Carnap and the Tractatus’ philosophy of logicOskari Kuusela

Introduction

A characteristic feature of analytic philosophy – or at least one strand of it – has been

the use of symbolic or formal logic as a philosophical tool. Given the methodological

importance of logic for analytic philosophy, developments in logic and the philosophy

of logic have played an important part in its development. A practically unanimously

accepted part of the history of logic and analytic philosophy is a particular account of

the relation between Wittgenstein and Carnap, and how Carnap in the 1930s

overcame the limitations of the Tractatus’ philosophy of logic, i.e. its condemnation

of logic to silence through the distinction between saying and showing. Carnap’s

achievement was an important step in the development of the contemporary model

theoretic account of logic which, so the story goes, left the Tractatus’ philosophy of

logic superseded. Arguably, however, this account of the Wittgenstein-Carnap

relation, adopted rather directly from Carnap’s The Logical Syntax of Language,

doesn’t do proper justice to the Tractatus. It downplays important similarities between

Carnap’s and Wittgenstein’s positions whose correct understanding is a reason to

regard Carnap’s position as a variant of Wittgenstein’s, rather than anything

particularly novel. Described in Carnapian terms, the Tractatus’ goal is to introduce,

by using only apparently metaphysical quasi-syntactical sentences, syntactical

principles and concepts that constitute a calculus designed for the purpose of

philosophical clarification in the formal mode. Hence, a distinction corresponding to

Carnap’s distinction between the material and formal mode is already part of the

Tractatus’ account of philosophy and logic. Moreover, arguably, a key point of

Wittgenstein’s saying-showing distinction is to clarify the difference between logical

or syntactical determinations and true/false statements, whereby logic is understood as

something that is not true/false and not justifiable by reference to any facts about

either language or reality. Thus construed, however, the saying-showing distinction

may be taken to underlie Carnap’s principle of tolerance which is based on the very

idea that logic is not true/false about anything. Similarly, the saying-showing

distinction, or an equivalent distinction, is assumed by Carnap’s distinction between

object-language and syntax-language. For abstractly conceived, Wittgenstein’s

distinction simply concerns the difference between statements in terms of a language

and logical determinations concerning that language. But this distinction is

acknowledged rather than rejected or overcome when distinguishing between an

object-language and a syntax- or metalanguage in logic. Hence, the key components

of Carnap’s philosophy of logic are already present in the Tractatus, even if in a

different form. Let us start the discussion from the generally acknowledged shared

features of Carnap’s and the Tractatus’ positions.

1. Logical syntax: agreements and departures

Carnap describes the early Wittgenstein’s influence on him in his ‘Intellectual

Autobiography’ as follows:

For me personally, Wittgenstein was perhaps the philosopher who, beside Russell and Frege, had the

greatest influence on my thinking. The most important insight I gained from his work was the

conception that the truth of logical statements is based only on their logical structure and the meaning

of the terms. Logical statements are true under all conceivable circumstances; thus their truth is

independent of the contingent facts of the world. On the other hand, it follows that these statements do

not say anything about the world and thus have no factual content. (Carnap 1963, 25)

The Tractarian conception of logic described in this quote, which Wittgenstein put

forward as a critique of Frege’s and Russell’s (early) view of logic as the most general

science, constitutes the common background for both Carnap’s and Wittgenstein’s

subsequent discussions of logic. Part of this conception of logic as tautological and

contentless is a conception of logic as syntax, according to which, logical relations are

syntactical relations determined by the rules of logical syntax. This is to regard

syntactical rules as determining, not merely what kind of sentences can be constructed

from subsentential constituents, but also the inferential relations between propositions

or sentences. Thus, logic becomes syntax, a study of the formal or structural

characteristics of language. (See, LSL, 2; Carnap 1963, 54; for relevant references to

the Tractatus, see below)1

More specifically, for Wittgenstein logical syntax determines the logical role

or the use of a sign in language, or put differently, it determines the logical form of an

expression, understood as its possibilities of combination with other expressions.

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Given the Tractatus’ conception that the function of language is the true/false

representation of reality, Wittgenstein ultimately understands the use of expressions in

terms of their contribution to true/false statements about reality. This leads us to an

important difference between his view and Carnap: despite their significant

agreement, and a number of very similar sounding remarks they make about the

notion of logical syntax, the Tractatus’ conception of logical syntax differs

importantly from Carnap’s. Whereas Carnap adopts a Hilbertian formalistic

conception of logical syntax as rules that apply to uninterpreted signs in the sense of,

for example, ink marks on a page, or to abstract patterns of such marks interpreted as

logical structures, for Wittgenstein syntax is concerned with signs with a significant

or meaningful (sinnvoll) use.2 How is this difference to be understood?

The difference is connected with – and easily obscured by the failure to notice

– certain terminological differences between Wittgenstein and Carnap, regarding the

notions of a ‘symbol’ and ‘expression’. While a symbol or an expression for

Wittgenstein is a sign with a significant or meaningful use (any part of a proposition

that characterizes its sense is a symbol or an expression), for Carnap a symbol or an

expression is a character or a mark not assumed to possess any meaning or designate

anything. (TLP 3.31; LSL, 4-6) For example, ‘a’ and ‘a’ printed on different points of

a page are, in Carnap’s terminology, different symbols, even if they may be

equivalent in syntactical design, insofar as their use is governed by the same

syntactical rules. (LSL, 15) Wittgenstein writes in the Tractatus: ‘In order to

recognize a symbol in a sign we must observe how it is used with a sense.’ (TLP

3.326) He explains this remark to Odgen, the book’s first translator as follows: ‘3.326

[…] The meaning of this prop[osition] is: that in order to recognize the symbol in a

sign we must look at how this sign is used significantly in propositions. I.e. we must

observe how the sign is used in accordance with the laws of logical syntax. […].’

(LO, 59) And once we understand their use, i.e. how signs signify, we understand

their syntax: ‘The rules of logical syntax must go without saying, once we know how

each individual sign signifies.’ (TLP 3.334) Accordingly, only signs with a

meaningful use have logical form: ‘A sign does not determine a logical form unless it

is taken together with its logico-syntactical employment.’ (TLP 3.327; cf. NB,

53/PTLP 3.253)

The significance of this difference between Wittgenstein and Carnap is that,

essentially, they are offering different accounts of the idea of the formality of logic –

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and therefore its nature, insofar as formality is essential to logic.3 Both characterize

the idea of formality by saying that syntax must be established without reference to

the meanings of signs4, with Carnap attributing this view to Wittgenstein, who ‘[…]

made clear the formal nature of logic and emphasized the fact that the rules and

proofs of syntax should have no reference to the meaning of the symbols.’ (LSL, 282,

cf. 284; IS, 156, 157, cf. 232). In the Tractatus this point about meaning and syntax is

presented as a criticism of Russell’s conception of logic and his theory of types as

involving a reference to meaning of signs (TLP 3.331). Accordingly, it is intimately

connected with Wittgenstein’s criticism of the idea of logic as a science whose

statements have factual content. Wittgenstein writes: ‘In logical syntax the meaning of

a sign should never play a role. It must be possible to establish logical syntax without

mentioning the meaning of a sign: only the description of expressions may be

presupposed.’ (TLP, 3.33) In accordance with his conception of expression as a sign

with a meaningful use, by the description of an expression (qua expression) he

understands a description of its use. More specifically, such descriptions are presented

by means of variables. The values of the variables are possible propositions that

contain the variable, whereby the determination of such a class of propositions

specifies the variable, and in this way the possible uses of the expression in question.

(TLP 3.313, 3.316, 3.317)

Carnap explains his conception: ‘By the logical syntax of a language, we mean

the formal theory of the linguistic forms of that language – the systematic statement of

the formal rules which govern it together with the development of the consequences

that follow from these rules. A theory, a rule, a definition, or the like is to be called

formal when no reference is made in it either to the meaning of the symbols (for

example, the words) or to the sense of the expressions (e.g. the sentences), but simply

and solely to the kinds and order of the symbols from which the expressions are

constructed.’ (LSL, 1) The syntax of a language, in other words, concerns the

structures of possible (serial) orders of its elements, or formal structures as

determined by syntactical rules. (LSL, 5, 6) Or as Carnap also explains the basic idea,

logical syntax as a theory of language is the ‘geometry of written pattern’ (Carnap

1963, 29) – though it is not essential here that the patterns should be written, but any

patterns will do in principle (cf. LSL, 6).5

This explains the sense in which for Carnap logical syntax is concerned with

signs irrespectively of whether they have any meaning, so that in principle

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uninterpreted meaningless signs too may be regarded as possessing a syntax and a

logic. This is characteristic of the Hilbertian conception on which signs are treated

meaningless, before an interpretation (or a model) is given to them. Wittgenstein’s

view, by contrast, excludes syntactic characterizations of meaningless signs.

