ATTEMPT TO UNDERSTAND WITTGENSTEIN'S PICTURE THEORY OF THE PROPOSITION
Kieran Cashell

Ludwig Wittgenstein

I use the words you taught me. If they don't mean anything any more, teach me others. Or let me be silent. [Pause.]

Samuel Beckett, Endgame. 1

I

Let us speak firstly of the attempt. Two senses of "Attempt to understand Wittgenstein's Picture Theory" can be indicated. On the one hand, functioning in its proper (intensional) context - as a title - it refers reflexively to the content of this essay. "Attempt", in this sense signifies the attempt made here tonight concerning Wittgenstein. On the other hand, one can perhaps predicate a certain extra-contextual, quasi-transcendent sense of "Attempt". Remove the scare-quotes, append an exclamation mark: Attempt to understand Wittgenstein's picture theory! becomes a didactic imperative to make the attempt to understand the picture theory.
Let us speak therefore of the attempt. 2
Thinking the attempt involves a caveat that at this stage gives us pause: namely, the attempt to understand involves a certain risk. Approaching the limit of understanding - this risk can be identified as the risk of failure. It means no more than that any attempt to understand must remain an attempt. What I seek tonight is nothing less than the attempt to understand the attempt.
Intensifying the attempt in this way gives it a performative structure. It attests to the refusal to take vicarious gratification in the fulfilment of an understanding that would masquerade as completion, as continuity, as consistency, as coherence.
The attempt signifies that something (is) taking place.
If the attempt is a project, what do we aim at? Hypothetically, can we speak of the horizon of an attempt? Eyeing an uncertain destination, our problematic snakes detour-wise across a faulty landscape, toward a kind of Zenonian non-place. This locus is not the place of understanding; it is not a discursive destination; having always already taken place, discourse takes (its) place somewhere inside the communicative trajectory: past the departure and short of the destination. A detour will take us outside that trajectory; it will deposit a broken inclination: this is the movement of discourse itself.
Discourse - all that can be said - shows itself in the detour of the attempt.
And this is what is to be understood.

II

Negative theology reminds us that every attempt to describe God adequately in communicative terms debases God to the level of ordinary reason, and so denigrates his absolute Otherness. The utterly hopeless attempt to understand God can only be understanding that we cannot understand God. Leading us to the point of despair, the following proposition: anything said concerning God is inadequate, turns back on itself recursively in the edifying recognition that - except for the following admission - anything said concerning God is inadequate.
This scepticism, this concession of defeat, is but a recognition of the fragility of our "transcendental" epistemological instrumentation. But the paradox of this scepticism is that there, amid the fault-lines that mar and undermine epistemic certainty, some objective (un)certain presence appears; there, stuck in the aporia, something presences. Abdicating to the limits of knowledge - there, there is an access - there there opens a way through the aporiai of discourse.
Apropos of Kierkegaard, Louis Mackey demonstrates that in the aftermath of a scepticism more sceptical than counterfeit Cartesian scepticism, a strange shape-taking emerges. 'Wherever all human possibilities - aesthetic, intellectual, moral - are exhausted, there God is present. … human attempts to make contact with God must be frustrated before God himself can break through' (1967; 76).
To speak unscientifically: alienated from something incommensurable to my cognitive categories - I become aware of something necessarily absent from my limited world. And yet it is in this moment - that is, in the moment I become aware of the limits of my world - I glimpse evanescent possibilities in the mesh of the profanely factual. In the negative delimitation, a gestural relation is maintained with the ambiguous region outside the boundaries of this cartography. In other words: the excluded necessarily (retributively - Anaximander) informs discourse. Negative form - what Kierkegaard might have called the 'shadowgraphy' of limits - involves an internal movement through to what lies beyond its limits. Installing a corruptive heterogeneity into Parmenidean identity, that which is limited maintains an ostensive relation with the other side of its limit. And yet contra Hegel's polemic against Kant, the transconceptual, being wholly indeterminate, is not just void.
Scepticism: a presence denied its presence and in this denial indicated, unsaid and in this unsaying said, unshown and shown, unseen and seen; and this counterplay of speaking and silence, of exhalation and inhalation, of positing and de-positing is the rhythm of Wittgenstein's Tractatus Logico-Philosophicus.

