov/mission pages/gpb/gpb results.html for details.


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http://www.nasa.gov/mission_pages/gpb/gpb_results.html

http://www.nasa.gov/mission_pages/gpb/gpb_results.html




Ideas that are immune from debate can never be in good standing in

science nor should they be in daily life. A primary distinction betweenscience and other attempts to describe and explain the world we live in isthat science, when it lives up to its ideals, tolerates – indeed encourages –critical discussion. As the philosopher David Miller put it: “ . . . every effortmust be made to provide criticism in the fullest measure. Reality must beransacked for refutations.” 10

Another benet of criticism is that it helps control the populationexplosion generated by prolic theorists. People can cook up theories fasterthan they can be thoroughly evaluated. As the biologist Edward O. Wilsonwrote, “Anyone can have a theory; pay your money and take your choiceamong the theories that compete for your attention. Voodoo priestssacricing chickens to please spirits of the dead are working with a theory.So are millenarian cultists watching the Idaho skies for signs of the SecondComing. . . . ”11 Many theories are rejected simply because scientists thinkthey would be a waste of their time.

Eventually, after debate has settled down, scientists usually reach aconsensus about the credibility of a theory. Using words similar to thosesuggested by Wilson, most scientists in a given discipline come to agreethat a theory in their discipline is either “suggestive,” “persuasive,”“compelling,” or “obvious.” 12 And, these appellations can change as ascientic eld matures.

Even after a consensus about a theory has been reached, however, newexperiments and observations might create unresolvable problems for thetheory – problems that cannot be solved by minor patches. In such cases,the old theory might eventually be replaced by a brand new and radicallydifferent one. The historian of science, Thomas Kuhn 13 , has called suchabrupt theory changes, “paradigm shifts.” In a paradigm shift, the oldtheory is rejected in favor of a new one, or maybe it is just put on a shelf

10 David Miller, “Sokal & Bricmont: Back to the Frying Pan,” Pli 9, pp. 156-73, 2000.http://www.warwick.ac.uk/philosophy/pli journal/pdfs/miller pli 9.pdf

11 Edward O. Wilson, Consilience: The Unity of Knowledge , p. 52, New York: AlfredA. Knopf, 1998.12 Edward O. Wilson, Consilience: The Unity of Knowledge , p. 59, New York: AlfredA. Knopf, 1998.

13 Thomas S. Kuhn, The Structure of Scientic Revolutions , Chicago: The Universityof Chicago Press, 1962.


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http://www.warwick.ac.uk/philosophy/pli_journal/pdfs/miller_pli_9.pdf

http://www.warwick.ac.uk/philosophy/pli_journal/pdfs/miller_pli_9.pdf




for occasional use under special circumstances. I have already talked about

one series of increasingly better planetary theories – Ptolemaic, Keplerian,and Newtonian – all examples of paradigm shifts. The moves to relativitytheory and to quantum mechanics are two more examples.

c Sidney Harris. Reprinted with permission, www.ScienceCartoonsPlus.com.

Although many aspects of the scientic method, such as performingcomplicated laboratory experiments, would not be applicable for evaluating

our everyday beliefs, we can, with some effort, adopt some of the practicesthat scientists routinely employ. For example, if a belief makes a predictionabout some future event, we can check to see if that prediction is fullled.If one of our beliefs contradicts another, we can try to resolve the conictby adjusting one or both of them. We can ask if a belief has a reasonable


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explanation. If a belief touches on a subject about which there is expert and

agreed-upon scientic opinion, we can compare our belief with that opinion.Most importantly, we can expose our beliefs to the reasoned criticisms

of others, just as scientists do. As the philosopher John Stuart Mill wrote,“[the person who] has sought for objections and difficulties, instead of avoiding them, and has shut out no light which can be thrown upon thesubject from any quarter . . . has a right to think his judgment better thanthat of any person, or any multitude, who have not gone through a similarprocess.” 14

14 John Stuart Mill, On Liberty , 1859.


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Chapter 8

Robot Beliefs

Like humans, many robots and other computer systems are capable of complex behaviors, both physical and cognitive. On the physical side, forexample, Google is developing automobiles that can drive themselvescompletely autonomously. According to the official Google Blog: 1

Our automated cars, manned by trained operators, just drovefrom our Mountain View campus to our Santa Monica office andon to Hollywood Boulevard. They’ve driven down Lombard

Street [which is very steep and curvy], crossed the Golden Gatebridge, navigated the Pacic Coast Highway, and even made itall the way around Lake Tahoe. All in all, our self-driving carshave logged over 140,000 miles [with only two humaninterventions].

In addition to their television-camera visual systems, GPS, and Lidarsensors, Google’s self-driving automobiles have access to maps, data fromGoogle’s “Street View” and vehicle driving codes, along with various othersources of knowledge needed for legal and competent driving behavior.

