"The analytic breakdown of , which was first rigorously performed hy Frege, is the unique and essential philosophical move of the analytic tradition." FREGE AND WITTGENSTEIN The Limits of the Analytic Style
















CLEARER WHEN THIS FAILURE IS EXAMINED CRITICALLY. I Gottlob Frege (1848-1925) aimed to formalize the language "The analytic breakdown of science such that the notation by which science ex- pressed itself corresponded to the rigorous objectivity of ultimately fails to achieve a the scientific worldview. Out of mathematics—specifically the of and equality—Frege derived a log- total reformulation.... ical system in which ordinary language is represented by "truth functions," and meaning is represented by equality. Language ultimately resists This novel representation of language as a formal syntacti- cal system purports to account for semantics as well. complete formalization." Frege's formal, objective systematization of language marks the beginning of the analytic tradition.

As pointed out by Edmund Husserl (1859-1938) in The The "conceptual notation"1 is made possible by two parallel Crisis of European Science, the philosophical move that I of ordinary language: (1) the reduction of have called the formal correlation has been and continues ordinary grammatical structure—that is, the — to be critical to the success of the scientific worldview. into subject and predicate, and (2) the breakdown of ordi- Galileo, Descartes, Newton, and others have used the for- nary semantics into sense (Sinn), (Bedeutung), mal correlation to describe shapes and physical bodies and idea. Subsequently, Frege correlated mathematical mathematically. Leibniz even proposed the idea of a uni- functionality with linguistic predication and mathematical versal notation, capable of accommodating everything

equality with linguistic ""—"the circumstance v within one formal system. Therefore, the formal correla- that it [the sentence] is true or false."11 The philosophical tion performed by Frege—although an interesting inter- path by which Frege arrives at his "formal language"1" con- pretation—does not constitute a new kind of philosophical sists generally in these two steps. move. I quite admire the ingenuity of Frege's application of the formal correlation, but I will not further discuss his I will refer to the reduction of ordinary syntax to predication "conceptual notation" and the correlation of argument and performed in parallel with the parsing of ordinary seman- function with subject and predicate, resulting in the "truth tics as the analytic breakdown. I will refer to the correlation function" formulation of language. of linguistic component to logico-mathematical as the formal correlation. The analytic style—as it was origi- The analytic breakdown of language, which was first rigor- nally conceived—fundamentally consisted of these two ously performed by Frege, is the unique and essential philo- philosophical moves. sophical move of the analytic tradition. This move aims to transform language—already a complex syntactical and se- Briefly, the formal correlation consists in ascribing formal mantic system—in such a way as to allow the application of notation and syntax (a formal system) to an informal sys- the formal correlation. tem. This usually involves the mathematization of non- mathematical content, but the formal system applied need Applying Husserl's method of remembering forgotten not be strictly mathematical. Frege's "conceptual notation" philosophical steps, I will trace the moves that Frege made is an example of a formal system that is not strictly mathe- in performing his analytic breakdown. This Husserlian matical, though it conserves the priority of logical relations analysis reveals that the analytic breakdown ultimately fails between symbols.lv to achieve a total reformulation—that language fundamen-

ELEM ENTS SPRING 10 tally resists complete formalization.^ The specific nature Consider a simple sentence: "The boy is German." This is of this failure limits the analytic tradition such that, at most, a grammatical English sentence, for the article ("the"), the it prescribes a philosophical style, which, like Socratic dis- noun ("boy"), the adjective ("German"), and the verb ("is") course, is a useful tool, but far from a strict philosophical perform functions within their linguistic jurisdiction as arti- method. In short, the general utility of the analytic break- cles, nouns, adjectives, and verbs. From the grammatical down for addressing philosophical problems is severely function of each word in the sentence—the syntax—I can constrained by its failure to clarify language to the point tell that the verb involved is being, the boy is the subject where it is sufficiently objective to be formalized. since he "does the being," so to speak, and German is the subjective complement—that which the boy is. II