Meaningless or nonsensical expressions whose meaning or sense has not been

determined do not possess a logic or a syntax. That is, while syntax indeed is

established without reference to the meanings of names or senses of sentences, only

signs with a meaningful use (i.e. propositions with a sense, and by entailment their

constituent expressions) have a syntax. Hence, although logic is not concerned with

meanings, but rather with forms that underlie the meaningful uses of language and

make the expression of meanings possible (TLP 3.34, 3.341, 3.344, 4.12), it does

presuppose the meaningfulness of linguistic expressions. As Wittgenstein notes about

the propositions of logic, i.e. tautologies, which he regards as bringing to view the

most general and abstract formal characteristic of language, the general propositional

form: ‘The propositions of logic […] presuppose that names have meaning and

elementary propositions sense; […].’ (TLP 6.124; see 6.12)6 Or as one might also

explain Wittgenstein’s view, there would seem to be no reason to think of a system of

marks or characters as a language and as possessing logic, unless it had a meaningful

use and the signs had meaning (cf. AWL, 43).

At this point Carnap departs from Wittgenstein also in certain other respects.

Wittgenstein’s conception of logic, Carnap maintains, leaves no room for talk about

syntax or the logic of language, or for philosophical elucidatory statements about

what is logically necessary or possible. As he says, in Wittgenstein’s view ‘syntax

cannot be expressed at all’. (LSL, 53) On these grounds Carnap then regards

Wittgenstein’s position as ‘certainly very unsatisfactory’ (LSL, 283; cf. Carnap 1934,

8; see below for a detailed discussion of Carnap’s disagreements with Wittgenstein).

On the background of Carnap’s dissatisfaction are issues about the methodology of

logic and philosophy. As he explains in the foreword to Logical Syntax with regard to

the former: ‘[…] a book on logic must contain, in addition to the formulae, an

expository context which, with the assistance of the words of ordinary language,

explains the formulae and the relations between them; and this context often leaves

much to be desired in the matter of clarity and exactitude.’ Given Carnap’s

recognition that ‘[…] in this context is contained an essential part of logic […]’, ‘[…]

the important thing is to develop an exact method for the construction of these

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sentences about sentences.’ Accordingly, the purpose of his book is to: ‘[…] give a

systematic exposition of such a method, namely, of the method of “logical syntax”.’

(LSL, xiii; cf. Carnap 1963, 55.) Given the use of relevant kind of symbolic languages

as tools of logical analysis, the point can also be expressed thus: ‘The aim of logical

syntax is to provide a system of concepts, a language, by help of which the results of

logical analysis will be exactly formulable.’ (LSL, xiii, cf. 7; cf. PLS, 58, 59)

Moreover, because Carnap regards logical analysis as the method that a

scientifically respectable philosophy must adopt, questions of the nature and

methodology of logic are of the greatest significance also in this sense. ‘The part of

the work of philosophers which may be held to be scientific in its nature […] consists

of logical analysis.’ (LSL, xiii; cf. 279) And as he intends to show: ‘[…] all

philosophical questions which have any meaning belong to syntax.’ (LSL, 280) Thus,

questions about the nature of logic, and logical analysis, are simultaneously questions

about the nature of philosophy. Later on in his autobiography, Carnap singles as ‘the

main thesis’ of his book ‘the importance of the metatheory for philosophy’. (Carnap

1963, 56; cf. LSL, xiii), where metatheory is a broader notion in the sense that it also

includes semantics.7 The point is that the adoption of the point of view of logical

syntax in philosophy would make it possible to formulate philosophical questions and

1 This characterization applies to Carnap before his ‘semantic turn’, i.e. in Logical Syntax and papers around this time. Later on Carnap characterizes logic ‘in the sense of a theory of logical deduction’ as ‘a part of semantics’, although he notes also that ‘This, however, does not contradict the possibility of dealing with logical deduction in syntax also.’ (IS, 60)2 Given the influence of Wittgenstein’s conception of logic on Carnap, one might also characterize the latter’s conception of logical syntax as a Hilbertian formalistic reinterpretation of Wittgenstein’s conception of logical syntax.3 Carnap writes: “[…] a ‘non-formal logic’ is a contradictio in adjecto. Logic is syntax.” (LSL, 259) Similarly, up to the early 1930s Wittgenstein regards logic as being concerned with calculi with definite and precise rules, assuming a conception close to Carnap’s who also characterises logical syntax in the widest sense as concerned with the construction and manipulation of calculi (see Ts213, 252v; LSL, 4-5; cf. IS, 156).4 ‘Meaning’ means here specifically what linguistic expressions refer to, as the names in the Tractatus refer to objects (TLP 3.203) or what sentences describe. It is in this sense that Wittgenstein maintains that logical constants and the negation sign do not have any meaning: they do not refer to any (logical) objects. (TLP 4.0312)5 More specifically, the last point goes for what Carnap calls ‘pure syntax’ which is concerned with the possible arrangements of elements, regardless of how they are realized whether any such arrangements are actually realized. Pure syntax only formulates definitions and develops consequences, and is wholly analytic. Descriptive syntax, by contrast, is concerned with the syntactical properties and relations of empirically given expressions. (LSL, 6, 7; cf. 15, 53, 168)6 Friedman makes a related observation concerning differences between Wittgenstein’s and Carnap’s respective conceptions of logical truth. (See Friedman 1999, 193-195.) On the basis of the preceding this point might be expressed thus: Wittgenstein’s conception of the contentlessness of logic assumes that linguistic expressions do have content, and differs in this way from Carnap’s conception.7 Modifications required to Logical Syntax from Carnap’s later semantical point of view are discussed in IS, 246ff.

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statements in an exact manner and enable one to sidestep the inexactitude of logical

and philosophical expositions given in natural language. Consequently, Carnap

believes, philosophers would be able to avoid the discussion of mere pseudo-

problems, such as the questions of metaphysics. Philosophy would become more

fruitful in that pointless disputes which in the garb of the traditional philosophical

vocabulary misleadingly appear to concern the nature of the objects in question, while

being really questions about the choice of appropriate forms of language for particular

tasks, can be set aside. We can then focus on questions concerning the choice of

language with a better self-understanding, and without the distraction of unnecessary

disputes about who is right or wrong, given that the choice of a language is a matter of

expediency, not of truth or falsity. (LSL, 277-281; see, Carus 2007, 232, 233 for

discussion.)

Thus, Carnap seeks to spell out a conception of philosophy as logical syntax,

according to which, pace Wittgenstein, the statements of philosophy are statements of

logical syntax. Here it is crucial that he believes to have found a way to formulate

syntactical sentences that are not ‘senseless, if practically indispensable, pseudo-

sentences, but […] perfectly correct sentences’ (LSL, 283). It is just to this end that

Carnap adopts the Hilbertian metamathematical point of view which allows for the

formulation of statements about logical forms and the syntax of an object-language in

a metalanguage so that syntactical sentences concerning the logical characteristics of

the object-language can be understood as sentences of a metalanguage. Thus it also

becomes possible to give logico-syntactical and philosophical statements an exact

formulation. From the point of view of Carnap’s conception it is then, ‘[…] just as

possible to construct sentences about the forms of linguistic expressions, and therefore

about sentences, as it is to construct sentences about the geometrical forms of

geometrical structures. […]’ (LSL, 282, 283) This possibility Carnap takes

Wittgenstein’s position to exclude, because there is no such formulation for any

nonsensical pseudo-sentences, which is what he takes the Tractarian sentences to be.

(LSL, 284)

Here Carnap clearly believes to have made advances over the Tractatus’

position by finding a way to make exact syntactic statements. As he notes about

Wittgenstein, ‘If I am right, the position here maintained is in general agreement with

his, but goes beyond it in certain important respects.’ (LSL, 282) In the history of

analytic philosophy this Carnapian account of the relation between Wittgenstein and

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Carnap has become widely accepted – Carnap’s reservations ‘If I am right…’ in

effect ignored. According to this prevailing account, merging influences from Hilbert,

Gödel and Tarski, Carnap managed to overcome the limitations of the

Wittgensteinian position, i.e. the silence imposed on logic by Wittgenstein’s saying-

showing distinction, according to which, it is impossible to speak about the logical

characteristics of language, and the conjoined Wittgensteinian conception of

philosophy as consisting of nonsensical elucidatory statements. By breaking out of

this Wittgensteinian prison Carnap made the Tractatus’ philosophy of logic obsolete,

superseded by what has subsequently become known as the model theoretic

conception of logic. Characteristic of this conception of logic is a distinction between

an object- and a metalanguage (corresponding to Carnap’s distinction between object-

and syntax-language), whereby the latter is a medium for statements about the logical

characteristics of the former. This view of Carnap’s achievement finds an early

expression in the reviews of Logical Syntax by Nagel and Quine in 1935 who seem to

have simply accepted Carnap’s account of his relation to Wittgenstein. This might

have partly contributed to Carnap’s account becoming engraved into the history of

analytic philosophy. (For recent interpretations of the relation between Carnap and

Wittgenstein along these lines, see Awodey and Carus 2009, Carus 2007, ch.9,

Friedman 1999, ch.8, Wagner 2009.)

