Laboratoire Philosophie, Langages & Cognition
Université de Grenoble PDF
Abstract: In a famous letter to Russell, Wittgenstein asserts that the ‘main point’ of his Logish-philosophische Abhandlung lies in the demarcation between ‘what can be expressed [gesagt] by propositions’ and ‘what cannot be expressed by propositions, but only shown [gezeigt]’. Drawing correctly this distinction between saying and showing is indeed presented as the ‘cardinal problem’ of Wittgenstein’s early philosophy. In fact, the author of the Tractatus seems to think that this prima facie enigmatic distinction provides us with the definitive ‘solution’ of every significant philosophical problem. Given the large variety of distinct matters the Treatise deals with, such an affirmation may sound extremely bold, and the careful reader must try to see if the book contains a definite idea of showing, or if ‘showing’ is, on the contrary, a mere name for an irreducible multiplicity of issues involving the limits of language. In this article, I try to sketch an elucidation of the form of the saying/showing distinction in order to indicate that it can be understood as the development of a single way of apprehending the most decisive ‘problems of philosophy’.
The presentation of Wittgenstein’s approach in the Preface of the Tractatus may sound very arrogant. After noticing that the Treatise would probably not be understood by readers who have not already had the thoughts which are formulated in it − thoughts which include several particularly complex logical developments −, the author explains that his work ‘deals with the problems of philosophy’ (without more precision) and concludes relatively quickly that ‘the problems have in essentials been finally solved’. Such a bold assertion is nevertheless partly elucidated by the expression of Wittgenstein’s viewpoint on the nature of philosophical problems. A central aim of the book is indeed to ‘show […] that the way of formulating (die Fragestellung) these problems rests on the misunderstanding of the logic of our language’. The author adds:
The whole sense of the book could be summed up in the following words: What can be said at all can be said clearly, and what we cannot talk about we must pass over in silence.
The repetition of the last words of this formula in the final sentence of the Treatise (‘What we cannot speak about we must pass over in silence’, 7) makes it obvious that Wittgenstein holds the idea of limits of linguistic expression to be a decisive point in his argumentation. In addition, the author of the Tractatus explains, in a famous letter to Russell written in August 1919, that his ‘main contention’ lies in the distinction between saying and showing, which is indeed present in his treatment of the major issues of the book.
The idea of ‘showing’, which appears as a very verbum ex machina, seems to be able to solve the large variety of problems at stake in the philosophical path of the Tractatus, especially: The nature of representation (or ‘picturing’), the logical features of propositions, the essence of logic and the nature of inference, the status of the operations it involves, the limits of thought, the criterion of a good life and what it is to see the world aright. The attempt to provide a single answer or a correct viewpoint corresponding to so many questions might be taken for a kind of intellectual delusion, but the task of the interpreter must consist in trying, through a precise analysis of the text, to attribute to the work the philosophically most ‘coherent’ conception, or at least the most unified approach. Every commentator of the Tractatus should therefore raise this decisive problem: Can we identify a uniform idea of showing in the Treatise, or are we to understand ‘showing’ as a mere name for an irreducible multiplicity of issues involving the limits of language? Is there some common characteristic present in each one of the different applications of Wittgenstein’s distinction between saying and showing? Is it possible to indicate some formal features which serve to unify this central distinction? In this paper, I try to sketch an elucidation of the form of the saying/showing distinction in order to indicate that it can be understood as the development of a single way of apprehending the most decisive problems, which seems to be essential in the Tractarian argumentation.
- The cardinal problem of philosophy and its definitive solution
A significant number of remarks in Wittgenstein’s Notebooks (Tagebücher and Geheime Tagebücher) explicitly suggest than he considered himself as fighting against a unique great problem, looking for a single solution to all the major philosophical issues. He thought that in getting a clear and correct overview (Überblick), he would become able to see that the various questions at stake in philosophy (according to the russellian background presupposed by the expression ‘problems of philosophy’) can be reduced to a single difficulty, that ‘every problem is the main problem (das Hauptproblem)’. Particular problems would be nothing but ‘reflections of the one great problem (Spiegelbilder des einen, grossen Problems) in the variously placed great and small mirrors of philosophy’. In conformity with such an idea, the young philosopher came to think that the solution to this Hauptfrage should be simple and unique: ‘The solution of all my questions must be extremely simple’. It should consist of a ‘fundamental thought’ (ein grundlegendes Gedanke), a single ‘key thought’ (der erlösende Gedanke), a ‘key word’ (erlösende Wort) or in a ‘clear vision’ (klare Sehen). Although the exact identification of this unique solution in the Notebooks remains problematic, it becomes obvious − at least from July 1916 − that Wittgenstein was convinced that such a solution would be able to solve at the same time logico-mathematical questions and difficulties related to what he calls the ‘problems of life’ (Lebensprobleme). In the coded entries of his notebooks, the search for a necessary relationship between logical and ethical issues appears as a very important aspect of Wittgenstein’s task, especially in the remarks dated from the 6th and 7th July 1916 in which the author evokes a ‘significant link’ between his mathematical interrogation and his conception of life, and writes: ‘This link will be established! What cannot be said cannot be said!’.
The nature of this link remains nevertheless cryptic. It is well-known that in a letter to Ludwig von Ficker, the editor of Der Brenner (in which Wittgenstein envisioned publishing his Logisch-philosophische Abhandlung), the Treatise is said to have an ethical value:
The book’s point is an ethical one. I once meant to include in the preface a sentence which is not in fact there now but which I will write out for you here because it will perhaps be a key to the work for you. What I meant to write, then, was this: My work consists of two parts: the one presented here plus all that I have not written. And it is precisely this second part that is the important one. My book draws limits to the sphere of the ethical from the inside as it were, and I am convinced that this is the ONLY rigorous way of drawing those limits. In short, I believe that where many others today are just gassing, I have managed in my book to put everything firmly into place by being silent about it. And for that reason, unless I am very much mistaken, the book will say a great deal that you yourself want to say. Only perhaps you won’t see that it is said in the book. For now, I would recommend you to read the preface and the conclusion, because they contain the most direct expression of the point of the book.
