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The Classics Explained
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Library of Congress Cataloging-in-Publication Data McGinn, Colin, 1950–.
Philosophy of language : the classics explained / Colin McGinn. pages cm
Includes bibliographical references and index. ISBN 978-0-262-02845-5 (hardcover : alk. paper)
1. Language and languages—Philosophy. 2. Language and languages—Philosophy— Textbooks. I. Title.
P107.M38 2015 401—dc23 2014021824
Preface ix
1 Frege on Sense and Reference 1 1.1 Background 1
1.2 Identity 3
1.3 Additional Machinery 10 1.4 The Conception of Sense 12 1.5 Reference 16
1.6 Ordinary and Extraordinary Use 18 1.7 Further Points on Sense and Reference 20 1.8 Problems with Frege’s Theory 23
1.9 Extension of Frege’s Theory beyond Singular Terms 25 1.10 Further Aspects of Frege’s Theory 31
2 Kripke on Names 35 2.1 Background 35 2.2 Kripke’s Critique 39 2.3 Rigid Designation 42
2.4 Kripke’s Epistemic Objections 45 2.5 The Causal Chain Theory 48 2.6 Objections to Kripke’s Critique 49 2.7 The Social Character of Names 51 2.8 Essential Descriptions 52 2.9 Impure Descriptions 53
3 Russell on Definite Descriptions 55 3.1 Indefinite and Definite Descriptions 55 3.2 Three Theories of Definite Descriptions 60 3.3 Indefinite Descriptions and Identity 63 3.4 Russell’s Rejection of Meinong’s Ontology 65 3.5 The Details of Russell’s Theory of Descriptions 67
3.6 Problems with Russell 72
3.7 Primary and Secondary Occurrences 74 4 Donnellan’s Distinction 77 4.1 Introduction 77
4.2 Referential and Attributive Uses 78 4.3 Denoting and Referring 84 4.4 Truth-Value Gaps 85
4.5 Evaluating Donnellan’s Distinction 87 4.6 Implication and Implicature 90
4.7 Further Objections to Russell’s Theory 94 5 Kaplan on Demonstratives 97 5.1 Intension and Extension 97 5.2 Kaplan on Indexicals 100
5.3 The Two Principles of Indexicals 102
5.4 Context of Use and Conditions of Evaluation 105 5.5 Possible Worlds, Meaning, and Indexicals 109 5.6 Kaplan on “Today” and “Yesterday” 113
6 Evans on Understanding Demonstratives 115 6.1 The Fregean Theory of Indexicals 115
6.2 The Point of Indexicality 118
6.3 Evans’s Theory of Sense and Reference for Indexicals 119 6.4 Saying versus Showing 122
6.5 Mock Sense 124 6.6 Empty Names 125 6.7 Evans’s View of Names 126
6.8 Evans on “Today” and “Yesterday” 128 6.9 Character, Content, and Information 130 7 Putnam on Semantic Externalism 133 7.1 Background 133
7.2 Twin Earth and “Water” 134 7.3 Meanings Are Not in the Head 135 7.4 Criticisms of Putnam 143
8 Tarski’s Theory of Truth 147 8.1 Background 147
8.2 Tarski’s Criteria of Acceptability 149 8.3 Aristotle and the Redundancy Theory 151 8.4 Object Language and Metalanguage 155 8.5 How to Derive the T-Sentences 157 8.6 Satisfaction 159
9 Davidson’s Semantics for Natural Language 165 9.1 Background 165
9.2 The Merits of Tarski’s Theory as Applied to Meaning 168 9.3 Applying Tarski’s Theory to Natural Languages 175 9.4 Empirical Truth Theory 181
9.5 Criticisms of Davidson’s Theory 185 10 Grice’s Theory of Speaker Meaning 191 10.1 Background: Speakers and Sentences 191 10.2 Two Types of Meaning 193
10.3 What Is Speaker Meaning? 195 10.4 Consequences and Criticisms 199 Appendix: Kripke’s Puzzle about Belief 203 Notes 211
This book is intended as a student text suitable for undergraduates taking a typical philosophy of language course. But it takes an unusual form: it undertakes to explain ten classic works in the field as clearly as I know how. So it is not the typical general survey of issues, but instead focuses on individual authors. It could also be used as an introductory text for gradu-ate students with no background in philosophy of language. The book is not geared specifically to students with a strong interest and background in analytic philosophy; it aims to include students who may not even be specializing in philosophy. The aim is to make difficult primary material accessible to people who might otherwise struggle with it.
The book consists of ten chapters (plus an appendix), each of which discusses in detail a single classic article. It is intended to be used in con-junction with an anthology of classic texts. The anthology I have used is Philosophy of Language: The Central Topics, edited by Susana Nuccetelli and Gary Seahy (Roman & Littlefield, 2008). It could also be used in conjunc-tion with A. P. Martinich’s The Philosophy of Language (Oxford University Press, 2006), though the selection of articles is somewhat different in the two books. I have found in teaching the subject that students need a thor-ough, clear explanation of the classic texts, which by themselves they find too difficult. Accordingly, the chapters in this book go through the classic texts carefully and systematically. There is no attempt to give a general survey of the literature, achieving complete coverage, and the book does not deal with some of the more recent literature. The instructor would use this book as a supplement to the original articles, sparing him or her a lot of arduous exegesis.
I have generally included some evaluation and criticism of the views and theories being expounded, but this is more to stimulate the student’s
thought (and class discussion) than to contribute to the subject to the sat-isfaction of my professional colleagues. I have always aimed to make the material as simple as possible, without sacrificing accuracy. Everything is explained from the ground up.
The book had an unusual gestation. It began when a student in my class at the University of Miami, Colin Mayer, suggested that it would be useful if there were a book offering the kinds of explanations I provided orally. I agreed but was reluctant to write such a book myself, not wanting to give up the time. He then suggested that he could transcribe the lectures from recordings he had been making of my classes. We decided to give it a try. He diligently set about the work. My task was to go over what he had written and revise it. I did that, finding it necessary to make many revisions (almost every sentence). I did, however, try my best to preserve the original spoken-word form of the lectures, thinking that this might make the material more accessible. In pure writing there is always a tendency to value succinctness and precision (not to mention elegance) over sheer comprehensibility. The end result is a mix of informality and careful formulation. I am grateful to Colin Mayer for undertaking this work, which could not have been easy, and for his original suggestion.
I also had the assistance of Monica Morrison, who went over the raw material of the transcriptions, cleaning up and formatting the text. All the final text, however, is due to me. It was a much tougher job than I bar-gained for, but I think the resulting book should be a boon for students and teachers alike. I first taught philosophy of language some thirty-eight years ago, and this is my distillation of many years of experience teaching the subject. I hope it achieves its aim of conveying a rich body of thought in an accessible form.
