[Formatting notes. Text in italics is bracketed by stars (*...*)] 

Cognitive Science and Wittgenstein's *Tractatus* 

Philip Swann 

Faculte' Psychologie et des Sciences de l'Education Universite' de
Gene've 1211 Gene've 4 Switzerland

swann@divsun.unige.ch 

Abstract 

Wittgenstein's philosophical work contains much of interest for
students of cognitive science. Attention so far has been largely
limited to the later philosophy of the *Philosophical Investigations*,
but a correct view must take into account the earlier work of the
*Tractatus* and the evolution of Wittgenstein's ideas. Starting from
David Pears' recent interpretation, this paper considers the
implications of the *Tractatus* for the foundations of cognitive
science. It is argued that Wittgenstein's early philosophy tackled
many of the theoretical issues facing cognitive science and proposed
imaginative solutions to the major problems. Taken with his later
criticism of some of these solutions, Wittgenstein offers a far deeper
and richer starting point for theory than is usually assumed in the
current debate concerning the foundations of cognitive science.


1 Introduction 

Wittgenstein's *Tractatus Logico-Philosophicus* (1922) is arguably the
most important work for the philosophy of language ever published.
This accolade, however, is usually reserved for its nearest rival, the
same author's *Philosophical Investigations* (1953), which is certainly
better known and more frequently cited. There is, in fact, a
wide-spread belief that the second book is a replacement for the first
and so the mental stress involved in "reading" the TLP can be avoided
with a clear conscience. This was not Wittgenstein's own view. In the
Preface to PI he says that he had planned to re-publish the TLP in the
same volume, since "the latter could be seen in the right light only
by contrast with and against the background of my old way of thinking"
(p.vi). He then goes on, however, to talk of "grave mistakes" in the
earlier work, setting the tone for the popular belief that PI
represents a rejection of TLP and the birth of a whole new way of
doing philosophy. In contrast, the posthumous publication and critical
study of W's many manuscript works, which began in 1960, has revealed
a great deal of continuity of method and doctrine from the earlier to
the later philosophy. This broader context has been put to good use in
recent studies of W's philosophical development and, as Anthony Kenny
says in his (1973), "as we move further in time from the writing of
the Investigations we can see that the likenesses to the Tractatus are
as important as the unlikenesses" (p.232). One might also add that we
shouldn't take for granted that W always moved in the right direction
as he revised and developed the early philosophy.
 
The TLP is, then, important for philosophers wishing to understand W's
work. But is it important for cognitive scientists concerned with the
theoretical foundations of the study of human language? I believe that
it certainly is, and for many more reasons than the fact that it is an
indispensable aid to the interpretation of the linguistic parts of PI.
In this paper, I shall present some of the main doctrines of TLP as
they emerge from the first volume David Pears' recent study of W's
philosophical development (Pears 1987). This central part (Sections
3-9) is bracketed by introductory and concluding remarks indicating
some of the connections between W's work as a whole and the concerns
of cognitive science. I suggest that these connections can only be
profitably exploited if, firstly, the early work in TLP is given its
proper weight and, secondly, due attention is paid to W's
philosophical doctrines: the W corpus is a gold mine for students of
semiotics, linguistics and psychology, but its proper use depends on a
correct reading of the philosophical problems that were its driving
motivation.

2 Cognitive Science and Wittgenstein 

Cognitive science results from the interaction between three main
disciplines: computer science (especially the branch known as
artificial intelligence), linguistics (especially formal and
computational linguistics) and psychology (especially cognitive and
developmental research in the Piagetian tradition). Here I shall give
a brief example of the impact of W on each of these disciplines.

There is a crisis in Artificial Intelligence research which sets the
*symbolic processing models* (founded in the 1950s by Allen Newell and
Herbert Simon) against the renascent *connectionist* models (also
founded in the fifties, by Rosenblatt and others, put to rest by
Minsky and Papert in 1970; and then resuscitated by Rumelhart,
McClelland and others in the early eighties). Dreyfus and Dreyfus
(1988), in an interesting discussion, suggest that the symbolic
processing models were founded on precisely the rationalist philosophy
that is proposed in the TLP; while the connectionist models are to be
justified by the holistic philosophy of PI. This allows them to treat
W as a kind of AI visionary who went through an anticipatory
philosophical version of the current crisis: 

[put this quote in smaller type]
It is one of the ironies of intellectual history that Wittgenstein's
devastating attack on his own *Tractatus*, his *Philosophical
Investigations*, was published in 1953, just as AI took over the
abstract, atomistic tradition he was attacking. After writing the
*Tractatus*, Wittgenstein spent years doing what he called phenomenology
-- looking in vain for the atomic facts and basic objects his theory
required. He ended by abandoning his *Tractatus* and all rationalistic
philosophy. He argued that the analysis of everyday situations into
facts and rules (which is where most traditional philosophers and AI
researchers think theory must begin) is itself only meaningful in some
context and for some purpose. (p. 26)

This is neat but surely simplistic. Firstly, it adopts the "two
philosophies" account of W's development, which is no longer tenable.
Secondly, it reads into AI theories and models a philosophical content
which they almost entirely lack. On the other hand, there is no doubt
that W's ideas would have to play a central role in any serious
foundation for AI: the collection of essays in which the Dreyfus and
Dreyfus paper appears is optimistically entitled *The Artificial
Intelligence Debate: False Starts, Real Foundations.*

W's influence on modern theoretical linguistics has yet to be
chronicled. It is probably far more pervasive than could be inferred
from the very limited communication between philosophers and
linguists. The increasing interest in the pragmatic and social aspects
of human language over the last couple of decade has certainly
received some of its impulse from ideas originating in W's later
philosophy, but the influence is largely indirect (via Searle, Austin
and others). An interesting exception is Chomsky, whose theory of
language played a central role in establishing the cognitive science
paradigm and who has never hesitated to engage in philosophical debate
with his critics and rivals. Now, many of these critics have
explicitly appealed to W's later philosophy -- to such an extent that
Pateman (1987) contains a chapter on the debate between
"Wittgensteinians and Chomskyans". The argument reached its peak,
when, in his (1982), Kripke published a now famous reading of the
"private language argument" in the *Philosophical Investigations* and
suggested in a footnote that "Modern transformational linguistics ...
seems to give an explanation of the type that Wittgenstein would not
permit" (p.97, n.77). Chomsky (1986) takes this attack seriously and a
whole chapter is devoted to an attempted refutation.  