III

If we ingenuously accept Wittgenstein's own insistent claim that the overriding theme of the Tractatus is ethical, then the ineluctable conclusion of that text (as its 'final imperative' 3 demonstrates) is that the axiological - the philosophy of values as opposed to facts - is sticto sensu ineffable. Candidly: the Tractatus says (NB this "says") that in order to do justice to the ethical we must (imperatively) observe a moratorium - that is, recognise a strict regime of ineffability - regarding value judgements.
It is this conclusion that leads Albert W. Levi (1978-9; 71), among others to hypothesise that the Tractatus represents a picture of traditional metaphysical dualism. Backing up his claim, Levi quotes Wittgenstein's famous 1919 letter to Ludwig Von Ficker (here I reproduce the pertinent passage of this letter in full from Ray Monk's biography, Wittgenstein, the Duty of Genius (1990)):

I wanted to write that my work consisted of two parts: of the one which is here, and of everything [note this "everything", in a sense, everything hangs on this "everything"] which I have not written. And precisely this second part is the important one. For the Ethical is delimited from within, as it were, by my book; and I'm convinced that strictly speaking, it can ONLY be delimited in this way. 4 In brief, I think: All of that which many are babbling about today, I have delved in my book by remaining silent about it. (in Monk: 1990; 178)
Levi concludes that Wittgensteinian reticence concerning the semantic 'displacement' of the axiological, promotes the radical exclusion of a transcendental value-domain from the empirical world; this implies (necessarily) a coterminous affirmation of the contingent status of the fact-world as reflected in linguistic sense (or more precisely, logical form). This strategy removes the moral beyond the legislation of rational (ad hominem) judgement (that is, it renders it outside and unanswerable to the categorical imperative) (73).
6.421 It is clear that ethics cannot be expressed.
Ethics is transcendental.
(Ethics and aesthetics are one.)
6.423 Of the will as the subject of the ethical we cannot speak.
Levi interprets this relativist 'strategy' with reference to apparently "incontrovertible" "facts" excised from Wittgenstein's biography. Thus, he claims (most bewitchingly) that Wittgenstein's ethical system (consolidated in the doctrine of 'moral inexpressibility' expounded in propositions 6.4 to 7 of the Tractatus) is associated with his haunted, self-deprecatory, and (ultimately) guilty conscience regarding his (homo)sexuality.
Granted, propositions 6.4 to 7 appear to ratify Levi's hypothesis; language cannot subsume anything of higher value than itself; the domain proper to the ethical is incommensurable to the language that we use to communicate contingent facts (or intentional objects) (6.42). And if read pari passu with Wittgenstein's tortured and self-deprecatory letters 5 (which Levi believes simply must relate to his guilty homosexuality) his hypothesis is admittedly enticing in a lurid, sleazy, tabloid way. However, interpreted in the light of my opening remarks, the tractarian inexpressibility thesis becomes perhaps more philosophically (even theologically) subtle than the sealed hermeneutic envelope of the Levian adaequatio can admit.
How?
In the following way.
Attempts to render the valuable in a suitable philosophic or scientific metalanguage surrogate the transcendent significance, the denial of which is the condition of its possibility. Thus (I argue) it is misleading to attribute a commitment to metaphysical dualism (ontological, axiological or otherwise) to early Wittgenstein, even if the geminate structure of the Tractatus itself appears to reflect this "two-worldism". The tractarian rejection of the translation of ethical values to significant speech is not an abstract negation. Rather it is a negation that conserves what it annuls; and thus it follows the (dia)logic of the negation characteristic of consciousness, i.e. the negating gesture that "casts away"and that yet maintains an ostentive relation with what it negates on a higher level. It is this negation (illustrated perspicuously in thesis 6.54 in terms of a certain climbed-and-thrown-away ladder) itself that intimates the ethical content of the Tractatus; and the task of that text is to show that the gesture of rejection itself provides its eliminated substance: 6 the content expunged through the parsimony of form returns like the spectre of "the repressed" to haunt the Tractatus.
(Negative theology shows that it is only through the performative denial per se that true transcendent, metaphysical experiences become possible - denial is their mode of actualisation [actualitas, entelechia].)
'There is indeed the inexpressible', Wittgenstein writes, 'This shows itself; it is the mystical [es ist das Mystische]' (6.522, my emphasis). Traditional philosophy errs in its attempt to reduce das Mystische to language. It is guilty of misunderstanding the logic of language in ways foundationally damaging to itself. Fundamentalontologie and Naturalistic ethics (for example) violate the rules of logic by attempting to make language do something it cannot do: namely, to represent metaphysical, transcendental or existential ("Subjective") experiences adequately in intentional ("objective") or scientifically accountable propositions. Such linguistic attempts to hypostatise (or reify) the metaphysical experience, as Wittgenstein says in the ante-penultimate proposition of the Tractatus, cannot signify; that is, the ambiguous signs of such language cannot do the work of hypostasis demanded of them. (Conversely, the Tractatus also shows that the positivist affirmation of the irrelevance of metaphysical, religious and aesthetic values from the episteme of philosophy is a facile and precipitate gambit.)
Yet again we recognise the gesture of negative theology in the tractarian delimitation of what can be communicated without ambiguity in language and in the necessity of silence concerning das Mystische. Wittgenstein maintains (in the Hegelian sense, and so: relieves) a relation to the meaningful aspects of life: those aspects that give form to the intuitive content of life and substantiate it - such as responsibility, decision and choice, the relation to the absolute, that wonder concerning the why of Being (Thaumazein), and simple indwelling with the self. 7 Eliminated from the general semantic, these forms of life are yet conserved under erasure (to use Derrida's term: sous rature8) in Wittgenstein's Tractatus. And yet far from avoiding the issue of the transcendental (what is common a priori yet cuts across all particular, contingent instances), the Tractatus recognises the aporia that we deny the transcendent only to represent it more clearly and unequivocally. In other words, we eliminate speaking of it in order to do justice to it.
The sentence: we admit the derelict inadequacy of our attempts to know the transcendent, paradoxically represents a fragment - a splinter (Splitter) - of adequate knowledge. Thus, in renouncing the possibility of a positive description of the metaphysical - through rejecting the reduction of transcendental possibility to positive atoms of language - a movement (as in a transport) of the radically transcendent takes place.
4.114 It [philosophy] should limit the thinkable and thereby the
unthinkable.
It should  limit the unthinkable from within through the thinkable.
4.115 It [philosophy] will mean the unspeakable by clearly displaying the speakable.
Reminiscent of the negative gesture, the meaning of the Tractatus is absent in that text. I deliberately use that paradoxical locution to demonstrate that what is excluded from the text is yet somehow still there.
It is absent, and in this absence, present.
Ineffability becomes the condition of possibility of (what I have termed, inadequately) "transcendent experiences". Attempts to express and adequately represent such experiences in language, therefore subsuming them in reflective concepts, founder against the limits of a hermetic conceptual economy. In other words: we tie ourselves in cognitive knots. For Wittgenstein, the philosophic performance is a matter of untangling those cognitive knots.
And yet.
In cataloguing the limitations of understanding, a certain negative shape emerges beyond the outer edges of discourse: the de facto absence of positive metaphysical facts in the world is yet a mark of their shadowed presence.
Let us therefore begin, with nimble fingers, to untangle some cognitive knots; let us face (up to) the attempt; let us await the phenomenal presence of das Mystische.