Language as we know it has both syntax and semantics. In addition to being grammatical, the sentence makes Specifically, the words and phrases we use have both gram- sense because it is reasonable to say, "The boy is German." matical meaning according to their function in correctly Why is this the case? The short answer is that the sentence formed sentences (syntax) and intrinsic meaning (seman- has properly coordinated semantic content. We know what tics). The reduction of grammar to subjection and predica- a boy is, having seen them running around our neighbor- tion concerns the syntax of language, while the parsing into hoods (some of us once were boys ourselves!). In the same Sense (Sinn), Reference (Bedeutung), and more broadly way, we know what it means to be of German origin, and we Idea concerns semantics. know what the act or state of "being" is. Consequently, we know that a boy is subject to any number of states, that the German nationality is one such state, and that "to be" is the


Negation —i- A - A ; -A Conditional A B-+A (implication) 1 B = A ' B Universal quantification Vy: «(y) —&— *00

Existential quantification r — ~\i'—^ * (u) 3y: <&(y) Content identity (equal sign) A = B A = B

FRECE AND WITTGENSTEIN proper verb for expressing a state or characteristic. the sentence, "The boy throws the ball." In order to express Therefore the sentence is reasonable. "The boy throws the ball," in predication syntax, the sen- tence must be reformulated to, "The boy is throwing the We can see from this simple example that although syntax ball." The action of the transitive verb "to throw" is con- and semantics are related, they are two different aspects of verted into a judgment about the boy mediated by "is." In language. This distinction necessitates at least two philo- an important sense, action is converted into a state or char- sophical moves—one addressing syntax and another ad- acteristic, and the subject is converted from an agent per- dressing semantics—in order to prepare ordinary language forming an action into an object undergoing judgment. for formalization. Frege recognized not only the necessity of this "pre-formalization," but specifically that this step The sentence above is, of course, a simple example demon- must result in both a rigorous simplification in grammati- strating the principle of converting grammatical syntax cal syntax and an elimination of intuition from semantics into predication syntax, but Frege dedicates a large portion "to keep the chain of reasoning free of gaps."vn Only such of the chapter entitled "Sense and Meaning" to articulating a step would enable the assimilation of ordinary language the method by which even complex sentences—sentences into conceptual notation. Thus Frege conceived the ana- in which whole phrases contribute to in grammatical syn- lytic breakdown as a syntactical reduction accompanied by a tax—may also be converted into predication syntax. Frege semantic . proposed that the method sketched above can restate a sig- nificant portion, if not all, grammatically syntactical state- Ill ments in predication syntax. The result is that even the In order to bring linguistic syntax down to size, Frege re- most complex sentences can be expressed as a subject and duces the complex grammatical syntax of language to pred- a judgment about that subject, achieving the requisite sim- ication. More specifically, he makes the case that all con- plification of grammatical syntax. crete statements can be reformulated into a subject-predicate structure, wherein the predicate articu- IV lates a "judgment" about the subject mediated by the verb While the syntactical reduction of Frege's analytic break- "to be."vm This judgment can either be true or false de- down is essential, the semantic deconstruction is at once pending on the subject, and this judgment becomes the pri- more difficult and more controversial. As we will see, the mary information communicated by the syntactical struc- success—or failure as I argue—of the analytic breakdown ture. The importance of the verb—particularly with regard depends on the success or failure of the semantic decon- to tense, but also with regard to voice and number—is struction. But let us first trace the deconstruction before downplayed dramatically. Given the large number of verbs analyzing it. in any language, this reduction is stunning. Again, an ex- ample can clarify this critical shift toward predication syn- As stated above, Frege's semantic deconstruction involves tax. parsing the semantic content of linguistic units or ""lx—usually words, but sometimes "several words or It is not so difficult to see how "The boy is German," fits into other signs "x—into two distinct aspects of meaning: Sense predication syntax. The boy comprises the subject, and the (Sinn) and Reference (Bedeutung). He later distinguishes predicate contains a judgment about German-ness related between Sense and Idea, but the critical importance of this to the boy mediated by a form of "to be." But how can a distinction cannot be clarified until the original distinction grammatically syntactical sentence containing a transitive is traced. Therefore to understand Frege's philosophical verb be accommodated by predication syntax? Consider move, we must first examine .