The difficulty with the proposed ‘key’ is that it may sound particularly hard to elucidate its intrinsic relation to the logical developments of the Tractatus, which cannot be reduced to the very general idea that some important things are unsayable. How are we to understand the link between the supposed ethical aim of the book and what is presented as Wittgenstein’s ‘fundamental thought’ (Grundgedanke), namely, ‘that the logical constants do not represent’, that ‘the logic of facts cannot be represented’ (4.0312)? Like the preface and the conclusion of the Tractatus, the letter written to Russell on the 19th August 1919, indicates that the main point of the book lies not only in the attempt to draw a limit, but also and more precisely in a distinction between saying and showing:
I’m afraid you haven’t really got hold of my main contention, to which the whole business of logical propositions is only a corollary. The main point is the theory of what can be expressed [gesagt] by propositions .− i.e. by language − (and, which comes to the same, what can be thought) and what cannot be expressed by propositions, but only shown [gezeigt]; which, I believe, is the cardinal problem of philosophy.
We may consider the content of the letter to von Ficker philosophically doubtful, insofar as it had a pragmatic goal (the publication of a baffling manuscript at a hard time for German-Austrian economy, sent to an editor who had no knowledge in philosophy of logic). However, this letter to Russell is clearly a decisive text for the understanding of Wittgenstein’s early thought. The distinction between saying and showing, presented as central here, is indeed involved in every other ‘key’ the philosopher provides us with to grasp the nature of his approach to philosophical problems in the Tractatus. Furthermore, Russell had been Wittgenstein’s teacher and, after Frege’s failure to grasp the meaning of the book, he was the single person the philosopher judged able to understand his work.
The characterization of the distinction between what can be said and what can only be shown, sketched in this letter, is significant; but it is also problematic for several reasons. First, the distinction is presented as the object of a ‘theory’, which seems difficult to reconcile with the 6.54’s demand to throw away the ‘ladder’ of the Tractarian discourse, and to recognize every philosophical theory as a mere nonsense (cf. 4.112: ‘Philosophy is not a theory, keine Lehre, but an activity’). Second, the distinction is said to be Wittgenstein’s ‘main contention’ and the ‘main point’ of the book, but also ‘the cardinal problem of philosophy’. A ‘contention’ is not exactly a ‘problem’, so that this assertion needs to be clarified. Although some specialists of the ‘resolute’ reading of the Tractatus don’t hesitate to claim that this distinction comes, as every ‘problem of philosophy’, from ‘the misunderstanding of the logic of our language’ (Preface) and is therefore to be thrown away with the famous Tractarian ladder, I would suggest a less radical interpretation: Given that in 1919 (i.e. after the final redaction of his book) Wittgenstein does not distinguish between his cardinal problem and the solution of this problem (or the essential means to get such a solution), and given that he doesn’t manage to identify clearly the status of his own philosophical discourse (this one is presented as a theory but it cannot consist of a theory), it is likely that the Tractatus is not a perfect expression of Wittgenstein’s thoughts. That is precisely what its author admits in his Vorwort:
If this work has any value, it consists in two things: The first is that thoughts are expressed in it, and on this score the better the thoughts are expressed – the more the nail has been hit on the head – the greater will be its value. – Here I am conscious of having fallen a long way short of what is possible. Simply because my powers are too slight for the accomplishment of the task. − May others come and do it better.
This sentence clearly suggests that Wittgenstein understood his work as an attempt to express some content (i.e. ‘thoughts’), and admitted a partial failure in respect to the quality of its expression in the Tractatus. There is a deep tension between his presentation of the work as having a positive content (thoughts considered as ‘truths’) and his insistence on not putting forward doctrines, theses or theories. Behind Wittgenstein’s apparent arrogance, there seems to lay a kind of modesty, and his radically dogmatic style hides a lack of certainty in his representation of the status of his own philosophical discourse. The explanation of the dogmatism of the Tractatus Wittgenstein gave to Waismann in 1931 is significant: ‘In my book, I still proceeded dogmatically. Such a procedure is legitimate only if it is a matter of capturing the features of the physiognomy, as it were, or what is only just discernible – and that is my excuse. I saw something from far away and in a very indefinite manner, and I wanted to elicit from it as much as possible.’ The idea that the Tractatus is not the perfect exposition of an ultimate truth but only an attempt to grasp a ‘physiognomy’, that is to say some formal features of which its author was catching a glimpse, may appear as very important for the task of the interpreter who intends to elucidate the unity of the book: It means that we must try to understand the Treatise better than its own author understood it. His apparent incapacity to provide us with a precise elucidation of the uniform character of his ‘main contention’, i.e. the distinction between saying and showing, doesn’t necessarily mean that this contention is deprived of a fundamental unity. What it indicates is that the interpreter must himself ‘hit the nail on the head’ in trying to reconstruct clearly the book’s fundamental distinction.
- Does the distinction between saying and showing have a single form?
The distinction between saying and showing has been variously apprehended by Wittgenstein’s scholars: according to some commentators it represents a key to understanding the overall unity of all his writings and it expresses the continuity of his philosophical path throughout his life; others specialists have claimed that this distinction is to be seen as a mere nonsense, either from the turning point of the 1930s, or already in the Tractatus. It has been noticed that the introduction of the idea of showing in the Treatise is baffling, not only because of its paradoxical aspect as a doctrine, but insofar as it is applied to radically different matters. Several interpreters have suggested lists or classifications of the main occurrences of the idea showing in the book, and in spite of small differences there seems to be an agreement on the identification of what is presented as showing itself. In a famous article, P.M.S. Hacker proposed the following presentation of ‘things’ that show themselves:
1°) The harmony between thought, language and reality;
3°) Logical relations between propositions;
4°) Internal properties and relations of things and situations;
5°) Categorial features of things and type classifications;
6°) The limits of thought;
7°) The limits of reality and the logical structure of the world;
8°) Metaphysical principles of natural science;
9°) Metaphysics of experience;
10°) Ethics, aesthetics and religion.
