According to Plato,?are the ideas of Beauty and Courage objectively real,?or are they notions that we invent in our minds whenever we want to? Do you think these ideas a

6.1 OVERVIEW: THE PROBLEM OF KNOWLEDGE

This is a serious question: Do you know anything? In other words, do you possess any knowledge? And here are some equally serious questions: If you do have knowledge, how did you attain it? And if you possess it, how much do you possess—that is, what is the extent of your knowledge? Do you know only the contents of your own mind or only mathematical or logical truths? Do you know that there is a God, that ordinary physical objects exist, that there is an external world (one existing independently of your mind), that unobservable entities such as electrons are real, that other minds besides your own exist, that events have occurred before the present moment? These questions probably seem odd to you, perhaps even absurd. But among serious thinkers, they are neither. Trying to find good answers to these is the main business of epistemology, the philosophical study of knowledge. It is the branch of philosophy that systematically investigates whether, how, and to what extent we know things. For well over two thousand years, philosophers have been searching for answers to these questions because, contrary to what most people believe, the answers are not obvious, and both the asking and the answering have theoretical and practical value. We value knowledge for its own sake, regardless of what we can do with it. When we are at our best, we crave the light simply because it is the light. But we also value knowledge because it can guide us to our goals, steer us away from error, and help us succeed in life, however we define success. Knowledge is power. Whatever our reply to the epistemological questions, if we take them seriously, they surely will affect how we see the world and what we do in it. Knowledge comes in different forms, and philosophy is usually concerned with only one of them. Knowing what something feels like (for example, what influenza feels like) constitutes one form of knowledge. Knowing how to do something The only good is knowledge and the only evil is ignorance. —Socrates Epistemology is the study of knowledge. 6.1 Overview: The Problem of Knowledge 283 284 Chapter 6 Knowledge and Skepticism (for example, how to throw a ball) constitutes another. Knowing that something is the case (such as knowing that an elm tree grows in the quad) is propositional knowledge—knowledge of a proposition. A proposition is a statement that is either true or false, an assertion that something is or is not a fact. This kind of knowledge has been the main focus of philosophers and is our primary concern in this chapter. Philosophers going back as far as Plato have said that propositional knowledge has three necessary and sufficient conditions: to know a proposition, (1) you must believe it, (2) it must be true, and (3) you must have good reasons for—be justified in—believing it true. On this traditional account, merely believing something is not enough; what you believe must be true. A belief does not count as knowledge unless it is true. But a mere true belief is not knowledge either, because you can have a true belief and yet not genuinely know. Let’s say you believe for no reason that three ducks are now swimming on Walden Pond, and suppose your belief is true—there really are three ducks swimming on Walden Pond. Does your true belief count as knowledge? According to the traditional view, no—because you have no reason to think that three ducks are now swimming on Walden Pond. You have only a true belief by accident, a lucky guess, and that’s not knowledge. To have knowledge, your belief must be true, and you must have good reasons to believe it true. Knowledge, then, is true belief that is justified. Philosophers disagree about the exact nature of the required justification, but most accept that knowledge is true belief that is in some sense backed by good reasons. Much of the work in epistemology centers around the questions of whether we have knowledge and, if so, how much we have. Most philosophers believe we have some knowledge but differ on its extent. They may insist that we possess knowledge of the existence of an external world, other minds, physical objects, the past and future, or self-evident truths. But some philosophers embrace skepticism, the view that we lack knowledge in some fundamental way. Skeptics may deny that we have knowledge in all of the areas just mentioned or maintain that we lack knowledge in only some of them. In any case, they hold that many or all of our beliefs are false or unfounded. Some skeptics argue that we lack knowledge because we have no way of distinguishing between beliefs that we take to be instances of knowledge from beliefs that are clearly not instances of knowledge. For all we know, we could be hallucinating, dreaming, in the grips of an illusion, or mistaken for some other reason. How do we know that we are not hallucinating or dreaming right now? Hallucinations and dreams can seem as real as our “normal” experience. If we cannot distinguish these two, the skeptic says, then we cannot have knowledge. Other skeptics raise doubts about the reliability of what we take to be our normal sources of knowledge—perception, memory, introspection, and reasoning. We realize that all these sources are fallible, that they sometimes lead us into Propositional knowledge is knowledge of a proposition. When you know a thing, to hold that you know it; and when you do not know a thing, to allow that you do not know it—this is knowledge. —Confucius 1 Do questions— such as “Is it raining?”