Carnap's Tractatus Logico-Philosophicus

In recent literature there has been a question as to the extent to which Carnap’s views in the Logical Syntax of Language departs from Wittgenstein’s views in the Tractatus LogicoPhilosophicus [1, 11, 3]. Carnap discusses his relation to Wittgenstein at various points of the Logical Syntax of Language, most notably in §§73-79. There he provides translations of several key propositions of the Tractatus into the so-called formal mode of speech. These propositions can be used to translate other parts of the Tractatus into the formal mode of speech that reveals Carnap’s own idiosyncratic reading of the early Wittgenstein. An investigation of how Carnap’s translation can be extended reveals the key points of Carnap’s view in the Logical Syntax of Language and how wide the gap between himself and Wittgenstein really is. This will be, as Friedman suggests, a “sketch, if you will, a Carnapian reading of the Tractatus [9, pg. 186] The translation1 shows decisively which of those propositions of the Tractatus that can be translated into the formal mode of speech Carnap would agree with and those that he would disagree with. This translation justifies Carnap’s claim that “the position here maintained [Logical Syntax of Language] is in general agreement with his [Wittgenstein’s] but goes beyond it in important respects” [7, §73]. It also makes explicit the respects in which Carnap’s view “goes beyond” Wittgenstein’s. In particular, Carnap admits a plurality of linguistic frameworks: his famous Principle of Tolerance first appears in Logical Syntax of Language. Wittgenstein, in contrast, countenances but one language. This divergence accounts for the differences between Carnap and Wittgenstein that show up in the translation. The question of their disagreement on the formulability of the syntax of a language in that language is, contra Kuusela [11], a red-herring because it follows from a more general disagreement. 1 Imperfect as the choice may be, throughout I will use the word ‘translation’ to refer to the act of restating passages in the Tractatus in the formal mode of speech. I will use ‘interpretation’ to discuss the relation between passages in German and their English interpretation in the Tractatus and less frequently Logical Syntax of Language. 1 2 Before looking at the translation itself several important aspects of Logical Syntax of Language need to be discussed. Carnap draws a distinction between object sentences, quasi-syntactic sentences, and syntactic sentences. Object sentences are sentences that feature names whose designation is straightforwardly a non-linguistic entity. For example, ‘This cat is sitting’ is a sentence about a cat, there is nothing linguistic about the content of the sentence. On the other hand the sentence ‘From a conjunction either conjunct can be inferred’, is a sentence about the rules of language that are adopted. Since for Carnap these rules are all syntactic, this sentence is about the syntax of a language, and so the sentence is called a syntactic sentence. To make these notions clearer and introduce the notion of a quasi-syntactic sentence, let L1 and L2 be two languages. Let L1 be a language that only speaks about some domain of objects, i.e. all the sentences of L1 are object sentences. In L1 there are terms, c, and predicates, E1 , such that the sentence E1 (c) is a sentence of L1 . Suppose that L2 has a term, c′ , and a predicate E2 , such that c′ is a name of the expression, ‘c’, in L2 . We will call L2 a syntax language for L1 . Suppose that we have a third predicate in L2 , E3 , where E3 holds of c when and only when E2 holds of c′ . The sentence, E3 (c), is then called quasi-syntactical. In this case E3 is a property that is “so to speak, disguised as an object-property, but which, according to its meaning, is of a syntactical character” [7, §63]. A quasi-syntactical sentence is one that corresponds to a properly syntactical sentence, in this case the sentence that ascribes the property E2 to a designation of ‘c’, c′ . For example, the sentence, ‘Red is a color’, is quasi-syntactic. This sentence has the same form as ‘Wise is a property’. Properly speaking ‘Red’ is a predicate, and so the correlated syntactic sentence is “Red’ is a color word’. Similarly, the correlated syntactic sentence of ‘Wise is a property’ is “Wise’ is a property word’, or to be more Carnapian, “Wise’ is a predicate’. There are two closely related notions that Carnap draws from the three part distinction between object, quasi-syntactic, and syntactic sentences: the formal and the material modes 3 of speech. Consider again two sentences, E1 (c1 ) and E2 (c2 ). Let the first be a quasisyntactical sentence, and the second be the correlated syntactical sentence. This means that c2 is a designation of the syntactical item ‘c1 ’, and that E2 is a property of an expression in a syntax. There are two cases to consider [7, §64]:(1) E1 (c1 ) means the same as E2 (c2 ), and (2) E1 (c1 ) does not mean the same as E2 (c2 ). In the first case, we know that E1 is also a property of syntactical expressions and that c1 designates itself. The sentence E1 (c1 ) is thus said to be in the autonymous mode of speech. In the second case, we have that E1 designates a property of objects, and the sentence E1 (c1 ) claims that property holds of the object that is designated by c1 . The sentence, E1 (c1 ), is then said to be in the material mode of speech. In contrast with this, the sentence, E2 (c2 ), which is the syntactic correlate of the quasi-syntactical sentence, E1 (c1 ), is said to be in the formal mode of speech. Carnap blames quasi-syntactical sentences, and the material mode of speech generally, for many philosophical problems. But because they can be translated into the formal mode of speech, careful use of the material mode of speech is admissible, and sometimes expedient [7, §80 - 81]. The admissibility of the material mode of speech rests on the ability to