Part 2

The Picture Theory of the Proposition
I

Ludwig Wittgenstein, supervising the searchlight of a captured Russian ship silently adrift on the Vistula in 1914, 9 was thinking about the mysteries of logic. And his quarry - to disclose the general, universal form of the proposition, that to which all empirical propositions of language (however complex) conform - would, he believed, solve at last those logical spectres haunting him since Cambridge, and which he alone, heroically, struggled to exorcise in Norway the year before.
During the first months of World War One he was working on the analysis of complex sentences into symbolic components; he believed that empirical language, if reduced to its elementary logical parts, could be shown to correspond to the irreducible (atomic) components that - taken in their totality - constitute reality. The direction of his thought was leading toward the conviction that only painstaking analysis could show the shared relational form of elementary proposition and associated portion of reality. In sum: if a proto-sign was discovered to represent the universal form of the general proposition, then such a sign would somehow also demonstrate the logical structure underlying language: that which enables language to describe (or at least give the appearance of logical correspondence with) a reality apparently indifferent to our description of it.
It was during his nocturnal supervision on the Vistula that he came to the conclusion that the relational form (logos) co-ordinating thought, language and the world was pictorial in nature. Prima facie, this says no more than that we picture facts to ourselves (2.1). Later the story was told how, while serving on the Eastern front, Wittgenstein read a report of a Parisian court case in which a model was used by witnesses to exhibit evidential facts (G.H. von Wright in Monk: 1990; 117).
No apocalyptic sign, or revelatory seal, merely the straightforward reconstruction of an accident used routinely in evidence: nevertheless it struck Wittgenstein (embroiled in his problematic) with the force of an epiphany.

II

Wittgenstein gradually became convinced that the ability to represent a positive fact through modelling it in its absence, thereby retaining and communicating its sense (inner logical form), contained the key to the general form of the proposition (logos). That an empirical chain of events can be modelled with ersatz objects standing in for the disposition of things in an objective (but absent, past, possible) event; that the truth of the event - "is this how it really happened?" - can thus be ascertained, gives crucial insight into how world, thought and language are logically co-structured.
Wittgenstein's notebook entry of 29 September 1914, catalogues the genesis of the idea that determines our attempt tonight:
The general concept of the proposition carries with it a quite general concept of the
co-ordination of proposition and situation. The solution to all my questions must be
extremely simple.
In the proposition a world is as it were put together experimentally. (As when in the
law-court in Paris a motor-car accident is represented by means of dolls etc.) This
must yield the nature of truth straight away (if I were not blind) … [there follows a
drawing of two figures fencing] … 'A is fencing with B'. The proposition in picture
writing can be true or false. It has a sense independent of its truth or falsehood. It
must be possible to demonstrate everything essential by considering this case.
(Wittgenstein, in Kenny: 1973; 53)
This, what we now recognise as "the picture theory of the logical proposition", was initially called 'The Picture Theory of Logical Portrayal' (Monk: 1990; 118); at its most skeletal, it is a description of our relationship with the world. And that that relationship is mediated, in the Hegelian sense, by language - that it is pictorial in nature - demonstrates that thought frames cells of reality (facts) in pictures; it demonstrates that language represents this depicting activity: we explain the world to ourselves by depicting it in language.
With the discovery that we explain reality to ourselves by picturing it, Wittgenstein believed he had discovered the solution to the problem intimated above, the problem of logical form.

