Thursday, 12 November 2009


I begin by referring to Alain Badiou, Infinite Thought, translated and edited by Oliver Feltham and Justin Clemens (Continuum, 2003), and in particular to pp 16-17 of the commentators’ Introduction. These pages bear on Being and Event, Meditation 3.

My question is: why should Badiou’s account of Frege’s understanding of the relation between ‘multiples and well-formed formulas’ be read as the editors and translators of Badiou’s text (and Badiou himself) would have us do?

To begin with, Frege’s definition of the relation is given by Feltham and Clemens as follows: ‘There exists a set b such that every term a which satisfies the formula F is an element of that set’. As they point out, such a reading leads to Russell’s Paradox. The paradox arises when the well-formed formula is ‘the set of all sets that which are not members of themselves’. If the set of elements which satisfies the formula belongs to itself, then by definition it does not do so, and if it does not belong to itself, then it does. In response to this, the axiom of separation was developed in ZF set theory so as to avoid Russell’s Paradox. Feltham and Clemens read it as: ‘If there exists a set a, then there exists a subset b of a, all of whose elements g satisfy the formula F’.

What is the point of this? Well, according to the editors, ‘the essential difference between Frege’s definition and the axiom of separation is that the former directly proposes an existence while the latter is conditional upon there already being a set in existence, a. The axiom of separation says that if there is a set already in existence, then one can separate out one of its subsets, b, whose elements validate the formula F’. They give the example in which F is the property ‘rotten’ and one wants to make the judgement ‘Some apples are rotten’. ‘Via the axiom of separation, from the supposed existence of the set of apples, one could separate out the subset of rotten apples.’ The significance of this is the bearing it has on the relationship between being and language: for Badiou, the axiom of separation stipulates that the existence of a multiple is no longer inferred on the basis of natural language (i.e. on the basis of confusions surrounding the use of the word ‘all’). It is rather the case that language separates out, within a supposed given existence (within some already presented multiple), the existence of a sub-multiple (BE 47). Badiou states: ‘Language cannot induce existence, solely a split within existence’ (BE 47). ‘The axiom re-establishes that it is solely within the presupposition of existence that language operates—separates…’ (BE 47). As the editors have it, ‘the very conditions of the inscription of existence in language require that existence be in excess of what the inscriptions define as existing’.

This last statement seems little more than a truism. Reality exists prior to and outside language. To call on set theory to establish or prove this bespeaks confusion. In any event, the point here is that neither the notation of Frege’s definition nor of the axiom of separation, need be read as Badiou and his commentators read them. One may simply invert the conditions of existence and conditionality as between the reading they give of Frege’s notation and the reading they give of the axiom of separation. In other words, it is possible to give Frege’s definition of the axiom in the following way: ‘If there exists a set b, such that for all a, a satisfies F, then a belongs to b’. Again, it is similarly possible to read the axiom of separation in a manner that differs from that of Badiou and his commentators: ‘For all a, there exists a set b, such that for all g, g belongs to a and g satisfies F and therefore g belongs to (is a member of) b’. And if the inversion goes through, then it would seem we are under no obligation to accept Badiou’s presentation/interpretation either of Frege’s logical definition or of the axiom of separation. As a result, we are not obliged to take Badiou’s account of the axiom of separation as any sort of justification for his account of the relations between language and being.

Not only that, but further inspection of set theory would appear to indicate that we are under no obligation to take the axiom of separation as the axiom that explicitly forbids x belonging to x, the condition that gives rise to Russell’s Paradox. Paul Cohen and Reuben Hersh, for example, give what they call the axiom of regularity as the axiom which serves that purpose. The formulation they present operates in terms of sets (or multiples) alone, and does not call upon the notion of a predicate, unlike the axiom of separation, as Badiou and his commentators present it. The formulation simply says that for all x, either x may be a set of elements that do not include x (x could be the set of whole numbers, say), or there is a y such that y belongs to x and for all z, if z belongs to x then no z belongs to y. Thus, the axiom of regularity, like the axiom of separation, precludes the possibility of x being a member of itself, although the two axioms can be seen to differ in other significant ways. Furthermore, it is by no means clear that the axiom of regularity can be used to muster support for Badiou’s notions concerning the relation between language and reality.

Part of Badiou’s purpose in all of this is to replace the ‘inadequacies’ of ordinary language with an ideal logical syntax. Now, the notion of an ideal logical syntax was subjected to critical scrutiny by the early Wittgenstein, as James Conant has made clear in a number of his readings of the Tractatus. This, then, raises a further question as to why we should take the notation that Badiou presents us with as requiring the prose interpretations that he ascribes to it. Logical propositions are senseless, and they are not to be confused with propositions which do have sense. The purpose and significance of logical notation is to be found in relation to what Wittgenstein calls ‘elucidations’. ‘In order to recognize the symbol in the sign we must consider the context of significant use’ (TLP 3.326), and it is central to the purpose of a logical notation to render perspicuous the mode of representation of intelligible propositions expressed in ordinary language where those propositions may be less than perspicuous, due to ambiguities or equivocations of one kind or another. But in logical propositions themselves, in tautologies (or contradictions), there is no symbol to be discovered in the sign. They have form, but no content.

It is precisely considerations of this order that Badiou is obliged to exclude from his enterprise. The assumptions underpinning his procedure require him to treat first order logical formulations, the predicate calculus in which the propositions of set theory are couched, as though they were propositions that do represent how things are, as though they were propositions that are as a matter of fact either true or false. One might wonder, therefore, if there is not, basic to Badiou’s approach, a confusion between sign and symbol of the kind that Wittgenstein in the Tractatus takes to be fundamental to what constitutes Scheinsätze, pseudo-propositions that generate an illusion of meaning. It is a confusion that stems from the projection of logic onto reality, a projection captured in the proposal that mathematics be taken as ontology.


Cohen, Paul, and Reuben Hersh. ‘Non-Cantorian Set Theory’, Scientific American 217 (October 1967), 104-116.
Conant, James. ‘The Method of the Tractatus’, in From Frege to Wittgenstein, ed. Erich H. Rech (Oxford: OUP, 2002), 374-462.

Friday, 6 November 2009


The standard reading of the Tractatus presents its project in terms of the demarcation of the bounds of sense. It is argued that the text develops a general theory of language which is then used to fix the bounds of sense. Wittgenstein’s purpose, on this view, is to draw limits to meaningful discourse. However, it has been made clear, by commentators like Cora Diamond and James Conant, that the task of a ‘proper theory of symbolism’ is to self-destruct in a manner that shows all theories of symbolism to be superfluous. ‘Logic must take care of itself’ (TLP 5.473). When Wittgenstein claims that you cannot give a sign a wrong sense, his claim is that there is no such thing as infringing on the bounds of sense and therefore there are no bounds of the sort that, according to the standard view, he was seeking to demarcate.

As Conant indicates, ‘the difference between an ideal logical symbolism and ordinary language, for the Tractatus, is that in the former—unlike the latter—one is able to read the symbol directly off the sign. Logical syntax for the Tractatus is not a combinatorial theory (which demarcates legitimate from illegitimate sequences of signs or symbols) but a tool of elucidation (which allows us to recognize the logical contributions of the constituent parts of a Satz, and the absence of such a contribution on the part of the constituents of a Scheinsatz)’. Elucidation, or the transition from unclarity to clarity, is not effected through the transformation in the logical character of the propositions of ordinary language, but rather through a transformation in the view we hold of their logical character. In Conant’s words, ‘It is a matter of making explicit the logical structure that has been implicit in our Sätze all along (and if our Sätze are Unsinn [nonsense], it is a matter making explicit that there has, all along, been no implicit logical structure but only the appearance of such structure)’.

Conant’s argument is that in the Tractatus Wittgenstein wants to show how Frege’s theory of Begriffsschrift—his theory of a logically perfect language that excludes the possibility of the formation of illogical thought—is in fact the correct theory of language as such. ‘Language itself prevents the possibility of every logical mistake. Ordinary language is in this respect already a kind of Begriffsschrift. What for Frege is the structure of an ideal language is for early Wittgenstein the structure of all language.’ Denis McManus argues that Wittgenstein's early work can be seen ‘as attempting to defuse all efforts to draw the bounds of sense, as attempting to expose as illusions anything that would give logic an impossible reality’. ‘Theories which make a proposition of logic appear substantial are always false’ (TLP 6.111). As McManus has it, ‘Anything that would seem to set the bounds of sense, to give substance to the laws of logic, is an illusion.’