translate the quasi-syntactic sentences of one language into proper syntactical sentences in another. In order for this to happen, and so for quasi-syntactic sentences to be meaningful, there must either be more than one language, or the syntax of a language must be formulable in the language itself. Just before Carnap began writing the Logical Syntax of Language, Gödel had discovered that with enough mathematics in a language it was possible to ‘code up’ the syntax of the language in the language [3]. This process is complicated, but the result is that sentence of the language is assigned a number, and then it is possible to describe operations on sentences by manipulating those numbers. Surprisingly, it turns out that the operations done on numbers can actually mirror what happens in the language. For example, let 3 be a number assigned to a sentence. There is a formula of the language, ‘P (x)’, such that 4 P (3) is true in that language if and only if the sentence represented by 3 is provable in that language. This discovery made it possible to discuss alternative syntax, and so alternative languages. As he indicates in his intellectual autobiography, Carnap always had pluralistic leanings towards the forms of language that could be used. As he says, “This neutral attitude toward the various philosophical forms of language, based on the principle that everyone is free to use the language most suited to his purpose, has remained the same throughout my life” [6, pg. 18]. Carnap had never adopted Wittgenstein’s view that there is one proper framework for formulating language. This comes out clearly in the Aufbau where he suggests that one could begin to construct the world from different phenomenalistic bases or materialistic bases [8, §§59 - 63]. It is this attitude that he suggests leads to the Principle of Tolerance [6], and which accounts for the divergence of his philosophical views from Wittgenstein’s. Because Wittgenstein did not recognize the possibility of there being multiple languages in the above sense, he did not recognize that it was possible to express the syntax of language in language [7, 1], though he could have accounted for ‘showing’ something about the structure of language [11]. This gap shows up in the sentences of the Tractatus that are translatable into the formal mode of speech, but that Carnap would say are false. An important point of contention on how far Carnap’s view in the Logical Syntax of Language is from Wittgenstein’s in the Tractatus is where to draw the line between sense and non-sense. Kuusela contends that the differences here are minor, and that Wittgenstein had the tools to do what Carnap had done in the Logical Syntax of Language. The translation suggests otherwise, supporting the claims that Carnap made in §73: There are two points especially on which the view here presented differs from that of Wittgenstein, and specifically from his negative theses. The first of these theses . . . there are no sentences about the forms of sentences . . . Wittgenstein’s second negative thesis states that the logic of science (“philosophy”) cannot be formulated. (For him, this thesis does not coincide 5 with the first, since he does not consider the logic of science and syntax to be identical) . . . [7, §73] The translation will show that the two areas of disagreement between Carnap and Wittgenstein are in how many languages there are, and in what this means for philosophy. Wittgenstein will see these as two separate questions because philosophical questions are non-sense along with many other sorts of sentences having nothing to do with philosophy. Once, however, it is possible to recognize a syntax language, it is obvious that the philosophical questions left over are ones about the syntax of language, these Carnap calls questions in the logic of science. So for Carnap, formulating the syntax of a language makes philosophy possible, and is itself what philosophy is. These two differences for Wittgenstein are one for Carnap. Wittgenstein suggests that philosophy has something to do with looking at language, “All philosophy is “Critique of language” ” [13, 4.0031]. As Kuusela points out, while the sentences about syntax are non-sense, when seen as such and discarded they leave behind some understanding of the structure of language. Correcting a person’s misuse of language is then the role of the philosopher for Wittgenstein [11]. This leads to his claim that “Philosophy is not a theory but an activity” [13, 4.112]. Carnap disagrees, and this may constitute a minor disagreement between the two. What the translation shows is that this disagreement is downstream of a more fundamental disagreement between the two philosophers: that there can be more than one language. The Translation The methodology of the translation is, whenever possible, to establish a syntactic correlate for each word in a proposition, and translate that word uniformly into the formal mode of speech. This will not work for all the lexical items or propositions of the Tractatus. In the first sets of propositions Carnap himself does not provide a uniform translation of words into the formal mode of speech, and there is controversy in the literature on the Tractatus 6 over how to interpret some key words. Later, it becomes necessary to translate propositions as whole entities because of complications that arise in the material mode of speech. One of the propositions that Carnap translates, 1.1, is in the first set of propositions considered. It, along with the other propositions of the set, provide a strong foundation to translate propositions in the ideal way: by establishing canonical translations of the words they are composed of. That such an accurate translation is possible here is not surprising since Carnap suggests that this is where his philosophical views overlap with Wittgenstein’s [7, §73].2 Tractatus Translation 1 The world is everything that is the case. Science is the set of admitted sentences. 