III

Wittgenstein's Tractatus begins with a precise and exiguous description of the world. Thesis 1.1 distinguishes between a fact and an object and identifies the world as the totality (Gesamtheit) of facts.
Why does Wittgenstein draw a distinction between a fact and an object? What is the distinction?
The answer is straightforward: empirical reality arranges itself into discrete facts - an indigenous potentiality to relate itself to other things, thus taking (its) place in the structure of a discrete fact represents the object's or thing's essential logical form (that without which it would not be itself); this potentiality is further defined as the 'internal property' of the object (Gegenstand) or thing (Ding).
Containing immanently all possible combinations with other objects, the given object virtually presents all other objects and hence virtually presents all potential states of affairs (groups) in which it can appear as a functional element. Wahl: 'These formal or internal properties of an object concern the range of its occurrences in atomic facts (Sachverhalten), the possibility of combining with other objects in a certain way'. 10
2.0123 If I know an object, then I also know all the possibilities of its occurrence in
atomic facts.
(Every such possibility must lie in the nature of the object.)
A new possibility cannot subsequently be found.
2.01231 In order to know an object, I must know not its external but all its internal
qualities.
2.014 Objects contain the possibility of all states of affairs.
2.0141 The possibility of its occurrence in atomic facts is the form of the object.
We could say that - in the tractarian account - the object / thing qua component of facts, wears its internal properties (potential to become a structural component of a possible fact) inscribed on it like the brush-stokes congealed on the surface of things in a painting.
A discrete fact is therefore essentially composite. It has a general form: it is a Gestalt figure. 11 The logical form of objects is such that we perceive configurations of objects in contrast to an isolated object, quarantined from its context of interrelations. That is to say, the logical form of perception is such that we perceive a morphological configuration of things as a single shape or form. In the Tractatus the notion of a unique, solitary object is a logical fallacy; thus "the thing" presents virtually, immanently, all possible configurations (or 'concatenations') that it can compose itself within or become a structural part of. And thus the simple or atomic fact is the fundamental ontological quantum of the tractarian cosmos.
Thesis 2.04 defines the world as the entire aggregation (Geshamtheit) of such existent (or subsistent: bestehen) simple facts. (The totality of atomic states of affairs that do exist, as opposed to those that do not, then equals the world.) Importantly in the next thesis (2.05), Wittgenstein maintains that all those simple facts that do exist (existent atomic states of affairs that do so exist) also decide (or contain virtually, immanently, in their logical form) those simple facts which do not exist, do not subsist. (Each fact contains its own antithesis. [To use Searle's example]: the sign communicating "No Dogs Allowed" [i.e. a schematic picture of a dog with a red line through it] is essentially the same sign as its affirmation, i.e. the "not" part is not a component of the picture. 12 Reality (Wirklichkeit) can now be defined as all independent existent / subsistent (Bestehen) and non-existent (Nichtbestehen) atomic states of affairs (or independent positive and negative facts). This determines (or defines) reality in general. Finally, the world is re-defined at 2.063 as the complete reality (Die gesamte Wirklichkeit).
Out of these initial cosmological reflections, a picture of the picture theory begins, gradually, to emerge.