Some elements of this classification (which respects as much as possible the order of Wittgenstein’s argumentation) are dependents on Hacker’s personal reading of the book, or don’t sound perfectly exact. That is why I would rather use a very close but different presentation, and classify the main occurrences of the notion of showing as follows:
a) The form of representation (Form der Abbildung, Darstellungsform);
b) The logical nature of a proposition and its relation to reality;
c) Logical truths and necessary relations between propositions;
d) Internal properties and formal concepts;
e) The limits of thought and philosophy as an activity;
f) The metaphysical subject and ‘solipsism’;
g) Ethics, aesthetics and the mystical.
The question is to determinate how a single distinction between saying and showing can operate in each one of these cases. If the Tractatus is not deeply mistaken on this point, we must be able to discern a unique idea involved in all the mentioned matters.
Several attempts have been made to explain the say/show distinction by means of some general concepts. For instance, it has been suggested that there is a link between this distinction and the Kantian opposition between a posteriori and a priori: According to such an interpretation, what is said would be a posteriori and what is shown is a priori. Another tendency to reduce the idea of showing could be identified in the use of the concept of world as a key to explaining the distinction: Showing would be a pure expression of the shape and the form of the world as a whole. The difficulty with such general explications is that they don’t take into account several occurrences of the idea of showing in the Tractatus. Wittgenstein explicitly asserts that the sense of a proposition is shown by the proposition (4.022: ‘A proposition shows its sense’), and it would be absolutely illegitimate to claim that the sense of a particular proposition is a priori, or that it is a pure expression of the world as a whole.
Those who have tried to take into consideration the showing of propositional sense, have sometime been led to emphasize the relation between this kind of showing and the idea of use, which is already present in Wittgenstein’s early work. For example, following an Austinian approach to the text, François Récanati suggested in La Transparence et l’énonciation that, contrary to the claims of what he calls the doctrine of ‘representationalism’, a sign has the power to show, i.e. to ‘indicate reflexively’ its own enunciation (its pragmatic nature). According to his interpretation, the distinction between saying and showing corresponds to the distinction between the representational aspect of a sign and the fact that this same sign is a speech act of a determinate category.
In a similar way, Michael Kremer attempted to elucidate the Tractarian distinction by means of Ryle’s famous demarcation between ‘Knowing-that’ and ‘Knowing-how’, suggesting that Wittgenstein’s idea of showing is nothing but the demand to overcome pure representation to understand ‘the demonstration of a technique’ (such an interpretation pretends to fit with the logical developments and equally with the ‘spiritual’ dimension of the book). A similar idea was already formulated by Donald W. Harward in his 1976’s essay: Wittgenstein’s Saying and Showing’s Themes, where the author claimed that an important category of the various uses (but not every use) of ‘showing’ in the Tractatus are ‘demonstratives uses’, that is to say references to situations involving an agent and an audience before which a practical demonstration is implemented. A major difficulty with such interpretations is that, contrary to the Philosophical Investigations, the Treatise doesn’t make any reference to concrete speech interactional situations and doesn’t contain any pragmatic analysis. In addition, although the book insists upon the importance of use, of the ‘meaningful employment’ (sinnvolle Gebrauch) of signs, and presents it as a means to show their symbolic nature (see e.g. 3.326), it doesn’t clearly express the idea that there is an essential correspondence between use and showing rather than between use and saying. As a consequence, the notion of use doesn’t permit us to distinguish precisely between saying and showing.
The irreducibility of the Tractarian idea of showing to a determinate concept led some authors to doubt if there is more than a strictly nominal notion of what ‘shows’ itself in Wittgenstein’s early work. Juliet Floyd and Warren Goldfarb have suggested that the text contains nothing we can legitimately call ‘the saying/showing distinction’ and that it develops several different uses of the verb ‘to show’. Nevertheless, the comparison between the varieties of the idea of showing in Wittgenstein’s argumentation and his claim that the same distinction is at stake in every case suggests that the interpreter must try to discern and to elucidate some formal properties of showing, and at least to construct a rough formal classification of the different uses of this complex notion. It may seem tempting to distinguish between the showing of the propositional sense, the showing of logical form, and the showing of what is called ‘the mystical’ (i.e. non-symbolic occurrences of ‘showing’). By following this path, some commentators have suggested a strict separation between ‘kinds’ of showing. Fabian Goppelsröder proposes to identify three kinds of showing: 1°) The showing of the sense of a proposition, presented as a ‘descriptive showing’ (deskriptives Zeigen); 2°) The showing of the transcendental character of logic; 3°) The showing of what is transcendent, i.e. ‘das Mystische’. We find a similar typology in Manfred Geier’s article: ‘Ludwig Wittgenstein und die Grenzen des Sinns’: the author distinguishes between: 1°) an external showing (externes Zeigen), related to the sense of a proposition and to the picture theory (for a proposition to have a sense means to represent an external fact); 2°) an internal showing (internes Zeigen) of the logical form: the form of a proposition cannot be said but shows itself in the proposition; 3°) a mystical showing (mystische Zeigen), which gives rise to paradoxical formulas in trying to indicate various transcendent realities.
At first sight, such classifications may seem convincing. They avoid a recurrent confusion between what is structural and what is properly formal in showing, and they emphasise the important difference between what shows itself in logic and what is shown as regards ethical, aesthetic, or ‘mystical’ matters. Unfortunately, they are not able to elucidate the fundamental nature of the distinction between saying and showing: in which manner can we distinguish between a ‘descriptive’ (or ‘external’) showing and a linguistic representation (i.e. an occurrence of saying)? And how can we identify the difference between the ‘mystical’ showing of ‘transcendent realities’ and a mere nonsense which pretends to refer to such a kind of things? Besides this, if these taxonomies of showing are correct, the argumentation of the Tractatus must appear as deprived of any real unity, contrary to what Wittgenstein obviously thought.