—count as propositions? Skepticism is the view that we lack knowledge in some fundamental way. Figure 6.1 Are you dreaming now? How can you tell? 6.1 Overview: The Problem of Knowledge 285 error. But skeptics ask how we know that these sources are not always in error. If all these sources are suspect, we cannot use one to check another. We cannot, for example, use our sense of sight to check the reliability of our sense of touch. And if we think one mode of perception is more trustworthy than the others, how do we know that? We seem forced once again into skepticism. Another view that challenges our commonplace ideas about knowledge is cognitive relativism, the doctrine that the truth about something depends on what persons or cultures believe. The notion that truth depends on what a person believes is known as subjective relativism, and the idea that truth depends on what a culture believes is called cultural relativism. We normally assume that truth is objective— that it depends on the way the world is. When we assert a proposition, we generally believe that the proposition is true if and only if it says the way things are in reality. But the relativist rejects this view, believing instead that truth is relative to what a person or culture accepts as true. Truth is a matter of what a person or culture believes—not a matter of how the world is. This means that a proposition can be true for one person, but not for another. If you believe that sheep can fly, then it is true (for you) that sheep can fly. If someone else believes that sheep cannot fly, then it is true (for him) that sheep cannot fly. You thereby can make something true Cognitive Relativism Undone Are you a cognitive relativist? Do you believe that truth is relative to persons or cultures—that the truth about something depends on what persons or cultures believe? If so, consider this common—and potent—criticism of the doctrine: The most serious flaw of relativism in all its forms is a purely logical one: It’s self-refuting because its truth implies its falsity. According to the relativist . . . everything is relative. To say that everything is relative is to say that no unrestricted universal generalizations are true (an unrestricted universal generalization is a statement to the effect that something holds for all individuals, societies, or conceptual schemes). But the statement “No unrestricted universal generalizations are true” is itself an unrestricted universal generalization. So if relativism in any of its forms is true, it’s false. As a result, it cannot possibly be true. Theodore Schick, Jr., and Lewis Vaughn, How to Think About Weird Things (2011), McGraw-Hill. 311. What Do You Believe? Are you still a cognitive relativist? Cognitive relativism is the doctrine that the truth about something depends on what persons or cultures believe. Subjective relativism is the view that right actions are those endorsed by an individual. Cultural relativism is the view that right actions are those endorsed by one’s culture. 286 Chapter 6 Knowledge and Skepticism by believing it to be true. Likewise, if a culture believes that the earth is flat and that adulterers should be beheaded, then it is true (for its people) that the earth is flat and that adulterers should be beheaded. If relativism in either form is correct, then knowledge would be easy to attain— perhaps a great deal easier than acquiring objective truth, which demands that our beliefs somehow link up to the objective world. But for a variety of reasons, most philosophers have rejected relativism. For one thing, they say, the doctrine implies several absurdities that render it implausible. They point out, for example, that if we could make a statement true just by believing it to be true, we would be infallible. We could not possibly be in error about anything that we sincerely believed. We could never be mistaken about what time it is or when the French Revolution took place or whether breaking a promise is morally permissible. Personal infallibility is, of course, absurd, and this possibility seems to count heavily against subjective relativism. The same point can be made about cultural relativism. Philosophers distinguish two ways to acquire knowledge: through reason and through sense experience. The former is called a priori; it yields knowledge gained independently of or prior to sense experience. The latter is known as a posteriori; it gives us knowledge that depends entirely on sense experience. We can come to know many propositions a priori—for example, that all bachelors are unmarried, that all triangles have three sides, that 2 + 3 = 5, and that something is either a cat or not a cat. We need not do a survey of bachelors to see if they really are all unmarried; we can know this just by thinking about it. And we know that “Something is either a cat or not a cat” is true; it is a simple logical truth—and we know it without having to observe any cats. It seems