Another discipline which has recently discovered W, also as a result
of a prolonged crisis in its foundations, is developmental psychology.
Chapman and Dixon (1987) is a collection of papers by eleven
psychologists who share the conviction that "if properly illuminated,
the figure of Wittgenstein will cast a shadow across the landscape of
developmental theory, method, and substantive research" (p. v). As
might be expected, it is very much the shadow of the later W that is
meant here, not the metaphysician and logician of TLP who, like Frege,
explicitly excluded psychological considerations from the domain of
philosophy. But, for these authors, the interest in the later W
derives is good measure from the desire to find an alternative to
various rationalist approaches in psychology; approaches that could be
considered to share at least some ideological roots with the early W.
The situation is analogous therefore to that in AI described by the
Dreyfus's.  


3 Pears on the *Tractatus* 

There are therefore good reasons for taking interest in new work on
the TLP: the book remains highly relevant and there is still much
progress to be made both in understanding the text itself and in
applying that understanding to linguistics. Volume 1 of Pears (1987)
is a substantial exegesis of some key parts of TLP, resulting from a
close and prolonged study of the entire W corpus. It is, however, very
much a philosophical text addressed to other philosophers: nothing is
said directly about the implications of the exegesis for cognitive
science.  Moreover, Pears makes no concessions to his reader: in many
cases, repeated and careful readings are required to grasp the point
he is making. The book is divided into eight chapters and two parts.
Part I (pp. 1-60) is an Introduction to the whole of W's philosophical
development with the following chapters: (1) A Wide-angle View; (2)
Close-up: The Early System; (3) Close-up: The Later System. Part II
(pp. 60-191) Inside the Early System is a detailed study of key
aspects of TLP: (4) Logical Atomism; (5) The Basic Realism of the
Tractatus; (6) Sentences and Pictures; (7) Solipsism; (8) Review and
Prospects.

Pears thus explicitly covers TLP three times and, together with
repetition over chapters within Part II, this leads to extensive
cross-references: the first page of Chapter 6 has no less than eight.
In part, this reflects the characteristic non-linearity of W's texts,
which applies not only to the order of exposition, but also to the
development of the doctrines and arguments themselves. The result is
that the W corpus resembles a hypertext system, in which each
paragraph or remark has an arbitrarily large number of implicit links
to other remarks. The hierarchical numbering of TLP is in fact the one
attempt W made to structure a text, but, as Max Black comments in his
(1964), "the device is so misleading here as to suggest a private joke
at the reader's expense" (p. 2). In other words, W has given us the
nodes of a hypertext without any clear map of which links we should
follow and in what order. But Pears non-linearity doesn't correspond
in any obvious way to the structure of TLP: the overall impression is
of a thinker circling round main topics looking for a way into
sub-topics, only to find himself again circling around the sub-topic
and so on recursively.

Pears' goal is almost purely exegetical: he seeks to establish what W
himself would have accepted as an exposition of the key ideas in TLP
at the time the book was written. He deals only with the central
philosophical ideas and arguments, excluding any discussion of the
formal logic. The whole corpus of W's writings is utilized, especially
the Notebooks that were preparatory to TLP and W's own later criticism
of his early philosophy. This results in an admirable feel for the
changing intellectual landscape that surrounds the text of TLP: Pears
shows very clearly how W struggled over many years with the
consequences of his extreme commitments. The only direct philosophical
influence considered by Pears is Russell. Kant, Schopenauer and Hume
also put in an appearance, as do a number of philosophical -isms
(Idealism, Platonism, Solipsism, Conventionalism etc.), but the
connections usually come across as either rather indirect or a bit
forced. This is not surprising, since W was notoriously indifferent to
other philosophers (with the exception of Frege, and to a lesser
extent Russell) and says so in the Preface to TLP.  With a couple of
exceptions, Pears makes little direct use of the secondary literature
in his text.  

Pears, therefore, writes in the narrow tradition of Wittgenstein
studies, following the majority of Anglo-American scholars (Anscombe,
Black, Fogelin, Kenny etc.). This means that he considers W's early
ideas and doctrines as a continuation of the work of Frege and
Russell, and of philosophical interest insofar as they engage directly
with what British and American professional philosophers consider
important. And it also means that he rejects the much richer context
of interpretation proposed by Janik and Toulmin in their (1973) and
supported, perhaps a little half-heartedly, in McGuiness (1988). This
richer interpretation supposes that W's early philosophy can only be
fully understood by considering its Austrian cultural matrix: not only
the music, painting and literature but also the philosophies of
language (especially that of Mauthner) and science (especially Mach
and Hertz).

  In the next six sections of this paper, I shall review the main
topics addressed by Pears, suggesting along the way some connections
with the concerns of cognitive science. The goal is not to evaluate
his textual exegesis, which seems to be scrupulously correct, nor to
argue with his broader philosophical reflections, some of which seem
rather strange. It is rather to identify Pears' contribution to the
critical problem of clarifying the conceptual space between the two
extremes: i.e. to giving the reader a plausible account of the mental
model, or models, from which W was working. It is possible, as some
critics have suggested, that such a model didn't exist, or that W
mixed and confused several different models resulting in a text that
is incoherent. It is also possible that he did have a coherent model
in mind, but that there is no sure way of recovering it. In the latter
case we should expect to (eventually) arrive at a number of competing
interpretations none of which could be eliminated by appeal to what W
actually wrote or is recorded as having said. There is a third
possibility: the model W worked from may be in part coherent and fully
defined and in part undefined. In this case, the coherent completion
of the parts that were left undefined may be possible or it may not.
Pears adheres quite clearly to this third possibility in its
pessimistic version: he believes that underlying the TLP is a model
that is coherent in so far as it is defined, but that cannot be
completed without becoming incoherent. Further, he claims that the
reason W left certain parts of the model undefined is not that he knew
or suspected the potential problems, but rather that he believed the
completion was unnecessary.  This certainly squares with W claims in
the Preface that he had solved all the problems of philosophy, and his
subsequent abandonment of the subject for some ten years; as well as
with his criticism of TLP in his later work.