Hence, the principle of charity demands that we search for an interpretation which manifests the essential unity of showing in its opposition to saying, i.e. which would be able to elucidate the form of the cardinal distinction of the work.
- An exegetical hypothesis to elucidate the form of the Distinction
A significant clue to understanding the say/show opposition as a single distinction may lie in the notion of reflexiveness. This complex and dangerous idea has been employed, often without being clearly defined, in the works of several scholars who were in quest of a characterization of the nature of showing in the Tractatus. For some of them, the assertion that the specificity of showing consists of a kind of reflexiveness essentially means that a sign can display its own pragmatic nature (see e.g., Récanati, supra). Others are more interested in the use of the words ‘reflexiveness’ or ‘self-reference’ in philosophy of logic, − for instance in Russell’s claim that ‘there is [in all the famous contradictions the theory of logical types intends to overcome] a common characteristic, which we may describe as self-reference or reflexiveness’ − suggesting that showing is reflexive or that it is a means to avoid discursive reflexiveness (and, therefore, teratological formulas). In addition, there is also a more metaphysical use of these expressions, related to the problem of the self-knowledge of the ‘thinking subject’ (the question of the possibility of a ‘reflexive consciousness’).
In their attempts to explain the Tractarian argumentation, some scholars have used the words ‘reflexiveness’ or ‘self-reference’ in a very general manner, applying this notion simultaneously to logical and metaphysical issues. In his essay on the saying/showing distinction, Daniel W. Harward claimed that all the uses of ‘showing’ which are not ‘demonstrative’ are ‘reflexive’, that is to say do not need any reference to an agent or an audience and are essentially of the structure: ‘a shows characteristic b’, or ‘the b of a shows itself’ (for example in the sentence: ‘That this is an English sentence shows itself’). A reflexive showing would consist of the possibility, for a given element x, to show itself, i.e. to indicate its own nature. It seems indeed that the Tractatus considers that a symbol cannot say anything about itself (contrary to what may suggest Harward’s example) but is always able to show its own symbolic properties, which dissolves several famous logical paradoxes. And this idea is apparently relevant to others major occurrences of showing, including non-discursive occurrences. That’s why one can be inclined to identify showing with a general ‘self-directed aboutness’ (opposed to the ‘other-directed aboutness’ of saying): Exactly in the same way as a proposition cannot refer to itself and shows its own nature, the metaphysical subject cannot represent itself and shows its formal character of ‘limit of the world’.
In other words, the idea of showing seems to be intimately related to the general conception that every apparent kind of self-reference is in fine a mere logico-philosophical fallacy. Indeed, we cannot hold showing to be self-referential because the notion of ‘reference’ involves a fundamental distinction between what is referring and the object of reference, distinction that the Tractatus presents as an essential characteristic of saying (or ‘picturing’). So, if we apprehend ‘saying’ as a case of reference (according to a very general use of this latter term), the Treatise appears as suggesting that every possible reference is reference ad extra, hetero-reference: Self-reference is, strictly speaking, a logical impossibility or a mere nonsense.
Such an assertion needs to be clarified, because it may seem that a great number of instances of self-reference can be found without any difficulty. A non-paradoxical (and true) proposition like: ‘This sentence contains five words’ (where ‘this’ refers to the sentence itself) is usually said to be self-referential. But we can doubt if the object of this sentence is exactly the sentence itself, or if it lies only in accidental features of a particular complex sign (the logical – symbolical – nature of the proposition as a living whole cannot be considered equivalent to a set of written words). What is at stake with this difficulty is the meaning of ‘self’ in the expression ‘self-reference’: it would be obviously wrong to claim that there is no case of self-reference at all (an element x can of course refer to one of its own parts, to its accidental characteristics), but it may seem necessary to acknowledge that there is, properly speaking, no absolute self–reference. The reason for this is in fact extremely simple: whatever x may be, x never needs to refer to itself because it is itself. And it cannot do it because the notion of reference presupposes an essential distinction between a subject (i.e. what refers) and an object (to which the former refers): without this distinction, there is no real reference (‘to refer – exactly – to oneself’ has no more meaning than ‘to go where you already are’). Being oneself doesn’t mean referring to oneself.
Identity is not a kind of reference. In fact, identity is − from the viewpoint of the Tractarian philosophy − nothing, i.e. nothing that can be said, although we are subject to the illusion that ‘identity propositions’ may have a content (that’s why identity is ‘the very devil’): ‘to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing at all’ (5.5303). The identity, that is to say the very nature, of a symbol, or more generally of a logico-philosophical ‘datum’, must show itself and cannot be represented at all. And it seems that showing always lies in the pure displaying of an identity.
Ultimately, every case of showing appears as characterized by a kind of non-referential reflexivity: what an element x shows is essentially itself, its own nature. Showing is not a self-reference, but it consists of an ability to reflect oneself, ability that we can metaphorically call ‘reflexibility’. It follows that there is no showing of something external to what operates the showing. More precisely, we must recognize, in every apparent instance of ‘something that shows something else’, an internal relation between the different elements involved, i.e. a ‘relation’ that expresses internal properties of its relata − their essence − rather than a proper relation between two really distinct elements. For example, the nature of a proposition can show the essence of the world, insofar as a ‘pictorial internal relation’ holds between these two elements (4.014), elements which are, in the final analysis, one and the same.
According to the preceding considerations, we can now formulate a general hypothesis to elucidate the form of the distinction between saying and showing:
(1) ‘Saying’ essentially means referring to an external reality (not necessarily an extra-linguistic fact but something distinct from the symbol which expresses it).
(2) ‘Showing’ consists only of an ability to reflect itself, to manifest its own identity.