For Badiou, Wittgenstein is, along with Lacan, one of the most potent of modern anti-philosophers. This is how he characterises the procedures of the early Wittgenstein:

The antiphilosophical act consists in letting what there is be manifested, insofar as ‘what there is’ is precisely that which no true proposition can say. If Wittgenstein’s antiphilosophical act can legitimately be declared archi-aesthetic, it is because this ‘letting-be’ has the non-propositional form of a pure showing, of clarity, and because such clarity happens to the unsayable only in the form of a work without thought (the paradigm for such donation is certainly music for Wittgenstein). I say archi-aesthetic because it is not a question of substituting art for philosophy either. It is a question of bringing into the scientific and propositional activity the principle of a clarity whose (mystical) element is beyond this activity, and the real paradigm for which is art. It is thus a question of firmly establishing the laws of the sayable (of the thinkable), in order for the unsayable (the unthinkable, which is ultimately given only in the form of art) to be situated as the ‘upper limit’ of the sayable itself.

This is a restatement of the standard, ‘ineffable’ reading of the Tractatus. However, if Conant and McManus (amongst others) are right, it is this very reading that the Tractatus causes to self-destruct. In Philosophical Remarks we find the following:

Any kind of explanation of language presupposes a language already. And in a certain sense, the use of language is something that cannot be taught . . . I cannot use language to get outside language. (PR 54)

McManus points out that a similar thought can be found in an early Notebook entry:

How can I be told how the proposition represents? Or can this not be said at all? And if that is so can I ‘know’ it? If it was supposed to be said to me, then this would have to be done by means of a proposition; but the proposition could only show it.
What can be said can only be said by means of a proposition, and so nothing that is necessary for the understanding of all propositions can be said. (NB 25)

As McManus indicates, ‘all explanations of propositions terminate at some point in our simply seeing what a proposition shows, and that will be a matter of our already understanding the world in the terms in which that proposition represents it. The proposal that a proposition must simply “show its sense” (TLP 4.022) and, with it, the world it represents, thus emerges here out of a sense of confusion in the notion that one might be told how propositions represent’.

The limits of my language mean the limits of my world. (TLP 5.6)

This sentence, as it is set out here, relating, as it would seem to do, to the question of the conformity between my language and my world, is in fact a sentence to which we given no sense. We have simply mistaken a combination of signs without sense for a combination of symbols with sense. If utterances are meaningless, that is not because they are beyond sense, or possess some illogical sense. It is because we have, as yet, given no meaning to the signs that make them up.

It would seem, then, that Badiou is right when he says that what he calls the ‘act’ is central to Wittgenstein’s notion of philosophy as an activity. 'Philosophy is not a body of doctrine but an actvity' (TLP 4.112). As Conant has argued, the nonsensicality of a sentence like ‘Caesar is a prime number’ is to be traced, not to the logical structure of the sentence, but to our failure to mean something by it. For Wittgenstein, the source of the problem is to be located in our relation to the string, not in the linguistic string itself. We think we are confronting a logically impossible thought—and that this involves a kind of impossibility of a higher order than ordinary impossibility. The desire for meaning is displaced onto the words themselves: it is as if they are aspiring to say something they can never quite succeed in saying. It is in this, and nothing more mysterious than this, that the archi-aesthetic nature of what is situated beyond the sayable consists.


Badiou, Alain. ‘Silence, solipsisme, sainteté: L’antiphilosophie de Wittgenstein’, BARCA! Poésie, Politique, psychanalyse, 3, (1994).
Bosteels, Bruno. ‘Radical Antiphilosophy’, Filozofski vestnik XXIX, 2 (2008): 155-187. The translation from Badiou is cited from Bosteels.
Conant, James. ‘The Method of the Tractatus’, in From Frege to Wittgenstein, ed. E.H. Reck (Oxford: OUP, 2002), 374-462.
McManus, Denis. The Enchantment of Words (Oxford: OUP, 2006).

Thursday, 15 October 2009


I want to suggest certain ways in which some reflections by P.M.S. Hacker on the distinction between object and event cast light on what it is that Badiou understands by the event. Obviously enough, Hacker, like Austin and Wittgenstein, is a philosopher of what Alain Badiou calls, dismissively, ‘the linguistic turn’. However, this point need not be taken too seriously. The issues Hacker raises concerning and object and event have a decided bearing on the relation between being and event.

Hacker points out that while objects occupy space, events occur in space, at a place: they do not fill or occupy space. He writes: ‘Two objects cannot occupy the same place at the same time, but two distinct events may occur simultaneously at the same place, as when an object in the fire simultaneously gets hotter and changes colour’. Events are unlike material objects in that they do not consist of matter. Not consisting of matter they have no size or texture, and they are neither solid nor not-solid. Since events do not occupy space as objects do, they are neither two- nor three-dimensional. While it is true that events need space in which to take place, they do not have dimensions. The component parts of an object are typically thought of as being spatial parts, and hence they are smaller than the whole of which they are parts. As Hacker indicates, the ‘analogue of part for an event is the notion of the phase’. As an object is made up of the sum of its parts, suitably ordered in space, an event is made up of the sum of its phases, appropriately ordered in time. But, as Hacker points out, ‘these “parts” of events are not … smaller than the event of which they are parts, but shorter (temporally) than it’.

If we take this distinction for what it is, a distinction in grammar (in both Wittgenstein’s and Austin’s senses of that term, which are not unrelated) between the spatial composition of objects into parts, and the temporal division of events into phases, then it makes no sense to say that an event is a multiple. That is, unlike an object, an event is not intelligibly to be understood as constituted in a way that lends itself to being described as a set, whether finite or infinite. Set theory is not designed to address that which is temporally constituted: an event, being thus temporally constituted, has no parts, and is thus not divisible into sets, subsets or power sets. Given that, for Badiou, mathematics (set theory) is ontology, it would thus seem that ontology has no significant bearing on the elucidation of what an event is. Now, Badiou allows for this: an event, after all, is a set that includes itself, a set that therefore violates one of the basic axioms of ZF set theory. To put this another way, it is a multiple that is indiscernible within the situation in which it occurs. An event is a generic set, a set which is not recognisable within the established parameters of knowledge as these are laid down by standard set theory, but nonetheless a set, albeit non-constructible.

That there is a difficulty in thus inscribing events among objects becomes clear if we think about how the attribution of perceptual qualities to events differs from the attribution of perceptual qualities to objects. As Hacker reminds us, one can watch the falling of leaves or the performance of a play. ‘But events have neither shape nor colour, just because they do not have spatial dimensions, do not fill space, and do not consist of stuff.’ How is it then that we can see events? To think of an event as a colourless and shapeless object is to think of what is an invisible object! However, events are not objects, and they are not amorphous or colourless. It simply makes no sense to attribute shape or colour to them. ‘A colourful event is not a multi-coloured event, but an event which consists in various transformations of vari-coloured objects or production of multi-coloured flashes, as in a firework display. To observe an event is to see something happening to certain material objects that are undergoing various changes. I may observe the event of the poker’s becoming hot. The poker changes from black to glowing red, but the event of its becoming red does not change from black to red, it is the change from black to red.’

In my previous entry on this matter, I drew attention to Peter Dews’ review of Badiou. Dews cites from Wittgenstein:

Even where the feeling that arouses joy is localised, joy is not: if for example we rejoice in the smell of a flower. – Joy is manifested in facial expression, in behaviour. (But we do not say that we are joyful in our faces.)

“But I do have a real feeling of joy!” Yes, when you are glad you really are glad. And of course joy is not joyful behaviour, nor yet a feeling around the corners of the mouth and the eyes.

“But surely joy designates an inward thing.” No. “Joy” designates nothing at all. Neither any inward or any outward thing. [Zettel §§486-87]

Dews remarks: ‘Like joy, the Badiouian event cannot be designated—and can be located neither in mental nor physical space. Indeed, one must surely conclude that joy is an event’. But in that case, events are very common: they ‘make up the very texture of the human world’, a point to which Hacker’s discussion gives full support.