4 What is the Tractatus about?  

In the Preface to TLP W sums up what he calls the whole meaning of the
book by paraphrasing its last sentence: "What can be said at all can
be said clearly, and what we cannot talk about we must pass over in
silence." What we must pass over includes all the problems of
philosophy, because when we try to talk factually about them the
result is nonsense. But this does not mean that there is no reality
behind the problems: on the contrary, what we mistakenly try to put
into words is already *shown* to us by the form of our language and its
relation to the world. Now the TLP is a philosophical treatise and
thus by its own definition nonsensical. W accepts this conclusion, but
also claims that the book definitively solves all the problems of
philosophy. It does this by *showing* the reader why it itself is
nonsense. Having seen what the book has to show, the reader can
discard it like a ladder used to climb up to a vantage point.  

This
paradoxical outcome may appear mystical or absurd: Pears himself
describes it as a "baffling doctrine bafflingly presented" (p. 143).
But there is no way around it: any study of TLP must surely accept W's
own statement of what the book is about. Faced with an apparently
absurd doctrine, a good move is to show that it is in fact related a
continuing theme, or themes, in Western philosophy.  Like some
previous commentators, Pears makes this move in his overview of W's
development by characterizing W's philosophy as critical in the
Kantian sense. By this he means that it seeks to mark out the limits
of the human intellect, the boundary between scientific sense and
metaphysical nonsense: "Kant offered a critique of thought and W
offers a critique of the expression of thought in language" (p. 3).
Like Kant, W rejects dogmatic or speculative metaphysics (of the kind
that would, for example, seek to show that Existence is prior to
Being) but admits the possibility of a metaphysic of experience: a
study of the necessary structuring of phenomena as we know them. While
admitting the possibility of such a metaphysic, he also denies that it
can be stated in factual language -- in contrast to Kant. Unlike Kant,
moreover, he does not believe is the existence of a transcendental
reality of things-in-themselves that cannot be experienced but only
thought: for W, the phenomenal world as we experience it is all that
there is or needs to be.  

Pears turns to Schopenhauer to help explain the mystical, almost
visionary tone of parts of TLP. This tone adds to the sense of paradox
mentioned above: if the book is nonsensical, then why is it written in
such an elevated, almost religious style? It is known that W read and
admired Schopenhauer (McGuiness 1988, pp. 39-40) but by the time of
TLP had abandoned the latter's Idealistic philosophy with its doctrine
of the world as a transcendental reality which we glimpse only through
the experience of our own agency (the Will). One thing he retained was
Schopenhauer's passionate spirituality, the belief that metaphysical
thought in some way is about our deepest emotional needs. As Pears
notes, this leads to something of a stylistic conflict in TLP:
"Wittgenstein's metaphysic is an affair of the head rather than the
heart ... However, the spirit of it and the sense that it gives of the
mystery of the world are more appropriate to a metaphysic derived from
human aspirations" (p.6). Pears, rightly I think, defends W by noting
that although TLP is a book about the world of everyday experience,
its theory is in fact a deep one that has a force equivalent to its
transcendental rivals. The style is thus justified: a conclusion which
few readers have challenged.

  What then is the metaphysics of TLP? First, W is a *realist*, in the
sense that he believes: (i) the world is independent of our experience
of it; (ii) what we experience is that same independent world: not a
veil of sense-data or an idealistic hologram projected by inaccessible
things-in-themselves. Second, W is a *critical* realist, in that he
believes (i) factual language represents the world accurately; (ii)
factual language as a representation, however, cannot say everything
about our experience; (iii) at least some of what cannot be said in
factual language is *shown* by its structure and the way that it
represents. Third, the main goal of TLP is to deduce the necessary
structure of reality from the logical analysis of factual language.
This deduction (although nonsense) allows the reader to grasp (at
least some of) what factual language shows.

The above immediately suggests two further questions. (i) Why can't
factual language say certain things? (ii) What are the things it can't
say? Pears answers the two questions briefly in Chapter 1, while
almost the whole of the rest of the book is devoted to enlarging on
the answers. His answer to (i) is that language cannot contain the
conditions of its own application, it cannot be grounded on itself;
and his answer to (ii) is that the things that can't be said include
the atomic, combinatorial nature of elementary objects and their
projection into sentence structure.

5 Logical Atomism deduced from the Analysis of Propositions

The elements of W's doctrine of logical atomism in the
TLP are relatively easy to state. The substance of the world consists
of a closed set of unchanging simples. Change is the result of the
varying combinations of the simples. There are no *a priori*
restrictions on these combinations: any simple can potentially combine
with any other. It is a matter of experience that some combinations
occur and not others. So far so good. But TLP does much more than
state an ontological theory: it claims that the truth of the theory
can actually be demonstrated from the analysis of natural language.
The claim, however, is not backed up with a detailed argument -- the
most we get are a few suggestive remarks. Faced with these remarks and
the evident centrality of the topic, Pears', like other commentators,
has two goals: (i) render explicit W's argument that establishes the
necessary existence of simples; (ii) add some substance to W's
telegraphic pronouncements regarding the nature simples (what are
they? what properties do they have?). He uses Russell's version of the
theory for contrast because W "reacted against Russell's views without
totally abandoning them" (p.64), and situates his interpretation as a
middle approach between those of Hintikka and McGuiness (see Section
6). The first half of Pears' Chapter 3 (pp. 63-73) sets out his
interpretation of W's argument. In the second half (pp. 73-87) he
reviews the textual evidence in support of his interpretation both of
the argument and the doctrine. Pears' version of the argument is as
follows.


			*Proposition to Prove*

Ordinary factual sentences can be analysed down to elementary
propositions in which only simples are named. These elementary
propositions never contradict each other because the simples named in
them are devoid of internal structure.