On the cognitive side, the IBM Watson computer defeated twochampion humans in the quiz show game Jeopardy! televised in February,2011. Watson had access to four terabytes of data, including millions of documents, dictionaries, encyclopedias, and other reference materials.

1 (http://googleblog.blogspot.com/2010/10/what-were-driving-at.html.


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http://googleblog.blogspot.com/2010/10/what-were-driving-at.html

http://googleblog.blogspot.com/2010/10/what-were-driving-at.html



CHAPTER 8. ROBOT BELIEFS

We certainly would say that human automobile drivers have beliefs

about driving and that human Jeopardy! contestants have beliefs aboutliterature, culture, sports, and other subjects. Couldn’t we say then thatGoogle’s self-driving automobiles and IBM’s Watson have beliefs too?

We ascribe beliefs (along with other mental qualities) to humansbecause, as the philosopher Daniel Dennett argues, doing so helps usexplain and predict their behavior .2 The same holds, he claims, for objectslike robots and computer systems. In ordinary conversation, we oftenattribute knowledge and beliefs to computer systems. It’s common to saythings like “the word-processing program believed I wanted that lower-case‘i’ capitalized.” Or “the chess-playing program knew it had mecheckmated.” It’s more convenient to describe computational behavior thatway than it would be, for example, to refer to the actual computer codethat automatically capitalizes a typed isolated lower-case “i.” Even thoughpsychologists and neuroscientists don’t yet know very much about whatexactly beliefs are or how they are represented in our brains, engineersknow exactly how knowledge is represented in the robots and computersystems that they build. They get to decide, if they want to, whether toinclude “beliefs” as part of the technical vocabulary used to describe howthese systems work.

The computer pioneer John McCarthy is one of those who has arguedfor ascribing beliefs to machines. For example, he claims we could say thata thermostat’s “belief” that a room is too cold is what leads it to turn onthe furnace. As he puts it, “When the thermostat believes the room is toocold or too hot, it sends a message saying so to the furnace.” 3 Although inthe case of a simple device like a thermostat, he admits, we wouldn’t needto talk about its beliefs because its operation is so easily understood usinga description involving a bi-metallic strip triggering an electrical switch.

For more complex systems though, such as computers, it is not onlypossible, but useful, to provide a technical denition for belief. I would saythat all of that information that is represented declaratively in a computersystem’s memory constitute its beliefs. For example, Shakey, the SRI robot

built in the 1960’s, had a large database of declarative sentences, including2 Daniel Dennett, The Intentional Stance , Cambridge, MA: Bradford Books, 1989.3 John McCarthy, “Ascribing Mental Qualities to Machines,” in Formalizing Common

Sense: Papers by John McCarthy , Vladimir Lifschitz (editor), page 104, AblexPublishing Company, Norwood, NJ, 1990.


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ones like “Doorway 17 connects Room 32 with Hallway 4.” (The actual

form of those sentences used a computer-friendly language called therst-order predicate calculus rather than English.) Shakey used “beliefs”such as these to help it decide how to navigate from room to room. Themost common type of database system represents its data declaratively inwhat is called a “relational” format. We could say, for example, that aprogram, such as Microsoft’s Outlook , believes “John Jones’s home addressis 1342 Elm Street” if it contained the computer equivalent of that sentencein its database. One could even say that it knew it if it represented itunequivocally, as Outlook does. It is common, for example, to saysomething like “My computer knows the names, addresses, and phonenumbers of many of my friends.”

Because so much of their information is represented declaratively, wecan say that Google’s driverless cars had beliefs about driving and thatWatson had beliefs about the many things needed to compete on Jeopardy! Watson’s beliefs, many of them in the form of actual English sentences,allowed it to conclude, for example, that Sir Christopher Wren designedEmmanuel and Pembroke Colleges. Watson believed that answer with acondence value of 85%, as the following snapshot from the telecast shows.It was condent enough to act on that belief by delivering that answer.

Many modern information systems organize their declarative knowledgein networks. The links and nodes of the network permit a compact


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representation of sentence-type information. The diagram below provides

an example.

For example, the diagram expresses sentences such as “Gio is a robot,”“Mia is a human,” and “Mia programmed Gio.” It can also be used toderive additional facts such as “Mia is an agent.” Such diagrams are oftencalled “semantic networks.” (In computers, they are represented, of course,by computer code – not by pictures. The picture equivalent is easier forhumans to understand than would be the computer code itself.) Becausethese networks express information about various entities and theirproperties, they are often called “ontologies,” using a term borrowed fromphilosophy having to do with “things that exist.” Ontologies are used toorganize information in the World Wide Web, in software engineering, inbiomedical informatics, in business enterprises, and in library science,

among other activities. Some psychologists think that humans store theirbeliefs in mental structures that are somewhat like ontologies.