1.1∗ The world is the totality of facts, not of Science is a system of sentences, not of things. names. 1.11 The world is determined by the facts, and Science is determined by sentences, and by by these being all the facts. those being all the sentences. 1.12 For the totality of facts determines both The system of sentences determine which what is the case, and also all that is not sentences are admitted and all those that the case. 1.13 The facts in logical space are the world. are not. The set of admitted sentences of a language is science. 1.2 The world divides into facts. Science is composed of sentences. 1.21 Anyone can either be the case or not be Any elementary sentence can either be adthe case, and everything else remain the mitted or not, independently of all the same. other elementary sentences. As bizarre as it may seem to translate ‘world’ as ‘science’ or ‘fact’ as ‘sentence’, it is fruitful to recognize that this is how Carnap would have read the Tractatus. Until the 2An asterisk (∗ ) marks the propositions translated by Carnap himself. All other translations are mine. 7 later parts of the translation, it is possible to translate each proposition word by word. Furthermore, these translated propositions together form a cohesive whole despite the prima facie awkwardness of Carnap’s interpretation. The first issue of the translation is to find a syntactical correlate for Wittgenstein’s phrase ‘is the case’. A natural first pass is to translate this as ‘is true’, but this is not something that is admissible in the formal mode of speech. Carnap says, “ ‘true’ and ‘false’ are not syntactical terms” [7, §82]. Because Logical Syntax of Language was written before Carnap adopted Tarski’s semantic machinery, terms such as ‘truth’, ‘falsity,’ and ‘meaning’, are not syntactic, and so must either be translated into syntactic notions or regarded as useless [12, pg.249]. It is in Introduction to Semantics that Carnap breaks from his syntactic approach to language, and adopts the use of semantic notions, including ‘truth’ and ‘falsity’. These terms, though, are not available to the Carnap of the Logical Syntax of Language. There does not seem to be a consistent phrase that Carnap uses to translate such notions into the formal mode of speech. At various points, he describes primitive sentences as being ‘laid down’, [7, §48], and at some points goes so far as to say that they are true [7, pg. 29]. other times he says that certain sentences are ‘taken as true’ [7, pg. 80], and some ‘have the character of hypotheses’ [7, pg. 318]. These uses are particular to different forms of sentences, and different things that are done with them in a given language. In order to capture what is done to a sentence when it is ‘assumed as true’ or ‘acknowledged’ [7, pg. 180], as well as what is done with the consequences of that sentence, the term ‘admitted’ is used. When a sentence is added to a language, or a law of transformation laid down, etc. it has been admitted.3 The second problem is due to Carnap’s translation of ‘fact’ as ‘sentence’ in 1.1. Since Carnap drew more distinctions than Wittgenstein did, it is possible to be more precise in the translation. This means translating ‘fact’ one way in one context, and in another way 3In several places Carnap does use the word ‘admitted’ in a similar way [7, pg. 124, pg. 279, pg. 321], though more often he uses it to discuss what operators are in the language. 8 in another. In particular, the translation of 1.21 is not uniform, if the ‘Anyone’ in this proposition refers to the ‘facts’ of the previous proposition. Translating the reference to a fact uniformly, however, makes proposition 1.21 clearly false: If a sentence of the form ϕ ∧ ¬ϕ, were admitted to classical logic, then every sentence would have to be admitted. It cannot be that any sentence can be admitted independently of the others. For the sake of charity in Wittgenstein interpretation the reference to facts in 1.21 cannot be translated as ‘sentence’. The property that is suggested here is that the facts are independent of one another, making a more appropriate translation one that uses ‘elementary sentence’. An elementary sentence is one which does not have any other sentences as parts [7, pg. 195]. Elementary sentences are what are commonly called atomic sentences. Tractatus 2 Translation What is the case, the fact, is the existence Which sentences are admitted is deterof atomic facts. mined by the admitted primitive sentences. 2.01∗ An atomic fact is a combination of objects A (elementary) sentence is a series of sym(entities, things) 2.011 bols. It is essential to a thing that it can be a Any symbol, constituent part of an atomic fact. nA i, can be combined with k other symbols and a predicate, n+1 Pr k , to form a elementary sentence, n+1 Pr k ( nA 1 , nA 2 , . . . , nA i , . . . , nA k ) 2.0123∗ If I know an object, then I also know all If the genus of a symbol is given, then all the possibilities of its occurrence in atomic the possibilities of its occurrence in (elefacts. mentary) sentences are given. A translation that takes into account both Carnap’s translation and what Wittgenstein says requires that ‘atomic fact’ not be translated uniformly. The conflict is between giving a translation of proposition 2 that Carnap would agree to, and being faithful to Wittgenstein 9 interpretation in understanding the distinction between ‘fact’ (Tatsache) and ‘atomic fact’ (Sachverhalt). For Carnap a primitive sentence is one which is admitted to a system either as an axiom, or ‘formulated as hypotheses’ [7, pg. 318]. The elementary sentences can all be primitive sentences, but a primitive sentence need not be elementary. Translating ‘atomic fact’ as primitive sentence’ in 2 is the most faithful to both Carnap and Wittgenstein. There are two plausible alternate translations: the first retains Carnap’s translation as ‘sentence’, the second remains consistent with the standard interpretation of Wittgenstein by using ‘elementary sentence’. On the first option, what Wittgenstein says is trivial, what sentences are admitted determines what sentences are admitted. On the second option, Carnap would have to say that strictly speaking, proposition 2 was false. Primitive sentences that are not elementary could determine which sentences are admitted into the system. If it turns out that the better translation of ‘atomic fact’ in proposition 2 is ‘elementary sentence’. Carnap’s disagreement with this may point to a deeper disagreement between the two. Wittgenstein has the set of true atomic facts determining what sentences are true in the rest of the language because it is the atomic facts that do the work of tying the language to the world, while the truth-value of other sentences, even quantified ones, depends on the truth-value of atomics [10, pg. 8]. That Carnap disagrees with this could be indicative of the fact that he had moved beyond a view of meaning that depended on a word-world tie, such as a picturing relation, to one that depends on the rules of inference and admitted primitive sentences, which need not be atomic. He discusses his move to this view of meaning in the preface: Up to now, in constructing a language, the procedure has usually been, first to assign a meaning to the fundamental mathematico-logico symbols, and then to consider what sentences and inferences are seen to be logically correct in accordance with this meaning . . . The connection will only become clear when approached from the opposite direction: let any postulates and any rules of inference be chosen arbitrarily; then this choice, whatever it 10 may be, will determine what meaning is to be assigned to the fundamental logical symbols [7, pg. xv] If the better reading of ‘atomic fact’ in proposition 2 is ‘elementary sentence’, this quote rejects the motivation to think that 2 is true. The sentences which are admitted as primitive need not be elementary because they need not have a meaning independent of the language. Friedman suggests that this is a place of disagreement between Carnap and Wittgenstein that is due to Carnap’s change in view on meaning [9, pg. 188]. This change in Carnap’s view on mean can be seen as motivated by his recognition that there are multiple legitimate forms of language, as opposed to Wittgenstein’s recognition that there is only one. Because this difference in their philosophies is clearer in Carnap’s translation of ‘picture’ below, the tentatively selected translation of ‘atomic fact’ in 2 is ‘primitive sentence’. This translation tries to preserve as much agreement between the two philosophers as possible. What this does indicate is that if a uniform translation is to be preferred, proposition 2 may be a symptom of a deeper disagreement that manifests itself later on in the translation. The second place that the translation of this set of propositions departs from the one given by Carnap is in the translation of ‘atomic fact’ as ‘elementary sentence’ in places other than proposition 2. This translation is more faithful to Wittgenstein. The interpretation of ‘atomic fact’ (Sachverhalt) and ‘fact’ (Tatsache) is a matter of dispute. Ayer [4, pg. 17], and Pears and McGuinness [10, pg. 9], suggest that the interpretation of ‘Sachverhalt’ should be ‘state of affairs’. Black suggests that ‘atomic fact’ is a better interpretation, “Here and nearly always, I prefer ‘atomic fact” ’ [5, pg. 39]. Hunnings also points out that in a note to Russell in 1919 Wittgenstein says that ‘Sachverhalt’ correspond to elementary sentences [10, pg. 7]. That Wittgenstein said this is enough to indicate that the best translation of ‘atomic fact’ is ‘elementary sentence’.4 4In the quote from his letter to Russell Wittgenstein uses the word ‘elementar Satz ’ [10, pg. 7], the same word that Carnap uses for elementary sentence in Logical Syntax of Language. 11 While Carnap’s translation is not uniform, translating both ‘fact’ and ‘atomic fact’ as ‘sentence’. He did this to make a point about the usefulness of translating quasi-syntactic sentences into the formal mode of speech: there is a tension between 1.1 and 2.1 when considered only in the material mode of speech. 1.1 suggests that facts are fundamental, as opposed to things; while 2.01 suggests that facts are composed of things, suggesting that perhaps things are fundamental. The thought here being that if a fundamental thing, such as an atom, were to have parts, we would likely consider its parts to be fundamental, and not the thing itself.5 Carnap’s translation of these two propositions into the formal mode of speech does away with this tension. Thus, not only is his translation charitable to Wittgenstein, but it also does exactly what the formal mode of speech is supposed to do, rid ordinary language of ambiguities that cause such tensions. Wittgenstein was talking about two types of fundamentality in propositions 1.1 and 2.01. This explains Carnap’s translation of both ‘fact’ and ‘atomic fact’ as ‘sentence’. He is here bringing out that there is a tension in what Wittgenstein is saying, and showing how that tension is dispelled in the formal mode. Had Carnap translated ‘fact’ as ‘sentence’ and ‘atomic fact’ as ‘elementary sentence’ the tension would have been less striking. The next set of propositions contains the translations for the Tractarian notions of ‘picture’ and ‘thought’ in the context that has been established above. Both these notions have uniform syntactical correlates in the formal mode of speech: 5This may not be a genuine tension, but it might be enough to motivate Carnap to show off how his translation into the formal mode of speech could clear up potential confusion. 12 Tractatus 2.1 Translation We make to ourselves pictures of facts A sentence has consequences. (Tatsachen). 2.11 The picture presents the facts in logical The consequences of a sentence are also space, the existence and non-existence of sentences of the language, among them are atomic facts. primitive sentences to be admitted, or denied admittance. 