Arguably, however, this account fails to do justice to the Tractatus. The

question may even be raised, whether what Carnap says about the Tractatus in

Logical Syntax might partly reflect a need to emphasize the originality of his own

position at Wittgenstein’s expense. The latter question arises in particular in

connection with a priority dispute between Wittgenstein and Carnap in 1932. Let us

begin the discussion of these issues by examining more closely this dispute and what

Wittgenstein says in its context as a clue to the interpretation of the Tractatus.

2. The Wittgenstein-Carnap plagiarism affair revisited

In 1932, in connection with Carnap’s article ‘Die Physikalishce Sprache als

Universalpsrache der Wissenshaft’, a dispute arose between Wittgenstein and Carnap,

whereby Wittgenstein accused Carnap of plagiarism. One reason for Wittgenstein’s

accusation was apparently that in his article Carnap presents without any

acknowledgement as the methodological framework for his discussion the Tractarian

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conception of philosophy, according to which, philosophy is the logical clarification

or analysis of language that dissolves misunderstandings, but doesn’t put forward any

true/false contentful statements of its own. Rather the propositions of logic are

tautologies. According to this view, the kinds of misunderstandings that philosophy

clarifies find their expression especially in metaphysical propositions and

philosophical pseudo-questions, but are avoidable through the use of a formal

language. (Carnap 1932, 432, 433, 435, 452, 456) There is no doubt that this

conception of philosophy is first spelled out in the Tractatus, and that Wittgenstein

was, at least to this extent, justified in his claim that Carnap had used his work

without due acknowledgement. Of course, this conception of philosophy is also the

core of Carnap’s own approach, and in Syntax he explicitly attributes it to

Wittgenstein (see, LSL, 282-284). It was apparently also meant to be part of the

collaborative book Wittgenstein and Friedrich Waismann were working on at the

time, which may have been part of Wittgenstein’s reasons for raising the issue.8

Nevertheless, in the form just stated, the Wittgensteinian conception of philosophy is

abstract enough to be compatible with the details of both his and Carnap’s different

views on logic. Thus, doesn’t help to decide how significant a departure Carnap’s

metamathematical conception is from Wittgenstein’s.9

More interesting in this regard is Wittgenstein’s statement to Schlick in

connection with the plagiarism affair: ‘That Carnap, when he is for the formal and

against the “material mode of speaking” [“inhaltliche Redeweise”], does not take a

single step beyond me, you know well yourself; and I cannot believe that Carnap

should have so completely misunderstood the last sentences of the Tractatus

[“Abhandlung”] – and so the fundamental idea [den Grundgedanken] of the whole

book.’ (GB, letter to Schlick 8.8.1932) How should this statement be understood?

Intriguingly, when Wittgenstein says that in promoting the formal mode as opposed

the material mode as the correct way of speaking in philosophy Carnap is not taking a

single step beyond his position, he seems to regard as a non-essential side issue

precisely the point that is for Carnap the most important, i.e. the possibility of

formulating syntactical statements and the identification of correct philosophical

statements with such statements. For although Carnap had not yet given in 1932 this

issue the full treatment it received in Logical Syntax, the view that philosophical

statements proper are ‘metalogical sentences’ that speak about ‘the forms of

language’ is an explicitly stated part of his introduction of the distinction between the

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material and formal mode in the article (Carnap 1932, 435). Wittgenstein therefore

could hardly have missed this part of Carnap’s characterization of his position. So,

how could he treat it as inessential? This can be explained as follows.

Regarding, first, the issue of the Tractatus promoting the formal mode as the

proper way to talk in philosophy, in his book Wittgenstein characterizes as ‘the only

strictly correct’ method the following: ‘To say nothing except what can be said, […]

and then always when someone else wished to say something metaphysical, to

demonstrate to him that he had given no meaning to certain signs in his propositions.’

(TLP 6.53) What such demonstrations and the strictly correct method amount to is,

arguably, the following. The strictly correct method is a method of logical analysis in

terms of a symbolic notation, whereby the logical, syntactical or formal properties of

unclear expressions are clarified by translating them into a logically perspicuous

notation or a calculus. This constitutes a formal mode of speaking in the sense of

Carnap’s 1932 paper in that here the object of discourse are the expressions uttered by

the interlocutor, not their meanings or what they talk about, and the objective of the

8 The article was published in 1934 in English as ‘Physics as a Universal Language’. Wittgenstein first starts the discussion of the affair with Schlick by saying that by browsing Carnap’s article, ‘[…] I found many of my thoughts stated anonymously’ (GB, letter to Schlick, 6.5.1932; all translations from the correspondence are mine). Wittgenstein worries to Schlick that since he has not published anything recently, although he has worked much and ‘constantly’ given oral accounts of his views, his work might be regarded merely as plagiarism or a ‘second brew’ of Carnap’s. Wittgenstein also says that ‘I see myself being pulled against will into what is called the “Vienna Circle”’, while ‘[…] I don’t want to belong to a circle’. (Ibid.) This suggests that for him the case is not just about plagiarism, but that he wants to avoid being read in light of the work of the Vienna Circle or Carnap in particular. For, to take Wittgenstein’s work as a second brew of Carnap’s would be to read it in the latter’s terms. By oral accounts Wittgenstein presumably refers to his discussions with the Vienna Circle, in some of which Carnap was present; other sessions were reported to the circle by Waismann and Schlick (see, WVC and Carnap 1963). Wittgenstein’s and Waismann’s manuscripts have been published as VW and earlier as a version completed by Waismann (Waismann 1995). See Kienzler 2008 for a detailed account of the unfolding of the affair on the basis of letters exchanged between Wittgenstein, Schlick and Carnap and discussion of the relevant philosophical issues. For discussions, see also Hintikka 1996 and Stern 2007. Whilst Hintikka too maintains that with respect to the notion of a formal mode of speech Carnap ‘[...] was merely repeating certain ideas of the Tractatus.’ (1996, 136), he does so on reasons entirely different from those spelt out in this article and on the basis of a Tractatus-interpretation very different from the one proposed here.9 Other points are also listed by Schlick and Wittgenstein as having been stated without acknowledgement, including, according to Wittgenstein, the very idea of the language of science as a universal language (GB, letter to Schlick 8.8.1932 and letter from Schlick to Carnap quoted in Kienzler 2008, 69, 70; cf. TLP 6.53). While Schlick agreed with Wittgenstein that an acknowledgement would have been in place, Carnap refused any need for it in a letter to Schlick, who was acting as a mediator. This convinced Wittgenstein that Carnap had not acted in good will, and that the case was not merely about oversight. (Ibid. and letter to Carnap 20.8.1932; see Kienzler 2008 for Carnap’s letter to Schlick.) After his letter to Carnap where Wittgenstein tried to clear up the matter, and a letter on the following day to Schlick, Carnap is never mentioned in Wittgenstein’s (published) correspondence and only on two distinct occasions (with seven repetitive occurrences) in his Nachlass, both times briefly and critically. Unlike Frege’s and Russell’s views Carnap’s views are not subjected to any sustained philosophical discussion by Wittgenstein.

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discourse is the clarification of their forms or syntactical properties (cf. Carnap 1932,

435, 436). With regard to this interpretation of 6.53, two points are important. Firstly,

the use of such a notation is what the Tractatus presents as the way we should seek to

get rid of philosophy’s ‘fundamental confusions’ (TLP 3.324): ‘In order to escape

such errors, we must employ a sign-language that excludes them […] that is to say, a

symbolism that is governed by logical grammar—by logical syntax.’ (TLP 3.325)

Secondly, by sticking to rewriting or translating the interlocutor’s statements into such

a symbolism one would be saying nothing except what, according to the Tractatus,

can be said in that one would not be making any contentful philosophical statements

of one’s own, especially not about formal properties. (Translating is logically distinct

from asserting.) Indeed, this is just the way the Tractatus says we can talk about

formal properties and concepts, in connection with his explanation why such

properties and concepts cannot be the object of true/false statements. (See TLP 4.122,

4.126 and discussion below.)10 In Carnapian terms, the employment of this strictly

correct method would consist of nothing but speaking in the formal mode and of

statements of translation (rules of transition from one language to another).