ELEM ENTS SPRING 10 The Sense of a is the part of its meaning "wherein the enced object is relatively defined, it serves perfectly well. mode of presentation is contained."5" This concept is diffi- cult to define precisely, and Frege himself can only illus- V trate it by examples, most prominently that concerning the Thus the meaning of a sign is divided into Sense and names "morning star" and "evening star" for the planet Reference. "The regular connection between a sign, its Venus.x" The Sense of "morning star"—a heavenly body sense, and what it means is of such a kind that to the sign appearing as a star in the early morning—is quite different there corresponds a definite Sense and to that in turn a def- from that of "evening star"—a heavenly body appearing as inite thing meant,"xlv says Frege. Certainly both are re- a star in the evening. In a similar way, the pronouns "I" and quired to obtain "comprehensive knowledge of the thing "me" are both names for myself, but their Sense is distinct: meant, "xv but these two aspects of meaning differ in some "I" acts as a subject in a sentence whereas "me" acts as an important ways. For Frege, the critical between object. Therefore the Sense of "morning star" differs from Sense and Reference is this: Sense is subject to change that of "evening star" as a result of the adjectival modifica- based on the particular sign and its use in context, whereas tion of the mode of presentation; the Sense of "I" differs Reference is unchanging within the of signs referring to from that of "me" as a result of the functional modification a given object. Put another way, a sign with a particular (change in grammatical function in the sentence) of the Sense has only one Reference, but a Reference can have mode of presentation. Even though in both cases the signs many signs, each with a different Sense. I can point to or at represent different names for the same thing, both the two least state the specific Reference of any sign independent of signs for Venus and the two signs for the first-person sin- the context in which that sign appears, and that Reference gular differ in meaning by differing in Sense. never changes. Whether I use "morning star" or "evening star," if you ask me what I mean, presumably I can say, Implicit in our discussion of Sense is the second aspect of "Venus!" or at least point it out in the sky. If the object is the meaning: Reference. Reference is the of signs as same for two signs, then the signs share meaning with re- designators of objects—that is, "any designation ... has as spect to Reference, but this sharing does not affect the sin-

"Sense is subject to change based on the particular sign and its use in context, whereas Reference is unchanging within [its] set of signs...."

its meaning a definite object (this word taken in the widest gularity of the object referenced. There are not two planets range)."X1H The signs "morning star" and "evening star" called Venus because it has two signs that reference it. may differ in their Sense, but because both refer to Venus, the signs are the same in their Reference. Concordantly, In contrast, the meaning of a sign with regard to Sense nec- because both "I" and "me" refer to the first-person singular, essarily changes depending upon the "mode of presenta- the two signs are the same in their Reference. Notably, the tion [i.e. the context]" of the sign. "Evening" is different object of Reference may be either a physical object (Venus) from "morning" by definition; thus, the two signs refer to or a concept (first-person singular). So long as the refer- different times of day. This modal dependence of Sense re-