Colin McGinn Miami, July 2012
1.1 Background
Before we begin to expound Frege’s views on sense and reference, a few words about the general aims of the philosophy of language might be use-ful. The most general thing we can say is that philosophy of language is concerned with the general nature of meaning. But this is not very helpful to the novice, so let us be more specific. Language is about the world—we use it to communicate about things. So we must ask what this “aboutness” is: what is it and how does it work? That is, how does language manage to hook up with reality? How do we refer to things, and is referring to things all that language does? Further, is referring determined by what is in the mind of the referrer? If not, what else might determine reference? Some parts of language we call “names,” but is everything in language a name? How is a word referring to something connected to a person referring to something? Do expressions like “Tom Jones,” “the father of Shakespeare,” and “that dog” all refer in the same way? In what way do these types of expressions differ in meaning? How is a sentence related to its meaning? Is the meaning the same as the sentence or is it something more abstract? Can’t different sentences express the same meaning? What is a meaning? Are meanings things at all? How is meaning related to truth? Whether what we say is true depends on what we mean, so is meaning deeply connected to truth? How are we to understand the concept of truth? What is the relation-ship between what a sentence means and what a person means in uttering a sentence? These are the questions typical of the philosophy of language. In this book we will consider these questions by reviewing what the great-est philosophers of language have said about them, beginning with perhaps the greatest of them all—Gottlob Frege.
Frege’s article “On Sense and Reference,” published in 1892, is the begin-ning of modern philosophy of language, shaping the field ever since. We shall therefore pay particularly close attention to its content, returning to it in later chapters. But before entering into detailed discussion of the article it is important we gain some familiarity with two concepts: sentences and propositions. A proposition is what is expressed by a sentence: the proposi-tion expressed by a sentence constitutes the meaning of the sentence. Thus it is possible for two different sentences to express the same proposition. Two sentences that are synonymous with one another will express the same proposition. Sentences can differ in their constituent words and be synony-mous, having the same meaning, and thus express the same proposition.
The following two sentences illustrate this point: (1) John is a bachelor.
(2) John is an unmarried male.
The terms “bachelor” and “unmarried male” are synonymous, that is, they have the same meaning; therefore, these two sentences express the same proposition. Hence two different, nonidentical sentences of English can express the same proposition. Two sentences from two different languages can also express the same proposition. Here we have two synonymous sen-tences of different languages, French and English:
(3) La neige est blanche. (4) Snow is white.
Despite the fact that these two sentences are made up of different words in two distinct languages, they still have the same meaning, and thus express the same proposition.
With this understanding of how sentences relate to propositions, we can now ask what a sentence is. A sentence is a collection of shapes, signs, or acoustic signals. Different shapes of letters on paper or acoustic signals in the air can correspond to the same proposition. Propositions, then, are very different from sentences—more abstract than physical. A sentence is the perceptible vehicle that expresses a proposition, and in addition can be uttered by a person. When you utter a sentence like “Snow is white,” you thereby make a statement. A statement is a relationship between three things: the speaker, the sentence, and the proposition. When a person speaks he utters a particular sentence, and in so doing he makes a certain
statement. If a Frenchman utters the sentence “La neige est blanche,” he is stating that snow is white, even though he did not utter that sentence of English. However, since the sentence “La neige est blanche” is synonymous with the English sentence “Snow is white,” the two different sentences express the same proposition. A sentence in one language can be used to report the same proposition expressed by a speaker who made a statement using a different language. Sentences, statements, and propositions are sys-tematically correlated, but they are not the same thing. A sentence is a physical sequence, a statement is a human action, and a proposition is an abstract meaning.
1.2 Identity
In “On Sense and Reference,” Frege is concerned with the relationship between a sentence and the proposition it expresses. He is concerned with discovering answers to the following questions: What exactly is the rela-tionship between a sentence and the proposition that it expresses? When is one proposition the same as another proposition expressed by a differ-ent sdiffer-entence? What constitutes a proposition? What is the meaning of a word? The questions that concern Frege lead one to wonder how a sen-tence, considered as an arrangement of shapes or a sequence of sounds, can be meaningful. That is, we are concerned with sentences and their mean-ings—how they are able to tell us things about the world. What kind of thing is meaning?
Frege’s article discussing these questions is not straightforward—it con-tains certain obscurities that are seldom if ever brought up by commenta-tors, because they are difficult to interpret. In what follows, however, we will bring out and clarify the obscurities in Frege’s article. First, let us exam-ine the opening of “On Sense and Reference”:
Equality gives rise to challenging questions, which are not altogether easy to answer. Is it a relation? A relation between objects, or between names or signs of objects? In my Begriffsschrift, I assumed the latter.1
Though Frege is not explicit about what he means by “equality,” he is using the term in a mathematical sense (not a social one!). The notion of equality can be illustrated with a mathematical statement: “4 × 5 = 20.” Contemporary philosophers use “identity” instead of “equality.” The exam-ple “4 × 5 = 20” would be called an identity statement, asserting that the
number 4 × 5 is identical to the number 20. It is these types of statements that Frege intends when he uses “equality.”
Identity can also apply to other nonmathematical cases. There are a few things about identity that Frege does not mention. Philosophers often distinguish between numerical identity and qualitative identity. Qualitative identity occurs when two things are exactly alike. For example, two cars that come from the same assembly line and have the same color and so on would be said to be qualitatively identical. Frege, however, is primarily interested in numerical identity. Numerical identity is the relationship a thing has to itself. The relation is a very primitive and trivial one: every-thing has the relation of identity to itself. Furthermore, numerical identity does not obtain between one object and another object, even if the two objects are qualitatively identical. For example, two twins do not have the relationship of numerical identity to one another—that relationship exists only between one of the twins and himself.
We can now ponder the following: Is identity a relation? There are all sorts of relations: left of, older than, belonging to a political party, or living in a certain place. Each one of these examples illustrates a nontrivial rela-tion, and therefore tells us something substantial about reality. However, in the case of identity, it has been argued that the relation something has with itself is trivial, and therefore gives no substantial information but provides only a tautology. Frege continues his explanation of identity in the follow-ing passage:
The reasons which seem to favor this are the following: a = a and a = b are obviously statements of differing cognitive value; a = a holds a priori and, according to Kant, is to be labeled analytic, while statements of the form a = b often contain very valuable extensions of our knowledge and cannot always be established a priori. The discovery that the rising sun is not new every morning, but always the same, was one of the most fertile astronomical discoveries. Even today the identification of a small planet or a comet is not always a matter of course.2
In the above Frege is concerned with statements that identify objects. An identity statement using different names will have this form: “a = b” (“a is identical to b”). There is one object that we have referred to with two names, “a” and “b.” For illustration, let “a” be “4 × 5” and “b” be “20.” We have referred to the object, a number, with the numeral “20,” as well as with the expression “4 × 5,” and now we form a corresponding identity statement. Two names that refer to the same thing create a true identity
statement when they are written down and have the symbol “=” between them. On the other hand, if “a” does not denote something identical to what “b” denotes, then we will produce a false identity statement.