IV

2.1 We make to ourselves pictures of facts [Wir machen uns Bilder der Tatsachen].
With this thesis, Wittgenstein inaugurates the initial discourse of the picture in the Tractatus (2.1 - 3.03). Facts can be presented in pictures; such presented facts have the ability to re-present reality as defined above: existent and non-existent simple facts; that is to say, we model reality through thought by picturing portions of it (2.12).
But how is this possible?
Pictures are reducible to their structural elements and the resultant elements (as in the reconstruction of the accident scenario), says Wittgenstein are substitutes for the objects combined in real facts (or states of affairs (2.131)). Like the objects disposed in a fact, the elements of a picture are configured in a determinate, logically necessary way; because its elements are linked together - that is, given in a context - the picture represents the atomic fact in which the objects are linked together ('concatenated') in an cognate way.
2.1511 Thus the picture is linked with reality; it reaches up to it.
2.1512 It is like a scale applied to reality.
Pictures frame cells of reality as between the prongs of a callipers; the picture is essentially composite: it is a Gestalt-figure (skhema). (And these characteristics of the picture endow it with factual status - but it is another day's work to unpack the implications of this proposition.)
A picture, in order to be representational must fulfil two criteria: On the one hand it must be somehow commensurate with the situation it depicts: fact-Gestalt, depicted in the picture, its objects becoming pictorial structural elements, means that it makes no sense to refer to - to depict - an isolated "object". Thus Wittgenstein (in 2.162) is able to say that 'there must be something identical' to both picture and depicted situation in order for the picture to function as a picture of the ontological state of affairs. The common identity that Wittgenstein discerns obtaining between picture and fact in the picture he terms 'representational form'.
2.171 The picture can represent [abbilden] every reality [Wirklichkeit] whose form
[Form] it has.
The spatial [räumliche] picture everything spatial, the coloured everything
coloured, etc.
Representational form can be seen as the capacity of the structural elements of the picture to meaningfully coalesce into a form reflexive of the Gestalt of objects in a fact. This, the minimal mutual relationship of "state of affairs" and picture means that the structural elements of both are co-ordinated in a one-to-one relationship. That is to say, the logical form of the disposition of things in the fact defines the form (or the sense) of the picture: where we may perhaps be able to depict illogical facts (in dreams or in our surrealist cartoons), we cannot depict impossible objects (like a rolling book, a spongy television screen or transparent milk).
On the other hand, in order to be a picture and not be confused with the possible ontological fact it depicts (something that - despite trompe l'oeil - never happens), the picture must be qualitatively different to the depicted fact; if the picture were identical to the fact represented, it would be the fact and not a picture of it: the logic of representation would be outside the synthetic grasp of our faculties. To claim that identity and difference are both central to representational form means that a picture is essentially heterogeneous. And that is only to say that the picture does not contain its depicted state of affairs; it does not bracket it as an eidetic content; it does not envelop it.
Although the picture is independent of the state of affairs it depicts, and thus assumes a perspective outside it, the picture cannot assume such a standpoint outside itself. The picture cannot stand outside itself as it were and depict its representational essence. Thus representational form, the condition of possibility of picturing a situation in general, is the one thing that the picture cannot depict about itself: it cannot represent what it is about itself that enables us to understand that it is the substitute for an ontological state of affairs and not this state of affairs itself. In sum, the picture cannot represent what it is about itself that makes it a picture - the representation of a possible fact.  Rather (Wittgenstein says in 2.172) the picture simply projects its representational essence forward: 'it shows it forth'; and we understand this implicitly, intuitively.
If the atomic fact represented by the picture exists in reality, the picture is true: if what it depicts does not exist, the picture is false ('2.21 'The picture agrees with reality or not; it is right or wrong, true or false'). While the activity or faculty of picturing and the grasp of the logic of representation may be a priori, Wittgenstein maintains that we are unable to determine from the picture alone if it is a true or a false picture; this can only be established a posteriori by referring to empirical reality. With the assertion that we always have to apply to experience to discover if the picture represents a case as it is, Wittgenstein suggests that no picture can be necessarily, analytically true. "No picture is analytically true" means that the truth of pictures cannot be recognised from the picture alone: a picture is always a picture "of something".
Of what? Of reality (existent and non-existent states of affairs).
The 50/50 probability of being false is essential to the logic of representation. And thus Wittgenstein maintains that the picture does not necessarily represent a state of affairs having a positive ontological status, but depicts rather, a possible state of affairs. This ability to depict ontological possibilities (the possibility of erroneous representation) is essential to the logic of representation; that is, for a picture to be capable of representing reality accurately, it must (i) be heterogeneous to what it depicts; (ii) be truth-functionally equivocal; and (iii) only ever be verified in a synthetic way.

V

Next, drawing on the discourse of the picture, there follows a short passage on thought.
Wittgenstein begins by characterising the thought as a logical picture: thought pictures the fact; that we can synthetically frame a possible fact in a picture is thus the same thing as saying we can think it. Through the universality of representational form (i.e. through the logical form that cognitive space shares with logical space in general), thought can frame existent facts in logical space; and hence the ability to conceptually construct possible facts is essential to the human cognitive processes of hope, of belief, of desire, of imagination, of dreaming (which some philosophers consider the defining characteristics of zoon logon echon). Identifying thought and logical picture enables Wittgenstein to draw out the consequences of his conclusions about the nature of picturing for his consideration of the proposition.