			      *Argument*

1. Assume that the complete analysis of a factual sentence includes an
elementary proposition that contains the name of a complex.

2. Then the sense of this elementary proposition would depend on the
truth of other sentences (not included in its analysis because it is
elementary) asserting the existence and correct arrangement of the
components of the complex.

3. But the question whether a sentence has sense can never depend on
the truth of another sentence about a constituent of the first.

4. Therefore we have a contradiction and (1) is false. The analysis is
not complete and we must continue until all words for complexes have
been replaced by genuine names for simple objects.

It is clear that the crucial step in this argument is given in (2) and
(3). Pears expands this as as follows. Consider the total demand made
on a sentence for it to be true. This can be divided into sense
conditions (roughly, what allows it to have meaning or semantic
content) and truth conditions (what determines if the sentence is true
or false). Given a sentence f(a), its sense conditions are (i)
existence of f and a; (ii) f is combinable with a; (iii) 'f' and 'a'
are attached to f and a as names.  The truth condition is that f and a
should be arranged in reality as f(a) says they are arranged. Now
suppose that a is actually a complex that can be analysed by the
sentence 'bRc'. Is the truth of bRc a sense-condition or a
truth-condition of f(a)? It must be a truth-condition, because
sense-conditions are ineffable and bRc is clearly not! We of course
now want to know why sense-conditions are ineffable (especially since
Pears has apparently just stated them for the sentence in question).
Pears says that this is a consequence of the Picture Theory, and will
have to wait until his Chapter 6 (see my Section 7). So this
establishes (2). But we are left with (3): why is it impossible for
the possession of sense by f(a) to depend on the truth of bRc? As far
as I can understand, Pears gives no answer to this question, leaving
the whole argument hanging in mid-air. Kenny (1973) offers the
following: "Whethera sentence has meaning or not is a matter of logic.
Whether particular things exist or not is a matter of experience. But
logic is prior to all experience. Therefore whether a sentence has
meaning or not can never depend on whether particular things exist."
(p. 78)

6 Realism 

Pears' reading of W's logical atomism is realist. The
elementary objects, or simples, exist independently of the human mind:
they determine the structure of reality and, by the process of
representation, the structure of language. At the level of complete
analysis all languages have the same structure mirroring the
atomic-combinatorial structure of reality: "Once a name has been
attached to an object, the nature of the object takes over and
controls the logical behaviour of the name, causing it to make sense
in some sentential contexts but not in others" (p.88). Put more
bluntly, W's realism is a version of the common-sense view that the
world exists independently of our experience of it, and that what we
experience is the world. In other words, the one and only world is the
world as we find it in ordinary experience. This is the very opposite
of a psychological theory that would treat our mental experience as
generated by a complex path of representations and manipulations that
distort and filter experience, so that Reality has to be painstakingly
recovered by intellectual investigation or shifted off into a
transcendental realm accessible only to mystics.  

In order to defend his realist reading, Pears' attacks two alternative
views of the nature of the simples in TLP. The first, espoused
especially by Hintikka, considers simples to be sense-data and their
properties; along the lines of Russell's version of logical atomism.
The second (proposed by Ishiguro and McGuiness) essentially reverses
the dependency between language and world: instead of making
elementary propositions depend on the simples named in them, it makes
the simples named in them depend on the elementary propositions.
Pears' lengthy rejection of these two alternatives is based on a
detailed study of the texts and appears well-founded.  

Pears establishes quite clearly, I think, that in TLP W left open the
possibility that simples could be sense data; but only because he
didn't think their precise nature was a problem. Similarly, he
postponed discussion of the relation between sense data and objective
phenomena and similar problems because he didn't really see that they
were problems. "This is really the most fundamental mistake he made in
his early work" (p.96). There is an important linguistic aspect to W's
realism which Pears also emphasizes here: just as the world is the
world as we find it, so human language in its material expression is
complete and irreducible just as it is. The main endeavour of TLP was
to show how ordinary language could be analysed to perfectly reflect
the nature of phenomena, but "the language in which this analysis was
expressed would not be an ideal alternative to everyday factual
language, but an ideal actually realized in it" (p.96).  

The TLP grounds language in the immediate relation between simples and
their names, but this relation is not explicitly described: we are not
told what names and simples are actually like or how they get linked
together. This makes it doubly difficult to grasp how the linkage is
maintained, or what Pears really means when he writes that "once a
name has been attached to an object, the nature of the object takes
over and controls the logical behaviour of the name, causing it to
make sense in some sentential contexts but not in others" (p.88). It
is clear, at least, that the world is considered the dominant partner
in the relation: W frequently uses the term "projection" and other
analogies with pictorial representation in a way that suggests
something closer to a theory of visual perception than intentional
linguistic construction. Ishiguro (1969) and McGuiness (1981) start
from the rather cryptic TLP 3.3, "Only propositions have sense: only
in the context of a proposition does a name have meaning", and invert
the dominance. This remark, Pears notes, echoes Frege's "argument that
numerals acquire their references from the propositional contexts in
which their insertion makes sense, not from any perceptual encounter
with numbers" (p.99, n.40). Ishiguro and McGuiness claim that W is
making the same point about names and simples in general. Here is
Pears' statement of their position:

[This quote in smaller type]

"...though the complete analysis of a factual sentence consists of
names in immediate combination with one another, the actual work of
analysis is finished at the penultimate level, where there are no
names but only quantifiers and variables. To put the point another
way, all the business of analysis is expressed in Quinese, and the
final step, which translates the result into Russellian is purely
decorative (Quinese contains quantification and variables while
Russellian contains names). Or, to put it in the terms used by
Ishiguro and endorsed by McGuiness, the names of the Tractatus are
dummy names, because they do not serve to distinguish one object from
another, but only to designate objects which have already been
distinguished from one another by the propositional contexts supplied
by the penultimate level of analysis in which their names can be
inserted. These propositional contexts contain predicative expressions
which can be understood without acquaintance with particulars
designated by Russellian proper names, and this makes it possible for
language to get off the ground." (pp. 100-101)

I have quoted this passage at length because it show how TLP
can be read as supporting symbolic AI: in particular, it strikingly
recalls Chomskian generative grammar, in which the penultimate stage
of derivation produces a string of category variables to be replaced
with actual words by "lexical insertion". Pears' goes on to show,
quite convincingly, that the text of TLP does not support such an
interpretation.  