A number of questions arise. To begin with, if joy is an event in Badiou’s sense (i.e. his account can be applied to it), then presumably the heating of the poker is also an event in Badiou’s sense, along with Hacker’s other examples (which include the French Revolution). How then can set theory, concerned as it is with multiples (sets and subsets, wholes and parts of wholes) illuminate the nature of an event, which, thus understood, is precisely not a multiple? That is, how would Badiou describe the kinds of event to which Dews and Hacker have given consideration? Again, on what principles are the events that Badiou privileges, Christ’s Resurrection, the French Revolution, the Cultural Revolution, for example, selected? Events are the stuff of life. Why should only these few, very rare, events be selected as events? Is it that fidelity is due to them? The suspicion must arise that the selection is the result of a certain political predetermination. Badiou’s ontology is static, the result of his set-theoretical parti pris. Once the original decision was made to cast ontology in mathematical form (Cantorian form), the event arises as that violates or ruptures the static nature of being as being. The event bears with it novelty, revolution. That there are problems with Badiou’s original decision is something that Peter Osborne has discussed, and I have referred to that discussion in an earlier entry. There is another worry that I have: in his book on St Paul, Badiou takes Christ’s Resurrection as exemplary of what an event is. And yet for him this event did not occur: it is, he says, ‘a fable’. In what sense is an event that has not occurred an event?

These are questions, not objections. It may be that Badiou’s achievement is to raise, in a mode not unlike that of Wittgenstein, problems that concern the foundations of philosophy. If one were to say of such an achievement that it is therapeutic, in the sense that Wittgenstein's philosophy is therapeutic, then one would also have to say that, if we are to understand Badiou himself, then that understanding is itself an event, the event of recognising his propositions for what they are, that is, nonsensical.


Dews, Peter. A review of Being and Event, tr. Oliver Feltham (Continuum, 2006), in Notre Dame Philosophy Reviews 2008.02.18. [online]
Hacker, P.M.S. ‘Events and Objects in Space and Time’, Mind 91 (1982), 1-19.
Hacker, P.M.S. ‘Events, Ontology and Grammar’, Philosophy 57 (1982), 477-486.
Osborne, Peter. ‘Neo-classic: Alain Badou’s Being and Event’, Radical Philosophy, 142 (March/April 2007), 19-29.

Sunday, 11 October 2009


I want to begin by making reference to a review by Peter Dews, published in 2008, of Badiou’s Being and Event. For Dews, Badiou’s philosophy derives from a tension between two basic propositions: mathematics is ontology and ontology is a situation. This means that ‘although ontology exhausts what there is, it cannot capture everything that occurs’. This division enlists Badiou in the tradition of anti-philosophy, despite his expressed opposition to it: what cannot be known is what it is most important to know, or, in a different version, what cannot be said is what must be said. Of course, for Badiou, ontology, the knowledge of being as being, is given to us by mathematics, and in particular by the set theory of Cantor. What exceeds the situation is the event and the event is that which cannot be known or said in that situation. An event is a multiple, but one that counts for nothing in the situation in which it takes place. If ‘the state of the situation’ is what is re-presented of what is presented (i.e. if it is the power set of the ‘original’ infinite set of multiples), then the event concerns those presented elements that are not re-presented in the state of the situation. An event is a multiplicity (a multiple of multiples) none of whose elements are re-presented in the state of the situation. As Dews notes, the event is what Badiou calls ‘totally abnormal’, which is to say that an event is a multiple comprised of those elements which were originally presented but not re-presented in the state of the situation. Such a multiple, an ‘evental site’, is ‘on the edge of the void’—in other words, it looks as though it does not exist, but this, it should be noted, is only how things appear from the point of view of someone within the situation. The event counts for nothing in the situation in which it emerges, or into which it erupts. Everything that exists in the situation is numbered or ‘counted for one’ in that situation. The event is thus said to be ‘supernumerary’. It is something that evades the count. To cite Peter Hallward, ‘As something that cannot be recognised as one in a situation, an event is the (necessarily ephemeral) presentation of inconsistency in the situation’. In Badiou’s book, the shift from being to event is the shift from Cantor to Cohen.

The emergence of the event is at the same time the emergence of the subject who recognises it, who nominates it as an event, an act which begins a process of fidelity to the event thus (retroactively) evoked. But, as Dews indicates, if we ask what exactly in the situation is being nominated, or what constitutes the evental site, all we seem to have is the multiplicity of elements from which the event emerged. As Badiou has it, the event consists of the elements belonging to the evental site, together with the event itself. Thus understood, the event can be seen as a set that belongs to itself (it thus violates one of the fundamental axioms of set theory—the axiom of foundation). Dews cites one of Badiou’s favourite examples, the French revolution, which is more than the innumerable (infinite?) list of doings that took place in France between 1789 and 1794. ‘It is rather something bound up in this assemblage, which the term “French Revolution” specifically names. But when we try to specify what this extra something is, we find ourselves again confronted only with the assemblage of happenings—plus that elusive addendum. The revolution is not simply the narrative of what occurred, but it cannot be filtered out from this narrative either.’

However, Dews goes on to argue that, given this way of defining them, events are far more widespread and common than Badiou allows for. He compares Badiou’s account of the event with the way Wittgenstein characterises the grammar of processes that have often been ascribed to a ‘mental’ domain. For example, expecting someone to arrive can consist of a wide range of different thoughts and activities. ‘There is no determinate set of thoughts and activities that can be said to be necessary and sufficient conditions of such expectation (and furthermore, activities which, in one context, are correctly taken as indicating expectation, may no longer have this meaning when transposed into a different context).’ We cannot therefore identify the event (of expecting someone to arrive) either with specific mental processes or with outward behaviour, or with a combination of both. Nonetheless, we cannot conclude that the event (of expectation) is something other than these processes and actions. Dews quotes the following imagined dialogue from Zettel:

Even where the feeling that arouses joy is localised, joy is not: if for example we rejoice in the smell of a flower. – Joy is manifested in facial expression, in behaviour. (But we do not say that we are joyful in our faces.)

“But I do have a real feeling of joy!” Yes, when you are glad you really are glad. And of course joy is not joyful behaviour, nor yet a feeling around the corners of the mouth and the eyes.

“But surely joy designates an inward thing.” No. “Joy” designates nothing at all. Neither any inward nor any outward thing. (§§486-87)

Like joy, as here characterised in Wittgenstein’s dialogue, Badiou’s event cannot be localised in either mental or physical space. For Dews, there is therefore no reason to think that joy, seen in this light, is anything other than an event, as Badiou is given to understand the term.

At this point, I would refer to two articles, published in 1982, by P.M.S. Hacker on the ontology of events and the relation of events to objects, articles that seem to owe as much, in their methods of analysis, to J.L. Austin as to Wittgenstein. In one article Hacker writes: ‘Events are neither substances nor indeed do they exist. Or, if one prefers the jargon, the “being” of events is to take place, happen, occur—but not to “exist”. Material objects do not take place and events do not exist. A volcano exists, but an eruption of a volcano cannot exist. It may have happened, be happening, or be about to happen. The death of Caesar never existed—it took place. Caesar existed and the event of his death was the termination of his existence. The termination of an object is not itself an “entity” which exists. It is an event’.

There is no immediate conclusion that I wish to draw from these reflections. However, I am certain that the matters here raised are of pertinence to a fitting acknowledgement of the power of Badiou’s thought. I would suggest that no just evaluation of that thought will be achieved without setting it in relation to the work of both Wittgenstein and Austin—the two of them representing positions Badiou has been deeply critical of.


Dews, Peter. A review of Being and Event, tr. Oliver Feltham (Continuum, 2006), in Notre Dame Philosophy Reviews 2008.02.18 [online]
Hacker, P.M.S. ‘Events and Objects in Space and Time’, Mind 91 (1982), 1-19.
Hacker, P.M.S. ‘Events, Ontology and Grammar’, Philosophy 57 (1982), 477-486.

Monday, 14 September 2009


In an essay on Wittgenstein’s later philosophy, Stanley Cavell raises the question of what rule-following is for Wittgenstein. He notes, amongst other things, that in those activities which could be said to proceed according to rules the activity is not (could not be) ‘everywhere circumscribed by rules’ (PI, sec 68). As Espen Hammer puts the point, rules do not circumscribe every aspect of a meaningful activity or speech act. There must always be projections of words to which it is not clear whether rules apply or not. (Consider here, for example, Wittgenstein’s discussion of secondary sense and aspect seeing.) again, every rule-following activity takes place against the background of innumerable other activities. These include taking and giving directions, obeying orders, and so on. As Cavell makes clear, these considerations suffice to show that the concept of a rule does not exhaust the concepts of correctness or justification: indeed, the concept of a rule would have no meaning unless these other concepts were already in place, and were possessed of meaning.