2.12 The picture is a model of realty. A set of consequences will impose constraints on which primitive sentences can be admitted. 3 The logical picture of the facts is the The set of all non-analytic consequences of thought. a sentence is its content. 3.01 The totality of true thoughts is a picture The content of all admitted sentences are of the world. the consequences of science. Picturing is an important relation for Wittgenstein. It is responsible for the link between language and the world. In his introduction to the Tractatus Russell says “the picture itself is a fact. The fact that things have certain relations to each other is represented by the fact that in the picture its elements have a certain relation to one another” [13, pg. xvii]. This shows that the picture of the a fact is a way of displaying the role that the sentence corresponding to the fact plays in the language. The picture of a fact will also display information about what atomic facts hold and which do not. It will show the ways that atomic facts are related to one another. Carnap does not think that the link between language and the world is something that can be captured syntactically. The correlated notion is ‘consequence’. The consequences of a sentence play a similarly foundational role in language, “From the systematic standpoint, however, it [consequence] is the beginning of all syntax. If for any language, the term ‘consequence’ is established, then everything that 13 is to be said concerning the logical connections within the language is thereby determined” [7, pg. 168]. The notion of consequence here also pins down the relation that a sentence has to the elementary sentences that compose it. Consider the sentence p ∧ q. Among the consequences of this sentence are p and p ≡ q. These serve show how the sentence p ∧ q fits into the language should it be admitted. Proposition 3 links up the notion of picturing with the content of a sentence. In the Tractatus a picture is what gives content to a sentence, and ultimately, this boils down to which atomic facts are pictured. As the translation of that proposition suggests, consequence plays the role in Logical Syntax of Language of determining the meaning of a sentence. This is because Carnap has “approached [the issue] from the opposite direction” [7, pg. xv]. Instead of letting the world determine the content of sentence by means of a picturing relation grounded in elementary sentences, Carnap’s view is that once we have selected postulates and inference rules “this choice, whatever it may be, will determine what meaning is to be assigned to the fundamental logical symbols” [7, pg. xv]. This conception of meaning is closely related to Carnap’s famous Principle of Tolerance: “It is not our business to set up prohibitions, but to arrive at conventions” [7, pg. 51]. Having a picturing relation give content of to a sentence ultimately in terms of a tie between language and a language independent world, forces there to only be one sort of inference, the one that goes from sentences that picture facts that exist to sentences that picture facts that exist. However, once the picturing relation is abandoned, there is no such rigid notion of inference, and no reason that one conception of inference is to be privileged as the right one. Underlying all of this is Carnap’s belief that there can be more than one language. Importantly, Carnap would not deny any of the propositions above. This is because they are only definitional. The results of the claim that there can be more than one language do not show up until later propositions. 14 Tractatus Translation 4 The thought is the significant proposition. A sentence with content is not a pseudosentence Proposition 4 shows both Carnap and Wittgenstein’s commitment to being precise about what sentences do actually have content. Sentences that are meaningless Carnap calls pseudo-sentences. In particular, it connects being a pseudo-sentence up with a well-defined notion, content. This makes it possible to give a rigorous account of what sentences are meaningful. The next set of propositions is the first place where there is an explicit disagreement between Carnap and Wittgenstein. There are sentences that have formal mode correlates that Carnap would say are false. Carnap cites this as a significant point of disagreement between himself and Wittgenstein. One point of the Tractatus is that a language cannot express its own syntax. It can only show what is the case, it cannot talk of its own structure. Carnap pointed out that it was possible for a language to capture its own syntax, or for one language to capture the syntax of another language. Tractatus Translation 3.332 No proposition can say anything about it- For any sentence, S, there is no sentence self, because the propositional sign cannot S(S). be contained in itself. 15 4.121 Propositions cannot represent the logical It is contradictory for a sentence to have form: this mirrors itself in the proposi- a name designating a sentence as a part: tions. That which mirrors itself in lan- this is syntax. Syntax is not an object of guage, language cannot represent. That lanuage. The structure of language is not which expresses itself in language, we can- an object of lagnauge. Syntax is not in not express by language. The propositions language. It is the structure of langauge. show the logical form of reality. They exhibit it. 4.1211 . . . If two propositions contradict one an- Whether two sentences are L-contravalid other, this is shown by their structure; depends solely upon the rules of applicasimilarly if one follows from one another, tion of the language (the syntax); whether etc. one sentence is a consequence of another depends solely upon the rules of application of the language (the syntax). 