FRECE AND WITTGENSTEIN quires some interpretation in order to apprehend. In many plays a role in the use and understanding of language. cases, this interpretation—like knowing the difference be- Frege asserts that Idea plays a trivial role in all but highly tween "morning" and "evening"—is relatively easy for a metaphorical forms of language, like poetry.xlx For him, person "sufficiently familiar with the language."XV1 the primary difference between "The boy is German" and "Let us go then, you and I,/ When the evening is spread out This modal knowledge requirement for apprehending Sense against the sky/ Like a patient etherised upon a table"xx is provides a point of entry for intuition and, therefore, for er- that the semantic content of the first sentence is accounted rors in determining the precise meaning of a sign. In other for by Sense and Reference, whereas that of the second re- words, Sense becomes dependent, however slightly, on the quires Idea in addition to Sense and Reference to be under- individual's capacity to interpret the language being used. I stood properly. will not apprehend the Sense of "morning star" and "evening star" if I do not know the definitions (again, in the The conceptual notation cannot be used for language in dictionary sense) of "morning" and "evening." Any pene- which Idea plays a significant role alongside Sense and tration of the subject's inherent linguistic capacity into the Reference in the determination of meaning precisely be- analytic breakdown cannot be tolerated, for this subjectivity cause a high degree of observer dependent assignment of insolubly resists the formal correlation. meaning precludes the objectivity necessary for semantic content to be formalized. In order for the semantic decon- VI struction—and consequently the analytic breakdown—to Frege knew that if the Sense of a sign could be even partially be even partially successful, Frege must relegate observer observer dependent, he would not be able to apply the formal dependent meaning only to certain forms of language. correlation, and his conceptual notation would be under- Were he to affirm Idea as equally determinant compared mined. Therefore, in an attempt to preserve Sense as a gen- with Sense and Reference, or to integrate Idea into Sense, eral, objective concept, he introduced a distinction between the analytic breakdown would fail to render any form of ordi- the modally dependent aspect of meaning (Sense), which nary language amenable to the formal correlation. The seman- remains objective through its grounding in the contextual tic content of all language would contain a fundamentally use of the sign, and the observer dependent aspect of mean- subjective aspect that could not be eliminated. ing (Idea), "an internal image, arising from memories of sense [sensory] impressions . . . both internal and Thus, he insists that there are "three levels of external... [and] imbued with feeling. "xvn difference ... at most the ideas, or the Sense but not the meaning [Reference], or, finally, the meaning [Reference] as In order for his conceptual notation to be applicable to any well" (SM i6i).xxl Sense and Reference, as Frege conceives statements at all in ordinary language, Frege must assert them, are definite aspects of a sign's semantic content. that Idea is not a universally significant aspect of a sign's This definitive, objective nature allows them to be rendered meaning. The decisive move of the semantic deconstruc- in conceptual notation by applying the formal correlation. tion is the insistence upon Idea as a third and categorically He admits that where observer dependent Idea is signifi- distinct aspect of meaning and its subsequent subordina- in the determination of semantic content, the formal tion to Sense and Reference in certain cases.xvm Frege's se- correlation cannot be applied. He contends, however, that mantic deconstruction outright rejects the notion that the in a significant portion of linguistic formulations, Idea has subject's (i.e. language user's) inherent linguistic sensibil- a trivial effect on the semantic content of signs. In this way, ity is, in all instances of language, inextricably linked to Frege implemented the first analytic breakdown of lan- subject's linguistic capacity. He rejects that Idea always guage and laid the foundation for the analytic tradition.

ELEMENTS SPRING 10 VII resemblances" argument—is sufficiently compelling to call into question the analytic breakdown, the original The propositional analysis of language enabled by Frege's philosophical move of the analytic tradition. analytic breakdown is in many ways carried to its logical conclusion in 's (1889-1951) first sem- It is notable that Wittgenstein's musings on this point in inal work, the Tractatus Logico-Philosophicus (1921). Philosophical Investigations appear as an informal series of Wittgenstein fully expounds the assertion that there is a thought experiments and observations, and not a formal ar- distinction between certain issues that philosophy can ad- gument. As a result of this presentation, philosophers dress and others that it cannot. The line is drawn between often get into trouble when attempting to interpret what is articulate—sufficiently objective to be formalized Wittgenstein's work, especially the concept of meaning as and analyzed—and what is inarticulate—too observer de- "." As I see it, the "family resem- pendent to yield to the analytic breakdown. We have just blances"™1 argument is fairly evident, so I aim only to ar- seen the origin of this distinction in the Frege's semantic ticulate and not to interpret. It is necessary, however, to do deconstruction. some "stringing together" in order to clarify the nature of Wittgenstein's criticism of Frege's semantic deconstruc- After publishing the Tractatus Wittgenstein retired from tion. In light of the body of literature on the topic, it is im- philosophy, believing that he had clearly defined this line portant to make clear to the reader my intended use of between what kinds of concepts and issues were "fair Wittgenstein's idea. game" and which could not be addressed. Wittgenstein then served as a schoolmaster in Austria, where he re- VIII mained until 1929, when he returned to Cambridge with a I stated in Section VI that the critical step in Frege's seman- reimagined perspective on the philosophical position that tic deconstruction—the step that allows the complete exe- he had been instrumental in solidifying. The powerful crit- cution of the analytic breakdown—is the separation of ob- icisms he leveled against his analytic contemporaries—par- server dependent meaning (Idea) from both Sense and ticularly against what I have called the semantic decon- Reference. The success of this separation is paramount. I struction—are put forward as collected musings in think that I have sufficiently explained why this is the case Philosophical Investigations (1953). The argument with and why Frege is so concerned with the sequestering of which Wittgenstein challenges the possibility of the seman- Idea to forms of language which he does not aim to formal- tic deconstruction—commonly referred to as the "family ize. It is precisely this situation that Wittgenstein's "family "Wittgenstein fully resemblances" argument questions. The essence of Wittgenstein's criticism is this: instead of expounds the assertion that "producing something common to all that we call lan- guage, I am saying that these phenomena have no one there is a distinction thing in common which makes us use the same word for all—but they are related to one another in many different between certain issues that ways . . . and it is because of this relationship that we call them all 'language.'"™11 He makes three assertions here: philosophy can address and (1) the Reference, not the Sense, is the point of entry for subjectivity, (2) as a result, a given word—or sign according others that it cannot." to Frege's terminology—has no concrete common refer-