The essence of Frege’s point here is that when he wrote the Begriffss-chrift, he thought that when we make a statement like “a = b” the relation expressed by “=” is a relation between the names themselves. In this case, the statement really is about the names “a” and “b” and not the objects to which the names “a” and “b” refer. The names of the objects are separate from the objects that they designate. During his Begriffsschrift days, Frege thought that when he made an identity statement he was concerned with the names that were in that statement. This is because the alternative view seems to lead to absurdity:
Now if we were to regard equality as a relation between that which the names ‘a’ and ‘b’ designate, it would seem that a = b could not differ from a = a (i.e. provided a = b is true). A relation would thereby be expressed of a thing to itself, and indeed one in which each thing stands to itself but to no other thing.3
It would seem that taking “=” to relate objects, not names, would make “a = b” express the same proposition as “a = a.” To illustrate this point more clearly, we can use the example of the two names, “Hesperus” and “Phos-phorous.” Venus is the planet that first comes up in the evening, and used to be called “Hesperus.” “Hesperus” is a proper name denoting Venus; it corresponds to the definite description “the evening star” (we discuss defi-nite descriptions in more detail in chapter 3). In using the name “Hespe-rus” we thus refer to Venus. Understanding advances in modern astronomy that the ancients did not, we know that “Hesperus” refers to Venus. The ancients, however, knew neither the name “Venus,” nor that Venus is a planet and not a star. The same heavenly body is also seen in the morn-ing—when viewed in the morning the ancients called it “Phosphorous, the bringer of light.” Frege points out that the two different acts of naming in fact correspond to the same object. In the example, the two different names “Hesperus” and “Phosphorous” in fact correspond to the same heav-enly body—Venus. It appears at one point in the sky in the evening and at another point in the sky in the morning. The ancients did not know that they were applying two names to the same planet. We can then say that Hesperus is identical to Phosphorous, stating a substantial astronomical discovery. The ancient Babylonians were not able to assert that Hesperus is
identical to Phosphorous, nor did they have any reason to think that. They were ignorant of the identity.
The example of Hesperus and Phosphorous is a general illustration of the following point: there are many cases where a single object has been given a name, and then in another time and another context, given another name, without anyone realizing that the object has been named twice. When the identity is discovered, what the observer has learned, intuitively, is that one thing has two appearances, and therefore that a = b. Therefore, the two differ-ent appearances correspond to the same object, thus producing substantial identity knowledge. In such a case “a = b” forms an informative identity statement. We have expressed a proposition that is not trivial and gives us genuine knowledge about reality. By contrast, an identity statement of the form “a = a” (“Hesperus is Hesperus”) is not an informative proposition—it is merely a tautology. The numerical identity—any numerical identity— can be seen to hold without any empirical observations about the world at all. In the case of Hesperus, if someone merely heard the name “Hespe-rus,” she could know without observation that the statement “Hesperus is Hesperus” is true. It is not possible to do the same with the statement “Hesperus is Phosphorus.” This statement is informative, whereas the pre-vious statement is not. Thus “Hesperus is Phosphorus” has empirical con-tent and is synthetic (from Kant); but “Hesperus is Hesperus” is analytic, or tautological, and is true simply in virtue of its meaning. To sum up, “a = a” expresses an analytic, a priori proposition; “a = b” expresses a synthetic, a posteriori proposition.
In the passages above from “On Sense and Reference,” Frege explains how these two propositions (expressed by “a = a” and “a = b”) are com-pletely different. For example, there could have been a time in the past when people thought that every morning, a different fiery heavenly body appears in the sky. Understanding that that heavenly body—the sun—is the same one that appears in the sky every morning is a substantial empir-ical discovery. We know that it has the same appearance, but sameness in appearance does not entail that it is the very same object. But Frege raises the following question: if equality is a relationship between an object and itself, how could there be any difference between the propositions expressed by “a = b” and “a = a”? Would they not both be saying the same thing, namely, that an object is identical to itself? In other words, wouldn’t “a = b” express the same thing as “a = a”? So isn’t it better to suppose that
identity is really a relation between the names themselves, because they are clearly different?
The sentence “a = a” expresses the proposition that a is identical to itself, and the statement “a is identical to itself” is analytic and a priori. However, there is no way to argue that the statement “a = b” gives us the same propo-sition as “a = a.” As we said, merely knowing a name allows one to say that the object named is identical to itself. Even the ancients knew that Hespe-rus is identical to HespeHespe-rus and that Phosphorous is identical to Phospho-rous. What they did not know is that Hesperus is identical to PhosphoPhospho-rous. Making the assumption that identity is a relation between an object and itself appears to lead to paradox when thinking about identity propositions. Frege therefore thought when writing the Begriffsschrift that identity could not be a relation between an object and itself. To avoid the paradox, the two different sentences must state different propositions—but how?
If identity is a relation between names and not objects, then something different is being stated in the two cases. Thus “a = a” informs us that the name “a” denotes the same thing as the name “a.” On the other hand, “a = b” informs us that the name “a” denotes the same thing as the name “b.” Here we are no longer concerned with the objects themselves but with the names of them. If we are really talking about the names, then we can see how the two sentences produce different propositions. Why? Because “a = a” contains the name “a” and only the name “a,” whereas “a = b” contains the name “a” and the name “b.” The second sentence accordingly refers to something the first one does not refer to, namely the name “b.” It contains the name “b” and in this analysis the sentence refers to that name. This explanation shows how these two sentences can express different proposi-tions: they are about different things, because they are really about names, not objects. The latter proposition is about the names “a” and “b” whereas the former is only about the name “a.” This way of thinking is a natural way to think about identity statements: an identity statement says that one name denotes the same thing as another name—not that one object is identical to itself.
It is not generally the case that sentences containing names are about those names. In fact, sometimes statements have nothing to do with names at all. Consider a statement where someone says, “Hesperus is bright”— here he does not appear to be talking about the name “Hesperus.” Rather, he is talking about a planet, which is Venus, and stating that it is bright.