More significantly, no specification of rules can ever explain what playing a game amounts to. Playing a game is ‘a part of our natural history’ (PI, sec 31), and until one has become an initiate of this form of life, this human form of activity, the citing of a rule can mean nothing. Many of our games can be learnt without ever learning or formulating rules, so that linguistic normativity does not involve the strong conception of inference and implication one finds in logical and mathematical systems. Again, language has no essence. There is nothing common to all games: they exhibit rather what Wittgenstein called family resemblances. For Wittgenstein, following a rule is just as much a practice as playing a game. Now, Cavell asks, what are its rules? There is typically no rule for following a rule. And yet following a rule can be done correctly or incorrectly. And that means that it can be done or not done. To follow a rule correctly is just to do it. To be an initiate of these practices is to be an initiate of a form of life. For Cavell, human speech and activity, sanity and community, rest upon nothing more, but nothing less than this. (Similar views may be found in such readers of Wittgenstein as Rush Rhees, Cora Diamond, James Conant, Rupert Read, James Guetti, Michael Kremer and Denis McManus, amongst a number of others.)

These considerations are of little significance to Badiou. He lists Wittgenstein high amongst the ‘sophists’ of the modern period, and in his fairly extensive writings on Wittgenstein he does not consider the kinds of question I raise here. (It is noteworthy that he does not refer to the work of Anglophone commentators on Wittgenstein; for instance, in his reading TLP he adheres to the traditional ‘ineffabilist’ account, and is oblivious to what may be called the ‘resolute’ reading of that text.) Badiou’s fundamental claim, that mathematics is ontology, aims precisely at the elimination of language from philosophy and at the overcoming of the ‘linguistic turn’. However, Cavell’s remarks on rule-following are not so easily dismissed, and any assessment of Badiou’s position (an assessment external to Badiou's own assessment of his achievement, that is) would need to consider them. The pertinence of Cavell's remarks may be seen when they are placed in relation to one of Zizek’s most telling criticisms of Badiou: ‘Against Badiou, one should insist that only to a mortal/finite being does the act (or Event) appear as a traumatic intrusion of the Real….Badiou remains blind to how the very space for the specific “immortality” in which human beings can participate in the Truth-Event is opened up by man’s unique relationship to his finitude and the possibility of death’. The implications of this last comment accord with what is already evident in Cavell's account of rule-following: the notion of a transcendent/ideal position such as that from which Badiou seeks to lay out an ontology is highly problematic. The elaboration of such a position is not to be characterised as an elaboration of the 'impossible': the idea is in fact nonsensical. (This, obviously enough, does not commit Cavell, or Wittgenstein, to relativism, post-modernism, or any of the other sins Badiou discerns in contemporary thought.) Hilary Putnam has written: 'There is always a cut between the observer's language and the totality of languages he generalizes over. The "God's-Eye View"--the view from which absolutely all languages are equally part of the totality being scrutinized--is forever inaccessible'.

Part of what I am saying can be placed in relation to what in Jean-Toussaint Desanti’s ‘remark’ on Badiou’s ‘intrinsic ontology’ touches on the question of the margin. Inasmuch as Badiou’s ontology is intrinsic, that is, concerned with being as being, it articulates itself in terms of ZF set theory. The margin is that which intrinsic ontology excludes by definition, and which it cannot recuperate. Desanti sees the margin as never silent. It is that which inscribes itself upon itself (marks itself), and is organised into a series of ‘writings’. The term has considerable resonance in French thought after Derrida, and Desanti draws on those connotations here: ‘I call writing anything which, as it is produced, leaves a trace’. He gives what he calls a ‘baroque’ list of examples, such as a falling leaf, a natural catastrophe, an utterance, an assassination, theft by a pickpocket, and so on. The obvious example he does not mention, that of a continuous line drawn between two points, but this is in effect the example that colours his discussion. Such a line is, obviously enough, the continuum, which cannot ultimately be defined by set theory.

The point of all this is to make it clear what Desanti means by a margin. He sees it as the writing of an excess (he italicises the word) which, he says, is not necessarily coordinated, though it is ‘susceptible to a localized coordination in the fragile wake left by some of its assemblages’. He gives no further clarification as to what he means, but perhaps one might think of the wreckage left behind in the wake of a hurricane. The fragile wreckage may be said to coordinate what has passed, in the sense that one can gauge the force of the passing of the storm from the detritus it has left behind. To draw on another idiom, though one not without relevance here, the margin is comparable, one might think, to the enunciation of the enounced, the uttering of the utterance. However, in set theory, which is itself a writing, the excess engendered by it must be recuperated back into the theory or else be excluded. Desanti concludes that ontological thought is therefore caught in the tension that binds these two writings together. Its task consists, he says, in trying to rewrite what is written in the margin and in capturing its excesses (an example being Cohen’s work on the continuum hypothesis). The margin can neither be abolished not excluded.

What this amounts to, I suggest, is a reworking in terms of ontology of what is given in Cavell’s account of rule-following. In other words, Cavell’s recognition of the relations between judgement and definition in the following of a rule, with its explicit recognition of what can only be called excess, is transposed here from what in Cavell’s case is a series of grammatical remarks into metaphysical statements, statements that purport to be true. A relevant example of this from Wittgenstein is the following: ‘The dangerous, deceptive thing about the idea: “the real numbers cannot be arranged in a series, or again “The set … is not denumerable” is that it makes the determination of a concept – concept formation – look like a fact of nature’ (RFM, II, sec 19, p.131). In a well-known study, Giorgio Agamben has gone to great lengths to recast the ontological/ontic distinction in terms of Benveniste’s distinction between enunciation and the enounced. The procedure there is the same: to recast what are distinctions in grammar as statements of fact, of a kind of hyper-fact.

Badiou does not seem to have escaped language. Mathematics—in his use of it—does not reach beyond language into a context free universe determined only by the offerings of ZF set theory (or now, under the influence of Desanti’s article, topos theory). What it would seem he has done is to transcode into the deliverances of set theory the structure of certain forms of language. So far from set theory escaping the toils of language, it would seem that it is to language that set theory has been brought to correspond. Language wears the trousers. Badiou would not of course deign to address any consideration of his position couched in these terms. But problems undoubtedly remain with the assumptions underpinning ontology as he presents it. (In this connection, an essay by Peter Osborne, in Radical Philosophy, 142 (March/April 2007), is to the point. I should note that objections to Osborne's position have been put by Oliver Feltham, especially in chapter 4 of his Alain Badiou: Live Theory (London, New York: Continuum, 2008). Feltham is critical of Osborne's suggestion that Badiou has transcoded certain linguistic concepts into set theory. He considers that this 'simply ignores the differences between mathematical and philosophical ideas' (p. 124). The point may rather be, however, that Badiou has simply blurred them.)

Agamben, Giorgio. Language and Death, trans. Karen E. Pinkus with Michael Hardt (Minneapolis, London: University of Minnesota, 1991).
Cavell, Stanley. Must We Mean What We Say? (Cambridge: Cambridge University Press, 1989).
Desanti, Jean-Toussaint. 'Some Remarks on the Intrinsic Ontology of Alain Badiou', in Peter Hallward, ed., Think Again: Alain Badiou and the Future of Philosophy (London, New York: Continuum, 2007).
Hammer, Espen. Stanley Cavell (Cambridge: Polity Press, 2002).

Sunday, 26 July 2009


These are some remarks on the poetry of Donald Davie, whose Collected Poems, edited by Neil Powell, were published by Carcanet in 2002.

In an essay of 1959 (reprinted in The Poet in the Imaginary Museum), Donald Davie presented himself, and those contemporaries associated with him in ‘The Movement’, in a light at once harsh and unforgiving. What underpinned his remarkably brutal self-exposure was the question of tone. The thing that stuck in his craw was what he came to see as the peculiarly deprecating and ingratiating mode of voice in which the poetry of the group had presented itself to the educated readers of its time. As Davie icily remarks, what in effect the poets of the Movement had succeeded in doing was to replace a poetry of self-expression (the poetry of Dylan Thomas and Edith Sitwell) with one no less egregious, namely, a poetry of ‘self-adjustment’—a poetry dedicated to getting on the right terms with the reader and to hitting off the right attitude towards him. Davie came to see the poetry he had written during the 1950s as an act of public and private therapy, in its own way another and no less contemptible mode of self-expression. His work, and that of those associated with him, was guilty of what during the 1960s and onwards he was to regard as the cardinal sin: the failure to respond creatively to the world as such. For the English poets of the 1950s, he believed, the world out there, in its quiddity, was accessible, if at all, only by way of an overweening irony, at once self-defensive and self-deprecating, which denied the world its integrity and otherness. Things in themselves were permitted no impact upon the poet unless submitted to categories and attitudes he himself had already imposed upon them. As Davie puts it: ‘This imperiousness towards the non-human goes along with excessive humility towards the human, represented by the reader’. To make the manipulation of ‘tone’ the central preoccupation of poetry was to deny the ontological in the interests of the social. The refusal, characteristic of English poetry from Yeats, Auden and Empson to the Movement, and on to Thom Gunn and others, to accept the reality of ‘alien modes of being’ was taken by Davie to be symptomatic of a deeper malaise: the catastrophic failure to acknowledge the reality of being as such. Awareness of this failure was to remain for Davie throughout his life a touchstone of what he saw as the peculiar deadness lying at the heart of English culture and mentality. Davie noted it especially in the willingness of modern English poets (including Hardy) to sell poetry short and in the diminished expectations and philistinism of the culture as a whole.

