Carnap and the Tractatus’ philosophy of logic
Oskari 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logic superseded.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.
2
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 –
3
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
4
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
5
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
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 pseudoproblems, 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, pseudo6
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
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 sayingshowing 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 objectand 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
7
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
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
8
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
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
discourse is the clarification of their forms or syntactical properties (cf. Carnap 1932,
9
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
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
10
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 socalled 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, 303304 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.
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
11
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.
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
12
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
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
13
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 socalled 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
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
14
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
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
15
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
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
16
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 objectand 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
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
17
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 ‘pseudoconcept 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 quasisyntactical 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
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
18
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
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 pseudostatements. 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
19
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
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
20
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
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
21
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
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 logicosyntactical 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
22
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,
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 syntaxlanguage. 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
23
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
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 sayingshowing 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
24
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
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 sayingshowing 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
this point Wittgenstein increasingly starts using the term ‘grammar’ instead of
25
‘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
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
26
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, 5759, 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
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
27
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.
References
Awodey, Steve and Carus, Andre. ‘From Wittgenstein’s Prison to the Boundless
Ocean: Carnap’s Dream of Logical Syntax’, in Wagner, P. ed., Carnap’s
Logical Syntax of Language. Basingstoke: Palgrave Macmillan, 2009.
Carnap, Rudolf. ‘Die Physikalische Sprache als Universalsprache der Wissenschaft’,
Erkenntnis, Vol. 2, No 5/6, 1932, pp. 432-465.
---. ‘The Physical Language as a Universal Language’, in Black, M. ed., The Unity of
Science. London: Kegan Paul, Trench, Trubner & Co., 1934.
---. ‘On the Character of Philosophic Problems’. Philosophy of Science, Vol. 1, No. 1
(1934), pp. 5-19.
---. Philosophy and Logical Syntax. London: Kegan Paul, Trench, Trubner & Co.,
1935.
---. The Logical Syntax of Language. London: Routledge & Kegan Paul, 1937/1967.
(LSL)
---. Introduction to Semantics. Cambridge, MA: Harvard University Press, 1942/1948.
(IS)
---. ‘Intellectual Autobiography’, in Schlipp, P. A. ed., The Philosophy of Rudolf
Carnap. La Salle, IL: Open Court, 1963.
---. ‘Empicism, Semantics and Ontology’, in Meaning and Necessity: A Study in
Semantics and Modal Logic. Chicago: University of Chicago Press, 1988.
Carus,
Andre.
Carnap
and
Twentieth-Century
Thought:
Explication
as
Enlightenment. Cambridge: Cambridge University Press, 2007.
Diamond, Cora. ‘Throwing Away the Ladder: How to Read the Tractatus’, in The
Realistic Spirit. Cambridge, MA; The MIT Press, 1991.
Frege, Gottlob, ‘On Concept and Object’, in Geach P. and Black, M. eds.,
Translations from the Philosophical Writings of Frege. Basil Blackwell:
Oxford, 1966.
28
Friedman, Michael. Reconsidering Logical Positivism. Cambridge: Cambridge
University Press, 1999.
Hintikka, Jaakko. ‘Ludwig’s Apple Tree: On the Philosophical Relations between
Wittgenstein and the Vienna Circle’. In: Selected Papers, Volume 1,
Dordrecht, 1996.
Kienzler, Wolfgang. ‘Wittgenstein und Carnap: Klarheit oder Deutlichkeit als Ideal
der Philosophie’, in Schildknect C., Teichert, D. and van Zantwijk T. eds.,
Genese und Geltung. Padrebon: Mentis, 2008.
Kuusela, Oskari. The Struggle against Dogmatism: Wittgenstein and the Concept of
Philosophy. Cambridge, MA: Harvard University Press, 2008.
---. ‘The Development of Wittgenstein’s Philosophy’, in Kuusela, O. and McGinn, M.
eds., The Oxford Hanbook to Wittgenstein. Oxford: Oxford University Press,
forthcoming-a.
---. ‘The Dialectic of Interpretations: Reading Wittgenstein’s Tractatus’, in Lavery,
M. and Read, R., Beyond the Tractatus Wars. London: Routledge,
forthcoming-b.