7 Elementary Propositions as Pictures 

The Picture Theory (PT) is the key element in W's explanation of how
sentences acquire and keep their sense. It grounds semantics in a
direct representational contact between elementary propositions and
states of affairs in the world: "names are correlated with objects
just as the flecks of paint in a pointillist picture are correlated
with points in the scene it depicts" (p.115).  The explanation has
three main aspects. (i) Separatism: each sentence independently
mirrors its own bit of reality. (ii) Analytical Depth: ordinary
sentences in everyday language would reveal their true pictorial
character only when fully analysed into elementary propositions. (iii)
What can be said using sentences depends on the actuality of other
things that can only be shown: language cannot get between an
elementary sentence and what it portrays.

Pears places the PT in the context of W's developing theory of
languages it is given in the *Notebooks*. In August 1914 he thought he
understood the relation between names and simples and he could see how
to use formal logic to build complex sentences from elementary
propositions. But he couldn't see how to get from naming to sentences:
in other words, how does one explain the sudden appearance of *sense*,
the fact that a sentence can represent non-existent states of affairs
and thus be true ot false? He rejected all solutions to this problem
that would make the sense of one sentence depend on the truth of
another (e.g. a sentence asserting the existence of a sentential form,
as in Russell's theory discussed below). The answer he finally gives
(in September 1914) is that a sentence makes sense if its components
represent objects in a situation as standing in a connection which is
*possible* for the situation.

Pears notes three illustrations of the PT. (i) Uttering a sentence is
like putting a spot of paint on a canvas. (i) A sentence is like a
model. (iii) Names are coordinates that determine a point in logical
space (TLP 3.4-3.411). What is common to all three analogies?  In all
three systems false claims are possible but not nonsensical ones. But
this is not true of natural language. W clearly meant that nonsense is
impossible within a system that gives words meaning. "So his idea was
that the best way to understand the restrictions imposed on signs by
the system that makes them the signs that they are is to start by
looking at the kind of system that we use when we represent spatial
facts spatially" (p.121).

Pears now takes a detour through Russell's contemporary Theory of
Judgement, which he maintains quite convincingly to be the major
source for the PT: *Russell's Theory of Knowledge, 1913* was published
in 1984 and "it was immediately clear that W's picture theory of
sentences had been developed against its incurably static conception
of sense" (p.122). Judgement is the psychological process by which we
assign truth or falsehood to a sentence (and clearly has as a
prerequisite our grasping the sense of the sentence). Russell
initially believed that the mere attachment of names to objects and
relations was enough to explain the sense of sentences; he claimed
that the fact "a judges bRc" is fully explained by the acquaintance of
a with b,c, and r -- together with the existence of a relation of the
form "judges(a, b, c, R)". When he realized that this was inadequate,
he tried (in *Theory of Knowledge*) to remedy the situation by
appealing to "pure forms of propositions".  For a given proposition,
p, the pure form is obtained by replacing all the names with
variables: so aRb would give xZy. Russell now claimed that in
judgement we are directly acquainted with this pure form, although it
is not a constituent of the proposition, p. But what does
"acquaintance with a pure form of a proposition" really mean?
Russell's reply is that it means acquaintance with the fact that r (
where r = 'something has some relation to something'): in other words,
grasping the truth of a concrete proposition. But this implies that to
use the pure form xZy to establish the sense of r, we must know that r
is true. Russell also accepted the corollary that the truth of r must
be self-evident, indeed necessary. This led to a proliferation of pure
forms, or logical objects, with which we are supposedly acquainted by
"logical experience".

As is well known and frequently recounted, W demolished the Theory of
Judgement and so demoralized Russell in the process that the latter
nearly gave up philosophy altogether (McGuiness 1988, pp. 172-76).
Pears carefully reconstructs the criticism from the text of NB and
TLP. W says that it is impossible to lay down a priori specific limits
to the possible forms of elementary propositions (i.e. postulate
logical objects) - nor can it be done by experience. This is a
dilemma. Horn One is based on the infinite regress provoked if the
sense of any sentence depends on the contingent truth of some other
sentence: if in general p depends on the truth of some q for its
sense, then q will also depend on the truth of some other sentence r
for its sense... and so. Horn Two. Russell tries to stop the regress
by treating fully generalized propositions as a priori, self-evident
and necessary truths. W has two objections. (i) There is no way to fix
the number of specific forms a priori. (ii) The nature of fully
generalized propositions is contradictory: they can't be both simple
and complex at the same time; self-evidence is a psychological not a
logical property; and just because they are generally applicable does
not mean they are necessarily true.  

In an interesting comment, Pears points out that the identification of
necessary truth highlights the difference between the two
philosophers. "Russell buries necessary truths in the foundations of
factual discourse, while Wittgenstein places them at its outer limit"
in the tautological patterns of formal logic (p.  129). Note how close
Russell's theory comes to the ideas underlying symbolic AI: he
essentially proposed to ground language on a set of primitive symbolic
forms with which we are "acquainted" directly, but of which we do not
have everyday propositional knowledge. This is pretty much the same
doctrine as that found in the work of Fodor and Chomsky. In TLP W
rejects it completely; and this confirms the view I expressed above,
that it is a bit simplistic to identify TLP with symbolic AI.

As we have seen, W rejected any theory of sentence form that would
appeal to pre-existing patterns (e.g.  n-place predicates).  He
believed that the direct concatenation of names for simples in an
elementary proposition was sufficient to produce the representation of
a possible combination of objects in the world. But this act of
representation is not accessible for inspection in our ordinary
language, since it takes place at the level of completely analysed
factual discourse. It is well known that W had arrived at his
conviction by reflecting on representation in general, especially the
use of pictures. He had been especially struck by the way in which
model cars were used to reconstruct road accidents in the Paris law
courts. Here was a system in which simple names (the models) could be
combined together in an unlimited range of configurations that
pictured possible configurations of real cars in the world. It is
obvious that the manipulation of the models represents directly,
without appeal to further linguistic apparatus such as a coordinate
system or names for types of configuration. W believed, quite
plausibly it seems to me, that sentences must do their job in
something like the same way. In TLP 4.016 he notes that hieroglyphic
writing "pictures the facts it describes" and suggests that the
alphabet evolved from it "without the essence of the representation
being lost."