FRECE AND WITTGENSTEIN ence, and (3) relatedness based on use (Sense), not common- important, again, is that each word must be used properly ality, is the fundamental feature of language. according to its standard uses (Sense) in a language in order for a valid sentence to be formed. These three ambitious claims are best understood sequen- tially, so first claim first. Frege certainly understood the Let us return to the example "The boy is German." Each of problem of the observer dependent aspect of meaning, but these words has Sense in that they are all used properly, re- he located subjectivity's point of entry in the Sense mean- sulting in an intelligible English sentence. But what is ing of a word—what Wittgenstein calls use. Wittgenstein meant by the word "German"? More specifically, what is thinks that this point of entry is incorrect because—in con- referenced by the word "German" and what actually hap- sideration of how language is actually exercised—the same pens when I conjure that reference? Earlier, "German- word appears in the same way in the same sentence, re- ness" sufficed as the Reference, but "German-ness" is quite gardless of the user. When I say, "The boy is German," and nebulous. Does it mean "of German descent"? or "from the when you say, "The boy is German," we are both using the country "? The same exists with "boy." words "the," "boy," "is," and "German" in the same way. A PHOTOGRAPH OF LUDWIG WITTGENSTEIN, PERHAPS THE

Proper use—being a function of both grammatical syntax MOST INFLUENTIAL PHILOSOPHER OF THE TWENTIETH CENTURY. and proper understanding of the words—cannot be de- pendent on the language user, or there would be no stan- dard grammar and we could use words however we pleased. This is not the case: "German is the boy," is unin- telligible because the speaker of this sentence has used the words improperly. Therefore, in order for any linguistic ex- pression to be intelligible to its speakers, not only must there be proper uses and improper uses of words, but the words composing the expression must conform to stan- dards of proper use. In other words, Sense cannot be per- sonal, or no one would be able to communicate.

If even some words had a subjective Sense, this would con- stitute a private language. Wittgenstein extensively consid- ers the possibility of a private language and comes to the conclusion that it is impossible by virtue of its impractical- ity. I will not elaborate much further on this point, but I think the principle is demonstrated by a simple example. Consider the gibberish a young child will concoct to com- municate with imaginary friends. The child understands this pseudo-language perfectly well (and, presumably, so do his imaginary friends!), but if he were to say, "Gaggle ben- ner gibblemony," instead of, "I like water," I will not have the foggiest idea what he means because I do not have ac- cess to the Sense in which those words are used. What is

ELEM ENTS : : SPRING 10 Does it mean "a small male," "a young male," or "an imma- boundary—for a special purpose,,,xxx narrowing "boy" to ture male"? There does not appear to be any "boundary"50^ "Jim Smith" only narrows boy so far because there is more designating what is referenced by "German" or "boy": "the than one boy named Jim Smith (I know at least two person- of the concept is not closed by a frontier."^ ally). Therefore, a certain subjectivity is inherent to Reference, therefore, is not really concrete at all. Reference and cannot be eliminated without denying criti- cal features of the way in which we actually use language. What is more, not only is meaning with regard to Reference not concrete, it cannot be concrete and specific. Here IX

