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"The analytic breakdown of language, 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 CHRISTOPHER SHERIDAN THE ANALYTIC TRADITION IN PHILOSOPHY STEMS FROM THE WORK OF GERMAN MATHEMATICIAN AND LOGICIAN GOTTLOB FREGE. BERTRAND RUSSELL BROUGHT FREGE'S PROGRAM TO RENDER LANGUAGE - PARTICULARLY SCIENTIFIC LANGUAGE - IN FORMAL LOGICAL TERMS TO THE FOREFRONTOF PHI LO SOPHY IN THE EARLY TWEN- TIETH CENTURY. THE QUEST TO CLARIFY LANGUAGE AND PARSE OUT GENUINE PHILO- SOPHICAL PROBLEMS REMAINS A CORNERSTONE OF ANALYTIC PHILOSOPHY, BUT IN- VESTIGATIVE PROGRAMS INVOLVING THE BROAD APPLICATION OF FORMAL SYMBOLIC LOGIC TO LANGUAGE HAVE LARGELY BEEN ABANDONED DUE TO THE INFLUENCE OF LUDWIG WITTGENSTEIN'S LATER WORK. THIS ARTICLE IDENTIFIES THE KEY PHILO- SOPHICAL MOVES THAT MUST BE PERFORMED SUCCESSFULLY IN ORDER FOR FREGE'S "CONCEPTUAL NOTATION" AND OTHER SIMILAR SYSTEMS TO ADEQUATELY CAPTURE SYNTAX AND SEMANTICS. THESE MOVES ULTIMATELY FAIL AS A RESULT OF THE NA- TURE OF LINGUISTIC MEANING. THE SHIFT AWAY FROM FORMAL LOGICAL ANALYSIS OF LANGUAGE AND THE EMERGENCE OF THE CURRENT ANALYTIC STYLE BECOMES 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 concepts of function 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 deconstructions of ordinary language: (1) the reduction of have called the formal correlation has been and continues ordinary grammatical structure—that is, the sentence— 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), reference (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 "truth value"—"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 symbols 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 COTTLOB FRECE PROPOSED A SYMBOLIC LANGUAGE FOR EXPRESSING FORMAL LOGIC, SHOWN I N TH E M I DDLE COLU M N. Basic concept Frege's notation Modern notations (A) = 1 Judging h-A, IK A p p(A) = i 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 deconstruction. 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.
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