4.1212 What can be shown cannot be said. If S is a sentence about the syntax of a language, then it is a pseudo-sentence. Carnap himself cites 4.121 as one of the points of disagreement between himself and Wittgenstein [7, §73]. While it is clear that he would have disagreed with three of the four propositions above, the crucial part here is that Carnap disagrees with Wittgenstein in two ways: First, Carnap thinks that these sentences are meaningful, since they can be translated into the formal mode of speech. Second, once the content of these sentences is made apparent, they are false. So a crucial distinction between Carnap and Wittgenstein is that he can express the disagreement that he has with Wittgenstein. Wittgenstein denies the possibility of doing this. That these sentences have correlates in the formal mode of speech shows that the dispute can be made explicit, and shows exactly what each philosopher takes the dispute to be about. 16 Kuusela takes this to be a superficial difference between Carnap and Wittgenstein, “Hence the difference in their views boils down to just this: while Wittgenstein doesn’t acknowledge the possibility of expressing logico-syntactic determinations by means of sentences, Carnap does” [11, pg. 16]. Wittgenstein can say that his discussion of language in the Tractatus is a way of ‘fixing’ misunderstandings of language. As Kuusela points out the best that a philosopher can do is to show that people under the spell of philosophical language are not making sense by correcting their logical form. These sentences, once they are discarded, will leave the person who was mistaken with an understanding of the logical form of propositions, but not the sentences themselves, which are neither true nor false [11, pg. 9]. For Carnap syntactical sentences are either true or false. They have content, and so the study of the syntax of language becomes a genuine field of investigation. Contrary to Wittgenstein, on Carnap’s view there is room for a study of syntax, and so room for philosophy. The translation brings this out clearly. While Wittgenstein may think that these sentences are useful, he does not think that they have a truth value, Carnap does. 4.1211 and 4.1212 are a preview of what Wittgenstein will say about the entire Tractatus with propositions 6.54 and 7. 4.1212 is assurance that the previous proposition that was helpful in seeing something about language was not itself a part of language, and so not meaningful. [5, pg. 190]. At this point, the propositions are no longer about languages, or how languages are formulated, they are about the limits of a language. These are things that Wittgenstein himself considers to be unsayable as in 4.1212. Thus, a translation that is as precise as earlier is impossible. The most that can be gotten out of this is a rough estimation of what Wittgenstein was trying to say. This should, however, be of no surprise. What this shows is the extent to which Carnap and Wittgenstein diverge on what can be said. The more of a proposition that cannot be accurately translated into the formal mode of speech the more that Carnap agrees it lacks content. A salient feature of the formal mode of speech 17 is that if a proper syntactic correlate cannot be found for each word, then the sentence as a whole will have to be translated [7, §64]. So much of the remaining sentences, which Carnap may think are metaphysical, will not have translations that preserve each word in the proposition. Tractatus Translation 4.111 Philosophy is not one of the natural sci- The logic of science does not have synences. thetic sentences. 4.112 The object of philosophy is the logical clar- The object of the logic of science is the ification of thoughts. Philosophy is not a clarification of content (of the language of theory but an activity. A philosophical science). No sentence of the logic of sciwork consists essentially of elucidations. ence is itself in this language. The logic of ... science cannot be expressed in the formal mode of speech. Any question that concerns the logical analysis of a scientific concept a question in the ‘logic of science’. These are questions concerning the proper logical framework for scientific investigation. Carnap proposes that what has traditionally been called ‘philosophy’ be replaced by the logic of science [7, §281]. On Carnap’s reinterpretation of philosophy, philosophical questions, questions in the logic of science, are meaningful and important areas of inquiry. Wittgenstein does not think that philosophical sentences are have meaning. This alone distinguishes philosophy from the natural sciences, since the sentences of natural science are meaningful sentences. For Carnap, any sentence with content is synthetic. So, in particular, a language that is useful for the natural sciences would be one that contained synthetic sentences. Carnap, however, distinguishes between two types of syntax: descriptive syntax and pure syntax. Pure syntax will contain only analytic sentences, and “is concerned with 18 the possible arrangements, without reference either to the nature of the things which constitute the various elements [of a syntax]” [7, §2]. Descriptive syntax on the other hand can have synthetic sentences. In particular, it will have sentences concerning the position of ink on a page, or sentences like ‘the fifth sentence on page n, contradicts the third sentence on page m’. 