VI

As it is with the picture so it is with the proposition.
4.1 The proposition is a picture of reality. The proposition is a model of the reality
as we think it is.
The facility with which Wittgenstein moves from the thought to the proposition suggests that he identifies the thought tout court with the proposition (c.f. 4). A proposition expresses a thought, he says: in the sentence, the thought realises itself in a material medium.
3.1 In the proposition the thought is expressed perceptibly through the senses.
(Im Satz druckt sich der Gedanke sinnlich wahrnehmbar aus: In the proposition,
the thought expresses its sensuous perceptibility).
A proposition is defined as the expression of a thought - i.e. the medium through which the thought is sensibly projected or inscribed; this is the same as saying that the sentence re-presents a thought in a form amenable to perception. Wittgenstein's characterisation of the thought in these terms suggests that for him the process of thinking (necessarily representational) was an aesthetic phenomenon. As is the case with the picture, we verify the truth or falsity of propositions expressive of thoughts through sense-experience - by relating them back to empirical reality (4.06).
To understand a proposition is to understand its sense. How can we understand the sense of a proposition without having seen or heard it before and without knowing if it is true or false? Because it is a picture and hence is reflexive of the logical structure of the fact: it makes sense. Having recognised that the sense of the proposition refers to the possible configuration of things in possible atomic facts, we relate the proposition back reflexively (i.e. mediated through concepts, or signifieds, in the Saussurean sense) to the relevant cell of reality, and thereby establish its truth / falsity. And thus the reference of the picture is recognised, and consolidated or refuted.
4.16 In order to understand the essence of the proposition, consider hieroglyphic
writing, which pictures the facts it describes.
And from it came the alphabet without the essence of the representation being lost.
4.02 This we see from the fact that we understand the sense of the propositional
sign
without having had it explained to us.
4.021 The proposition is a picture of reality, for I know the state of affairs
presented
by it, if I understand the proposition. And I understand the proposition, without
having had its sense explained to me.
Three points can now be enumerated: 1) the proposition is a picture; 2) it images the facts it describes; 3) it exhibits its sense.
As with the representational form of the picture, the proposition cannot say what it is about itself that makes it a picture of the facts it depicts; rather it projects its sense, its logical form, silently from within itself. Like the hands of a speaker, silently gesticulating, soundlessly shaping thoughts in the air,
4.22 The proposition shows its sense.
The proposition shows how things stand, if it is true. And it says that they do so
stand.
Propositions are thought-vectors, their sense consists in the indicative ability of their elements to pick out objects and articulate possible states of affairs. As objects configure themselves into facts in the world, so signs are 'articulated' in the propositional sign; they are articulated in the anatomical sense, like the limbs of a skeleton
3.14 The propositional sign consists in the fact that its elements, the words, are
combined in it in a definite way.
The propositional sign is a fact.
Wittgenstein gets us to imagine the propositional sign as composed of 'spatial objects (such as tables, chairs, books) instead of written signs'. This thought experiment elucidates the essence of the proposition. Of extreme significance for Wittgenstein, is the 'mutual spatial' disposition of the taken objects, tables, chairs etc. This 'expresses the sense of the proposition' (3.14131). In the ideal logical symbolism, the spatial disposition of symbols in the propositional calculus would correspond precisely to the disposition of the objects in the atomic state of affairs.

VII

As clothing conceals the form of the body, the sentence as it phenomenally appears, does not look like a picture. Ordinary language obscures its underlying logical form. Wittgenstein compares this obscuring relation to the relation a musical score has with the narrative of sounds it represents. Similarly, the graph only superficially appears to bear a relation to the dynamic system it represents - but we say it makes sense when we discern the definite homology of pattern informing it: 'these symbolisms' Wittgenstein writes, 'prove to be pictures - even in the ordinary sense of the word - of what they represent' (4.011). A proposition expressed in symbolic notation is pictorial in this sense. As a signifier, Wittgenstein writes, it bears an 'obvious' material similarity to its signifieds [Bezeichneten]. The internal relation associated with all these phenomena is that minimal logical structure shared by the logical picture, the thought, the proposition and the fact: it is the form of reality itself.
With the category of internal properties, Wittgenstein simultaneously differentiates and identifies picture and fact. An internal property is the defining or exclusive characteristic that gives a particular thing its identity. It is that "whatness" of the thing that it is impossible that something should lack and still be itself (4.123). Without internal properties, the objects informing the fact would cease to be themselves. In this context, Wittgenstein also speaks of an "internal relation" or 'relation of structure' obtaining between objects in atomic facts (4.122). Again these internal properties are the essential characteristics defining the simple fact.
It is through their internal properties (which he says are like facial features) that a relation of structures - an internal relation - can subsist between different facts in the world. We can now say that the proposition can represent and communicate the essential properties of a state of affairs because the proposition also possesses essential (its own) properties: And this it shares with the factual state of affairs. What they share, in sum, is the logical form of reality. It is this universality of logical structure that co-ordinates the elementary propositions of language to the atomic constituents of facts.
An internal relation whereby the proposition qua picture both accommodates and excludes the state of affairs it represents is the condition of possibility of representation in general. Representing the possible ontological fact means we must understand at once the similarity and the difference underlying their structure. Logical picture and reality, fact and proposition are homologous structures, they are ostensibly different yet they follow an identical logic. What it is that gives a fact its defining characteristics - those aspects that preclude its being something else - that make it incommensurable with other atomic facts? They are precisely those aspects that enable it to be depicted accurately in pictures, in language. The conditions of possibility of the picturing function of language are the self-same aspects that make it impossible for the picture to be the thing pictured.
Most significant about this notion of homologous structure, for Wittgenstein, is that it cannot be expressed in denotative (or communicable) language.
4.12 Propositions can represent the whole reality, but they cannot represent what
they must have in common with reality in order to be able to represent it - the
logical form.
To be able to represent the logical form, we should have to be able to put our
selves with the propositions outside logic, that is outside the world.
4.121 Propositions cannot represent the logical form: this mirrors itself in the
propositions.
That which mirrors itself in language, language cannot represent.
That which expresses itself in language, we cannot express by language.
The propositions show the logical form of reality.
They exhibit it.
Wittgenstein here (again) insists on the opposition between what can be said and what cannot be said but shown (the informing gesture of the Tractatus). According to Monk, the showing / saying distinction is the crucial nexus between Wittgensteinian logic and the ascetic silence concerning metaphysico-ethical meaning. As I tried to show in the opening sequence of this paper, despite a moratorium of silence concerning the axiological or the transcendent, events of higher value yet manifest themselves, not in the world yet somehow in my world. When I begin to appreciate the world as a limited whole, there, I apprehend the metaphysical and ethical. And so it is with logic: when we understand language as a limited whole, its underlying logical form becomes manifest, informing it - like the body its loose and baggy garments.
But why does Wittgenstein place a prohibition on naming the internal properties, the logical form of language?
If there is an answer to this question, perhaps it is this: No Archimedian point exists outside language from where we could analyse it thoroughly - thus there always an essential aspect of language that remains inscrutable to us. This ineffable aspect is essential to our understanding of language - it is logical form - it is shown forth. We are intuitively aware of the ineffable aspects of language: they show themselves in our use of language. In fact it is essential to language that there be something about it that cannot be expressed but makes itself manifest in those pictorial, pictogrammatic aspects of language.
What they show (and this is the fundamental thesis of the Tractatus) about language and monadologically about the world cannot be said. I am unable to express the truth of the relationship between my world and the language I use to describe that world. All that can be unequivocally said must be worked through, rung by tortuous rung. Until one night, elucidation gleams darkly behind the stripped and denuded, skeletal and anorexic propositions we are limited to. And in that nocturnal Penelope work of recognition that is philosophy, we recognise the propositions of the Tractatus as senseless (Sinnlos) 13: we negate their negation. And in this night, understanding returns to where it was most rigorously expunged - in the attempt as such. Just as the underlying logical structure of language is made manifest when we experience the limits of language, when we experience the world as a limited whole with the "I" as the limiting case - the ethical becomes manifest. At this limit, the relationship of language and the world "as such" cannot be expressed in language - or in the world - but rather becomes manifest in the experience of the limits of language, in the experience of the aporia as such, in the experience of the hopeless attempt "as such".