What Davie’s Collected Poems reveal is a constant struggle to overcome these failures, as he saw them, within himself.

Worry hedges my days
Like a roil of thick mist at the edge of a covert
Fringing a tufted meadow. In that field
Monuments of art and sanctity
Arise in turn before
The clouded glass of my eye.
Last year two churches of St Francis
Were piled up there, at the lowest verge of Assisi.

This poem, ‘On Not Deserving’, from Poems of 1962-1963, is suggestive in its ambiguities. There is in place a ‘roil’ of thick mist obscuring the edge of a covert which is compared to the ‘worry’ hedging the poet’s days. The first line implies that worry not only limits or sets bounds to the speaker’s days, it also allows him to hedge his bets and to trim, to hold to the middle course and avoid extremes. ‘Roil’, which as a verb means to rile, vex or annoy, or to make water muddy or unclear by stirring, has become a substantive, a displacement of use which effects precisely the blurring of boundaries essential to the poet’s strategy here. Furthermore, the boundary or edge in question is the edge of a covert, itself a hiding-place, a thicket hiding game. The field thus delimited by the poem is of uncertain definition. However, it is here that ‘Monuments of art and sanctity’, invoking the transcendence of Yeats’s ‘Monuments of unageing intellect’ and the humility of St Francis, are said to ‘arise’, and ‘arise in turn’. ‘Turn’ evokes ‘verse’ and ‘before’ points to what comes next, which is, as we pull over the line end: ‘The clouded glass of my eye’. Here, the poem is showing itself for what it is, a ‘turn’—a turn that clarifies what it clarifies with respect to an eye whose glass is ‘clouded’. To clarify is thus an obscuring. The opacity of the situation is marked in the last line by the spatial deictic ‘there’, suspended before the caesura and pointing back to the equally unfocussed temporal marker of the previous line—‘Last year’. Just as the poem seems poised to impose its images on the world, so, in the same gesture, the flat, almost paratactic phrasing seems on the ‘verge’ of withdrawing them, as too overweening an importunity. What is piled up is piled up at ‘the lowest verge of Assisi’, a phrase that fails to point to anything, except perhaps itself, engaged in the act of pointing. The speaker is not ‘deserving’, not worthy—of what, we don’t know—on the evidence of the very act he has just performed. He has accomplished his own failure, and, as it were, by pleading his innocence established his guilt. The poem’s lack is the possibility of its being.

‘The Hill Field’ (Events and Wisdoms (1964)) is a more extended and complex piece in the same vein:

Look here! What a wheaten
Half-loaf, halfway to bread,
A cornfield is, that is eaten
Away, and harvested.

How like a loaf, where the knife
Has cut and come again,
Jagged where the farmer’s wife
Has served the farmer’s men,

That steep field is, where the reaping
Has only just begun
On a wedge-shaped front, and the creeping
Steel edges glint in the sun.

See the cheese-like shape it is taking,
The sliced-off walls of the wheat
And the cheese-mite reapers making
Inroads there, in the heat?

It is Brueghel or Samuel Palmer,
Some painter, coming between
My eye and the truth of a farmer,
So massively sculpts the scene.

The sickles of poets dazzle
These eyes that were filmed from birth;
And the miller comes with an easel
To grind the fruits of earth.

This poem, like the first I quoted, refers to other writing. The reference here is to ‘The Solitary Reaper’. The poem also refers to itself, as the singular act of composition that it is. That is, in referring to itself, it simultaneously refers us to another writing. This is to stress, not intertextual reference in general, but rather the singularity of the act of referral itself. What Davie has here constructed is a poem that is open and closed at once. Because of the uncertainty of context this play of reference creates, an uncertainty concerning who is saying what to whom, the poem’s tone—its explicit ‘address’ to the reader—can no longer be understood as it was by Davie in 1959. That this is so can be seen at the beginning of the opening line. The imperative, ‘Look here’, serves to confirm the identity of this text (or, at any rate, of this phrase) by moving outside or beyond itself, in order to point to itself from the position of an other, the reader who is addressed by words that apparently refer only to the event of the poem itself—the event of the poem’s depicting what is depicted by it. (This ‘event’, it would seem, is the poem’s ‘wisdom’.) The phrase, ‘Look here’, can of course also be read as an expostulation. The status of the poem’s beginning is thus rendered immediately problematic.

This point may be made clearer with respect to the image of the field which is in play here, as in ‘On Not Deserving’, and which fulfils much the same role in this poem as it did in that. The image of the field is what the poem is in the process of constructing, and part of what the image is an image of is the process whereby it is being constructed. In effect, what the poem shows is itself as it emerges from, or is engendered by, the process of being said. As a critic, Davie had elaborated on this kind of symbolist configuration in essays on Eliot, Pound, Mallarmé and Pasternak, some of which were written prior to or during the composition of the poetry of this collection. Thus, in ‘The Hill Field’, as with many other poems he wrote during the same period, one can see the poet developing a complex modernist poetry based on that of the earlier masters, but as it were transposed into what looks like the minor key of a poet who also has his eye on Hardy, a poet who was, according to Davie, unlike Eliot and the other major modernists in that he failed to transform or displace ‘quantifiable reality or the reality of common sense’. In ‘The Hill Field’, symbolist techniques are present, and signalled as such. ‘Wheaten’ is reduced to ‘eaten’ as the ‘half-loaf’ of the field set up by the poem is reduced by the removal, or harvesting, of the letters ‘wh‘. In stanza three, ‘the wedge-shaped front’ is there on the page, shown in the shape constructed by the way the words ‘and creeping’ in line 3 protrude beyond the second and fourth lines. The apostrophe ‘how’, beginning at line 5, is only revealed to be an apostrophe, rather than a question, by the end of line 12. The opening ‘See’ of line 13 looks like another apostrophe, but by the end of line 16 it is seen in retrospect to be a question. The palpability of the words is further emphasised by sound: ‘ee’ provides a kind of basic pattern, through which other vowels intertwine in a series of complex variations.

More generally, the poem doubles back on itself, as though it were referring to itself referring to itself. It separates itself from itself and by so doing opens a gap within its structure across which reference can operate. This is signalled and effected by the temporal displacement at the opening, whereby the cornfield is presented as already the loaf it has not yet become, a loaf baked before the harvest is gathered in. It is in this temporal shifting that we see what gives rise to the various metaphors of violation carried by words like ‘knife’, ‘cut’, ‘cheese-mites’ and the ‘sickles’ (inevitably evoking ‘versicles’) that occur throughout the text. By means of a folding or turning back of time on itself, something that occurs only in the order of writing, the end is enabled to precede the beginning, and the beginning to come after the end. The device results in so profound a rupturing or undoing of intelligible order that, as Davie describes it, in an essay on syntax and music, there remains to the reader only one order of time which he can trust: ‘the one time the tales takes in the telling, the time which the poem takes to be spoken or read’. This foregrounding of the device, or ostranenie, is a procedure central to the poetry of Pasternak, as Davie’s essays and book on him make abundantly clear, and it is central also to his own:

Most poems, or the best,
Describe their own birth, and this
Is what they are – a space
Cleared to walk around in.
('Ars Poetica')