4.111 suggests that either Wittgenstein would not have accepted such a syntax, or he would not have called it syntax. Carnap would, however, say that pure syntax was not one of the natural sciences since it could be done without any synthetic sentences, while descriptive syntax could be a sort of scientific study. Carnap denies 4.112 though, at least when it is translated into the formal mode of speech. In particular, Carnap does not think that the logic of science cannot be expressed in the formal mode of speech. The goal of Logical Syntax of Language is to do precisely that, “The book itself makes an attempt to provide, in the form of an exact syntactical method, the necessary tools for working out the problems of the logic of science” [7, pg. xiii]. Their disagreement here, though, should not force us to overlook the fact that Carnap would agree that the object of philosophy was some sort of linguistic analysis. Wittgenstein says, “All philosophy is “Critique of language” ” [13, 4.0031]. Carnap thinks of philosophy, if it is possible to do it at all, as linguistic analysis, “the logic of science takes the place of the inextricable tangle of philosophical problems which is known as philosophy” [7, §72]. It is this agreement that leads Kuusela to claim that Wittgenstein and Carnap are not so far apart in their views. They both think that philosophy can be done by analyzing the forms of language that are available. But Wittgenstein thinks this can only be done using ‘elucidations’. An elucidation being the type of thing that cannot be spoken about, but only shown to be the case [5, pg. 115]. On this point Carnap says such a view is wanting, it is ‘unsatisfactory’ [7, §73]. So while Wittgenstein may be able to do philosophy, there 19 will be no formulation of syntax, and so no genuine study of philosophy, since as Carnap reads him, no sentence of philosophy can be in the same language one uses for science.6 Tractatus 5 Translation Propositions are truth-functions of ele- Elementary sentences, nsa 1, nsa 2, . . . , nsa m, can be combined with an m place senten- mentary propositions. tial junction, Vkm , to form a sentence, the characteristic of which is a function of the product of the ranges for Vkn . 5.54 In the general propositional form, proposi- For any two sentences, S1 and S2 , if S1 tions occur in a proposition only as bases occurs in S2 , then there is a sentential junction Vk, such that S2 is Vk(S1 ). of the truth operations. The general form of a truth-function is: Any sentence of a language is a 0sa or a 6 [p, ξ, N (ξ)]. This is the general form of a n+1N k( nsa 1, nsa 2, . . . , nsa k )[5, pg. 311-312]. proposition. 5.5301∗ Identity is not a relation between objects. The symbol of identity is not a descriptive symbol. 5.6 The limits of my language mean the limits The language determines science. of my world. Proposition 5 explains the possibility of forming sentences by means of truth-functional connectives. Proposition 5.54, explains that this is the only way for one sentence to have another as a part. This proposition, in particular rules out non-extensional sentences, such as ‘A is impossible’ and ‘Charles says A’ [7, §67], since the truth value of each sentence is not a function of the truth of ‘A’. Proposition 6 is Wittgenstein’s particular way of expressing that all sentences are built according to a recursive operation, N , on sentences. In particular, the notation means take from the set of sentences, p, some subset, ξ, and 6Here 0 sa is the expression for an elementary sentence, and for a sentential junction. n+1 N k () is Wittgenstein’s general expression 20 form a negated conjunction of each of the members of ξ, N (ξ), and repeat this process some number of times. [2, 5, pgs.132-133, pg. 311]. In this way a language is generated from a set of atomic sentences. Carnap discusses his views on extensionality in contrast to Wittgenstein in §67, where he mentions propositions 5, 5.54, and 6. He points to these as expressing the claim that language is extensional. While he admits that he agrees with this is spirit, as it stands it is ‘incomplete’ [7, pg. 245] since there are languages which are not extensional. The sentences which are not extensional, can be translated into extensional sentences because they are quasi-syntactical. Contrary to 5.54, once properly stated they contain designations of the some of the sentences that appear as sub-sentences. The possibility of such a translation allows Carnap to present the ‘complete’ claim, which is that the language of science could be formulated extensionally. Though he is careful to point out that this is “presented here only as a supposition” [7, §67]. Because Carnap thinks that intensional sentences are quasi-syntactical, he can say that many of them are meaningful, an option not open to Wittgenstein [13, 4.124]. Carnap remarks that Wittgenstein does not recognize that these sentences can be meaningful because he didn’t recognize the possibility of there being more than one language. Once this is admitted, it is possible to have sentences that take names of other sentences as objects, and so to give a syntactic analysis of sentences involving predicates such as ‘is possible’, or ‘it is believed’. Similarly, Wittgenstein doesn’t recognize that identity claims can be meaningful, which he points out in 5.5301 [5, pg. 290]. This is because the identity relation cannot say that two objects, a and b, are one [13, 5.5303]. With this in mind, Carnap translates this proposition as claiming that the identity is not descriptive in the above sense, it is not about objects, but designations of objects. This, for Carnap, is not problematic. But for the reasons discussed above, Wittgenstein cannot think any such relation is meaningful. 21 5.6 is where this discussion of syntax languages comes to light. For Wittgenstein science will be constrained by the one language [1, pg. 150]. Once Carnap develops the tools in Logical Syntax of Language, it is possible to broaden the notions of what science can be. A notion that is unavailable in one language, such as syntax, may be expressible in another. The formal mode of speech presupposes this flexibility, while it also “makes it quite clear that the language intended must be stated” [7, §78]. Without noting that there is a formal mode of speech with which to discuss the forms of language, there can be an “erroneous conception of philosophical sentences as absolute” [7, §78]. Wittgenstein appears to make such absolute claims following 5.6 on the nature of solipsism and the subject. The propositions of the last group are translated as whole sentences, not as functions of the translations of their parts. The translations, however, provide support to Carnap’s claim that 6.54 and 7 are in some sense by-products of 4.121-4.1212. [7, pg. 283] Tractatus Translation 6.54 My propositions are elucidatory in this The sentences of this book have no correway: he who understands me finally rec- lates in the formal mode of speech. ognizes them as senseless, when he has climbed. . . 