He is not saying the name “Hesperus” is bright. It is, of course, still possible that the name “Hesperus” is bright (e.g., the name “Hesperus” is written as a neon sign). However, in general, if someone says, “Hesperus is bright,” he is not saying that the name “Hesperus” is bright. We are not generally talk-ing about our words, but ustalk-ing them to talk about somethtalk-ing else.
Notice that there is a huge difference between a name occurring in an ordinary statement where it refers to its bearer, and a name occurring in quotation marks in a statement when it refers to the name. Generally speaking, statements that use a name do not refer to that name. Therefore, making the claim that an identity statement like “Hesperus is identical to Phosphorous” refers to the names is to say something quite revisionary about that sentence. In actuality, the speaker intends for that statement to refer to the planet Venus, and does not intend for that sentence to refer to names of the object at all. This is sometimes called the use–mention distinc-tion: we use the name to mention an object; we don’t use the name to men-tion itself—except when we expressly want to talk about words, not things. Looking back on his view in the Begriffsschrift, Frege now thinks he was wrong to take the view that identity is a relation between names. He illus-trates this point in the following passage:
What is intended to be said by a = b seems to be that the signs or names ‘a’ and ‘b’ designate the same thing, so that those signs themselves would be under discussion; a relation between them would be asserted. But this relation would hold between the names or signs only in so far as they named or designated something. It would be mediated by the connection of each of the two signs with the same designated thing. But this is arbitrary. Nobody can be forbidden to use any arbitrarily producible event or object as a sign for something. In that case the sentence a = b would no longer refer to the subject matter, but only to its mode of designation; we would express no proper knowledge by its means. But in many cases this is just what we want to do.4
Frege had tried to avoid the problem in supposing that identity is a relation between an object and itself because that would make identity proposi-tions trivial. Bringing in the names themselves was intended to solve this problem. The phrase “mode of designation” in the above passage is meant to include the names themselves. But then the statement would refer to a mode of designation, not to a state of affairs in the world. The mode of designation then becomes what he here calls the “subject matter” of the statement. Frege now finds this objectionable, because we would not be expressing what he calls “proper knowledge.” The reader will wonder what
Frege means by the phrase “proper knowledge.” To learn that Hesperus is Phosphorous is to learn something substantial, empirical, and a posteriori. But what proposition have we learned? It is clearly not the proposition that a is identical to a. The proposition instead states that the name “a” denotes the same thing as the name “b,” according to the earlier theory. However, Frege raises the objection that knowing that one name co-denotes with another is not enough to acquire “proper knowledge.” If we suppose that proper knowledge is knowledge that goes beyond a tautology, does the knowledge that “a” co-denotes with “b” go beyond tautology? Contrary to what Frege implies, it can be informative to learn that one name refers to the same thing as another name—very informative. It would be impossible to possess this knowledge ahead of time by just knowing the names inde-pendently. Through knowing the name “Hesperus,” one also knows that Hesperus is identical to Hesperus. However, to discover that in addition to this the name “Hesperus” denotes the same thing as the name “Phos-phorous” is to learn something previously unknown. Effectively, we have learned that two different symbols denote the same thing. Isn’t this “proper knowledge”? It certainly isn’t a tautology.
But Frege is suggesting that learning that Hesperus is Phosphorous is not only learning a linguistic fact but also understanding something significant about reality and the objects in the world. This statement has revealed a genuine empirical fact about two heavenly bodies. Frege’s earlier theory does not capture the fact that the person who comes to know the statement has learned something about the world. It reduces the fact learned to a merely linguistic fact, but the fact learned is not merely linguistic in nature. What one learns is not merely that the names have the same reference, but that two appearances correspond to the same object. The object of one’s knowledge, then, is not the same as that of someone who learns that one name refers to the same thing as another name. That would be learning something about two names, not two appearances. The real knowledge in the sentence “Hesperus is Phosphorus” comes from understanding some-thing empirical about reality, not just somesome-thing about language. Frege’s idea of “proper knowledge” is knowledge of the world, and not merely linguistic knowledge. Thus he rejects the linguistic theory of the content of identity statements, as well as the simple object theory—the theory that identity statements are only about objects, not linguistic items.
1.3 Additional Machinery
To capture what is grasped when someone learns that “a = b” is true, we need another analysis of the proposition expressed by that statement. So far, we have seen two propositions that “a = b” might express:
(5) a = a (the object is identical to itself). (6) “a” denotes the same thing as “b.”
Of course, these two things are both things one can know, but they are not what one learns from the proposition expressed by the sentence “a = b.” It may seem that we have exhausted all the possibilities on this matter. If so, this leads to a huge logical problem, because it means that we cannot even explain such simple identity statements as “2 +2 = 4.” This logical problem is why Frege is faced with the task of trying to account for something that seemingly cannot be accounted for.
The purpose of “On Sense and Reference” is to bring in extra machinery to account for the meaning of “a = b” beyond what we have talked about so far:
If the sign ‘a’ is distinguished from the sign ‘b’ only as object (here, by means of its shape), not as sign (i.e. not by the manner in which it designates something), the cognitive value of a = a becomes essentially equal to that of a = b, provided a = b is true. A difference can arise only if the difference between the signs corresponds to a difference in the mode of presentation of that which is designated.5
Frege here introduces the notion of a “mode of presentation” without much fanfare or explanation, and he contrasts it with a “mode of designa-tion.” For Frege, the mode of presentation is what is essential to the mean-ings of the names “a” and “b,” the modes of designation—where the mode of designation is simply the name considered as a sign. What is needed in this account is a mode of presentation associated with the objects where that mode is not to be identified with the objects themselves or with their names. Frege states:
Let a, b, c be the lines connecting the vertices of a triangle with the midpoints of the opposite sides. The point of intersection of a and b is then the same as the point of intersection of b and c. So we have different designations for the same point, and these names (‘point of intersection of a and b,’ ‘point of intersection of b and c’) likewise indicate the mode of presentation; and hence the statement contains actual knowledge.6
This is a mathematical example, but we can think of other examples, by returning to the evening star and the morning star, that illustrate the point more clearly. The description “the evening star” refers to the same thing as “the morning star,” because those things are just Hesperus and Phospho-rous, respectively. There are many instances of this same possibility, where two descriptions pick out the same object. It need not be obvious to people that these descriptions do refer to the same thing. All Frege wants his read-ers to undread-erstand through the example is that two descriptions can refer to the same thing—the intersection of these two lines and the intersection of these other two lines are the same point.