Nagel, Ernest. ‘Review of Carnap’s Logische Syntax der Sprache’. Journal of
Philosophy, Vol. 32, No. 2(1935): 49-52
Quine, W. V. ‘Review of Carnap’s Logische Syntax der Sprache’. The Philosophical
Review, Vol. 44, No. 4 (1935): 394-397.
Stern, David. ‘Wittgenstein, the Vienna Circle, and Physicalism, a Reassessment’, in
Richardson, A. and Uebel, T. eds., The Cambridge Companion to Logical
Empiricism. Cambridge: Cambridge University Press, 2007.
Wagner, Pierre. ‘The Analysis of Philosophy in Logical Syntax: Carnap’s Critique
and His Attempt at Reconstruction’, in Wagner, P. ed., Carnap’s Logical
Syntax of Language. Basingstoke: Palgrave Macmillan, 2009.
Waismann, Friedrich. The Principles of Linguistic Philosophy. Basingstoke: Palgrave
Macmillan, 1995.
Wittgenstein, Ludwig. Tractatus logico-philosophicus. Translated by Ogden, C. K.
London: Routledge & Kegan Paul, 1951. (TLP)
---. Preliminary Studies for the “Philosophical Investigations” Generally Known as
the Blue and Brown Books. Oxford: Basil Blackwell, 1958. (BB)
---. Notebooks 1914-1916. Anscombe, G. E. M. and von Wright, G. H. eds, translated
by Anscombe, G. E. M. Oxford: Basil Blackwell, 1961. (NB)
29
---. Prototractatus: An Early Version of Tractatus Logico-philosophicus. Ithaca, NY:
Cornell University Press, 1971. (PTLP)
---. Letters to C. K. Ogden with Comments on the English Translation of the Tractatus
Logico-Philosophicus. von Wright, G. H. ed. Oxford: Blackwell, 1973. (LO)
---. Philosophical Grammar. Rhees, R. ed., translated by Kenny, A. Oxford: Basil
Blackwell, 1974. (PG)
---. Wittgenstein’s Lectures, Cambridge 1932-35. Ambrose, Alice, ed.Oxford: Basil
Blackwell, 1979. (AWL)
---. On Certainty. Anscombe, G. E. M. and von Wright G. H. eds., translated by
Anscombe, E. and Paul, D. Oxford: Blackwell, 1993. (OC)
---. Philosophical Investigations, Second Edition. Anscombe, G. E. M and Rhees, R.
eds., translated by Anscombe, G. E. M. Oxford: Blackwell Publishers, 1997.
(PI)
---. Ludwig Wittgenstein: Cambridge Letters, Correspondence With Russell, Keynes,
Moore, Ramsey and Straffa. McGuinness B. and von Wright, G. H. eds.
Oxford: Blackwell, 1997. (CL)
---. Culture and Value. Revised Edition. von Wright, G. H. in collaboration with
Nyman, H. ed., rev. ed. by Pichler, A., translated by Winch, P. Oxford:
Blackwell, 1998. (CV)
---. Philosophical Remarks. Rhees, R. ed. Blackwell, 1998. (PR)
---. Wittgenstein’s Nachlass, The Bergen Electronic Edition. Oxford: Oxford
University Press, 2000. (Quotations by manuscript or typescript number
following von Wright’s catalogue.)
---. Wittgenstein, Ludwig and Waismann, Friedrich, The Voices of Wittgenstein: The
Vienna Circle, Ludwig Wittgenstein and Friedrich Waismann. Baker, G., ed.,
London and New York: Routledge, 2003. (VW)
---. Ludwig Wittgenstein: Gesamtbriefwechsel/Complete Correspondence. Inssbrucker
Electronic
Edition.
Monika
Seekircher,
Brian
McGuinness,
Anton
Unterkircher, eds. InteLex, 2004. (GB)
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.
1
30
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.
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 Tractatusinterpretation 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.
10
I discuss this strictly correct method and its relation to the method employed in the Tractatus itself in
more detail in Kuusela 2011.
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
31
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)
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
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.
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 quasisyntactical 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)
17
Carnap translates this as: ‘29b Science is a system of sentences, not of names.’ (LSL, 303)
18
Other Tractarian sentences he uses as example of untranslatable and therefore unacceptable
metaphysical statements. (See, LSL, 314)
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)
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).
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.
32