that we can also come to know many propositions a posteriori—for instance, that John the bachelor has red hair, that he just drew a triangle on paper, that he is holding five pencils, and that Tabby the cat is on the mat. To know these things, we must rely on our senses. Through the centuries, philosophers have debated whether our knowledge of the world is fundamentally a priori or a posteriori (if indeed we have knowledge), and these arguments continue today in many forms in both philosophy and science. On one side of this divide are the rationalists, who believe that through unaided reason we can come to know what the world is like. They maintain that some or all knowledge of the empirical world is a priori, discoverable simply through the workings of our minds. On the other side are the empiricists, who contend that our knowledge of the empirical world comes solely from sense experience. We acquire knowledge entirely a posteriori. We may come to know logical and mathematical truths through reason, but we can know nothing of empirical reality except through our senses. At this point, you may find yourself being more sympathetic to the empiricists than to the rationalists. After all, you seem to acquire an enormous amount of information via your five senses. Through them, you grasp that the grass is green, the stove is hot, the music is loud, the lime is tart, and the rose is sweet. But what can you know through reason alone? Rationalists would say that you can know a great deal. Without making any empirical observations, mathematicians can not only The recipe for perpetual ignorance is: be satisfied with your opinions and content with your knowledge. —Elbert Hubbard 2 Are you a cultural relativist? Is the point about personal fallibility a valid criticism of the doctrine? A posteriori knowledge is knowledge that depends entirely on sense experience. Rationalism is the view that through unaided reason we can come to know what the world is like. Empiricism is the view that our knowledge of the empirical world comes solely from sense experience. A priori knowledge is knowledge gained independently of or prior to sense experience. True knowledge exists in knowing that you know nothing. —Socrates 6.1 Overview: The Problem of Knowledge 287 discover new mathematical truths, but also develop mathematical models that can accurately describe the empirical world. They can, for example, accurately predict the existence of astronomical objects and their movements without once looking through a telescope. Likewise, we know the fundamental truths of logic, without which reasoning itself would be impossible. We know, for example, that nothing can both have a property and lack it at the same time, and that for any particular property, everything either has it or lacks it. Thus we know without looking that nothing can both be a dog and not be a dog at the same time, there are no square circles, and married bachelors don’t exist. Some rationalists have gone further and asserted that reason alone can reveal the most important, basic truths about the world—such as “Every event has a cause” and “The shortest distance between two points is a straight line.” Many of the greatest thinkers in history have taken the rationalist approach to knowledge. Among these we can count Plato (c. 427–347 BCE), René Descartes (1596–1650), Benedict Spinoza (1632–1677), and Gottfried Leibniz (1646–1716). The most influential rationalist theory comes from Descartes, the inventor of analytic geometry and founder of modern philosophy. He thinks sense experience is an unreliable source of knowledge, so he looks to reason to give all our knowledge a foundation as firm as that which supports unshakeable mathematical truths. Through reason he hopes to defeat skepticism. His method is first to doubt everything that he cannot be certain of, a process that leaves him knowing hardly anything. But through reason alone he soon uncovers what he considers to be selfevident, certain truths from which he derives other indubitable propositions. In this way he tries to build an edifice of knowledge that, like an inverted pyramid, rests on one or two rock-solid foundation stones that support all the others. The empiricist view of knowledge has been advanced most famously by the British empiricists John Locke (1632–1704), George Berkeley (1685–1753), and David Hume (1711–1776). They want to turn Descartes’s pyramid right side up, resting all knowledge on a vast foundation of sense data (the content of our experience) that supports the upper stones. Among these thinkers, Hume probably has been the most influential, arguing for an uncompromising empiricism that leads to a far-reaching skepticism that not all empiricists have shared. He holds that all our knowledge (aside from purely logical truths) is derived from sense perceptions or ideas about those perceptions. Like other empiricists, he believes that the mind is empty—a blank slate—until experience gives it content. We can have knowledge of something only if it can be sensed, and any proposition that does not refer to what can be sensed is meaningless. Guided by this latter empiricist principle, Hume is driven to skepticism about many things that others have taken for granted, including the existence of the external world, causation, a continuing self, religious doctrines, and inductive reasoning. His skepticism arises because he thinks that even though all our knowledge is based on sense experience, we cannot know how the objects of our sense experience are related. We cannot know, for example, that there is a cause-and-effect relationship between associated objects. To infer such a connection is to go beyond what our senses tell us. Our notions of causal connections are merely matters of custom and habit. To be conscious that you are ignorant is a great step to knowledge. —Benjamin Disraeli 3 What facts about the world can we know based solely on our reasoning? 