The reader would naturally infer at this point that the mode of presenta-tion is connected to perceppresenta-tion—it is the mode in which something percep-tually appears, such that two different modes of presentation of something correlate with different perceptual appearances. It is natural to assume that two different ways an object is presented to somebody could produce two entirely different appearances of that object to that person. A famous example is of a mountain where someone approaches it from the east and upon seeing it calls it Atlan. The same explorer approaches the very same mountain from the west and calls it Athla. Of course, our explorer eventu-ally discovers that he approached the same mountain twice, but from dif-ferent perspectives. All of these examples illustrate the same point as Frege’s triangle intersection example.
In addition to a name and its bearer, then, Frege has added the mode of presentation of the bearer to somebody who uses the name. This brings in additional machinery—some mode of presentation of both a and b. Let “a” be associated with the mode of presentation MP1 and let “b” be associ-ated with the mode of presentation MP2. Frege is arguing, in effect, that if “a = b” is true the statement tells us truly that MP1 presents the same object as MP2. Here the modes of presentation have replaced the names. So understood, names are words with associated modes of presentation. Now we see the difference between “a = a” and “a = b.” In “a = a” there is only one mode of presentation, MP1, making that statement trivial. In “a = b” there are two modes of presentation, MP1 and MP2, thereby creating a nontrivial statement. It is nontrivial to find out that a single object has these two different modes of presentation. Hence, Frege’s solution to the problem of identity statements is to bring in modes of presentation as the missing ingredient.
1.4 The Conception of Sense
The last sentence from the passage quoted above illustrates Frege’s view of what he calls “actual knowledge.” We have already discussed how actual knowledge is knowledge of the nonlinguistic world. It is not the names as such that are important in this case, but the references of the names and how they can appear or be “presented.” He continues:
It is natural, now, to think of there being connected with a sign (name, combina-tion of words, letter), besides that to which the sign refers, which may be called the reference of the sign, also what I should like to call the sense of the sign, wherein the mode of presentation is contained. In our example, accordingly, the reference of the expressions ‘the point of intersection of a and b’ and ‘the point of intersection of b and c’ would be the same, but not their senses. The reference of ‘evening star’ would be the same as that of ‘morning star,’ but not the sense.7
In addition to the term “mode of presentation,” Frege has now introduced another piece of theoretical machinery, the “sense.” He has so far explained the sense as connected to the mode of presentation of the reference. Thus in “a = b” the names “a” and “b” have the same reference but not the same sense. To account for the proposition expressed by a sentence it is not enough to look at the sentence itself or at the reference of the words in the sentence. To account for the proposition expressed by a sentence, another level of semantic reality must be recognized—that of the sense. So, in addi-tion to the reference of an expression in a language, the expression also has a sense.
At this point Frege has established to his satisfaction that the meaning of a name cannot be explained purely by its reference. Instead, the name must be assigned a particular mode of presentation of its reference, and the mode of presentation of the reference shows the true definition of the name. Although the name refers to an object in the world, the real meaning of the name comes not from what it refers to but from the mode of pre-sentation. Therefore, Frege has shown us that a theory of language cannot have only reference—it must have sense over and above reference.
So far, the word “sense” is merely a label. Frege has introduced this ter-minology so that there is a mechanism to differentiate the various names, since we have shown that it can be neither the reference nor the names themselves that play this role. The sense, then, accounts for the cognitive differences in names. But what is a sense? Frege uses the phrase “mode of
presentation,” and given his example of the triangle, it is natural to suppose that the mode of presentation is a perceptual or psychological notion. Of course, it is possible to see an object from different angles and perspectives and not realize it is the same object you are seeing. The idea of sense can be generalized beyond what we have talked about with the examples of Hesperus and Phosphorous, or Frege’s own example of the triangle. But in our examples and his it seems as though sense has something to do with perceptual perspective—way of seeing. Notice in the previous passage that Frege is not saying that the sense is identical to the mode of presentation; rather, he says that the sense contains the mode of presentation. Strictly speaking, then, Frege has introduced two extra levels of meaning: sense and mode of presentation, where the former “contains” the latter.
Not every expression in language that designates an object would natu-rally be considered a proper name. A proper name is normally considered an ordinary name, such as “Charles Dickens.” However, Frege also includes other expressions under the heading of proper name that are generally not called proper names. For instance, “the president of the United States in 2012” is said by Frege to be a proper name because it designates a particular person, Barack Obama. Usually, such expressions are called definite descrip-tions; however, Frege considers definite descriptions to be proper names. Consequently, he thinks that both proper names and definite descriptions have a sense and reference. In chapter 3, we will see that Bertrand Russell argues that definite descriptions are not proper names at all, and that logi-cally proper names are completely different from definite descriptions. In his essay, however, Frege assumes that proper names and definite descrip-tions are logically the same.
Frege’s main point is that every expression in either of these two catego-ries—ordinary proper names and definite descriptions—has both a sense and a reference. Further, it is the sense that contains informative value for identity statements containing those proper names. Frege outlines this idea in the following passage:
It is clear from the context that by ‘sign’ and ‘name’ I have here understood any des-ignation representing a proper name, which thus has as its reference a definite object (this word taken in the widest range), but not a concept or a relation, which shall be discussed further in another article. The designation of a single object can also con-sist of several words or other signs. For brevity, let every such designation be called a proper name. The sense of a proper name is grasped by everybody who is sufficiently
familiar with the language or totality of designations to which it belongs; but this serves to illuminate only a single aspect of the reference, supposing it to have one. Comprehensive knowledge of the reference is not to be obtained.8
Here Frege attends to the fact that people who understand a language will grasp the senses of the names in that language. Hence the connection between sense and understanding—one who grasps the sense will under-stand the meaning of the names in the language.
A close scrutiny of the paragraph just cited will help us to figure out the exact meaning of the term “sense.” There is a vital clue to the meaning of “sense” when Frege states that the sense is something that “illuminates only a single aspect of the reference.” From this, we can deduce that a sense is akin to a single aspect of an object. For it is natural up until this point for the reader to assume that senses are something like concepts or ideas in people’s minds. However, the above passage illustrates Frege’s rejection of the idea that senses are anything mental. If the sense is an aspect of an object, then it cannot be something in the person’s mind who understands the expression—it is a part of the object, not the individual cognizing it.
Another way of interpreting this “aspect of an object” is viewing the sense as a certain property an object has. For example, one of the proper-ties of the moon is that it is arid. Obviously, objects have many differ-ent properties, and differdiffer-ent expressions can latch on to each one of those properties as distinct from others. The sense, then, consists in latching on to a particular property of the given object. As stated in the above pas-sage, the mode of presentation is an aspect of an object. Those aspects will exist regardless of whether anyone is there to know them, perceive them, or apprehend them; objects have these properties, these aspects, indepen-dently of human minds.