We could add to these two points the following remark on Wittgenstein’s use of the distinction, which may be relevant to understanding his conception of philosophy from an historical point of view:
(3) The idea of showing is first related to fundamental logico-philosophical ‘data’. By ‘fundamental logico-philosophical ‘data’’ I mean the Tractarian − non-empirical and content-less − equivalents of concepts which often play a decisive role in foundational matters in logic or in philosophy, especially: The formal aspect of propositions/pictures, simple objects as conditions of possibility of meaning, logical truths, internal properties, the thinking subject, philosophical discourse itself, the ethical/aesthetic/’mystical’ sense of life as a limited whole. Although this aspect of Wittgenstein’s use of the idea of showing doesn’t permit us to conclude that he was trying to solve the traditional problem of the search for an absolute foundation (the Tractatus tends to replace this quest with the question of the essence of logic/of the world), it suggests that his cardinal distinction may be apprehended as an original answer to interrogations which logicians and metaphysicians have considered of great importance.
- Application of the hypothesis to some significant occurrences of the say/show distinction
The above formulated general hypothesis needs to be confronted with a detailed analysis of Wittgenstein’s argumentation in the Tractatus. Though such a test would require long developments and cannot be completely achieved in the present paper, we can sketch an overview of the way this exegetical hypothesis may be applied to some of the most significant occurrences of the saying/showing distinction in the Treatise.
The relevance of our hypothesis for the elucidation of the ‘picture theory’ appears clearly in Wittgenstein’s introduction of the notion of ‘pictorial form’. After presenting the world as ‘the totality of facts’, the Tractatus affirms that ‘we picture facts to ourselves’ (2.1). Pictures (Bilder) are facts that are in an internal relation with other facts thanks to a determinate ‘pictorial form’, which permits that the picturing facts and the pictured facts have a common structure (2.151). The nature of a picture essentially depends upon its pictorial form: A picture is not only a particular structure, but ‘also includes the pictorial relationship, which makes it into a picture’ (2.1513). This fundamental aspect of every picture is its condition of possibility, it is what permits its (correct or incorrect) depiction of any reality which form it has (2.171). Generally speaking, a ‘spatial picture’ can represent any spatial fact, a ‘colored picture’ can represent any colored fact. And the logical form, which is present in every picture (2.18), permits the representation of anything. But the essential limit of picturing is directly indicated by Wittgenstein:
2.174 A picture cannot, however, depict its pictorial form: It displays it (weist sie auf).
2.173 A picture represents its subject from a position outside it (von ausserhalb). (Its standpoint is its representational form.) That is why a picture represents its subject correctly or incorrectly.
2.174 A picture cannot, however, place itself outside its representational form (ausserhalb seiner Form der Darstellung stellen).
Through the spatial metaphor of interiority/exteriority, this presentation of the nature and of the limits of picturing (the genus including ‘saying’ as particularly significant specie) seems to be in perfect agreement with the hypothesis we have formulated. A picture can ‘depict’ (bilden), ‘represent’ (darstellen), in as much as it can refer to an external reality (i.e. a reality which differs from itself); what it cannot represent and what it must necessarily ‘show’, ‘display’ (aufweisen), is its own pictorial form, i.e. its own identity as a picture.
The conception of the proposition as a logical picture of reality leads to similar remarks on the nature of linguistic pictures, especially as regards the status of the logical form. Here we must notice that, contrary to what is sometimes assumed, Wittgenstein doesn’t consider that a picture cannot be represented at all by another picture, or that a proposition (i.e. a linguistic picture) cannot be described at all by another proposition. A great part of what we often call ‘metalinguistic statements’ is not forbidden by the Tractarian ‘semantics’. The impossibility for a particular picture to represent its own pictorial form doesn’t entail the impossibility for another picture to represent the pictorial form of the former. The point which remains nevertheless doubtful is if the latter picture (proposition) can represent completely the pictorial form of the former. The problem is that this pictorial form already involves a decisive constituent of the second picture: the logical form. And, in opposition to particular pictorial forms, the logical form cannot be represented at all because it is the form of reality itself and, as a consequence, it is present in every possible pictorial form. We cannot go ‘outside’ logical form to represent it:
4.12 […] In order to be able to represent logical form, we should have to be able to station ourselves with propositions somewhere outside logic, that is to say outside the world (ausserhalb der Welt).
4.121 A proposition cannot represent logical form: It is mirrored in it (sie spiegelt sich in ihm). What finds its reflection in language (Was sich in der Sprache spiegelt), language cannot represent (darstellen). What expresses itself in language, we cannot express by means of (durch) language. A proposition shows (zeigt) the logical form of reality. It displays it (weist sie auf).
So, the possibility for a picture to represent another picture (or another ‘pictorial form’) remains problematic: on the one hand, the second picture cannot represent the logical form of the first; on the other hand, it has itself in common with the first picture this general form of every possible representation, and must be able to reflect it. Anyway, the distinction between saying and showing is here characterized by the same recurrent formal trait: It is impossible to say what logical form is (i.e. to represent it by means of propositions) because no proposition can stand outside it, apprehend it as an external ob-ject; and, logical form being the formal nature of language, it shows itself in language. Language says insofar as it refers to an external reality, it shows insofar as it displays its own identity. Saying and showing are here presented as two modes of expression (Ausdruck), which differ only according to their respective ‘aboutness’: The former corresponds to the expression (of something, of some state of affairs) ‘by means of language’ (durch die Sprache), the latter to the autonomous expression of language in language itself (‘Was sich in der Sprache ausdrückt’). This idea can be seen as a clue to understand the famously obscure remark 4.022 in which the saying/showing distinction seems to disappear. A few pages before asserting that ‘what can be shown cannot be said’ (4.1212), Wittgenstein notices: ‘The proposition shows its sense’ (zeigt seinen Sinn). The proposition shows how things stand if it is true. And it says that (sagt dass) they do so stand’ (4.022). Do we have to admit that saying and showing can sometimes be identical? The only way to avoid this dissolution of the distinction is to recognize that what the proposition shows is its own sense – its own identity as a proposition – and that what is said by the proposition is the external fact it represents.