288 Chapter 6 Knowledge and Skepticism Applying his own theory of knowledge, John Locke rejects skepticism about external objects. Like a good empiricist, he believes that all we are directly aware of is sense data. Our sense experience is caused by external objects, and we can have knowledge of those objects because our sense data resemble or represent them. Berkeley, like Locke, also thinks his brand of empiricism can defeat the skeptic, but he differs with Locke and other empiricists on how sense data relate to the external world. He accepts the empiricist notion of our being aware only of sense data but rejects Locke’s belief in the existence of material objects. He argues that not only do we know just our own ideas, but there is no reason to suppose that they resemble or are caused by material objects. Locke, like most people, presumes that material objects exist independently of our sense experience, that they are, even when we do not perceive them. But Berkeley denies this, insisting that it is logically impossible for physical objects to exist, for we cannot “conceive them existing unconceived.” All that exist, he says, are minds and their ideas, a view known as subjective idealism. Immanuel Kant (1724–1804) was shocked by the skepticism that seemed to be lurking in empiricism in general and in the thoroughgoing empiricism of Hume in particular. Hume’s view is that we constantly experience countless sensations associated in various ways, but we cannot know about any necessary connections between them, the kind of connections that are the central focus of science. Kant agrees that all our knowledge begins with the raw data of sense experience, but he argues that our minds impose order on it. Like a cookie cutter stamping out shapes in dough, our minds mold our sensations into conceptual patterns that determine how we see the world. Thus our minds impress the concepts of cause and effect, space, and time onto our experience. Therefore we can know—a priori—that there are necessary connections between causes and effects and that space and time have definite characteristics, because our mental powers impose this structure on our perceptions. In this way, Kant tries to save science and our everyday experience from Hume’s radical skepticism. In the process he initiates two hundred years of critical scrutiny of his ideas by generations of philosophers.

Chapter 6.2

So rationalists hold that we have knowledge, that skepticism is false, and that through reason we can come to know the most important truths of reality. They differ, however, on how such knowledge is possible and how they arrive at their rationalist conclusions. Historically, two giants stand on the long road of rationalist thought: Plato at the beginning in ancient Greece and Descartes in Europe at the intersection of modern philosophy and science. Plato’s Rationalism Plato maintained that sense experience alone could not be the source of knowledge, although many of his contemporaries claimed otherwise. Some of them assumed that since knowledge must be based on sense experience, and since sense experience can vary from person to person or culture to culture, cognitive relativism must be true. If one person says a grape is sour and another says it’s sweet, there must be no objective fact of the matter, just truth relative to different persons. Other thinkers thought that since our perceptions are often illusory, distorted, or otherwise mistaken, sense experience is not a reliable source of knowledge. And since our perceptions are the only possible route to knowledge, we must not know anything. Thus skepticism, they said, is the proper epistemological attitude. Plato thought that our perceptions were just as unreliable a guide to genuine knowledge as the relativists and skeptics assumed. But he argued that since we clearly do have knowledge, we must derive it from a reliable source— and that source has to be reason. 3. Suppose a rationalist declares that scientists can know (without once looking through a telescope) about the physical characteristics of planets in our solar system. Would this be a plausible claim? Why or why not? 4. Suppose Locke is right that all we are ever directly aware of is sense data. Would this fact make it impossible to know about external objects? How could we ever know that there is something on the other side of our sense data? Explain how Locke’s view can lead to skepticism. 