Exegesis of the PT involves showing how W could have translated his
insight into a genuine theory of representation for elementary
propositions. This is no easy task since it involves reconciling a
series of apparent or real contradictions. As usual, the text of TLP
gives just enough information to reconstruct the general lines of his
thought, but not nearly enough to fill in much of the detail. Pears
sticks very closely to what W actually says in TLP and NB and makes a
valiant attempt to extract the elements of a theory. I take his
interpretation to involve the following main assertions. (i) An
elementary proposition contains only names of simples (i.e.
particulars, not qualities or relations) in concatenation. Each name
represents a single simple and so the proposition has the same
cardinality as the atomic fact it represents. (ii) To know a simple
means to know all its combinatorial possibilities, to know all its
possible occurences in atomic facts. To know a set of simples is
therefore to know a space of possible atomic facts. (iii) A name for a
simple must respect the combinatorial possibilities of its referent,
otherwise the proposition in which it occurs will be nonsense. (iv) A
set of names can be considered as a system of coordinates defining a
space of elementary propositions that represents the corresponding
space of possible atomic facts. The statement of an elementary
proposition is equivalent to the claim that the corresponding atomic
fact holds in the world. (v) Each atomic fact is logically independent
of all others. Each elementary proposition is logically independent of
all others.

This brings out well the tension in W's key ideas. On the one hand, we
have the *holistic* notion of system in (iv): anyone who thinks of a
point in a grid or co-ordinate system will see it in relation to other
points. On the other hand, there is what Pears calls the *separatism*
implied in the doctrine of logical independence (v).  "The two
tendencies are reconciled and held together by the thesis that all the
possibilities of combination that belong to an object are inherent in
it and so can be found in it (2). This was a rather forced
reconciliation and it produced an unstable equilibrium" (p.133).

The central difficulty for the PT then may be stated as follows. (i)
An elementary proposition represents a possible atomic fact by setting
up a relation between names for simples that correspond to a possible
relation for the simples. If the relation actually holds in reality,
then the proposition is true otherwise it is false. (ii) But
elementary propositions only contain names for simples in
concatenation, so how can they possibly also represent the relation
holding between the simples? W's short answer is that they must do it
in the way pictures and models represent spatial and temporal
relations. But of course an elementary proposition has none of the
representational resources of physical models, and so the short answer
is no real answer at all. W's longer answer, according to Pears, is
that the relational information is inherent in the simple and knowing
the name for a simple is the same thing as knowing all its
combinatorial possibilities. Now this seems patently absurd. How can a
simple carry around heaps of information? Of course it is possible to
think of analogies which reduce some of the absurdity. Chess, for
example, could be played with identical pieces that would only differ
in the constraints on their moves: but then the information would not
be inherent in the pieces but rather in the minds of the players; and
this would introduce exactly the kind of psychological explanation
that W insistently rejected at the time of TLP. Pears does not offer a
real defence of W's answer and goes on to show how the conflicting
assumptions underlying it led W to abandon the theory in his later
philosophy. The reader is left feeling let-down: surely W and/or Pears
could have done better!


8 Showing and Saying 

Pears discusses the doctrine of the unsayable as part of the picture
theory, but it appears to be logically independent. The assertion is
that certain things cannot be said but only shown. In TLP W does not
explain or really argue for this. Pears explains the intuition behind
the doctrine with use of pictorial representation as an example. A
painting relies on projective geometry but does not itself represent
the principles of projection (if it tried we would end up in an
infinite regress). Likewise, if someone wants to say that 'p' is
correlated with the possibility that p, they will have to use the same
method of correlation in order to identify that possibility. They
could use an equivalent sentence, but if 'p' is elementary then there
is no equivalent and they will have to use the same sentence: "If we
try to say that the object a occurs in the sense of 'fa', we shall
fail, because the only way to pick out the object that we mean is to
use the method of correlation used by 'fa' and then the result will be
a tautology" (p.145). A positive consequence of the above is that the
structure of language is perspicuous. The philosopher who achieved a
commanding view would see not only the far-reaching senses of
individual factual sentences, but also the lateral connections
(logical and combinatorial) of language. "We can see all the way to
the edge of language, but the most distant things that we see cannot
be expressed in sentences because they are the pre-conditions for
saying anything" (pp.146-47).


9 The Solipsist's Dilemma 

A solipsist is a person who maintains that nothing exists beyond his
own conscious experience. He will usually argue that the only things
with which he is acquainted are sense data (or introspection of stored
sense data), and that he cannot possibly imagine, or know, anything
else. The brief, dense and more than usually obscure two pages devoted
to solipsism in TLP 5.6 - 5.641 serve a crucial function in the
philosophical programme of the book. They both tie the formal logic
and theory of language into a general philosophy of mind and
illustrate the thesis that any such philosophy is inexpressible. As
with the other central ideas of TLP, the general outline of what W is
driving at is clear, but elaboration and argument is almost entirely
missing. The forty or so pages that Pears devotes to the two pages of
TLP attempt to elaborate and argue, but the result is often as
difficult as the original text. This is a pity because Pears'
interpretation does in fact appear to get close to the heart W's
imaginative insights. As before he uses other philosophers (Russell,
Schopenhauer and Hume), a detailed textual study of TLP and NB and W's
own later writings.