Evidently, it is therefore a central part of the Tractatus’ outlook to promote the

formal mode of speech as the correct way of speaking in philosophy. Nevertheless,

this doesn’t yet justify Wittgenstein’s claim that Carnap doesn’t take a single step

beyond his position. For from the point of view of how Carnap presents the issue in

Logical Syntax, the novelty of his position is his account of the possibility of making

statements about syntax, and of introducing syntactical concepts and principles in this

way. However, in this regard it is important to notice the following. Clearly the

possibility of the employment of Wittgenstein’s method of clarification in terms of a

symbolic notation presupposes that a relevant kind of notation has been introduced, or

that we have in our command relevant principles and concepts of logical syntax in

whose terms the analysis is carried out. Arguably, this work of introducing syntactic

principles and concepts is done in the Tractatus by means of elucidatory statements

that Wittgenstein says are ultimately to be understood as nonsensical. (See TLP 6.54

and below.) But if this is what Wittgenstein’s nonsense aims to achieve, then

Carnap’s proposed way of using a syntax-language for the purpose of introducing

syntactical concepts and principles can be regarded simply as a different way of doing

10 I discuss this strictly correct method and its relation to the method employed in the Tractatus itself in more detail in Kuusela 2011.

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the same. While for Carnap the way to set up a symbolic notation is by means of

definitions given in the syntax-language, for Wittgenstein the way to do this is by

means of elucidatory statements, such as those of the Tractatus. Moreover, as I will

explain later in connection with a discussion of Wittgenstein’s saying-showing

distinction, there is no obstacle for Wittgenstein to allow for Carnap his syntactical

method, as long as it respects Wittgenstein’s fundamental idea that logical statements

are not contentful true/false statements. And of course Carnapian statements of

syntactical rules do meet this requirement: a rule is not a true/false statement. What

these considerations suggest is that there might indeed be less distance between

Carnap and Wittgenstein than Carnap acknowledges, and that Wittgenstein might be

right to say that Carnap is not going beyond him. But to make this clear we need to

discuss in detail the function of Wittgenstein’s nonsensical elucidatory statements,

and the saying-showing distinction.

Notably, it can also be argued that by Carnap’s own lights his position should

be recognized as a variant of Wittgenstein’s. As I explain below, from his point of

view the Tractatus can be interpreted as an instance of the employment of the so-

called material mode to introduce syntactical principles, i.e. as employing for this

purpose what Carnap calls ‘quasi-syntactical’ or ‘pseudo-object’ sentences, and

whose use Carnap regards as an entirely acceptable method, as long as caution is

exercised to avoid confusions. But, alas, this is a point where Carnap’s understanding

of the relation of his project to Wittgenstein’s doesn’t seem very secure. While

making suggestions that this is how the Tractatus could be read, and giving a number

of examples from the book as translatable into his syntactical mode (see LSL, 303-

304 and below), Carnap nevertheless contends that, while such a reading of the book

would be preferable to a metaphysical one, it is not the intended interpretation. His

failure to appreciate that this might indeed be the intended reading may then be

plausibly taken to be what Wittgenstein refers to in the letter to Schlick quoted above,

when expressing his disbelief that Carnap had not comprehended the fundamental

idea of the book. For this fundamental idea is that the statements of logical or

syntactical principles and concepts (including ones used to introduce such principles

and concepts) must be distinguished from contentful true/false statements, which is

the gist of Wittgenstein’s showing-saying distinction (see section 5). Clearly, Carnap

had comprehended this idea in some sense, given its centrality to his notion of

syntactical statements, but he doesn’t ascribe the idea to the Tractatus.

12

If it is correct that the point of the Tractatus’ nonsensical sentences is the

introduction of syntactical concepts and principles, with his proposal to (re)interpret

the Tractatus’ propositions as quasi-syntactical sentences, Carnap came closer than

either Frege or Russell to a correct understanding of the book as a treatise in logic

rather than a bizarre metaphysical opus. But while not realizing or acknowledging that

this could be the intended reading he thereby made the distance of his own position to

Wittgenstein’s appear greater than it is.11

3. The possibility of speaking about syntax

Let us now examine more closely the sense in which it is (and is not) possible, from

the Tractatus’ point of view, to speak about syntax. In this regard Carnap maintains

that Wittgenstein has wrongly sentenced philosophy to silence through his view that

logic or syntax is inexpressible. Carnap speaks in this connection about

Wittgenstein’s two negative theses (although their relation remains somewhat

unclear). The first thesis relates to Wittgenstein’s distinction between saying and

showing: 1) According to it, ‘there is no expressible syntax’, because logic (logical

form, syntax) cannot be represented in statements, but only shown (LSL, 282). The

second thesis relates to Wittgenstein’s conception of philosophy: 2) According to it,

‘[…] the logic of science (“philosophy”) cannot be formulated’, i.e. philosophy is not

a theory but an activity of clarifying statements that doesn’t result in any statements

of its own. ‘According to this, the investigations of the logic of science contain no

sentences, but merely more or less vague explanations which the reader must

subsequently recognize as pseudo-sentences and abandon.’ (LSL, 283) But this

Carnap regard as ‘certainly very unsatisfactory’. (Ibid.) It results in lack of exactitude

and leaves the difference between Wittgenstein’s elucidations and nonsense produced

by metaphysicians entirely unclear: ‘[…] he draws no sharp line of demarcation

between the formulations of the logic of science and those of metaphysics.’ (LSL,

284) Arguably, however, Carnap misunderstands Wittgenstein on both accounts.

11 Kienzler also remarks on Carnap’s ambivalent relation to the Tractatus. On the one hand, Carnap applies his method of translating from the material into the formal mode to the propositions of the Tractatus, showing that it can be advantageously read in this way. On the other hand, Carnap never asks, whether Wittgenstein might have been consciously employing the material mode and expecting from his reader just the kind of interpretational work Carnap undertakes. In this case Carnap’s translations would exemplify (approximately at least) just what Wittgenstein hoped from his reader. (Kienzler 2008, 79, 80)

13

Firstly, it is crucial that Wittgenstein only denies that syntax is expressible in

terms of true/false statements, not in every possible sense of ‘to express’ or ‘to

speak’. As he says: ‘We can speak in a certain sense about formal properties […] and

in the same sense about formal relations [… or in the case of facts about internal as

opposed to contingent external properties and relations]. It is impossible, however, to

assert by means of propositions that such internal properties and relations obtain:

rather this makes itself manifest in the propositions that represent the relevant states

of affairs […].’ (TLP 4.122; my square brackets; cf. 4.124) A further remark on the

theme of 4.12 makes a parallel point about formal concepts: ‘In the sense in which we

speak of formal properties we can now speak also of formal concepts.’ (TLP 4.126)

Evidently, Wittgenstein therefore is not denying the possibility of speaking about

formal concepts and properties as such. This means more specifically that, in cases

where formal properties do not readily manifest themselves, but natural language

obscures or disguises them, we may need to make such properties manifest through

the transformation of expressions, i.e. by translating the expressions into a logically

perspicuous notation. Hence, a sense in which we can, according to Wittgenstein,

speak about formal or syntactical properties is by doing logical analysis by means of a

symbolic notation. Accordingly, the results of such analyses are not presented in

propositions about logic or syntax – in either true/false factual statements or

nonsensical metaphysical sentences – but by means of the expressions of the

symbolic notation. Although distinct from assertion, however, analysis as the

transformation of expressions constitutes a perfectly respectable mode of language

use. This is just what Wittgenstein understands by the ‘strictly correct method of

philosophy’ characterized earlier.

A second way to speak about syntax (also already referred to above) is the

introduction of syntactical concepts and principles governing the logically

perspicuous notation to be used for the purpose of logical analysis. Such concepts and

principles – for example, that logical connectives do not stand for logical objects

(TLP 4.0312) or the notion of a general propositional form (see below) – Wittgenstein

seeks to introduce by means of sentences that his reader is expected to come to

recognize as nonsensical. Thus, this way of speaking about syntax seems to

correspond to what Carnap understands under the second negative thesis, i.e. the

conception of philosophy as an elucidatory activity by means of statements to be

ultimately abandoned. Contrary to what Carnap assumes, however, such elucidatory

14

statements are not simply ‘pseudo-sentences’. As I will explain shortly, they can be

understood as Carnapian pseudo-object sentences or quasi-syntactical sentences (or

something very close to such Carnapian sentences). But however exactly the role of

the Tractatus’ nonsensical sentences is characterized in Carnap’s terms, in order to

grasp the nature of this mode of language use it is important that ultimately the

expression of these principles and relevant logical insights is, not the nonsensical

sentences themselves, but the perspicuous notation that they are used to introduce.