The peculiar character of the propositions of logic is that they do not say anything, i.e. that they do not refer to any particular fact except themselves. On the contrary, they must appear as pure opportunities of self-manifestation of their ‘object’ (which cannot be an ob-ject): Logic itself. The distinction between the content-less (sinnlose) propositions of logic and factual propositions (sinnvolle Sätze) is grounded in the absolute auto-nomy of logic. Factual propositions consist of representations and their truth or falsehood depends on external represented facts. The Treatise’s Grundgedanke is that the propositions of logic do not represent at all (that’s why there is no ‘logical constant’, 4.0312). If we need to compare a proposition with reality in order to judge its truth or falsehood, the ‘peculiar mark of logical propositions’ is ‘that one can recognize that they are true from the symbol alone’ and – Wittgenstein adds – ‘this fact contains in itself the whole philosophy of logic’ (6.113). It couldn’t be otherwise because there is nothing outside logic, and insofar as the laws of logic have no content they ‘cannot in their turn be subject to laws of logic’ (6.123).This self-manifestation of logic (‘Every tautology itself shows – zeigt selbst – that it is a tautology’, 6.127) does not concern the arbitrary part of the symbols but their necessary formal correspondence with the world: Logic is a field ‘in which the nature of the absolutely necessary signs speaks for itself (sagt … selbst aus)’ (6.124). This is the fundamental meaning of the optical metaphor of reflection in a mirror (logic reflects itself in ‘the great mirror’, 5.511, it is ‘a mirror-image of the world’, 6.13).
This formal autonomy of logic (that is to say of the world, because logic is the form of the world, 5.61) consists of the displaying of internal properties or relations which are not, strictly speaking, properties or relations at all. These formal and logical properties of language and world are shown, e.g. by tautologies (that propositions of logic are tautologies ‘shows the formal – logical − properties of language and the world’, 6.12) or by the use of definite variable signs (cf. 5.24: ‘The operation shows itself, zeigt selbst, in a variable’). The general form of a proposition is itself a variable, that is to say expresses no function, i.e. no genuine content, but only an ‘operation’ applied to any possible content. The ideas of an operation (corresponding to what we try to represent by means of ‘formal concepts’, see 4.126 & sq.) and of a function are to be distinguished. The most significant difference between these two notions lies in the fact that ‘a function cannot be its own argument, whereas an operation can take one of its own results as its base’ (5.251). As an explicit way of saying, a function must refer to something different from itself (it cannot be its own argument, because ‘the sign for a function already contains the prototype, Urbild, of its argument, and it cannot contain itself’, 3.333); as a pure way of formal and content-less showing, an operation possesses a power of ‘reflexibility’, i.e. the possibility to be reiterated to its object. Wittgenstein’s argument against the teratological function sign: ‘F(F(fx))’ and his argument against self-referential propositions are essentially one and the same. According to the Tractatus, the fundamental error which gives rise to Russell’s paradox (and other antinomies of the same kind), and by this way to the theory of logical types, lies in the necessity for the author of the Principles of Mathematics to speak about the meaning of the signs (when establishing their syntactic rules). According to Wittgenstein, such a procedure is indeed a logical impossibility, for the following reason:
3.332. No proposition can make a statement about itself, because a propositional sign cannot be contained in itself (that is the whole of the ‘theory of types’).
3.333. The reason why a function cannot be its own argument is that the sign for a function already contains the prototype of its argument, and it cannot contain itself.
For let us suppose that the function F(fx) could be its own argument: In that case there would be a proposition ‘F(F(fx))’, in which the outer function F and the inner function F must have different meanings, since the inner one has the form φ(f(x)) and the outer one has the form ψ(φ(fx)). Only the letter ‘F’ is common to the two functions, but the letter by itself signifies nothing.
The (hetero-)referential character of saying forbids any formulation of logico-syntactical rules, because such ‘rules’ are essentially constitutive of every possible proposition, in such manner that they ‘must go without saying’ (müssen sich von selbst verstehen) if we only know how every single sign signifies (3.334).
What is at stake here is nothing but the limits of propositional thought, that is to say the principal ‘object’ of philosophy according to the Tractatus. To present something in indicating that it ‘goes without saying’ (or more precisely that it must be ‘understood by itself’) amounts to asserting that it depends on an original kind of understanding, which does not consist of picturing particular facts but in the way we represent reality. The task of philosophy as a positive activity is essentially to operate a kind of showing, i.e. to clarify several dangerously unclear propositions. Philosophy has no proper object (that’s why it is not one of the natural sciences) and therefore no proper propositions. It is not a ‘theory’ but a pure activity of clarification (4.112). Its ‘elucidations’ (Erläuterungen) have indeed a pragmatic value: they are means to clarify propositions or, more exactly, to let propositions become clear by themselves (das Klarwerden von Sätzen). Its main question is to grasp the essence of propositional thought, which cannot be done without a non-representational kind of understanding. There can be no propositional representation of propositional representation, because its nature is essentially hetero-referential. That’s why the understanding of the essence of (representational) thought must be a delimitation: Philosophy should ‘set limits to what can be thought; and, in doing so, to what cannot be thought’ (4.114). Due to the impossibility of stationing ourselves outside language and thought (i.e. to get an external standpoint on language and thought), it must ‘limit the unthinkable from within (von innen) through the thinkable’ (ibid.). And showing is but this internal manifestation of the clear meaning of every proposition: To ‘signify what cannot be said’ and to ‘present clearly what can be said’ are in fine one and the same activity (4.115).