Nur um der Hoffnungslosen willen ist uns die Hoffnung gegeben.
- Walter Benjamin 14

NOTES

1.   In The Complete Dramatic Works; London and Boston: Faber & Faber 1986, page 113.
2.   Those familiar with critical theory will perceive the unconcealed reference to Adorno's 1965 essay on Beckett's Endgame "Versuch das Endspiel zu verstehen" in all this. They will also no doubt recall the negative work that Adorno demands of the word "understand" (Verstehen) in that essay. To understand Endgame is to understand that it cannot be understood. I refer also to Simon Critchley's excellent analysis of the modality of "Versuch" in Adorno's essay in his 1997 Very Little … Almost Nothing; Death, Philosophy, Literature. See especially page 147.
3.   7 Wovon man nicht sprechen kann, daruber muss man schweigen (Whereof one cannot speak thereof one must be silent).
4.   Again, I am using Ray Monk's translation of this letter here; this line appears in Levi as: ' "to set limits to the domain of the ethical from the inside - which is the only way it can be rigorously done"' (in Levi: 1978-9; 72); See Monk, Wittgenstein, The Duty of Genius. London: Jonathan Cape, 1990 page 178.
5.   Levi draws mostly on William Warren Bartley's book Wittgenstein for his biographical material. He cites Wittgenstein's correspondence to Paul Englemann between December 1916 and September 1925 ('The letters are both highly personal [he writes] and enigmatic. But one thing runs through them like a trail of blood [!] - a deep consciousness of personal guilt' (66). This guilt is occasioned by Wittgenstein's 'not being able to get over a particular fact … It was [William Warren] Bartley's not entirely sympathetic function to ground this unmistakably in Wittgenstein's role as guilty homosexual' (67). In this context it is worth reading the Appendix ("Bartley's Wittgenstein and the Coded Remarks") of Monk's biography. 'In writing this book, I have had unrestricted access to all the coded remarks in possession of the literary executors, and permission to quote any of them that I wish. I have chosen to quote virtually all the remarks that are in any way revealing of Wittgenstein's emotional, spiritual and sexual life. … I have left nothing out that hat would lend support to the popular notion that Wittgenstein was tormented by his homosexuality, although I myself believe this to be a simplification that seriously misrepresents the truth' (585).
6.   I borrow this idea and phrasing from Theodor W. Adorno's "Towards an Understanding of Endgame": in Twentieth Century Interpretations of Endgame, A Collection of Critical Essays. edited by Bell Gale Chevigny; Prentice Hall, Inc, 1969 p 83.
7.   These ideas are taken from a lecture Wittgenstein delivered in November 1929 to the Heretics Society in Cambridge. See Wittgenstein: "A Lecture on Ethics", Philosophical Review Volume 74, January 1965, in Philosophical Occasions 1912-1951. Edited by James C. Klagge and Alfred Nordmann; Indianapolis and Cambridge: Hackett Publishing Company 1993, pp 37-44.
8.   See Derrida, Jacques: Of Grammatology pp 19 and 45 (1974, translated by G. C. Spivak) for an example of his use of the Heideggerian-influenced (from The Question of Being, [see Heidegger, 1956 page 81 where Being is famously put "under erasure"]) strategy of materially placing the signifiers of concepts sous rature. I stress in this context that a concept cannot be "said" while "under erasure". See also Christopher Norris's (1991) Deconstruction, Theory and Practice page 69 for a discussion of the Derridean use of the sous rature.
9.   See Monk, Wittgenstein, The Duty of Genius. op. cit. page 117.
10.   See Wahl, Russell. "Impossible Propositions and the Forms of Objects in Wittgenstein's Tractatus" The Philosophical Quarterly Vol. 46, no. 179, April 1995 page 190.
11.   See Stenius, E.: Wittgenstein's Tractatus. Oxford: Basil Blackwell, 1960.
12.   See Magee, Bryan. "Wittgenstein, A Dialogue with John Searle" in The Great Philosophers, An Introduction to Western Philosophy. 1987 pages 324-325.
13.   See Wahl on the distinction between Sinnlos and Unsinnig in the Tractatus. Wahl, Russell. "Impossible Propositions and the Forms of Objects in Wittgenstein's Tractatus" 1995 op. cit. page 190.
14.   Walter Benjamin. Goethes Wahlverwandtschaften, in Gesammelte Schriften I . 1, 1980 page 201