The ramifications of this reach very far. A word that has special privilege in Davie’s earlier poetry is ‘edge’, and there are others related to it, like ‘knife’, cut’, ‘sculpture’, ‘stone’ and words and names associated with art more generally. ‘Edge’ seems to have the same role here as ‘blanc’ in Mallarmé. Like Mallarmé’s writing (or Pasternak’s), Davie’s is a writing of spacing—in the sense that it foregrounds spatio-temporal differing—and words like ‘edge’ or ‘cut’ or their substitutes refer to the very spaces or cuts that make possible the series of which they are themselves members. (One may be inclined to see something paradoxical here, comparable to the problem arising when we consider the set of all sets that are not members of themselves. Is this set a member of itself? If it is then it is not. If it is not then it is.) The edge thus understood is what gives to the poem the conditions both of the possibility of meaning and of its impossibility. Thus, in ‘The Hill Field’, the names of the artists, Brueghel and Samuel Palmer, constitute a movement of undecidability: they mark what makes the poem possible and what stands outside, or transcends, that possibility, inasmuch as they mark what conditions it, ‘coming between/My eye and the truth of a farmer’. The final stanza takes this further: in acknowledging that the poet’s eyes were ‘filmed from birth’, a play is engendered on ‘from’ (inasmuch as ‘from’ may mean both ‘since that time’ and ‘due to’) that is repeated in the double genitive in the last line: ‘fruits of earth’ allows or constitutes a doubling which in turn allows (or calls forth) a play on ‘earth’ itself, a word resonant with implication and connotation. The complex play of meaning and counter-meaning at the end of the poem is thus shown to be an effect internal to the conditions of writing as such. For an instance of a poem that can be said to take this procedure to the limit, see the extraordinary ‘Bolyai, the Geometer’: it is a fully achieved symbolist poem in the mode of Pasternak.

And it is this excess, the excess of syntax over semantics, that Davie’s work continued to explore, throughout Events and Wisdoms and beyond. To align Davie in this way with an advanced modernism, may seem, despite Davie’s own critical clarification of these very modes of writing, perverse, wrong-headed. And yet, in ‘Sonnet’, a poem of the 1980s, Davie writes: ‘the scarp/Of language you would quarry, poet, whirls/Indeterminately shaped in/Helix on nebulous helix, not to be netted’. In ‘Thomas and Emma’, which, according to the editor, Neil Powell, is the last poem Davie wrote, in July 1995, two months before his death, he wrote:

Hyperbole, analogy, allusion
Build up what is no lie, although so wishful:
Conspiratorial, conjugal collusion.

The alliterations hark back to what ‘builds them up’ and suggest that the ‘collusion’, which is no lie, depends upon a poetic understanding of language that is hyperbolic, dependent upon analogy and allusive. I am not offering a modish characterisation or deconstruction of texts against the grain of an author who would have been resistant to readings of this kind. I am attempting rather to point to ways in which Davie came to see how the foundation of meaning in what is itself without meaning was inseparable from the vision his poetry gives us of what poetry, and so life, can or might be. It is here that his earlier self-castigation finds itself assuaged. In the enhanced sense his poetry shows of terms such as ‘between’, ‘before’, ‘after’, and so on, terms which resist being straightforwardly conceptualised or being turned into nouns, as well as in its sensitivity to the syntactic exploitation of the different values of words, a thematic or moral reading of the texts must give way to something else—something more ‘nebulous’, ‘not be netted’:

Moreover, space is encoded
to signify lapses of time.
(One verse-line under another;
this one after that one.)

The nearness of God is known as
an aching absence:
the room the reception-desk
cannot locate nor account for,

in a fictitious or
analogous space that does not
answer to or observe
the parameters of Newton,

any more than a page of verse does.

This, from a late poem, ‘Thou Art Near At Hand, O Lord’, is not an attempt to identify the language of modern poetry, with its predilection for negativity and a dialectic of lack, with that of negative theology. The lines serve only to suggest that the thematic or didactic, often seen as typical features of Davie’s poetry, may not be as easy to identify there as we might like to think. The play of wit and irony, the play, that is, of the sudden idea and its ironic realisation or separation out into paradox, allows Davie a writing at once playful and serious. Davie’s poetry is one of an interminable oscillation between meaning and the loss of it, between rapidity and the discursive. In this, Davie, the exponent of late Augustan order, is also the exponent of the romantic fragment, in which both creation and destruction are sustained. ‘He branches out, but only to collapse,/Imprisoned in his own unhappy knack,/Which, when unfailing, fails him most, perhaps’. Perhaps, for Davie, the truth of literature is captured in that ‘perhaps’.

Wednesday, 10 June 2009


During the nineteenth and twentieth centuries art reached an awareness of itself that developed contemporaneously with the need for a new kind of criticism, one requiring a judgement not simply as to whether a given work is deficient in this or that respect but as to whether the work in question is art at all. From the beginning of the nineteenth century, with the onset of Romanticism, art began to make the matter of its own status central to what constituted it, and by so doing incorporated the problematic and ambiguous into its very essence. One need look no further than the titles of the early masterpieces of European horror cinema, Nosferatu and Vampyr, or the American classics, Frankenstein and Dracula, to see that horror cinema is also a product of the Romantic movement. And it too confronts us with the question of its status: films were, and regularly still are, found to be offensive and trivial. Lacking the redemptive powers of art, they are thought especially worthy of censorship. Within this ethos, horror films are frequently linked with pornography, by critics and the censorious generally, as well as by the filmmmakers themselves, obvious examples being Franco and Buttgereit.

Condemned as trashily exploitative and sadistic, the films suffer as a consequence from mutilation, neglect and, what is worse, contempt. It is not to be denied that extreme violence, sexual degradation and grotesque forms of death are legion in the films of Argento, Cronenberg, Craven, Hooper, Fulci, Deodato, and many others, and yet I would argue that this is precisely the point: its confronting us with death presented in especially offensive and unacceptable ways, and its provoking of scandal and outrage, are what constitute the real significance of the horror film in our culture, and what of authentic value attaches to it attaches to these very images of death and dying.


Horror films have, on occasion at least, addressed themselves to the procedures and forms whereby they create what they create, and it is not too extravagant to suggest that films like Vampyr, Peeping Tom, Tenebrae and Dead Ringers exhibit an order of self-interrogation that has many features in common with the literature of modernism, features brought out by questions such as `why write all?' and `how can the act of writing be justified?' Within modernism, literature becomes literature only as it becomes a question as to what counts as literature, and in order to show something of the significance of this degree of self-questioning, both for literature and cinema, I want to begin by considering what I have already pointed to as one of the abiding preoccupations of Romantic and modern writing, the ground of representation itself.

To take a cinematic instance, the exploration of this issue is central to the project of Dreyer’s Vampyr. Aporia and contradiction are fundamental to it, and Dreyer accords them a particularly vivid and focused expression. The action of the film is situated ambiguously, in a world poised between life and death, in a landscape self-consciously created out of cinematic effects. For instance, Gray’s first walk to the mill is both a narrative event and at the same time a disruption of the logical sequence of that narrative event. The disruption of the intelligibility of the relations between the shadows, as the corporal’s shadow separates itself from his physical body, the sudden irruption of dance music and the appearance of what seem dancing cut-out figures, the commanding voice of the vampire, these and similar elements compromise the narrative order, rendering the narrative presentation suspect. This means that the narrative order of the film in its totality can no longer be trusted. The status of what we are seeing has become undecidable, and as a result the temporal progression of the events we see has also become uncertain, if not discredited. The only order of time that we can trust is the time it takes for the film to be seen, the time it takes for the reels of film to pass through the projector and to cast an image on the screen and to bring up sound through the speakers. It is in this sense that Vampyr can be said to resemble music. The action that is represented and the process of representing that action have been collapsed into one, so that the time it takes the events we see to elapse and the time it takes show us those events are the same. What Vampyr narrates, we might say, is the occurrence of the events that compose it, in the very instant that it is narrating the events themselves.

It is writing conceived of on the model of post-symbolist procedures that Vampyr most nearly answers to. It is when the events a poem narrates are the events that constitute its own unfolding that we are cast into what the French critic, Maurice Blanchot, has called a time before the world, before the beginning. In the symbolist poem, the work says what it says in the very gesture of saying what there is for it to say. The only happening in the poem is the happening of the poem itself: a world is described, and, in that same act of description or definition, created. Here, the act of creation turns back upon itself, becoming other than, and exterior to, itself. Hence it is possible neither to begin nor to end, since the words of the poem are already beyond themselves, elsewhere. As Eliot has it, in Burnt Norton: `the end precedes the beginning,/And the end and the beginning were always there/Before the beginning and after the end./And all is always now'. We cannot begin, since the beginning is always already begun, and we cannot come to an end, since the end is always already completed, in a time before the beginning. If, with Blanchot, we think of names on the Hegelian model, as effecting the murder or annihilation of the things they name, then the negation, by which the poem sustains itself and which in turn it sustains, must enter paradoxically into the poem, effecting its failure, and (in Blanchot's idiom) betraying the work of the poem to worklessness (désœuvrement). By this he means that the poem is split from itself, in a movement of double negation that turns it towards the outside, the exterior, beyond language and concept, where, as he puts it, there is no intimacy, no place to rest. The work says the nothing that is the condition of its simultaneous possibility and impossibility:

What are the roots that clutch, what branches grow
Out of this stony rubbish? Son of man,
You cannot say, or guess, for you know only
A heap of broken images . . .