5. Berkeley denies the existence of material objects. How would you argue that he is mistaken about this? Hint: Why do you normally assume that material objects exist and are not merely creations of your mind? Why do you assume that the world exists while you are sleeping? Figure 6.2 Plato (c. 429–347 bce). Every great advance in natural knowledge has involved the absolute rejection of authority. —Thomas H. Huxley WRITING TO UNDERSTAND: CRITIQUING PHILOSOPHICAL VIEWS (continued) SECTION 6.1 290 Chapter 6 Knowledge and Skepticism Plato deduced that we must be able to acquire knowledge because we can identify false beliefs, and we obviously possess knowledge because we can grasp, through reason, mathematical, conceptual, and logical truths. We know that 2 + 5 = 7; that a triangle has three sides; and that if A is larger than B and B is larger than C, then A is larger than C. Plato pointed out that these truths are objective: They are true regardless of what we think. We do not invent them out of our imaginations; we discover them. No matter how hard we try, we cannot make 2 + 5 equal 9. Plato reasoned that if such truths are objective, they must also be about real things. They must refer to an independently existing, immaterial reality that is beyond sense experience. In addition, he insisted, these truths must also be immutable and eternal, existing in the immaterial realm unchanged for all time. Only through our powers of reason can we reach beyond the physical world to take hold of real knowledge of fundamental truths. Sense experience, in contrast, can yield only transitory, ever-changing information— mere opinion that is vastly inferior to everlasting truths. So for Plato, reality comprises two worlds: the fleeting world of the physical accessed through sense experience and the eternal, nonphysical, changeless world of genuine knowledge accessed only through reason. In spelling out the contents of the latter, Plato articulates the central notion of his philosophy: the Forms. The Forms (also called Ideas) are perfect conceptual models for every existing thing, residing only in the eternal world penetrated by reason alone. They are the ideals, or 4 Is the number five an objective entity? Is the preposition over objectively real? Explain your reasons. Do your answers to these questions give any support to Plato’s notion of the Forms? All men by nature desire knowledge. —Aristotle Modern Platonism Platonism refers to views derived from Plato’s doctrines, especially his theory of Forms. In the twenty-first century, Platonism is alive and well in the form of mathematical Platonism, a kind that has widespread acceptance among mathematicians. Mathematical Platonism says that mathematical entities—such as the number 3; 2 + 2 = 4; all prime numbers; and pi—are abstract objects that exist independently of the thoughts and practices of rational beings. Suppose you think of the number pi—what is it exactly you are thinking about? Platonists might say you are thinking of an object that exists somewhere beyond space and time and that has certain properties regardless of what you or anyone else thinks or does. A typical objection to mathematical Platonism is that it proposes a great divide between mathematical concepts and the human mind, between the mathematical world and the world we live in. If such a divide exists, it would seem to make human interaction with the mathematical realm inexplicable or maybe even impossible. How can the mind, living as it does in this material world, know anything about the imperceptible, strange mathematical entities that exist in an entirely alien sphere that is neither physical nor mental? Mathematical Platonists have offered answers to this question, and the debate continues—all because of something Plato said almost twenty-five centuries ago. Philosophy Now Do you think mathematical Platonism is plausible? Why or why not? 6.2 The Rationalist Road 291 standards, that we can first come to know and then use to assess the notions and objects we encounter in our lives. Through reason, we can access the Form of “table” and thus know the ideal template of “table.” With this knowledge we can understand the essence of a table and use this understanding to make judgments about all physical tables. Likewise, when we access the Form “courage,” we know what the ideal of courage is and can use this knowledge to appraise a particular instance of courage. As Plato sees it, the truly real world is the world of the Forms—the domain of the perfect and everlasting. With knowledge of the really real, we can understand the “less real” realm of the imperfect and transitory. In Plato’s account, the Forms are universals—properties that can be had by several particular things. Every blue thing is a particular instance of the universal property of blueness. Every triangular thing is a particular example of the universal of triangularity. Particulars reside in the temporary, imperfect world of the material; universals are found in the eternal, perfect world of the really real. We can rise above mere opinion and attain knowledge only by reasoning our way to the Forms. To do this is to travel down the rationalist road marked by Plato, the greatest rationalist of all time. How is it that we seem to have knowledge of the Forms, however dimly, even though our senses can tell us nothing about them? Our sense experience can acquaint us only with material objects, but the Forms are not material. It’s as if these universals were already in our minds waiting to be uncovered. Plato’s answer—and the answer of most other rationalists—is the