It is important at this point to note a natural interpretation of sense that is flawed. Take the example of the definite description “the president of the United States.” The reference of this definite description is a certain object with various properties. Each of those properties that the object has is (or corresponds to) a potential sense. In the case of this definite description, one of these properties is an actual sense, because we have an expression in our language that expresses that property—“the president of the United States.” That would seem to be the notion of sense that Frege has expressed so far. However, there is a hole in this seemingly natural interpretation. Since we know that the sense serves to illuminate this single aspect of the
reference, is it correct to suppose that the sense is an aspect of the refer-ence? No, because a thing that illuminates an aspect is not identical to that aspect. There is a distinction between the sense, the illuminator, and the thing illuminated, the aspect. The thing illuminated is an aspect of the object, a property. The sense is not identical to the aspect, though it is closely related to it. The purpose of the sense is to illuminate the aspect; it expresses it or contains it. To say that they are identical would be to ignore a vital point in the above passage.
This distinction is a significant one for our purposes—if the sense were identical to the aspect and the aspect is not itself representational, then it follows that the sense is not representational. On the other hand, if the sense illuminates the aspect without being identical to it, then it can be a representational entity. With this interpretation, sense becomes something that represents an aspect of something. It is highly likely that this inter-pretation of sense is the one Frege was going for—sense is something that represents an aspect of an object. If we are trying to analyze an expression like “the president of the United States,” we thus have four levels to exam-ine: (i) the linguistic expression, (ii) the sense that illuminates the aspect, (iii) the aspect illuminated by the sense, and (iv) the reference, an object. In fact, very strictly, we might identify five levels in Frege’s theory, because there is also the notion of a mode of presentation, which is contained in a sense without being identical to a sense, and which serves to present an aspect of the reference. The name expresses the sense, which contains the mode of presentation, which illuminates the aspect, which is possessed by the object of reference.
Several questions arise concerning the possibility of a regress of expla-nation in trying to understand how reference works. If we think of sense as referring to an aspect, then the idea of referring is presupposed by the theory rather than explained. It matters whether or not we think that the sense represents something because representation is a form of reference. We must give a theory of reference to aspects before we can understand ref-erence to objects. If the relationship between the sense and the aspect is one of representation, we may question whether the relationship of reference here is mediated by a further sense that presents the aspect. If the sense and the aspect were related in representation, it would appear that this relation would cause a regress. There is now something that lies between the sense and the aspect—the mode of presentation of the aspect, that is, an aspect
of an aspect. The possibility of regress raises an uncomfortable question for Frege: is the sense to be taken as an aspect or something that represents an aspect? Neither possibility appears satisfactory. If it is neither, then what is it exactly?
We saw in the previous passage that the expression illuminates a single aspect of the reference but it does not illuminate every aspect of the refer-ence. This is crucial to the whole picture Frege is painting, because a given object can have several aspects and two proper names can latch on to these different aspects. Therefore, when they are put together in an identity state-ment, the statement becomes informative. If we knew every aspect of every object, we would not gain information with identity statements, because we would already know everything. For example, we would know that the evening star is the morning star. But because we do not know a given object in all of its aspects we are in a position to be informed of something when we are told that a = b. I can know one thing about an object without know-ing everythknow-ing about it.
1.5 Reference
We should examine the following passage to aid in the discussion of the relationship between signs, senses, and references:
The regular connection between a sign, its sense, and its reference is of such a kind that to the sign there corresponds a definite sense and to that in turn a definite reference, while to a given reference (an object) there does not belong only a single sign. The same sense has different expressions in different languages or even in the same language. To be sure, exceptions to this regular behavior occur. To every ex-pression belonging to a complete totality of signs, there should certainly correspond a definite sense; but natural languages often do not satisfy this condition, and one must be content if the same word has the same sense in the same context. It may perhaps be granted that every grammatically well-formed expression representing a proper name always has a sense. But this is not to say that to the sense there also corresponds a reference.9
The relationship as explained above is rather fluid—the very same sense can be expressed by two different signs, as in the case of synonymy. Synonymy can exist within a language or across different languages. For example, Eng-lish speakers would say “snow” and French speakers would say “neige.” Fur-ther, because of ambiguity it is possible to have one sign that corresponds to two different senses—“bank” could mean a bank of a river or a bank for
money. Ordinary proper names, such as “Bob,” in our language have a simi-lar problem of ambiguity since many people have the same name. The same name has many different senses depending on whom or what it names.
Concerning reference, Frege believes that a single reference can have many senses corresponding to it and can have many signs corresponding to it. However, there cannot be one sense that corresponds to several different things, since a sense uniquely determines its reference. In Frege’s system, the reference does not determine the sense, because there can be many dif-ferent senses for the same reference. In contrast, the sense does determine the reference, because the same sense cannot fix two different references. A sense must always have one specific reference to which it corresponds. Therefore, the determination goes from sense to reference but not con-versely. Furthermore, there is no determination from the sign to the sense. Although every expression should have a definite sense, it is possible for expressions not to have senses. For example, someone could make up words like “fedneep” that are nonsense—they are signs that lack a sense. However, to make a statement with meaning Frege states that the sign should have a sense:
The words ‘the celestial body most distant from the Earth’ have a sense, but it is very doubtful if they also have a reference. The expression ‘the least rapidly convergent series’ has a sense; but it is known to have no reference, since for every given conver-gent series, another converconver-gent, but less rapidly converconver-gent, series can be found. In grasping a sense, one is not certainly assured of a reference.10
The general point may be lost to the reader since Frege’s examples are rather technical. Only astronomers would understand the former example, and mathematicians the latter. The general idea underlying the examples is that you can form definite descriptions that do not refer to anything. Take the following example of a definite description: “the polka dotted president of the United States.” There has never been a polka dotted President of the United States, so descriptions like those do not refer to anything at all. There is a reason why descriptions such as “the polka dotted president of the United States” must have a sense even though they do not have refer-ence. For us to be able to construct meaningful and true statements such as “the polka dotted president of the United States does not exist,” the definite description itself must be meaningful. This is just one example, but there are infinitely many definite descriptions that have sense and are therefore meaningful, but lack reference. Therefore, it is possible to have
sense without reference, and to form proper names that have sense but no reference.