Wittgenstein uses a helpful example. If I am shown a se- Accepting the subjectivity of Reference "with blurred ries of pictures of leaves and told, "These are leaves," I will edges,"XXX1 Wittgenstein himself asks the key question: "Is obtain a usable definition of "leaf" such that I am competent it only other people whom we cannot tell exactly?',XXX11 Put to identify another, different leaf as "leaf."xxvl How do I do another way, "if the concept ... is uncircumscribed like this? One might say that it is because I have an idea of what that, you don't really know what you mean."'00011 This is ap- "leaf" is, or more clearly, a "schema" of "what is common to parently false, for I certainly know what I mean when I say, all shapes of leaf."xxvn In order for this to be the case, this "The boy is German" even if I cannot specify the exact ref- schema of "leaf" must appear in my mind "not as the shape erence of each word. Were it not the case that I had work- of a particular leaf."50™111 If the "leaf" schema were specifi- ing definitions of these words, I would not be able to use cally representative of a particular leaf, if I saw any other them correctly. It is clear that I know what I mean because leaf I would not be able to identify it as "leaf." This is not correct use implies a correct usable definition. the case because I certainly can identify leaves of many shapes and colors as "leaves," and any language user can do The first question is more interesting and more difficult. this as well. How do other people know what I mean when I properly use words if that proper use is based on a usable definition Furthermore, what is true of "leaf" is true of "boy" and of the word derived from a "blurred edge" Reference. "German," and I see no reason why it could not be true of Wittgenstein employs the concept of "game" to explain this any word's usable definition. And it must be so, for phenomenon in terms of "family resemblance"50™^ be- Reference must be sufficiently non-specific to accommo- tween each person's usable definitions of a word. Chess is date all instances of a word's use—even previously un- different from tennis, and yet they are both "games."xxxv known use. But if behind each word lies an unbounded They are both games not because there is "something com- mental schema of what that word means that is necessary mon to all, but [because] similarities, relationships, and a for proper use of the word, then Reference is inherently ob- whole series of them at that" link chess and tennis.xxxvi In server dependent. This is because "if someone were to passing between games, "many common features drop out, draw a sharp boundary I could not acknowledge it as the and others appear," but what remains are "correspon- one that I too always wanted to draw, or had drawn in my dences with the first group."xxxvn mind.',xxlx

Such is the case with a word. When passing between indi- This "unbounded-ness" may seem odd, but consider the vidual's usable definitions of a word, there is no one thing way we actually use language. We do not have a word for in common, but many correspondences. Where my usable every specific leaf in the world, as would be the case in a lan- definition of "German" might include my friend Matthis guage with concrete Reference. Even efforts to make refer- (who is German), the spoken language ("scheissekopf" ence concrete only go so far. Although "We can draw a could be my favorite word in any language), Faust and

FREGE AND WITTGENSTEIN "The strength and incredible utility of language lies .. .in the very capacity of a word to accommodate richness in meaning."