doctrine of innate knowledge. He thinks that knowledge of these immaterial ideals is already present at birth, inscribed in our minds (our immortal souls) in a previous existence. We are born with this knowledge, and we somehow acquired it before our present lives. Accessing this knowledge, then, is a matter of using reason to recall what we previously knew in another life. To many ears, this recall theory may sound preposterous. But in Meno, Plato attempts a brilliant demonstration of it. In the dialogue, he depicts the character of Socrates discussing innate knowledge with Meno. To prove his point, Socrates calls over an unschooled slave boy and asks him a series of questions about a geometry problem. Socrates draws a two-foot-by-two-foot square (four square feet) and then tells the boy to draw another one that is twice the size of the first. Initially the boy thinks that doubling the length of each side of the square will produce a square twice as large as the first. So he draws a four-foot-by-four-foot square (sixteen square feet) but sees right away that that answer cannot be correct. As Socrates asks further questions, the boy comes to the right answer on his own. Socrates says that he merely helped the boy recollect knowledge that he already possessed, bringing innate knowledge to consciousne

In Descartes’s time, the world must have seemed to many to be turning upside down. Time-honored ideas, established religious doctrines, and traditional attitudes were being called into question by both new discoveries in science and radically different religious outlooks on the Continent. This was the era of Galileo, Copernicus, Kepler, Bacon, Newton, and Martin Luther—thinkers who were dismantling the old ideological structures piece by piece. Into this world of upheaval and change came the brilliant Descartes, determined to see if there could be any epistemological certainties in an age of doubt. He hoped that knowledge could be given a foundation as sturdy as that which buttressed mathematics. If only knowledge of the world could be as certain as knowledge of geometry! Oddly enough, Descartes begins his quest for knowledge by first plunging into skepticism. He sees that a great many things he thought he knew appear now to be false. So he decides to “raze everything to the ground and begin again” from a firm foundation, doubting all beliefs except those that are “certain and indubitable,” beliefs that cannot possibly be false. Only beliefs that are certain can count as knowledge, he says. If he has reason to doubt any of them, they are not knowledge. Here he is at the start of his quest: René Descartes, Meditations on First Philosophy It is now some years since I detected how many were the false beliefs that I had from my earliest youth admitted as true, and how doubtful was everything I had since constructed on this basis; and from that time I was convinced that I must once for all seriously undertake to rid myself of all the opinions which I had formerly accepted, and commence to build anew from the foundation, if I wanted to establish any firm and permanent structure in the sciences. But as this enterprise appeared to be a very great one, I waited until I had attained an age so mature that I could not hope that at any later date I should be better fitted to execute my design. This reason caused me to delay so long that I should feel that I was doing wrong were I to occupy in deliberation the time that yet remains to me for action. To-day, then, since very opportunely for the plan I have in view I have delivered my mind from every care [and am happily agitated by no passions] and since I have procured for myself an assured leisure in a Figure 6.3 Roman fresco painting of Socrates. There comes a time when the mind takes a higher plane of knowledge but can never prove how it got there. —Albert Einstein 294 Chapter 6 Knowledge and Skepticism peaceable retirement, I shall at last seriously and freely address myself to the general upheaval of all my former opinions. Now for this object it is not necessary that I should show that all of these are false—I shall perhaps never arrive at this end. But inasmuch as reason already persuades me that I ought no less carefully to withhold my assent from matters which are not entirely certain and indubitable than from those which appear to me manifestly to be false, if I am able to find in each one some reason to doubt, this will suffice to justify my rejecting the whole. And for that end it will not be requisite that I should examine each in particular, which would be an endless undertaking; for owing to the fact that the destruction of the foundations of necessity brings with it the downfall of the rest of the edifice, I shall only in the first place attack those principles upon which all my former opinions rested.2 Descartes soon finds reason to doubt all beliefs based on sense experience, arriving at this conclusion via his famous dream argument. He notes that “there are no certain indications by which we may clearly distinguish wakefulness from asleep.”3 Our dreams can seem like reality, and in dreams we often don’t know we are dreaming. So it is possible that we are dreaming now, he says, and that what we take to be the real world is in fact not real at a

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