It follows from this that the important idea of a limit must appear as the indication of another viewpoint on a same reality rather than the authentic signification of some transcendent entity. This is clearly perceptible in Wittgenstein’s treatment of the notion of a metaphysical subject (5.631 & sq.), which equally seems to corroborate the exegetical hypothesis we have proposed. The metaphysical subject is not some reality beyond the world, but the pure showing that corresponds to the impossible representation of the essence of thought. The notion of representation consists of an intended adequacy between a subject and an object (i.e. some definite fact), so that there cannot be representation without any distinction between what (or who) represents and what is represented. That’s why the subject cannot be itself an object of its own representation. As its field of possible representation is the world as the totality of facts, the subject cannot itself be a factual part of the world (it is not the human being, not the human body, or the object of psychology, but ‘the limit of the world – not a part of it’, 5.641). So there can be no authentic representation of (and therefore no saying about) the ‘representing subject’; this one must show itself, display its own identity in its internal relation to the world. The incapacity of propositional thought to represent the subject leads to contradictory judgments about its existence or non-existence (compare 5.631: ‘In an important sense there is no subject’, with 5.641: ‘Thus there really is a sense in which philosophy can talk about the self…’).
Such judgments are in fact elucidatory sentences which aim is not to refer to a positive reality, but to suggest a particular way of seeing. With the explicit introduction of the idea of limit, Wittgenstein’s style becomes more and more complex, so that his spatial metaphors are sometimes inverted. His remarks on ethics, aesthetics and the mystical may, prima facie, suggest that there is a reality external to the world, reality which can be shown and cannot be said. This presentation risks leading to the idea that showing is in some cases a reference to an external and transcendent world whereas saying would remain related to what is the case ‘in’ the world of facts. To avoid misunderstanding these developments, it is particularly important to see that there is just one single world, and that this unique world can be apprehended in different ways. When Wittgenstein employs the term ‘world’, he sometimes intends to indicate the world as a ‘totality of facts’ (i.e. the factual aspect of the world), sometimes the form of reality (i.e. the logical form or the ‘limit of the world’), and sometimes the pure existence of ‘something’ (5.552, 6.44). In order to stress the strict delimitation between the factual aspect of the world and its other aspects, the end of the Tractatus presents these other aspects as being ‘outside the world’ (that is to say: outside the pure content of facts). But the non-factual aspects of the world are not related to ‘another’ world: They remain internal characters of the same single world. Actually, they show themselves in the unsayable factuality of facts, i.e. in their formal traits which themselves presuppose the pure existence of something (dass etwas ist). The ‘experience’ of the existence of the world, that is to say what Wittgenstein calls the ‘mystical’ (6.44) is not something hidden behind the facts, but what is logically prior to every possible fact and present in every existing structure. This pure existence appears only when we manage to see the world as ‘limited whole’ (6.45), to recognize that the totality of facts is limited by formal properties which constitute others aspects of the world. To see the world aright (die Welt richtig zu sehen, 6.53), we need to understand that the world possesses non-factual (and therefore unsayable) aspects, which give rise to nonsensical sentences. But the nature of the saying-showing distinction remains the same: whereas saying means representing facts by means of other facts, showing is the pure displaying of an identity, of the nature of something: In this case, of the complete essence of the world.
Although an important exegetical work remains to be accomplished to verify our general hypothesis, it seems likely that this formal characterization of the Tractarian distinction between saying and showing permits an understanding of the unity of Wittgenstein’s first book and provide us with a coherent explanation of how it has been possible that he thought to have found a single solution to all the major problems of philosophy. For the author of the Tractatus, the idea that there is a unique way to solve philosophical problems does not only mean that these problems must be dissolved by the logical analysis of their formulation. Its means that all the important logico-metaphysical difficulties which appear in philosophical discourse share a same formal characteristic, and therefore that they can be overcome by a unique distinction. That Wittgenstein was not himself able to elucidate the essential form of this main distinction, and that he didn’t manage to apprehend in a clear and constant manner the status of his own discourse, does not imply that there is no uniformity in his various applications of the idea of showing. The Tractatus can pretend to be the swansong of philosophical discourse insofar as this one is always victim of a single great formal problem, which perfect expression and definitive solution would lay in the idea of showing.
 I am grateful to Marie McGinn and Denis Vernant for their helpful suggestions and comments on earlier versions of this paper, and to the Région Rhône-Alpes for its financial support. My work was presented at the University of East Anglia (Norwich) during a session of the Wittgenstein Workshop in May 2012. I thank Oskari Kuusela, Rupert Read, and all the participants of the workshop, who provided me with valuable feedback at this occasion.
 Cf. letter to Russell, 13.3.1919: ‘I’ve written a book called Logisch-philosophishe Abhandlung containing all my work of the last six years. I believe I’ve solved our problems finally. This may sound arrogant but I can’t help believing it.’ B. McGuinness (ed.) Wittgenstein in Cambridge. Letters and Documents 1911-1951, Oxford, Wiley-Blackwell, 1995, p. 89.
 Geheime Tagebücher 1914-1916, Wien, Turia & Kant, 1991, 29.9.14.
 Tagebücher, in Werkausgabe Band 1, Berlin, Suhrkamp Verlag, 1984, 6.3.15.
 Tagebücher, 29.9.14.
 Geheime Tagebücher, 9.10.14
 See G.H. von Wright, Wittgenstein, Cambridge, Cambridge University Press, p. 82-83.
 B. McGuinness & G. H. von Wright (eds.), Ludwig Wittgenstein: Cambridge Letters: Correspondence with Russell, Keynes, Moore, Ramsey and Sraffa, Oxford, Blackwell, 1997, p. 124-125.
 M. Kremer, ‘The Purpose of Tractarian Nonsense’, Noûs 35 (2001), 3973; ‘The Cardinal Problem of Philosophy’, in A. Crary (ed.) Wittgenstein and the Moral Life: Essays in Honour of Cora Diamond, Cambridge, MIT Press, 2007, p. 143-176.
 On the one hand, we must agree with Oskari Kuusela to notice: ‘that it is tempting to read Wittgenstein’s statements as theses, and that it may be hard to see how else to construe them, does not mean that they should be read as theses – especially if this makes his philosophy contradictory’ (The Struggle against Dogmatism: Wittgenstein and the Concept of Philosophy, Harvard, Harvard University Press, 2008, p. 6). But, on the other hand, the idea that the Tractatus contains no doctrine at all is itself inconsistent with the affirmation of the Vorwort that the book communicates truths.