Goethe, Nietzsche, Berlin, etc. whereas my friend Matthis' mate failure of the semantic deconstruction. The analytic usable definition might include different people, sounds, style in its current conception—emphasizing the use of rig- literature, philosophers, places, etc. which are nonetheless orously clear language and formal logic in argument—has of the categories people, sounds, etc. By these correspon- proven invaluable in considerations of language, aesthet- dences "German" is communicable in any proper use be- ics, science, and even philosophy itself. In addition to his tween Matthis and I, even though we do not have a com- contributions to philosophy, it should not go unnoticed that mon usable definition of "German." Thus the proper modern computation has its roots in Frege's work. In fact, conception of language is not a set of defined Frege himself intended his notation to be a philosophical as Frege asserts (at least in certain areas), but rather "a com- tool. He says as much: "my 'conceptual notation', further plicated network of similarities overlapping and criss- developed... can become a useful tool for philosophers."xl1 crossing."5™™111 The strength and incredible utility of lan- guage lies not in universality, but "in the overlapping of I believe the lesson of the failure of the analytic breakdown many fibres"—in the very capacity of a word to accommo- is this: the task of philosophy is to articulate, clarify, and ex- date richness in meaning.xxxix amine those phenomena that are the case. The task is not, as Frege puts it, "to break the power of the word over the X human mind ... freeing thought from that which only the Wittgenstein's criticism of Frege's conception of Reference nature of the linguistic means of expression attaches to as specific and concrete—"an area" with clear bound- it."xlil It is not generally the case that we experience thought ariesxl—is quite powerful. It reveals that the semantic de- detached from language, although this is certainly true for construction—the critical step in the analytic breakdown of some forms of thought—like prayer. To assume otherwise language into propositions—is executed by means of a cannot lead to clarification of philosophical issues, for one false premise. In doing so, Wittgenstein calls into question is performing operations on artificial constructs that do not any transformation, analysis, and conclusion about lan- exist in "the life world,"xlm as Husserl would say. When guage and about philosophical issues performed on the these constructs become complex and compelling—as a shoulders of the analytic breakdown. As a result, this ap- formal notation encompassing language certainly is—it re- proach to analytic philosophy cannot serve as the basis for quires the clear thinking of a Ludwig Wittgenstein to bring a system able to address a wide range of pressing philo- us back to the world in which we live. sophical issues; it makes assertions about linguistic form and meaning that are demonstrably false. ENDNOTES i. Frege 2000 (104) ii. Frege 2003 (163) I would like to say in conclusion that I do not wish to belit- iii. Frege 2000 (104) tle the astounding intellectual effort displayed by Gottlob iv. Frege 2000 (111) Frege in the formulation of his conceptual notation. Nor v. Frege 2000 (105) vi. Husserl (57-59) am I asserting that his work is useless because of the ulti- vii. Frege 2000 (104)

ELEM ENTS SPRING 10 viii. Frege 2000 (111) Wittengenstein, Ludwig. Philosophical Investigations. Trans. G. ix. Frege 2003 (158) E. M. Anscombe. 3rd ed. Blackwell Publishing, New York: 2001. x. Ibid. xi. Ibid. xii. Ibid. xiii. Ibid. xiv. Frege 2003 (159) xv. Frege 2003 (158) xvi. Ibid. xvii. Frege 2003 (160) xviii. Frege 2003 (161) xix. Frege 2000 (104-105) xx. Eliot (w 1-3) xxi. Frege 2003 (161) xxii. Wittengenstein (67) xxiii. Wittengenstein (65) xxiv. Wittengenstein (69) xxv. Wittengenstein (68) xxvi. Wittengenstein (73) xxvii. Ibid. xxviii. Ibid. xxix. Wittengenstein (76) xxx. Wittengenstein (69) xxxi. Wittengenstein (71) xxxii. Wittengenstein (69) xxxiii. Wittengenstein (70) xxxiv. Wittengenstein (67) xxxv. Wittengenstein (66) xxxvi. Ibid. xxxvii. Ibid. xxxviii. Ibid. xxxix. Wittengenstein (67) xl. Wittengenstein (71) xli. Frege 2000 (106) xlii. Ibid. xliii. Husserl (48-53)

REFERENCES Eliot, T. S. "The Love Song of J. Alfred Prufrock" in The Complete Poems and Plays: igog-1950. Harcourt Brace & Co., New York: 1980.

Frege, Gottlob. "The Conceptual Notation." In The Conceptual Notation and Related Articles, trans. TerrellWard Bynum. 3rd ed. Oxford University Press, New York: 2000.

Frege, Gottlob. "On Sense and Reference." in The Frege Reader, trans. Michael Beaney, 151-171. Blackwell Publishing Ltd., New York: 2003.

Husserl, Edmond. The Crisis of European Sciences and Transcendental Phenomenology. Trans. David Carr. Northwestern University Press, Evanston, II: 1970.