This symbolism is the proper expression of these principles. As Wittgenstein says (in

a remark from 1929) ‘The notation is the last expression of a philosophical view.’

(Ms105, 12) His nonsensical sentences therefore are used only ‘transitionally’12 to set

up the symbolic notation. In this capacity they function similarly to Fregean

elucidations that require the reader to meet the author half-way, but will be ultimately

thrown away, because what they say is not expressible in the logically preferable

notation introduced (TLP 6.54; cf. Frege 1966). Nevertheless, given their use to

introduce the principles governing a symbolic notation, once the reader throws away

these explanations, she is not simply left with nothing, as would be the case with so-

called metaphysical nonsense. What the reader is left with is a comprehension of (the

principles and concepts of) the notation introduced, i.e. the ability to operate with it

and to understand and analyse the function of expressions in its terms. Thus, contrary

to what Carnap maintains, Wittgenstein’s nonsense is clearly demarcable by reference

to this function from mere metaphysical nonsense. Accordingly, the measure of the

exactitude of such elucidations is, whether they manage to unambiguously introduce

relevant syntactical concepts and principles.

Hence, we can conclude that it is not Wittgenstein’s view that ‘syntax cannot

be expressed at all’ or that it can only be presented by means of pseudo-sentences

indistinguishable from metaphysical nonsense. Pace Carnap, Wittgenstein’s position

does allow for the exact formulation of syntax by means of the expressions of his

symbolic notation, even though not in the form of true/false statements whose subject

is the syntax, logic or logical form of expressions.13

4. Wittgenstein and the quasi-syntactical mode of speech

12 For the notion of a transitional remark, see Diamond 1991.13 For discussion and justification of the interpretation of the Tractatus assumed here, which is a variant of the so-called resolute reading, see Kuusela 2008, forthcoming-a and in particular forthcoming-b

15

With respect to the question of how exactly Carnap’s position relates to

Wittgenstein’s, what Wittgenstein is doing in the Tractatus might be described in

Carnapian terms in the following way (with certain complications and reservations to

be discussed later). Mostly the book is concerned to introduce and spell out syntactic

concepts and principles by speaking in a metaphysically sounding manner reminiscent

of Carnapian quasi-syntactical sentences in the material mode of speech. That is,

Wittgenstein proceeds as if making true/false metaphysical statements about language

or what language speaks about, while really concerned to introduce syntactic

principles and concepts constitutive of his logical system. I will give two examples to

illustrate this and then return to the issue of the aptness of the Carnapian locutions as

characterizations of the method employed in the Tractatus.

i) When in the beginning of the Tractatus Wittgenstein states that the world is

a totality of facts, not things (TLP 1.1), he is saying that, from the point of view of his

logically perspicuous notation this is just what the world is: when regarded as the

object of true/false representation it is a totality of obtaining states of affairs, where

objects figure only as the constituents of states of affairs, not independently.

Accordingly, as he fills in the details of his account of representation and language,

the logical role of names is similarly subordinate to the task of representation, as

things are subordinate to states of affairs. Like objects are constituents of states of

affairs, so names, whose logical function is to stand for objects, are constituents of

true/false propositions that, through the arrangement of names in them, represent

possible states of affairs. Thus Wittgenstein’s apparently metaphysical account of the

nature of reality is really a component of an account of language and thought as

true/false representation, whose proper expression is his notation. The core of this

account is an idea of representation and reality possessing an identical logical

structure, first described in the book by reference to reality.14 The point is that what

looks like a metaphysical account of the nature of reality and representation is really a

way to explain the principles of a symbolic notation or a logical system. Stated in a

summary fashion, this is a calculus that treats complex propositions as analysable

truth-functionally into elementary propositions that are true/false representations of

reality, and on their part further analysable at a subsentential level into concatenations

14 See TLP 1-2.25 for these points explained abstractly as an account of reality and representation, or picturing; from 3 onwards these notions are used to build up a corresponding account of thought and language.

16

of names that stand for objects. That, Wittgenstein believes, gives us the proper

framework for the analysis of language and thought.

ii) When introducing the core syntactical concept of his notation, the general

propositional form, i.e. the notion of propositions as true/false representations that can

enter into truth-functional relations, Wittgenstein again speaks as if giving a

metaphysical account of the nature of language, and as if stating something about the

essence of language. As he also explains, however, the general propositional form is a

logical constant (a formal characteristic that all propositions have in common), and in

the logically perspicuous notation it is therefore represented by means of a variable.

(See TLP 3.31-3.313, 4.5, 4.53, 5.47-5.472, 6) But this means that this formal

characteristic cannot be the object of true/false statements; that way of presenting the

matter fails to clearly distinguish the generality of the notion of general propositional

form from the merely accidental generality of general facts – which is the

fundamental confusion of Russell’s logic, according to Wittgenstein (see, TLP 6.111,

6.1232). Rather, the logically correct expression for this idea of the logical form of

propositions is the rendering of propositions in the relevant way in Wittgenstein’s

notation, i.e. as possessing the relevant form so that every possible proposition can be

understood as a substitution instance of the propositional variable.

Again, therefore, the way in which Wittgenstein speaks is to be understood as

a particular way of introducing logical or syntactical notions or principles. Such talk,

if we take it literally, fails to respect the distinction the Tractatus seeks to clarify

between a) true/false statements about reality, including language as an object of

description and b) proper expression of the logic of language. The logic of language

cannot be described in terms of true/false statements, but made manifest by means of

concepts and principles that belong to the perspicuous notation. However, as just

explained, Wittgenstein’s statements in the Tractatus can be readily understood as

intended to introduce the principles of his calculus which is the proper expression of

relevant logical insights. In this case the apparent confusion is harmless. And notably,

such a possibility of giving expression to syntactic principles (or something close to

this) Carnap too accepts in Logical Syntax when admitting that the material mode of

speech (to be explained presently) can be used to speak about syntax. As he writes:

‘We do not mean […] that the material mode of speech should be entirely eliminated.

Since it is in general use and often easier to understand, it may well be retained in its

place. But it is a good thing to be conscious of its use, so as to avoid the obscurities

17

and pseudo-problems which otherwise easily result from it.’ (LSL, 288; cf. 309)

According to another characterization, sentences in the material mode are not

incorrect but incomplete. However, ‘[…] in every domain incomplete, abbreviated

modes of speech are employed with profit.’ (LSL, 301) Accordingly, not only is the

use of the material mode ‘non-contradictory’, ‘when systematically carried into

effect’ (LSL, 308), it ‘[…] is frequently expedient.’ (LSL, 312; original italics; the

same basic point about the acceptability of material mode is also made in the article

connected with the plagiarism affair: 1932, 456) Hence, Wittgenstein’s manner of

proceeding should have been unobjectionable to Carnap, as I will now explain in

more detail.

Carnap characterizes the material mode as follows: ‘The material mode is a

transposed mode of speech. In using it, in order to say something about a word (or a

sentence) we say instead something parallel about the object designated by the word

(or by the fact described by the sentence respectively).’ (LSL, 309; for more exact

definitions of the material mode, see 287.) Correspondingly, characteristic of

Carnapian pseudo-object sentences, which are quasi-syntactical sentences in the

material mode (LSL, 287), is that they ‘[…] are formulated as though they refer

(either partially or exclusively) to objects, while in reality they refer to syntactical

forms, and, specifically, to the forms of the designations of those objects with which

they appear to deal’, thus belonging to an intermediate field between genuine object-

and syntax-sentences (LSL, 285; for a formal definition of quasi-syntactical

sentences, see 233, 234). However, when presenting his logical ideas as if he were

making metaphysical statements about propositions, or about what and how they

represent, Wittgenstein is speaking in just this manner: he is ascribing a property to an

object of description, for example, he says that all propositions possess a certain

characteristic such as the general propositional form, and that this is their essence,

something common to them all (TLP 5.47, 5.471). But, really, this is meant as a way

to introduce a syntactical designation or formal concept that belongs to the calculus

whose idea he seeks to spell out. For the concept of a proposition as defined through

the notion of general propositional form, and as presented in the symbolic notation by

a variable, is indeed a syntactical or formal concept. What Wittgenstein’s remarks that

employ the concept of a proposition and other connected concepts then are meant to

do is to explain the role of this syntactical concept in Wittgenstein’s notation. And

generally, the same applies to other concepts in the Tractatus too, such as, state of

18

affairs, complex, object, name, function, negation, number, some, all, and so on. They

all can be understood as quasi-syntactical concepts in the sense that, while used in the

Tractatus in a fact stating manner, as if presenting a metaphysical theory of language

and reality, they are really intended to explain the role of corresponding syntactical

concepts and principles in Wittgenstein’s notation.