 Wittgenstein and the Vienna Circle, Conversations recorded by Friedrich Waismann, ed. & trans. J. Schulte and B. McGuinness, Oxford, Blackwell, 1979, p. 184.
 See Christiane Chauviré, ‘La monstration, unique mode de donation de l’a priori chez Wittgenstein’, Revue de Métaphysique et de morale, 101 (3), p. 291-301, 1996 ; Marie McGinn, ‘Saying and Showing and the Continuity of Wittgenstein’s Thought’, The Harvard Review of Philosophy, 9 (1), p. 24-36, 2001 ; Mark Sultana, ‘Bridging the Gulf Between Wittgenstein’s Works: A Matter of Showing’ , Forum Philosophicum, 12.2, p. 207–25, 2007 ; Martin Pulido, ‘The Place of Saying and Showing In Wittgenstein’s Tractatus and Some Later Works’, Aporia, Vol. 19.2, Fall, 2009, p. 11-32. The idea was already present in: Donald W. Harward, Wittgenstein’s Saying and Showing Themes, Bonn, Bouvier Verlag Herbert Grundmann, Abhandlungen zur Philosophie, Psychologie und Pädagogik, Band 109, 1976; Paul Holmer, ‘Wittgenstein: Saying and Showing’, Neue Zeitschrift für Systematische Theologie und Religionsphilosophie, vol. 22, p. 222-235, 1980; Philip R. Shields, Logic and Sin in the Writings of Ludwig Wittgenstein, Chicago, University of Chicago Press, 1993.
 This is the thesis of several tenants of the ‘new’ reading of the Tractatus: Thomas Ricketts, James Conant, Michael Kremer. See Juliet Floyd, ‘Wittgenstein and the Inexpressible’, in A. Crary (ed.) Wittgenstein and the Moral Life: Essays in Honor of Cora Diamond, MIT Press, 2007, p. 177-234, especially p. 180 & sq.; Jean-Philippe Narboux, ‘Making Sense of Showing’ (2011, draft available on the Internet).
 P.M.S. Hacker, ‘Was He Trying to Whistle It?’, in A. Crary, R. Read (eds), The New Wittgenstein, London, Routledge, 2000, p. 353-354.
 For instance, Hacker’s use of the terms ‘metaphysics’ and ‘religion’ seems especially misleading.
 Due to the nature of the Tractarian argumentation, it is not possible to divide precisely the book into several distinct parts. This ‘classification’ has therefore first a pragmatic value: the thematic entries roughly correspond to the order of the Tractatus, but I do not pretend that it is a perfect representation of its structure.
 See Marie McGinn, ‘Wittgenstein and the Pure a priori’, in Wittgenstein and the Future of Philosophy: A Reassessment after Fifty Years, Vienna, Ontos-Verlag, 2002. The idea is also suggested in Christiane Chauviré, ‘La monstration, unique mode de donation de l’a priori dans le Tractatus’, Revue de métaphysique et de morale, Paris, PUF, vol. 101, n°3, 1996, p. 291-301.
 See A.W. Moore, ‘On Saying and Showing’, Philosophy, n°62, 1987, p. 473-497.
 Commentators who present showing as being a priori may only mean that it is prior to truth (and falsehood) and independent of experience (at least of subsisting states of affairs). But what we picture consists of facts, that is to say empirical structures which are not a priori, and there is no rigorous positive use of this expression in the Tractatus.
 F. Récanati, La Transparence et l’énonciation, Paris, Seuil, 1979, p. 124-126.
 G. Ryle, ‘Knowing How and Knowing That’, Proceedings of the Aristotelian Society, New Series, Vol. 46 (1945-1946), p. 1-16; Michael Kremer, ‘The Purpose of Tractarian Nonsense’, Noûs 35, 3973, 2001, p. 39-73; ‘Mathematics and Meaning in the Tractatus’, Philosophical Investigations 25, 2002, p. 272-303.
 Op. cit.
 Juliet Floyd, ‘Wittgenstein and the Inexpressible’, p. 180 & sq.
 Fabian Goppelsröder, Zwischen Sagen und Zeigen, Wittgensteins Weg von der litterarischen zur dichtenden Philosophie, Bielefield, Transcript, 2007, p. 27.
 In Chris Bezzel (ed.), Sagen und Zeigen. Wittgensteins Tractatus, Sprache und Kunst, Berlin, Parerga Verlag, 2005, p. 15-31.
 ‘Mathematical Logic as Based on the Theory of Types’ (1908), in Logic and Knowledge. Essays 1901-1950, London, Routledge, 1956, p. 61.
 See Christiane Chauviré, ‘La monstration, unique mode de donation de l’a priori dans le Tractatus’, p. 295 : ‘The main interest of showing is that in ‘showing’ signs can teach us something on themselves, without having to say it : showing is reflexive (in a non-technical sense), it exempts us from self-reference, which is besides forbidden by Wittgenstein in 3.333: a proposition cannot say anything about itself, and certainly not that it is true, because a fonction cannot be its own argument.’ That a sign cannot be employed to construct formulas which give rise to vicious circles is shown by the symbol itself, so that a ‘theory’ of significance appears useless (and is also impossible).
 See Pete Mandik, ‘Picturing, Showing, and Solipsism in Wittgenstein’s Tractatus Logico-Philosophicus’, Analysis and Metaphysics 6 (1), 2007.
 A case of absolute self-reference would be such that it is impossible to distinguish between what refers and the object of reference. There can be not example of this, because it must be a logical impossibility. Every example of reference, including the so-called cases of ‘self-reference’, presupposes the distinction between two different elements (even if this distinction may sometimes remain very unclear).
 See B. McGuinness (ed.) Wittgenstein in Cambridge: Letters and Documents 1911-1951, Oxford, Blackwell, 2012, p. 49.
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