1.6 Ordinary and Extraordinary Use
Frege applies his discussion of sense, signs, and reference to the ordinary use of words in our language, but not only to this:
If words are used in the ordinary way, what one intends to speak of is their reference. It can also happen, however, that one wishes to talk about the words themselves or their sense. This happens, for instance, when the words of another are quoted. One’s own words then first designate words of the other speaker, and only the latter have their usual reference. We then have signs of signs. In writing, the words are in this case enclosed in quotation marks. Accordingly, a word standing between quotation marks must not be taken as having its ordinary reference.11
If words are used in an ordinary way, then in using a word one is intend-ing to speak of the object the word refers to. For example, when someone uses the words “Barack Obama,” he will usually intend to speak of Barack Obama, and therefore Barack Obama is his reference. However, words are not always used in an ordinary way. Therefore, it is not in every case that we are speaking of the reference of a word. It is also possible that one can talk about only the words themselves. Likewise, one can talk about the sense of a word. For example, “the sense of ‘Barack Obama’” refers to the sense of that name, not to its reference. Take caution when parsing these sorts of sentences. For example, if one writes “the sense of Barack Obama” instead of “the sense of ‘Barack Obama’” one has confused the sense of a human being (whatever that may be) in the first case with the sense of a name in the second case. Barack Obama does not have a sense, because he is a per-son, not a piece of language. Quotations give us a device to prevent us from falling into such a logical error. When writing about the sense of an expres-sion as opposed to the reference of an expresexpres-sion, quotation marks can be used to form the appropriate expression. Therefore, when talking about signs and the sense of signs we must be careful about our use of quotation marks so that what we say makes sense.
Further, when reporting what someone else has said, words do not have their usual reference. In this case, the quoted words are signs of signs. Most of the time words are signs of objects, but in the case of quoting the words of another person the quoted words become signs within signs. Therefore,
“‘Barack Obama’” is a sign of a sign. Let us look at two examples to further illustrate these points:
(7) The word man (8) The word “man”
The second example is correctly expressed because the quotation marks show that it is a word that is referred to. In the first example without quota-tion, “man” refers to a certain species or gender, not to the word itself. In spoken language, we can use such techniques as intonation of voice, body language, or say “quote” and “unquote.” Frege thought that ordinary natu-ral language was quite defective in this way and that it should be clearer when one attempts to talk about words themselves and not what they are about.
There are many other places in “On Sense and Reference” where Frege attempts to deal with how words function in normal and abnormal speech. He writes:
In order to speak of the sense of an expression ‘A’ one may simply use the phrase ‘the sense of the expression “A”’. In reported speech one talks about the sense, e.g., of another person’s remarks. It is quite clear that in this way of speaking words do not have their customary reference but designate what is usually their sense. In order to have a short expression, we will say: In reported speech, words are used indirectly or have their indirect reference. We distinguish accordingly the customary from the
in-direct reference of a word; and its customary sense from its inin-direct sense. The inin-direct
reference of a word is accordingly its customary sense. Such exceptions must always be borne in mind if the mode of connection between sign, sense, and reference in particular cases is to be correctly understood.12
Consider someone who says, “John said that Barack Obama is great.” Notice here that “that” has been inserted in the sentence with no quotation marks at all. This example illustrates indirect speech. Someone also could have said, “John said, ‘Barack Obama is great,’” and it would have served much the same purpose. But it may be that John, contrary to the latter statement, is not an English speaker. For example, John could have uttered an Italian sentence, “Barack Obama e meraviglioso” (translation: “Barack Obama is wonderful”). An English speaker would take the Italian words and trans-late them into an English sentence, thus forming a statement of indirect speech. Frege thinks that in indirect speech the expressions that follow a word like “that” do not have their ordinary reference. Instead, these words refer in that context to their ordinary sense not their ordinary reference.
To give you a better sense of what Frege has in mind, let us take an example of someone who utters a sentence containing an expression that has no reference. Suppose John says, “The polka dotted president of the United States is great.” In this case, that statement has no reference, and we have reported the sentence in the direct speech form. However, if we put it into the indirect speech form, then we might be taken to suppose that there is such a thing as a polka dotted president, contrary to our intentions. If the definite description were taken to refer to its normal reference, then that part of the sentence would have no reference at all. Furthermore, if the part of the sentence had no reference, something true could not have been said. To avoid these consequences, Frege thinks that we refer instead to the customary sense of the expression and use it abnormally in that particular context. Since the customary sense exists, there is no part of that sentence that lacks a reference. Paraphrasing the idea into explicit form, what is really being said when someone says “John said that Barack Obama is great” is “John said something expressing the proposition that Barack Obama is great.” It is almost as though the individual who utters these words is talking directly about the sense that someone’s words have and not the reference of what he says. When we are reporting what someone said, the interest does not lie in whether or not what the person said was true or really achieved objective reference. Rather, the interest lies in the content of what the person said, and therefore in the sense of the words he used. In this complex sentence, there is no reference to Barack Obama at all. The only thing that is referred to is the sense of the name “Barack Obama.” This solves the potential puzzle of reporting a thing that a speaker says that may not refer to any real object. So there may not be a reference for “the polka dotted president,” but there is a sense of that expression, and that is what matters in reporting the content of what someone said.
1.7 Further Points on Sense and Reference
It is wrong to suppose that words can be used only to talk about their cus-tomary references. We have seen how it is possible to talk about words, and the sense of words, without talking about the reference of those words. Concerning this point, Frege states the following:
The reference and sense of a sign are to be distinguished from the associated idea. If the reference of a sign is an object perceivable by the senses, my idea of it is an
in-ternal image, arising from memories of sense impressions which I have had and acts, both internal and external, which I have performed. Such an idea is often saturated with feeling; the clarity of its separate parts varies and oscillates. The same sense is not always connected, even in the same man, with the same idea. The idea is subjec-tive: one man’s idea is not that of another. There result, as a matter of course, a vari-ety of differences in the ideas associated with the same sense. A painter, a horseman, and a zoologist will probably connect different ideas with the name ‘Bucephalus’. This constitutes an essential distinction between the idea and the sign’s sense, which may be the common property of many and therefore is not a part of a mode of the individual mind. For one can hardly deny that mankind has a common store of thoughts which is transmitted from one generation to another.13
In this passage, Frege sharply distinguishes between ideas present in peo-ple’s minds and the sense and reference of words. To reiterate a point made above, Frege does not think that the ideas present in people’s minds have anything essentially to do with sense and reference at all. A psychological idea may be necessary for a human being to grasp a sense, but that does not mean that the sense is the same thing as the idea.
First, depending on who you are, a certain word will bring different ideas to mind. For example, an equestrian will have a different idea come to mind when he hears the word “horse” uttered than when a zoologist hears the same word. Frege thinks that the sense of the word “horse” is the same for both of those individuals—the only difference lies in the different men-tal associations each person has for that word. Furthermore, over time an individual can come to have different emotional associations with the same word. In that case, Frege does not think that the sense changes; rather, the mental associations do. Mental associations can change, but the sense will stay the same.