The Waste Land, exemplary in this regard, is nothing other than what it constitutes itself as, namely `this stony rubbish', and the reader, caught within the language of the poem, unable to move beyond it, is, at the same time, exterior to it as it narrates the passage of its own negation:

A heap of broken images, where the sun beats,
And the dead tree gives no shelter, the cricket no relief,
And the dry stone no sound of water.

Blanchot's prose, which often reads like a rhapsodic commentary on The Waste Land, says of this mode of writing: `The work declares being - and says choice, mastery, form - by announcing art which says the fatality of being, says passivity, and formless prolixity'. At the conclusion of Vampyr, the mechanism driving the mill wheels that are drowning the doctor in flour finally stops, under its own volition and without visible cause. The doctor has been assimilated to the whiteness of the flour, a whiteness which is finally inseparable from a whiteness that has come to dominate the balance of light and shadow across the whole film, a fact made evident in the penultimate sequence, when Gray and Gisèle move across the water into the light of the dawn sun. As they step out of their boat onto the river bank, they walk into, and are transfigured by, the intensifying rays of light streaming through the forest. Suffusing the mist rising around the branches, the light comes to acquire almost as palpable a material presence as the objects it illuminates. And at this juncture, we cut back to the mill. The whiteness of the flour has by this time so filled the projected image that there appears no discernible difference between it and the whiteness of the screen behind the image, and it is in this moment of assimilation of the image to its support that the movement of the mechanism comes to a halt. The seeming coincidence of the image and the screen behind it is doubled by the fact that the movement of the mill gears and that of the projector showing the film also appear to coincide. The two movements collapse into a single duration, as the teeth of the gears and the sprockets of the projector gears appear to mirror one another, in a concurrence that effectively links an action internal to the film with an action external to it. It is as though the film were being completed in a time that had already been superseded, inasmuch as it has been this same action, the action of the mechanisms of the projector, that began the film and that has continued to sustain it throughout the time of its showing.

Tuesday, 28 April 2009


I have suggested (on this site) that in TLP, so far as language and logic taken together are concerned, we are dealing with something that can be seen in terms of the Lacanian ‘il n’y a pas de rapport…’: what leads Lacan to the assertion that there is no sexual relation can also be taken to support the assertion that there is no relationship between language and logic. There is no meta-language enabling us to grasp the two levels of language and logic from the same neutral standpoint. They are inextricably intertwined. If the structure of such a relationship, of such an ‘impossible’ relationship, one might say, is to be represented, it is imperative that we look at a form favoured by Lacan, that of the Moebius strip: first, we move from language to its logical form, its logical infrastructure; then, we have to confront the irreducible dimension of language at the heart of logic itself. We derive the logical form of the proposition by means of what is called in TLP an operation, only to find that what constitutes an operation returns us, by virtue of what Lacan determines as the logic of the ‘not-all’ (pas-tout), to the context of significant use, to the specific occasion of an actual utterance. The attempt to step outside language, in order to say what it is that constitutes meaning as such, results in nonsense.

In The Parallax View (pp.37-40), Zizek has some comments that bear on the matter. He raises the question of how Lacan’s binary signifier, S1-S2, manifests itself in the context of the symbolic order. ‘What the symbolic order precludes is the full harmonious presence of the couple of Master-Signifiers, S1-S2 as yin-yang, or any other two symmetrical “fundamental principles”. The fact that “there is no sexual relationship” means precisely that the secondary signifier (that of the Woman) is “primordially repressed,” and what we get in place of this repression, what fills in its gap, is the multitude of “returns of the repressed,” the series of “ordinary” signifiers’. Zizek illustrates this by reference to Woody Allen, but so far as TLP is concerned we can see how the general form of the proposition marks the place of S1, inasmuch as it functions as the quilting point of the ‘multitude’ of empirical propositions (T/F).

This is not a binary logic, divided between the polar couple Masculine/Feminine (or logic/language). The split is not between the One and the Other, it is inherent in the One itself: the split comes between the One and its empty place of inscription (a theme made explicit by Wittgenstein in his presentation of the ‘operation’). In what looks like a critical aside aimed at Badiou, Zizek insists that the multiple is not ‘the primordial ontological fact’—an assumption that underpins Badiou’s system as a whole. The ‘transcendental’ genesis of the multiple, he argues, resides in the lack of the binary signifier: ‘the multiple emerges as the series of attempts to fill in the gap of the missing binary signifier’. What we are dealing with here is the minimal difference between a signifier and its place of inscription, between one and zero.

On the one hand, we have S1 as the empty signifier, together with S2 as the signifying chain in its incompleteness. It is in order to fill in this incompleteness that S1 intervenes, as the quilting point. This is the ‘masculine’ side, in which a multitude is organised into a totality, into an All, through the exception, S1, which fills in its void. On the other hand, the binary signifier, the symmetric counterpart of S1, is ‘primordially repressed’. It is in order to supplement the void of this repression that the chain of S2 emerges. Here, as Zizek has it, ‘the original fact is the couple of S1 and the Void at the place of its counterpart, and the chain of S2 is secondary’. It is in these terms that we may understand the ‘feminine’ non-All. It is the logic operative here that accounts for the emergence of the inconsistent multitude characteristic of the non-All: the emergence of the multitude must be seen in relation to the void or lack of the binary signifier.

In his later work, Wittgenstein elaborates his notion of ‘grammar’, and it becomes clear—from the perspective opened by Lacan—that such an idea can be seen in relation to the non-All. Wittgenstein writes, in Philosophical Remarks, as follows:

If I could describe the point of grammatical conventions by saying they are made necessary by certain properties of the colours (say), then that would make the conventions superfluous, since in that case I would be able to say precisely that which the conventions exclude my saying. Conversely, if the conventions were necessary, i.e. if certain combinations of words had to be excluded as nonsensical, then for that very reason I cannot cite a property of colours that makes the convention necessary, since it would then be conceivable that the colours should not have this property, and I could only express that by violating the conventions. [PR 53]

I do not call a rule of representation a convention if it can be justified in propositions: propositions describing what is represented and showing that the representation is adequate. Grammatical conventions cannot be justified by describing what is represented. Any such description already presupposes the grammatical rules. That is to say, if anything is to count as nonsense in the grammar which is to be justified, then it cannot at the same time pass for sense in the grammar of the propositions that justify it (etc.). [PR 55]

Rules of grammar, which he also calls grammatical conventions, cannot be justified by appeal to the supposed fact that they enable us to represent reality correctly. If it makes sense to say that an object cannot be reddish-green all over, then it must also make sense to say that it can be reddish-green all over. But then the grammatical convention is superfluous. Further, if one supposes that the colour word conventions are necessary, one could not say what property it is that makes them necessary, for then it would be conceivable that the colours might not have this property, and one could only express this fact by violating the very convention one was trying to justify. In effect, one has to say that there is no such thing as reddish-green, which means that the phrase ‘reddish-green’ is nonsensical, i.e. we have no use for it in making intelligible statements about how the colours are. (Analogously, there is no such thing as a double fault in chess, which is just to say that in chess there is no use for the phrase ‘double-fault’.) The nature of propositions of very many kinds can be elucidated by reference to the grammar they exhibit, but any attempt to impose a limit on grammar as such results in nonsense. This is part of the significance of the notion of a language-game: by means of it, language is exhibited in all its inconsistent and contingent multiplicity, and this in turn means that there is no point from which it can be surveyed in its totality. Language use is without justification, and language is without essence—a statement that is itself nonsensical.