Here, with respect to the issue of the relation between Carnap and

Wittgenstein, Carnap’s discussion of the pseudo-object concept universal word,

which he inherits rather directly from Wittgenstein, is quite instructive. By a universal

word Carnap means a word ‘that expresses a property (or a relation) which belongs

analytically to all objects of a genus’ (LSL, 293). An example is ‘thing’, which can be

predicated of anything belonging to the genus things, and sensibly of nothing else. A

universal word then is a pseudo-object concept expressed in the symbolic notation by

a syntactical concept, a variable, and the pseudo-object concept functions, basically,

as an index for a variable that indicates the genus of its values (or a logical category).

(LSL, 294-295) So far Carnap is doing little more than rehearsing a point made by

Wittgenstein, when the latter introduces the idea of variables as the proper expression

of formal concepts (i.e. of constant forms), his example being similarly the ‘pseudo-

concept thing’, whose proper expression is the variable name ‘x’, given that things are

just what names name. (TLP 4.1271, 4.1272) Carnap writes with reference to 4.1272,

using the opportunity to explain the difference of his position from Wittgenstein’s:

‘Here the correct view is taken that the universal words designate formal (in our

terminology: syntactical) concepts (or, more exactly: are not syntactical but quasi-

syntactical predicates) and that in translation into a symbolic language they are

translated into variables (or again more exactly: they determine the kind of variables

[…]). On the other hand, I do not share Wittgenstein’s opinion that this method of

employing the universal words is the only admissible one.’ (LSL, 295) Rather, Carnap

says, there also cases in which universal words can be employed as proper concept

words.

But here is something remarkable: As the most important case of the kind that

constitutes an exception to Wittgenstein’s view Carnap now mentions the use of such

words in pseudo-object sentences, characterizing this role ‘in the simplest form’ by

saying: ‘[…] a universal word is here a quasi-syntactical predicate; the correlated

syntactical predicate is that which designates the appertaining expressional genus.’

(LSL, 297) An example is ‘1 is a number’ whereby the ‘correlated syntactical

19

predicate’ is ‘number word’ (LSL, 297). This is remarkable because in the Tractatus

Wittgenstein numerous times employs universal words in just this or a very similar

way. For example, this is the way he employs terms such as ‘general propositional

form’ and ‘proposition’; in the Tractatus ‘general propositional form’ can be

understood as a quasi-syntactical predicate used to ascribe a quasi-syntactical property

to the quasi-syntactical subject-term ‘proposition’.15 Here the corresponding

syntactical concept proper is the propositional variable in Wittgenstein’s system.

Another example, to be understood in the same way, is ‘An elementary proposition

consists of names.’ (TLP 4.22) that aims to explain the relation between the

propositional variable and the syntactical concept of a variable name. But if

Wittgenstein is making this kind of use of relevant terms, it is quite misleading to say

that he doesn’t regard it as admissible to employ statements with universal words in a

quasi-syntactical way. Given that he is himself doing just that in the Tractatus, then

clearly he must regard it as admissible in some sense. This sense has already been

explained: they are admissible as a method for introducing syntactical notions and

principles.

Now my argument can be stated quite straightforwardly. This point about

universal words generalizes to all other syntactical expressions introduced by using

the material mode in the Tractatus: Wittgenstein’s purpose there can quite generally

be characterized as the introduction, by means of quasi-syntactical statements, of

syntactical concepts and principles that together constitute his logical system or

calculus.16 But if this is Wittgenstein’s purpose, then we can say that in spelling out

his metalogical point of view, Carnap has not ventured very far at all beyond

Wittgenstein’s position. Carnap’s syntactical sentences employed to define syntactical

15 An example of the use of ‘general propositional form’ as a quasi-syntactical predicate is Wittgenstein saying that all propositions share this form in TLP 5.47; a related use of another quasi-syntactical concept occurs in 4.1, where he says that propositions present the existence and non-existence of states of affairs, thus employing the locution ‘presentation of a state of affairs’ to characterize the concept of a proposition. The same goes for the concept of a picture in 4.01, where a proposition is characterized as a picture of reality. These remarks are examples of successive characterizations of the quasi-syntactical concept of proposition in terms of quasi-syntactical predicates aiming to give an idea of the proper syntactical concept of a propositional variable which is at the centre of Wittgenstein’s system.16 This is not quite correct but serves to illustrate the fundamental similarity between the Tractatus and Carnap’s conception. The Tractatus also seeks to introduce in the same way concepts that might be classified as semantical, such as sense or meaning and truth. Remarking later on the notion of a theory of systems that covers both semantical and syntactical questions, Carnap also observes: “(Wittgenstein seems to use this terms likewise ‘(logical) syntax’ for an analysis which, in our terminology, combines syntactical and semantical questions but also covers what we call descriptive syntax and descriptive semantics, and perhaps even something of pragmatics.)” (IS, 240)

20

concepts and principles may be regarded as a variant or a particular outgrowth of the

quasi-syntactical method used by Wittgenstein.

However, here a possible objection to the conclusion just stated requires

discussion. This has to do with Carnap’s more precise definition of quasi-syntactical

sentences and the notion of translation. For according to Carnap’s definition, it is

characteristic of quasi-syntactical sentences that they are – indeed, apparently always

must be – translatable into syntactical sentences (LSL, 233, 234). The requirement

translatability is important for him from a methodological point of view, because

‘[t]ranslatability into the formal mode of speech—that is, into syntactical sentences—

is the criterion which separates the proper sentences of the logic of science from the

other philosophical sentences—we may well call them metaphysical.’ (LSL, 284) For

Carnap translatability into the syntactical mode, therefore, is the feature that

distinguishes philosophical statements proper from those to be abandoned as pseudo-

statements. But given that Wittgenstein characterizes his elucidations as nonsensical

(TLP 6.54), which means that in his view there are no translations for them, his

remarks seem to automatically disqualify from being quasi-syntactical. Indeed, in

connection with his discussion of the concept of a universal word, Carnap cites just

this untranslatability as what distinguishes his view from Wittgenstein’s. According to

him, when a universal word is employed in a quasi-syntactical sentence, ‘[…] it is a

question of sentences of the material mode of speech which are to be translated into

syntactical sentences. Sentences of this kind with a universal word are held by

Wittgenstein to be nonsense, because he does not consider the correct formulation of

syntactical sentences to be possible.’ (LSL, 295, 296; my square brackets) Does this

mean that Wittgenstein cannot, after all, be characterized as making quasi-syntactical

statements? No; there seem to be more than one sense in which Wittgenstein might be

understood as making such statements.

On the one hand, as noted earlier, Carnap himself proposes in Logical Syntax a

number of translations of statements from the Tractatus into the syntactical mode

(LSL, 303-304, 307). An example is: ‘29a The world is a totality of facts, not things.’

(LSL, 303), which Carnap regards as translatable, despite it containing two universal

words, ‘fact’ and ‘thing’.17 In this connection he comments: ‘Similarly many other

sentences of his which at first appear obscure become clear when translated into the

formal mode of speech.’ (LSL, 303) Evidently, Carnap therefore maintains that at 17 Carnap translates this as: ‘29b Science is a system of sentences, not of names.’ (LSL, 303)

21

least some of Wittgenstein’s statements could be understood as quasi-syntactical in

the sense of being possible to translate into syntactical sentences proper.18 But if,

according to Carnap, such a way to understand Wittgenstein is possible, it becomes

quite unclear what his philosophical grounds are for saying that Wittgenstein’s

position is ‘certainly very unsatisfactory’. For, if translations of Wittgenstein’s

statements into the syntactical mode are possible by Carnap’s lights, then apparently

he can in such cases at most criticize Wittgenstein for poor self-understanding:

Wittgenstein doesn’t realize that what he is doing is making quasi-syntactical

statements, and he should accept the possibility of their translation into syntactical

statements proper. But if Wittgenstein’s work can be understood in this way, i.e. if he

is making quasi-syntactical statements of the sort hailed by Carnap as a very

important and ‘frequently expedient’, his work should to that extent be perfectly

acceptable to Carnap. But then it seems that Carnap’s own approach is little more than

a variant of Wittgenstein’s. What Carnap has achieved is an important clarification of

the status of the statements of the Tractatus as quasi-syntactical, but this is to clarify a

feature of Wittgenstein’s approach and to adjust and modify it, not to spell out a novel

rivalry approach.