Before presenting the solipsist's dilemma, the
nature of his commitments should be explained in more detail. A
central notion in TLP is that of *closure*: all possible worlds (i.e.
the one and only world) result from the combination of simples; since
language perfectly mirrors the logical structure of the world, the
logical structure of any possible situation may be represented in
language. If there are any limits to language, they coincide with the
limits of the world itself. But the solipsist claims that the world is
*his* world, that its boundaries are the psychological boundaries of *his*
conscious experience (not the metaphysical limits of some external
independent reality of things in themselves). Extended to language
this becomes the claim that *my* language describes *my* world. Now,
Wittgenstein accepts the solipsist's insight as valid but claims that
any attempt to state it leads to nonsense, because it belongs to the
realm of what cannot be said but only shown. What he hints at in the
text is a dilemma that reveals both the source of the solipsist's
insight and the absurdities it leads to. It is this dilemma that Pears
identifies and develops as his interpretation.  

By claiming that the only things that exist are the objects of *his*
experience, the solipsist presupposes the identification of his own
ego. It is this act of identification that W targets rather than the
claim that all experience is sense data. He uses an analogy with the
visual field.  Our visual experience has two striking properties: (i)
there is no reference-point *within it* from which to plot its
structure: the eye cannot see itself; (ii) although the field is
clearly bounded, it has no obvious edge or limit: indeed we cannot
even imagine what such a edge or limit would be like (what would be on
the other side?). Now take the visual field as analogous to our total
experience: the ego corresponds to the eye (or rather to the
geometrical focal point behind the retina). No ego appears in the
field of consciousness, just as no eye appears in the visual field.
The second point of analogy is not made in the TLP by W, but Pears
claims it "can certainly be discerned...below the surface of the
thoughts that are actually developed in the text". It corresponds to
W's strong sense of the world as a limited whole. Trying to think
one's way out to the edge of the Universe is a good way of grasping
the intuition: that the Universe should end somewhere seems as absurd
as that it should go on for ever.

In TLP, W gives a linguistic turn to the solipsist's commitments. For
the solipsist the limits of language coincide with the limits of the
world because both depend on using the (same) ego as a reference
point, and, since for the solipsist the ego is personal, both world
and language are limited to the personal. The analogy to the visual
field can be applied: "W's idea would be that one of the things that
cannot be mentioned in any language is the ego which serves as the
point of view from which language can be understood" (p.  167).

The dilemma may now be stated as follows. (i) The solipsist claims
that there is nothing in the world beyond his own conscious
experience. (ii) To identify this experience as his own, he
presupposes that he can use his self as a reference point. (iii) There
are only two ways to do this: (a) identify the self with his physical
body; (b) indentify the self with his psychological ego. Now (a)
obviously contradicts (i), since much of our body and its history is
inaccessible to conscious experience. But (b) is also impossible, as
the following shows. We cannot find the ego *in* our field of
conscious experience (just as we can't find the eye in the visual
field). But nor have we anyway of establishing the existence of our
ego *outside* of our field of conscious experience (just as there is
nothing in the visual field that allows us to establish its focal
point). The ego must therefore be the *limit* of our experience, since
the two alternatives are absurd. It cannot therefore be identified in
factual language and used to delimit the objects of the solipsist's
experience.

The conclusion to be drawn is that the solipsist's insight cannot be
stated in factual language, it belongs to what can be shown but not
said. The way out of the dilemma is to allow the ego to dissolve back
into the material reality from which we misguidedly isolated it, and
this is perfectly coherent with realism: "Here it can be seen that
solipsism, when its implications are followed out strictly, coincides
with pure realism. The self of solipsism shrinks to a point without
extension and there remains reality coordinated with it" (TLP 5.64).

Pears identifies the origin of the solipsist's dilemma in the
uniqueness of the phenomenal world. There is only one world and it has
certain properties, such as closure, just because it is the only one.
Any attempt to set up a miniature world in contrast to it is doomed to
failure. And because language is co-extensive with the world the same
restriction applies. So you cannot set possibilities expressible in
language against a background of candidate possibilities (i.e. cut out
a miniature language). "For that would apparently presuppose that we
can exclude certain possibilities, and this cannot be the case since
otherwise logic must get outside the limit of the world: that is, if
it could consider these limits from the other side also" (TLP 5.61).
Nor can you use an existing language to set up a more restricted one:
to do this, you would have to "cross the limits of the inner language
in order to put them in their place" (p.172).


10 Conclusions 

In this concluding section, I shall first bring together and comment
on the main features of Pears' interpretation of TLP. Then I shall
make some suggestions about the potential significance of early W for
the study of human language and the cognitive science paradigm.  Pears
critical approach has three main aspects. Firstly, as a philosopher in
the traditional sense of the word he is concerned with the Big
Questions about the relation of the thinking self to the world; and
reads W for what he has to say about these questions, not for the
technical theory of logic and language.  In doing so he is undoubtedly
close to the real concerns of the book. Secondly, he treats W's
thought as a whole and makes use of the whole corpus of writings. This
approach is certainly fruitful and allows Pears to clarify many
obscure passages. Thirdly, the points of germination of W's ideas are
often to be found in the intensive collaboration with Russell when W
was his student at Cambridge in the year 1911-13, and Pears shows how
many of the TLP doctrines are properly understood as a critical
reaction to ideas of Russell. But W was the more powerful thinker and
rapidly overtook his teacher, to such an extent that the space and
weight given to Russell in Pears' exposition seems out of proportion
-- adhering to the narrow interpretation of W as a British academic
philosopher. There is no doubt that W made full use of Russell's vast
knowledge and experience, and that their common enthusiasm for Frege
engendered a genuine collaboration. But there is equally no doubt that
the philosophy of TLP, as opposed to its theory of logic, derives from
a radical, visionary style of thought that was foreign to Russell.
This is apparent in Russell's own *Preface* to the book, and even more
so in his famously negative judgement on the later W. Pears does
counterbalance the influence of Russell with that of Schopenhauer and
Kant, but it seems to me that this is an inadequate substitute for the
richer context of interpretation proposed by Janik and Toulmin in
their book.