References

Adorno, Theodor W. "Towards an Understanding of Endgame", in Twentieth Century Interpretations of Endgame, A Collection of Critical Essays. Edited by Bell Gale Chevigny; Prentice Hall, Inc, 1969 pp 82-114.
Beckett, Samuel. "Endgame" in The Complete Dramatic Works. London and Boston: Faber & Faber 1986, pp 89-134.
Benjamin, Walter. "Goethes Wahlverwandtschaften" in Gesammelte Schriften I . 1, Frankfurt am Main: suhrkamp Verlag 1980.
Critchley, Simon. Very Little … Almost Nothing: Death, Philosophy, Literature; London and New York: Routledge 1997.
Derrida, Jacques. Of Grammatology. Translated G. C. Spivak Baltimore and London: Johns Hopkins University Press, 1974.
Heidegger, Martin. The Question of Being. Translated with an introduction by William Kluback and Jean T. Wilde; New York: Twayne Publishers inc., 1958.
Kenny, Anthony. Wittgenstein. New York and London: Penguin Books, 1973.
Kiekegaard, Søren. Either/Or Volume One. Translated by David F. Svenson and Lillian Marvin Svenson, with revisions and a foreword by Howard A. Johnson; New Jersey: Princeton University Press 1919.
Levi, Albert W. "The Biographical Sources of Wittgenstein's Ethics" in Telos 38 Winter 1978-79.
Mackey, Louis. "Søren Kierkegaard: The Poetry of Inwardness" in Existential Philosophers: Kierkegaard to Merleau-Ponty. Edited by George Alfred Schrader Jr. New York: Mc Graw Hill Inc., 1967.
Magee, Bryan. "Wittgenstein, A Dialogue with John Searle" in The Great Philosophers, An Introduction to Western Philosophy. Oxford University Press, 1987; pp 320-347.
Monk, Ray. Wittgenstein, The Duty Of Genius. London: Jonathan Cape, 1990.
Stenius, E. Wittgenstein's Tractatus. Oxford: Basil Blackwell, 1960.
Wahl, Russell. "Impossible Propositions and the Forms of Objects in Wittgenstein's Tractatus" in The Philosophical Quarterly Vol. 46, no. 179, April 1995 pp 190-198.
Wittgenstein, Ludwig. "A Lecture on Ethics" in The Philosophical Review vol. 74, no. 1, January 1965 pp 4-14; in Philosophical Occasions 1912-1951. Edited by James C. Klagge and Alfred Nordmann; Indianapolis and Cambridge: Hackett Publishing Company 1993, pp 37-44.
Wittgenstein, Ludwig. Tractatus Logico-Philosophicus. Translated by C. K. Ogden with an introduction by Bertrand Russell; London and New York: Routledge and Kegan Paul, 1922.

Copyright © 1998 Minerva. All Rights Reserved.

A version of this paper was presented to the Limerick Philosophical Society in 1998.
Kieran Anthony Cashell, M.A. is a tutor in Philosophy at Mary Immaculate College, University of Limerick and a lecturer in Critical and Contextual Studies at the Limerick School of Art and Design, Ireland.
Mail to: Kieran Anthony Cashell

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