On the other hand, if we accept Wittgenstein’s view that the sentences of the

Tractatus are nonsense and therefore untranslatable, he can still be characterized as

making quasi-syntactical statements in a sense close to Carnap’s. In this case his

statements might be characterized as quasi-syntactical on the grounds that their

purpose is the introduction of syntactical concepts and principles, as explained above.

More specifically, some words that occur in Wittgenstein’s sentences could be said to

correspond to syntactical concepts in that they can be taken as stand-in notions to be

replaced by proper syntactical ones, even though the statements of the Tractatus

would not be translatable into syntactical statements. Thus, although the

correspondences between some words in the Tractatus’ sentences and expressions in

Wittgenstein’s symbolic notation would not mediated by syntactical sentences as a

kind of a bridge between two modes of expression, one might still speak of there

being such correspondences. The situation resembles the relation between the

everyday concept of a concept and that concept in Frege’s concept-script. Although

statements of everyday language in which the concept of a concept occurs in the

18 Other Tractarian sentences he uses as example of untranslatable and therefore unacceptable metaphysical statements. (See, LSL, 314)

22

subject position cannot be formulated in Frege’s system, there is still some kind of a

relation of correspondence between his and the everyday concept.

5. The saying-showing distinction and Carnap’s philosophy of logic

But why does Wittgenstein reject the possibility of statements about logic or syntax?

How should one understand his saying-showing distinction, according to which

logical syntax or the formal characteristics of language cannot be the subject matter of

statements, or represented in language? Wittgenstein’s rejection of the notion of

statements about syntax, as I will explain, is best understood as an attempt to

distinguish clearly between statements made in terms of (or within) a language and

statements about that language, i.e. as a way to emphasize a difference in the status of

the two kinds of statement. Given that a clear comprehension of this distinction is

absent in Frege’s and Russell’s logic (for whom the laws of logic are truths among

other scientific truths and distinguished from those other truths only by their subject

matter and generality), and that just this distinction is presupposed when talking about

an object-language and a meta-language, Wittgenstein should be recognized as

playing an important role in making it possible for Carnap to spell out the distinction

between an object-language and a syntax-language in Logical Syntax, rather than

negatively as someone from whose influence Carnap had to liberate himself, as he is

portrayed in the secondary literature. (See Awodey and Carus 2009.) Wittgenstein’s

saying-showing distinction is also what opens up the space for Carnap’s principle of

tolerance in the sense that, by means of his saying-showing distinction, Wittgenstein

is the first to spell out the idea that the statements of logic are not true or false about

anything, which Carnapian tolerance presupposes. Let us look at these issues more

closely.

The basic idea of the saying-showing distinction can be characterized as

follows. If we assume that the function of language is the making of true/false

statements, as in Wittgenstein’s calculus given its notion of the general propositional

form and truth-functional account of logical inference, then there is no such thing as

making statements about what is logically necessary or possible. Rather, logical

possibility is something that, so to speak, finds its expression in the possibility of

formulating statements that describe states of affairs. In other words, what is logically

possible is just those states of affairs that can be described in language. (cf. TLP

23

2.203, 3.02) What is logically necessary, by contrast, is that which the possibility of

such descriptions presupposes. The latter we can come to grasp through a certain kind

of process of abstraction, by coming to understand what underlies possible

descriptions and is common to them. (TLP 3.34-3.3421) What such a process of

abstraction then leads us to, Wittgenstein maintains, is the Tractarian calculus. And it

is by spelling out the principles of such a calculus that Wittgenstein believes we

should seek to present the logical laws that govern true/false thinking. Such logico-

syntactical laws are to be made perspicuous by means of a symbolic notation that

doesn’t conceal the principles of its operation, like everyday language does. In

particular, according to Wittgenstein, the laws of logic cannot be presented by means

of true/false statements, because in so doing we are making use of what we are

supposed clarify, assuming that in making true/false statements we must rely on the

laws of logic. This is also to fail to distinguish clearly between the generality of

general facts that hold without exception but still accidentally, and what holds by

without exception by necessity.

The motive behind the distinction between what can be said and what can only

be shown in the Tractatus is therefore to clarify the distinction between true/false

statements and the expression of logical possibility and necessity. Because logical

possibility and necessity is what is determined by the rules of logical-syntax, we can

also say that the saying-showing distinction is an attempt to distinguish between

statements that can be made within a system of language and the rules that determine

the system, whereby Wittgenstein wants to emphasize that the status or role of the

rules of syntax is entirely different from that of the true/false statements that

presuppose such rules. As he comments later (sometime between 1929 and 1936) on

this distinction: “The difference between ‘saying’ and ‘showing’ is the difference

between what language expresses and what is recorded in the grammar [was in der

Grammatik steht].” (VW, 130) In other words, the term ‘that which is shown’ refers

to the logico-syntactical determinations of what is logically necessary and possible, as

opposed to statements that presuppose those determinations. Wittgenstein then

continues by explaining why he chose to speak about something being shown in this

connection: “The reason for choosing ‘it is shown’ was that one sees a connection in

the notation. What one learns from the notation is indeed something different from

what the language expresses, and this in turn means nothing other than that grammar

can’t be derived from facts. […] I learn internal relations only from the grammar,

24

even before I have used language, i.e. even before I have said something.” (VW, 130,

131) Assuming that by ‘seeing a connection’ Wittgenstein means here ‘seeing an

internal relation’, i.e. a logical or syntactical relation, that which is shown, and can be

seen in the notation, may be characterized as that which is laid down in the rules of a

language or a calculus and which, in this sense, logically precedes any statements

made in that language. And while the statements made in the language may be

justified by reference to the facts they describe, there is no corresponding justification

for the rules of logical syntax. This is the sense in which logical syntax and grammar

cannot be derived from facts.

But if this is the way to understand Wittgenstein’s distinction between what is

said and what is shown, then this distinction closely corresponds to what Carnap

wants to capture in terms of the distinction between the object-language and syntax-

language. For what language, according to Wittgenstein, shows is just those formal

characteristics or logico-syntactical determinations that according to Carnap’s

conception are determined in syntax-language and spelled out in its terms. As Carnap

characterizes the notion of syntax language, it is ‘the language in which we speak

about the syntactical forms of the object-language’ (LSL, 4). In other words, by

rejecting the possibility of true/false statements about formal characteristics,

Wittgenstein emphasizes the very same distinction that Carnap marks by talking about

an object- and a syntax-language, thus distinguishing between the rules that determine

a system and statements made in that system, and between the status or role of the two

kinds of statements. Now the reason why the Tractatus says it is not possible to speak

about the syntax or the formal characteristics of language can be explained as follows:

It is characteristic of the Tractatus’ system that it regards or treats all statements as

true/false statements, that is, all statements within that system are of this type. That

logic or syntax cannot be spoken about, but only shown, then simply means that it

cannot be the object of true/false statements – and therefore also cannot be justified by

reference to reality. That logic cannot be the object of true/false statements, and that

the laws of logic are not comparable to scientific statements in this sense, is

Wittgenstein’s key criticism of Frege and Russell.

Here we come to an important point about the relation between Carnap and

Wittgenstein. If the way to understand the saying-showing distinction is as just

explained – and it seems to be so by Wittgenstein’s own testimony –, then, pace

Carnap, the key issue is not that syntax cannot be spoken about. Rather, the point of

25

Wittgenstein’s distinction is that the status of determinations of syntax is different

from the status of statements made in the system that those determinations define, and

in particular that the determinations of syntax are not true/false statements. The latter

is something that Carnap also recognizes: that syntactical statements are not true or

false about anything is a central feature of his philosophy of logic. However, in

Logical Syntax he doesn’t connect this point with the saying-showing distinction, but

only with Wittgenstein’s view of the tautologousness of logical truth.19 Regardless of

Carnap’s failure to connect the point that logic is not true/false with the saying-

showing distinction, however, just this view that statements about syntax or logic are

not true/false statements lies at the bottom of his famous principle of tolerance.

Without the Wittgensteinian ‘non-cognitivism’ about logic the principle of tolerance

is not possible, but a crucial part of it is that logic is not true/false about anything.

Accordingly, it is Carnap’s explicitly stated intention in Logical Syntax to question

the idea that logical languages must be justified by reference to their correctness and

should constitute “a faithful rendering of the ‘true logic’.” (LSL, xiv) Rather, he

characterizes it as one of the chief tasks of the book to eliminate this standpoint,

together with the pseudo-problems and controversies that arise as a result. (LSL, xv)

More specifically, the principle of tolerance, he says, relates to all questions of logic.