The second reason he gives for making this distinction is that mankind acquires a stock of knowledge, a series of propositions we believe, and we pass those propositions on from generation to generation. Therefore, in a nonpsychological sense, the same thought (or proposition) is transmit-ted from one generation to another. This process concerns something that transcends the individual persons and the minds that are responsible for the transmitting. For example, consider Isaac Newton in the eighteenth century with various thoughts going through his mind. Suddenly, he states that gravity obeys the inverse square law and writes it in his Principia. After this event, everyone who reads Principia acquires that thought, down the ages, until the present day. Knowing such a thing is different from knowing
Newton’s subjective, psychological ideas. Hence, when Frege speaks of thoughts he refers to something that is objective and transcends time— a thought is the objective unchanging sense of a sentence. Thoughts, in Frege’s use, are abstract entities.
Ideas are not the same as senses; rather, they are things that perish when the mind that has them perishes. Ideas are not really shared by people. Senses, however, are shared by people and do not perish with an individual mind. For Frege, senses have the same objectivity and mental independence as references. The sense of the word “gravity” existed back in Newton’s time and we grasp that same sense now. Therefore, many subjective ideas can correspond to the same objective sense. Frege’s general purpose in arguing for senses to be objective is to show the objective basis for mathematics and science in general.
It is important to note that ideas can also be objects of reference. In normal speech, people do not typically talk about ideas. People have ideas all the time, but they do not usually refer to them. For example, if someone says, “It’s raining outside,” she is not saying anything about ideas at all. If she were talking about ideas, she would say something like, “My idea that it is raining outside is well founded.” Just as senses and words can be the objects of reference, so too can ideas be the object of reference.
Frege constructs a complete picture for organizing all of these aspects of language by forming a system of levels—words, ideas, senses, and refer-ences. He illustrates his leveled system with an analogy:
The reference of a proper name is the object itself which we designate by its means; the idea, which we have in that case, is wholly subjective; in between lies the sense, which is indeed no longer subjective like the idea, but is yet not the object itself. The following analogy will perhaps clarify these relationships. Somebody observes the Moon through a telescope. I compare the Moon itself to the reference; it is the object of the observation, mediated by the real image projected by the object on the glass in the interior of the telescope, and by the retinal image of the observer. The former I compare to the sense, the latter is like the idea or experience. The optical image in the telescope is indeed one-sided and dependent upon the standpoint of observa-tion; but it is still objective, inasmuch as it can be used by several observers. At any rate it could be arranged for several to use it simultaneously. But each one would have his own retinal image. On account of the diverse shapes of the observer’s eyes, even a geometrical congruence could hardly be achieved, and an actual coincidence would be out of the question. This analogy might be developed still further, by as-suming A’s retinal image made visible to B; or A might also see his own retinal image in a mirror. In this way we might perhaps show how an idea can itself be taken as an
object, but as such is not for the observer what it directly is for the person having the idea. But to pursue this would take us too far afield.14
There is the telescope, the object observed through the telescope, the opti-cal image on the lens of the telescope, and the retinal image on the eye of the observer. The retinal image is also an optical pattern that is projected through the lens of the eye and passes on to the retina. There appear to be three levels: the object out there, the optical image on the lens, and the retinal image. Frege compares the optical image to the sense, and the idea to the retinal image. The retinal image is different for each individual per-son who looks through the telescope because we all have different retinal structures. However, he thinks that the optical image is the same, even though people observe it with different retinas. Therefore, the sense is an objective thing in the same way that the optical image is an objective thing, and different from the retinal image, which is subjective and depends on an individual’s physiological makeup.
1.8 Problems with Frege’s Theory
In an earlier section, we discussed how Frege explains that “a = b” could not state what he had previously held, namely that the name “a” denotes what the name “b” denotes. He argued that his earlier thoughts on this were incorrect because if the sentence says that “a” denotes what “b” denotes then it is about not the objects those names designate but the names them-selves. His solution to this problem is to bring in the notion of sense, which contains the mode of presentation of the object. Associated with the name “a” and the name “b” there are particular modes of presentation, and this fact accounts for the informative value of “a = b.”
To analyze “a = b” with Frege’s notions of sense and mode of presenta-tion, we can consider a situation where MP1 is associated with the name “a” and MP1 presents what MP2, associated with the name “b,” presents. According to his theory, what makes a sentence such as “a = b” informative is that one mode of presentation presents the same thing as another mode of presentation.
Some readers may wonder why the same objection Frege makes against the name theory could not be raised against his own theory. On the surface, the statement “a = b” appears to be about the objects a and b. However, Frege’s theory is focused not on the objects themselves but on the mode
of presentation of those objects. Common sense would tell us that “a = b” does not seem to be about modes of presentation at all but about objects. For example, few people would think that a statement involving the name “a” (e.g., “a is a planet”) is about a mode of presentation, unless the mode of presentation itself is explicitly under discussion. It is natural to assume that the statement is about an object and that the object is a planet. If names are generally not about modes of presentation, we may wonder how identity statements could be about modes of presentation. The problem is that the subject matter of “a = b” is not the name “a” or the name “b,” nor the mode of presentation of a and the mode of presentation of b, but the objects a and b. At no point are we talking about words or the modes of presentation they allegedly express.
Frege raises no objections to himself in regard to this matter. However, the question is a rather uncomfortable one because it exposes a gaping hole in the theory he proposes in “On Sense and Reference.” If “a = b” is only about objects, then he has regressed to his original problem: “a = b” states that an object is identical to itself. Frege solves the problem of informative value, but the way he solves it seems to raise the same kind of objection he has against the names theory, which we discussed at the beginning of this chapter. The only difference between these two is that one theory deals with purely linguistic knowledge and the other deals with knowledge of modes of presentation. Through the latter theory, Frege has shown us that one mode of presentation can correspond to the same object as another, but that does not allow the identity statement “a = b” to be about the actual objects themselves. There is definitely a challenge here that Frege fails to address, considering that his own theory commits him to something objec-tionable by his own standards.
Philosophers have approached this problem differently. In Tractatus Logico-Philosophicus, Ludwig Wittgenstein claims that these sorts of iden-tity statements are ill formed. In natural language, Wittgenstein argues, we can make such statements, but they express trivial propositions and not substantial propositions. Wittgenstein thought that statements like this must be eliminated from an ideal language because they do not make any sense. However, Frege does not make any objection of that sort—instead he attempts to make a seeming triviality into something substantial. Though Wittgenstein’s solution to this problem is to eliminate that sort of sentence from an ideal language altogether, Frege tries to give a theory of it. He never considers Wittgenstein’s more radical eliminative suggestion.