7 Whereof one cannot speak, thereof one Any quasi-syntactic sentence is a pseudomust be silent. sentence. 4.121 claims that the syntax of a language cannot be part of language. 6.54 is the follows from this claim. If there can be no language about the syntax of language, then there can’t be a formal mode of speech into which the quasi-syntactic sentences of the book are translated. This means that there is no way to understand the sentences as having content. From the translation of 4, this entails that they are pseudo-sentences. Such propositions are not formulable in the language of the Tractatus, and because Wittgenstein thinks this is the only language, there cannot be a language in which they have content. 22 If, as is natural, propositions 6.54 and 7 are read as the climax of the Tractatus, Carnap will disagree with the main thrust of the work. He thinks not only that these propositions do have content, but that because of this they are false. All this is due to there being multiple languages, some of which can formulate the syntax of others. From this account of language Carnap can precisely formulate what a quasi-syntactic sentence is, as well as the material and formal modes of speech. It is also possible to describe alternative languages, and to do so in a rigorous way. The translation gives insight into how Carnap read the Tractatus, and so provides insight both into his own philosophy and the places that he takes himself to depart from the Tractatus. For Wittgenstein what syntactic sentences do is illuminate language so that we can see when we are being misled by it [11]. But we cannot use them to communicate things that are true or false. This makes it is hard to see how we could have an area of research into syntax. It is this that Carnap was after, “. . . the important thing is to develop and exact method of construction of these sentences about senteces. The purpose of the present work is to give a systematic exposition of sch a method, namely, the method of “logical syntax” ” [7, pg. xiii]. This disagreement and its ramifications are made clear in the translation. Carnap thinks that important sentences of the Tractatus are meaningful, e.g. 4.1212, 6.54 and 7. He also thinks that these sentences are false. On Carnap’s view it is possible to have disputes about a language. There are true and false things to say about the syntax of a language, it can be the proper object of study. This is the sense in which his view “goes beyond” Wittgenstein’s. In §73 Carnap says with respect to Wittgenstein’s view that syntax is not formulable, “Such an interpretation of the logic of science is certainly very unsatisfactory” [7]. While Carnap could say that Wittgenstein’s method of elucidation described above is admissible [11], Wittgenstein’s view has not gone far enough. If syntax is to be an object of study, which is what Carnap and others at the time were doing, there have to be true and false sentences about it. 23 Wittgenstein’s view is unsatisfactory in that it makes it impossible to study logic or syntax. Wittgenstein’s belief that language was limited in not being able to formulate a syntax was an important aspect of his philosophy [5, pg. 192]. The translation reveals the connection between the one language thesis and the rest of Carnap’s work. From there being multiple languages, it is possible for there to be a syntax language. But if there is a syntax language, we can explicitly and meaningfully describe the syntax of a language. There is a strong sense in which this leads to all the differences between Carnap and Wittgenstein. Carnap acknowledges this by saying that it is the only difference between himself and Wittgenstein [7, §73]. Though, Wittgenstein would probably recognize two differences: that there were multiple languages, and that philosophy was the syntax of the language of science. Wittgenstein would only not recognize this latter point because he would put philosophy in with all the other nonsense that he has floating around, even though he seems to recognize the importance of critique of language for philosophical claims. However, once it is possible for syntactic sentences to be meaningful, it is obvious that these are the philosophical sentences. So for Carnap there is just one difference, but for Wittgenstein there are two. References [1] A. Angelides, Carnap’s 1934 Objections to Wittgenstein’s Say/Show Distinction, Erkenntnis, 76 (2012). [2] G. Anscombe, An Introduction to Wittgenstein’s Tractatus, Hutchinson University Library, 1959. [3] S. Awodey and A. Carus, From Wittgenstein’s Prison to the Boundless Ocean: Carnap’s Dream of Logical Syntax, in Canap’s Logical Syntax of Language, P. Wagner, ed., Palgrave Macmillan, 2009. [4] A. Ayer, Wittgenstein, Random House, 1985. [5] M. Black, A Companion to Wittgenstein’s Tractatus, Cornell University Press, 1966. [6] R. Carnap, Intellectual autobiography, in The Philosophy of Rudolf Carnap, P. A. Schilpp, ed., Open Court, 1963. [7] , Logical Syntax of Language, Routledge, 2001. 24 [8] R. Carnap, The Logical Structure of the World, Open Court Classics, 2005. [9] M. Friedman, Reconsidering Logical Positivism, Cambridge University Press, 1999. [10] G. Hunnings, The World and Language in Wittgenstein’s Philosophy, State University of New York Press, 1988. [11] O. Kuusela, Carnap and the Tractatus’ Philosophy of Logic, Journal for the History of Analytical Philosophy, 1 (2012). [12] T. Oberdan, The Concept of Truth in Carnap’s “Logical Syntax of Language”, Synthese, 93 (1992), pp. 239 – 260. [13] L. Wittgenstein, Tractatus Logico-Philosophicus, Barnes & Noble, 2004.