In logic ‘[…] we have in every respect complete liberty with regard to the forms of

language; […] both the forms of construction for sentences and the rules of

transformation […] may be chosen quite arbitrarily.’ (LSL, xv, cf. 51, 52; see also

Carnap 1988, 221) Rather than trying to justify the choice of logic or the forms of

language by reference to any facts, in logic only the syntactical consequences to

which a choice of language leads matter. Thus, in the end the choice of a language

becomes for Carnap a practical question of expediency. (LSL, xv)20

19 See, LSL, 44 and the first quote in section 1. Carnap is not without right to connect the point about logic not being true/false with the view of the tautologousness of logic only, and to disagree with the claim that we must be silent about logic. The Tractatus was confused about this very issue in the sense to be explained shortly. Interestingly, however, Wittgenstein remarks in a letter to Russell about the order of priority of these two conceptions: ‘Now I’m afraid you haven’t really got hold of my main contention, to which the whole business of logical prop[osition]s is only a corollary. The main point is the theory of what can be expressed (gesagt) by prop[osition]s -- i.e. by language -- (and, which comes to the same, what can be thought) and what can not be expressed by prop[osition]s, but only shown (gezeigt); […]’ (CL, 124)20 The principle of tolerance is assumed also in the following characterization of the nature of philosophical statements: ‘It is especially to be noted that the statement of a philosophical thesis sometimes […] represents not an assertion but a suggestion. Any dispute about the truth or falsehood of such a thesis is quite mistaken, a mere empty battle of words; we can at most discuss the utility of the proposal, or investigate its consequences.’ (LSL, 299, 300)

26

Carnap therefore occupies in Logical Syntax a fundamentally Wittgensteinian

position in the sense that, like Wittgenstein, he distinguishes sharply between the

statements of logic or syntactical statements and true/false factual statements.21 The

function of syntactical sentences for Carnap is to determine the logic of the

expressions in the object language. And here both him and Wittgenstein agree that

syntax (and its determinations in syntactic sentences), is not answerable to any facts in

the sense of logic being true or false about anything, and not to be articulated in

true/false factual statements. Besides their agreement on this point, spelt out in the

Tractatus by means of the saying-showing distinction, the fact that Carnap admits

syntactical sentences, while the Tractatus doesn’t, is of no comparable significance.

As argued earlier, there are no great obstacles to Wittgenstein’s acceptance of such

statements, given that he is already employing in the Tractatus something like

Carnapian quasi-syntactical sentences, granted that syntactic sentences are clearly

distinguished from true/false statements, as they are in Logical Syntax. Perhaps this

then explains, why in connection with Carnap’s paper from 1932 Wittgenstein

thought Carnap was not taking a single step beyond his own position by introducing

the distinction between material and formal mode. For this is just the distinction that

the saying-showing marks: it delineates statements in the material mode from the

formal. In between these two modes are Wittgensteinian quasi-syntactical

elucidations.

The point might also be put like this: the key to understanding the saying-

showing distinction is not Wittgenstein’s declaration of silence; in the end this not the

essential point. In fact, as Wittgenstein came to realize, the requirement of silence

involves a confusion, the merging of two distinct issues that he should have kept apart

(see below, section 6). Rather, the distinction should be seen as an attempt to drive

home the point that logic is not true/false about anything. Indeed, soon enough

Wittgenstein separated the latter point from the urge to silence. Expressed as the

principle of the arbitrariness of grammar, i.e. that grammar cannot be justified by

reference to what statements describe, he continued to hold the view that logical

statements are not true/false until the end of his career. Apparently he first formulated

the principle in these terms in March 1930, stating it also about syntax, although at

21 Carnap occupies this position until the end of his career, despite Quine’s attempts to dislodge him through the criticism of the analytic-synthetic distinction. Wittgenstein comes to loosen up the distinction: the distinction between grammatical and empirical statements, according to his later view, is not clear cut and fixed (see for example OC §96-99).

27

this point Wittgenstein increasingly starts using the term ‘grammar’ instead of

‘syntax’ (Ms108, 104 and PR, 322; see also PI §370-373). Historically speaking, the

saying-showing distinction had therefore already been transformed in this way well

before the priority dispute, and before Carnap’s formulation of the principle of

tolerance (in 1932, according to Carus 2007, ch.10). Accordingly, Carnap too already

knew to write in his foreword to Logical Syntax in 1934: ‘[…] in opposition to

Wittgenstein’s former dogmatic standpoint, Professor Schlick now informs me that

for some time past, in writings as yet unpublished, Wittgenstein has agreed that the

rules of language may be chosen with complete freedom.’ (LSL, xvi) Regardless of

whether this is an accurate way to describe Wittgenstein’s new conception, Carnap

was aware of criticizing in his book a view Wittgenstein no longer held, and indeed,

Wittgenstein himself had been characterizing his earlier view as dogmatic since 1931,

also in the sessions of the Vienna Circle. (See Ms111, 119/CV, 21, 22; WVC, 182ff.)

To conclude, let us discuss briefly the confusion involved in the saying showing

distinction.

6. Wittgenstein’s confusion

As noted, Carnap was not without right to identify the saying-showing distinction

with a exclusion of syntactical statements: Wittgenstein himself was not clear about

matters at this point, merging together different issues. Wittgenstein’s unclarity is

directly connected with what he came later to see as the crucial mistake of the

Tractatus. For the aspiration of the book had been to put forward a method of

clarification in which philosophical claims or theses would play no part. But as

Wittgenstein came to realize later (by the early 1930s), philosophical or metaphysical

claims about the nature of language and philosophy – of what language must be and

what philosophy must be – had found their way into the book, disguised as

methodological claims.22 Basically, one might say that Wittgenstein failed to

distinguish between two distinct issues: i) spelling out principles of a logical system

or a calculus, and ii) the claim that this system or calculus captures what our language

or natural language actually is like. For if it is the case that natural language is like the

Tractatus’ calculus, and the notion of the general propositional form really captures

22 I discuss the Tractatus’ failure in detail in and spell out an interpretation of Wittgenstein’s later methodology as a response to it in Kuusela 2008; see especially chapters 2 and 3.

28

its essence, then any statements about logic would turn out to be nonsense. But that

our language actually is like this, or that language must by its very nature be like this,

is a claim that is distinct from merely spelling out or introducing syntactical concepts

and principles. And while simply to do the latter is not to present any claims or theses

(to state rules for a calculus is not to claim anything), the former claim that our

language, or natural language, actually functions like a particular calculus – or any

calculus – is a substantial claim.

This distinction can be clarified as follows. Language can in a certain sense be

described by spelling out syntactical principles. Such descriptions, however, are

merely descriptions of a language in the sense of a design; to give such a description

is to describe a possible language, like by stating rules for a game one can describe a

possible game. (Giving descriptions in this sense corresponds to what Carnap in the

Logical Syntax calls ‘pure syntax’.) But this also means that it is a further logically

distinct step to claim that any actual language in fact corresponds to such a design, i.e.

functions according to relevant rules. Here the word ‘description’ is used in a different

sense, i.e. in the sense of a true/false description. (For discussion of this distinction,

see, Ms113, 22r-23v, 28v; Ts211, 569–570, 576; Ts213, 240–242r, 245r; Ms115, 57-

59, Kuusela 2008, 115-116.) This further step can be understood in several ways,

corresponding to different types of claims that might be made. To take this further

step might be to make an empirical claim about language (as in Carnap’s descriptive

syntax, or for example in linguistics), or also to make a metaphysical claim,

understood as a claim about the necessary nature of something. In effect, Wittgenstein

came to make the latter kind of a claim – a metaphysical claim about what language

must be – thus putting forward a philosophical thesis against his intentions.

It is important for understanding Wittgenstein’s mistake that it was not his

intention to present such a thesis about language. This would directly contradict the

Tractatus’ aim of philosophizing without theses. Rather, he relapsed into advancing

such a thesis through the methodological claim that all philosophical problems can be

resolved by logical analysis in terms of the Tractarian calculus, or that by introducing

this method of analysis he had solved all philosophical problems ‘in essentials’ (TLP,

Preface). For even though the introduction of a scheme for logical analysis as such

doesn’t constitute a thesis about anything, to claim that the scheme of analysis is

universally applicable to any proposition whatsoever, is to put forward a thesis. In this

sense metaphysics of language, part of which was the exclusion of syntactical

29

sentences, disguised itself in the gown of philosophical methodology in the Tractatus.

Consequently, as Wittgenstein came to realize later, the methodology needed to be

reconceived. This task then led him to his so-called later philosophy, where he also

recognizes the possibility of statements about logic or what he calls ‘grammatical

statements’ (cf. e.g. BB, 30, 55). The discussion of how his later philosophy of logic

relates to Carnap’s (or to the model theoric conception), and how it might possibly

solve problems that arise for Carnap’s syntactical method and his later method of

explication, however, must be left to another time.

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