A computer system’s beliefs can be updated by additions,modications, or deletions of sentences. Human programmers can makethese updates directly, and the systems themselves can also make them


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during interactions with their environments. Robots have perceptual

apparatus such as visual and auditory systems, touch sensors, and sonarsystems. It is possible for robots to sense anything that engineers can buildsensors for. Information about the environment gained by sensoryperception can then be used to make appropriate changes to a robot’sdeclarative models. Computer systems can learn new beliefs and modify oldones in manners similar too (but still more limited than) those of humans.

Powerful “machine learning” techniques have been developed byarticial intelligence researchers and by statisticians to produce useful newinformation for computer systems from many sources, including data fromsensors, from large databases, and from the World Wide Web. For example,computer systems such as Picasa and iPhoto can learn to recognizeindividual faces in photographs based on large samples of known faces.Machine learning methods are used in many other applications, including“data-mining” (by Amazon to guess your reading preferences), detectingpossible credit-card fraud, and translating languages.

The goal of machine learning is to construct an abstract representationof data. For example, given a sample, such as {1, 5, 3, 11, 7}, drawn from alarge set of numbers, a machine learning algorithm might attempt to guesssomething about some property of all of the numbers in the set from whichthe sample was drawn. It might, say, guess that they are all odd numbers.Of course, the guess might be incorrect; the large set of numbers mightactually include or more even numbers, which just didn’t happen to showup in the sample. Perhaps a larger sample would have included them.Typically, the larger the sample of data that a machine learning systemworks on, the better its performance. There are several machine-learningmethods for building such abstractions. These include neural networks,decision-tree induction, nearest-neighbor methods and others. To build auseful abstraction, one usually needs a lot of data. Analogously, scientictheories constructed to explain particular observations are also abstractionsthat make guesses – more-or-less correctly – about new observations.

If the data set is insufficient, however (there are rule-of-thumb measures

for such insufficiencies), the abstraction won’t do very well at makingpredictions. Attempting to generalize from limited data causessuperstitions. These can only be ameliorated by more data. Probably it’sthe same for humans. When someone dreams that his grandmother has


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died and then wakes the next day to hear that she did die, that person

might adopt the theory that dreams foretell the future: a superstition basedon limited data. Recognizing that the data is limited (which many peopleprobably wouldn’t note) and wanting to extinguish a possible superstition(which many people might not want to do), one would have to gather muchmore data about dreams, most of which would fail to predict the future.Sufficient additional data would lead to the conclusion that dreams areirrelevant as far as predicting the future is concerned.

What do the beliefs of computers and robots have to do with humanbeliefs? Our various engineering devices have often served as inspirationsfor understanding biological phenomena. The heart is a kind of pump, theeye is a kind of lens and camera, arms and legs are like cables pulling onlevers, the ear is a kind of microphone, and the brain was once a hydraulicapparatus, then a telephone switchboard, and now a computer. Consideringhow computer systems acquire, create, organize, and evaluate beliefs mightprovide a useful guide for us. Comparative studies often help illuminate thesubjects being compared. For example, studying geologic processes on Marsand other planets leads to generalizations that give us a betterunderstanding of Earth’s geology. Studying different languages contributesto useful generalizations about linguistics. I think additional perspectiveabout human beliefs might be gained by studying those of computers. Likerobots, I think that we humans are machines – albeit very, very complex

ones, still little understood. Thus, I think we are pretty much in the sameboat as robots regarding our ability to form useful beliefs about ourenvironment.

We can shed light on several philosophical conundrums by consideringwhat they would be like for robots. For example, some philosophers worryabout whether or not a belief has to be something that is being consciouslyconsidered rather than being locked away in some momentarily inaccessiblepart of our brains. Robots and computer systems also have various levels of data storage. Some might be in active use by current computations, somemight be ready for use in random access memory, and some might be stored

more remotely in secondary or tertiary storage. Do all of this data count asbeliefs? Well, we get to decide that as we decide what is the most usefuldenition of belief for a computer. Similarly, I think, psychologists andneurophysiologists get to decide what a technical denition of belief shouldbe for humans.


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Although I have written this book to help people wrestle with questions

of belief, our beliefs are only one aspect of our lives as humans. Unless theyserve us in other important parts of life, such as warm interactions withfamily, friends and others; fulllment in “good work;” appreciation,preservation, and enjoyment of our various cultural achievements; andachieving and maintaining good health; what good are they? The writerJoseph Campbell has said that what we all seek is the “experience of beingalive.” 4 Being able to enjoy that experience, however, depends on thequality of our beliefs. See to them!

Documents

Beliefs by Nilsson