Turning now to the content of Pears' interpretation, I think the
spirit of it is best captured by glossing a quote from the *Notebooks*:
"My work has extended from the foundation of logic to the nature of
the world" (NB 2/8/16). W started his work with Russell in the heroic
period of symbolic logic, when it seemed that all of mathematics and
consequently all hard science could be reconstructed in formal logic.
Logic had the same kind of absolute necessity and universality as had
Euclidean geometry in Newton's world. But why was logic universal and
absolute, indeed prior to metaphysics? Why was it impossible for us to
think illogically? This was the question that W decided to tackle,
because he believed that metaphysics would fall out as a consequence
of the answer: "The great problem round which everything that I write
turns is: Is there an order in the world a priori, and if so what does
it consist in?" (NB 1/6/15).  His search for an answer led him to
study a whole menagerie of philosophical problems, culminating in the
relation between self, thought, language and the world.  

The solution was radical and simple: logic is the essence of the
common form of language and world, which allows the first to perfectly
mirror the second. This common form is the a priori scaffolding not
only of all experience and expression but also of the world itself: it
exhausts the possibilities of language and world. But precisely
because language is co-extensive with the world, we cannot use it to
represent its own form: to do that we would have to get outside of
logic and the world. Consequently, there are things that cannot be
*said* in language but that nonetheless are *shown* by it. A key
example is logical form itself: we cannot state this in language, but
at least some aspects of it are shown by the truth-table calculus of
tautologies. The only necessary truths of logic are these tautologies:
they define the empty limit of language as the mere formal possibility
of logical statement.  The problems of philosophy arise because we
insist on trying to say what can only be shown. This does not mean
that the philosophical impulse is a worthless relic. On the contrary,
it is the symptom of our belief that all that is really important in
human life is ultimately unsayable: "We feel that even when all
possible scientific questions have been answered, the problems of life
remain completely untouched. Of course there are then no questions
left, and this itself is the answer. The solution of the problem of
life is seen in the vanishing of the problem" (TLP 6.52-6.521). The
job of the philosopher is thus to protect the silence of the mystic by
revealing the absurdity of any attempt to make of philosophy a branch
of science.

Let us now briefly consider those TLP themes that are closes to the
more empirical concerns of cognitive science. There is no place in TLP
for *psychology*: following Frege, and in contrast to Russell, the
exclusion is radical and complete. W is concerned with the necessary
logical form of the world and language. How the human mind processes
language is no more relevant to his concerns than biology is relevant
to physics. There is a clear parallel with Chomsky's distinction
between competence and performance in its earlier versions, where the
study of grammar was considered to be concerned solely with linguistic
competence, itself a branch of mathematics. W does distinguish between
thought and language: a thought is a logical picture of a fact, while
a sentence is a thought expressed in a manner expressible to the
senses (TLP 3, 3.1). When pressed by Russell to explain this, W
replied that "the kind of relation of the constituents of the thought
and of the pictured fact is irrelevant. It would be a matter of
psychology to find out" (NB p. 129). The rejection of psychology
extends to its philosophical parent, epistemology, which is dismissed
in TLP 4.1121 as the "philosophy of psychology." W continues: "Does
not my study of sign-language correspond to the study of thought
processes which philosophers held to be so essential to the philosophy
of logic? Only they got entangled for the most part in unessential
psychological investigations, and there is an analogous danger for my
method."

The centrality of *natural language* in TLP is one of its most
original features and marks the beginning of the 'linguistic turn' in
modern Anglo-Saxon philosophy. But there are numerous passages which
show that W started not from everyday speech but with very general
considerations regarding symbolic systems. Pears writes that W
"treated language as the universal medium of all thought, and his
theory is really about any possible mode of symbolization." I would go
further and agree with Kenny (1973, p.54) that W views human language
at its most abstract level as a system of representation, and TLP can
be read as a theory of representation in general (and logical form
then becomes the minimum requirement for any system of
representation). Indeed, it is precisely the arbitrary, conventional
and creative nature of semiotic systems that is conspicuously absent
from TLP: Pears shows very clearly how in the picture theory atomic
facts are projected into elementary propositions in a determinate,
almost mechanical fashion. Once the correlation between names and
simples has been established, changes in configurations of simples are
mapped into changes of elementary proposition, like shadows projected
onto a wall. In contrast there are passages where W emphasizes the
complexity and richness of natural language, which show that he was
far from unaware of its multidimensional character. He also emphasizes
that natural language is in perfect order and complete just as it is:
anything that can be said at all can be said clearly and in natural
language.  

W view of *logic* is as radical as his view of psychology.
All of formal logic is considered reducible to propositional logic,
and the "truths" of logic are merely the tautologies that may be
mechanically calculated using truth tables. Logic is therefore a
purely syntactic theory dealing with the manipulation of symbols. (One
is forcefully reminded of the binary logic underlying computers: a
complete system of representation built from two digits and three
logical constants.) Moreover, this logic is the a priori form of all
possible worlds and all possible languages. An immediate consequence
is that there can be no theory of logic stated in factual language: we
can see the logical form of language, even manipulate it by juggling
with tautologies, but we can never say what it is -- because that
would presuppose a language without logical form (otherwise we would
be taking for granted what we are supposed to be explaining). It also
means that logic is autonomous: it has no "semantic" content
whatsoever. (cf. Kenny 1973, pp. 43-53)  

The theory of logic in TLP summarized in the previous paragraph is at
least partly independent of what might be called the *semantic* theory
of the book, i.e. the picture theory of elementary propositions and
logical atomism. It has been repeatedly noted that this semantic
theory belongs with the unsayable: logic (and so language) is grounded
in the world by a process that is prior to them and which cannot be
stated. But the theory is also apparently practically empty, because
semantics is reduced to the manipulation of tautologies at the
boundary of the sayable. It seems to me possible to read TLP as an
attempt to prove, *via reductio ad absurdum*, that formal semantics is
either impossible or trivial. If that is the case then the relevance
for cognitive science is clear.

In conclusion, then, I believe that in TLP W was concerned with much
the same intellectual territory as cognitive science. He succeeded in
mapping out what might be called a "theory space" using a number of
conceptual dimensions: atomism versus holism, solipsism versus
realism, syntax versus semantics, natural language versus formal
language and so on. Further, he built the theory of the TLP on extreme
positions for these various dimensions. It is still unclear whether
the positions he took can actually be developed into a workable
theory, let alone be used to draw the negative conclusions that he
does. It is clear, however, that W was asking many of the right
questions.  

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