One consequence of this view of grammar may seem paradoxical: it is that language is non-normative. Grammar is non-normative (a remark that flies in the face of most commentary on Wittgenstein). This is, however, a position that has been argued for by Stanley Cavell, and others, such as Steven Affeldt, James Guetti and Rupert Read. To see grammar in terms of the non-All is to see meaning in terms of the future. In this connection, Zizek cites a phrase of Brian Rotman’s: meaning is something which is always ‘borrowed from the future’, relying on its ever-postponed fulfilment to come [The Parallax View, p.51]. As Cavell has put it, ‘Is the issue one of a leap [not of faith, but, let us say, of reason] from a ground that is implied or defined by the leap? Or is the leap from grounds as such, to escape the wish for such definition [as if reason itself were a kind of faith]?’ Steven Affeldt glosses this by saying: ‘The idea is that to speak intelligibly is to define the ground from which you speak, it is to articulate the position that you are assuming and from which you speak’. To cite Zizek again: ‘subjects cut the impasse of the endless probing into “do we all mean the same thing by ‘bird’?” by simply taking for granted, presupposing, acting as if they do mean the same thing. There is no language without this “leap of faith”’ [p.54]. Guetti and Read have examined in close detail the operation of an example very similar to this—the use of the word ‘waxwing’ [I have discussed this elsewhere on this site].

Wittgenstein remarks: ‘If language is to be a means of communication there must be agreement not only in definitions but also (queer as this may sound) in judgments’ [PI sec.242]. Affeldt glosses the force of this remark by saying that our intelligibility for one another depends continuously, from moment to moment, and in each act of speech, upon precisely our agreement in judgment. ‘It is not that our shared language is the ground of our intelligibility. Our language is the vehicle through which, or the medium within which, we continuously undertake to make ourselves intelligible to one another by projecting the ground that we individually, at a given moment, occupy.’ One might reposition Zizek in these terms by saying that, for him, it is the status of such an agreement in judgment that it is not normative, nor could it be. It cuts across ‘the debilitating deadlock of language, its ultimate lack of guarantee, by presenting what we should strive for as already accomplished’ [p.52]. Language is a system that lives on credit it can never pay off.

Steven Affeldt, “The Ground of Mutuality: Criteria, Judgment and Intelligibility in Stephen Mulhall and Stanley Cavell”, European Journal of Philosophy 6:1 (April 1998): 1-31.

Stanley Cavell, “The Division of Talent”, Critical Inquiry 11:4 (1985).

James Guetti and Rupert Read, "Acting from Rules", International Studies in Philosophy 28:2 (1996): 43-62.

Wednesday, 25 March 2009


The notion, shared by Blanchot, Bataille, Lacan and others drawing on the tradition of Hegel, that a conception of naming can provide a sound basis for the explanation of meaning in language is seriously flawed. The opening of Philosophical Investigations is aimed at precisely this question, and the implications of that opening are drawn out by G.E.M. Anscombe, in her essay ‘A Theory of Language?’, published in 1981 [see: I. Block, ed., Perspectives on the Philosophy of Wittgenstein (Oxford: Blackwell, 1981), pp. 148-158]. Professor Anscombe is concerned here with Wittgenstein’s remarks in the first section, about naming, and with subsequent remarks in sections 2 and following that make use of a primitive language whereby builders call out to each other for materials, such as slabs and beams. She summarises the main purpose of these opening sections as being ‘to persuade us not to look at the connection between a word and its meaning either as set up or explained (a) by ostensive definition, or (b) by association, or (c) by mental pictures, or (d) by experiences characteristic of meaning one thing rather than another, or (e) by a general relation of reference or naming or naming or designation which has (logically) different kinds of objects as its terms in different cases’ [p. 154]. In order to see what Wittgenstein was fundamentally about here Anscombe believes that we must turn our attention to what he means by ‘grammar’. It has been frequently urged by commentators that what for Wittgenstein belongs to grammar differs in significant ways from what grammarians would see as their field. Anscombe argues, on the contrary, that the difference in opinion about what belongs to grammar ‘arises from belief in and practice of a “formal” science of grammar on the one hand, and a study of what a given use of words amounts to or achieves or tells us on the other’ [p. 156]. This latter idea sees grammar as an expression of the roles words play in our lives, of the place our diverse concepts, of pain, colour, truth, doubt, fear, naming, and so on, have within our forms of life. Whereas the first idea of grammar results in an account of how rules operate to determine patterns and structures of language, an account given in terms of a purely linguistic structure, the second works rather differently. For example, in the latter case, Anscombe argues, one might consider contrasts between say ‘For how long did you forget that?’ and ‘For how long did you reflect on that?’, or between intermissions of intention and intermissions of attention. There is, she makes clear, nothing odd about applying the word ‘grammatical’ to the observation of the different temporalities involved in these different cases. Another example, addressed by Wittgenstein, is the difference between the first-person avowal of pain and the ascription of pain to others. There is similarly nothing strange about describing as ‘grammatical’ the very significant differences involved here. As Anscombe points out, this is not the kind of observation that we expect from traditional grammarians, whose attention is turned elsewhere, to the structures of language considered essentially on their own terms and for their own sake.

The nature of Wittgenstein’s interest can be seen from the following passage, cited by Anscombe from Philosophical Investigations, section 240:

The agreement, the harmony, between language and reality consists in this: if I say falsely that something red, then, after all, it isn’t red. And if I want to explain ‘red’ to someone in the statement that this is not red I do it by pointing to something red.

What is of immediate significance here is that ‘The harmony between language and reality is found in the false statement no less than the true. This false statement says (of what is) something that it is not — but something nevertheless, which is. Here we can point to that which the thing is not’ [pp. 156-7]. This, for Anscombe, shows how close Wittgenstein is to Plato on this issue, a point she clinches by citing Sophist (262-3B):

A statement does not consist of names spoken in succession or verbs apart from names . . . it does not merely name something, but gets you somewhere by weaving together verbs with names . . . those that fit together make a statement . . . stating something of something (of you, say) . . . the false statement stating of you, as being, things which are different from the things that are of you, and so things which are not, but all the same things which do exist.

The matter comes to a focus by way of Wittgenstein’s remark: ‘if I say something falsely that something red, then all the same it isn’t red’. If I am able to change a false statement to a true one by negating it or by negating a negation this is ‘because of the distinction of the different kinds of words which fit together to make descriptions’ [p. 157]. It is not merely experience of the colour that determines the grammar of ‘red’, but its place in our lives with language. Anscombe cites Wittgenstein once more:

If you trained someone to emit a particular sound at the sight of something red, another at the sight of something yellow, and so on for other colours, still he would not yet be describing objects by their colours. Though he might be a help to us in giving an description. A description is a representation of a distribution in a space (in that of time, for instance).
If I let my gaze wander round a room and suddenly it lights on an object of a striking colour, and I say “Red!” — that is not a description. (Philosophical Investigations, II, ix)

For Anscombe, to say of the object that it was red, or to say that my visual field was not suffused with (or that it did contain) red, would be to give ‘a representation of a distribution in a space’. What we can say is that the act of conferring or citing of names has meaning only within our grammar as a whole.

This suggests that notion of naming found in Blanchot and others, that is, the idea of the power of the word, the name, to found language by an act of negation, of ‘murder’, requires to be significantly redescribed in the light of Wittgenstein’s thought, who in the examples cited uses negation (the negated or false statement) to show how it is that meaning may not intelligibly be thought to derive from names. Names act as names only in the context of a statement, description or other kind of utterance: only in the context of the language-game, of our life with language, as a whole, do names have their part to play. That is, names function as names only insofar as they have a place within our grammar. Because names are simply part of our grammar, they are not privileged over other parts of that grammar, and hence it makes no sense to see them as the unique foundation of it. The same holds for negation: since negation is an operation within our use of language, any attempt to found language on it would require the removal of negation from language as such, in order to establish it outside language, as the condition of its possibility. To do so would result in negation acquiring a meaning other than the one under consideration, so that ‘negation’ would undergo an alteration such that, if it meant anything at all, it would no longer mean what it formerly meant. This latter point will become fundamental to the case I will seek to present later, concerning the seeing of aspects. Wittgenstein has himself addressed this area of thought, and it is a concern that continues to engage him from his earliest thought, in the Tractatus, to his last reflections, gathered together in On Certainty.

In order to draw out the implications of Wittgenstein’s earlier approach to language for my larger argument, I will now turn to the Tractatus. It would seem that, in the Tractatus, there is a decisive statement of what it is for language to have meaning based on the correlation of name and object. In giving his picture theory of the proposition, he gives an explanation of how propositions have sense, i.e. are true or false, which invokes ontological categories. ‘The possibility of propositions is based on the principle that objects have signs as their representatives’ (4.0312). Or again: ‘One name stands for one thing, another for another thing, and they are combined with one another. In this way the whole group — like a tableau vivant — presents a state of affairs’ (4.0311). A proposition or picture is the fact that its elements are combined in a certain way. In a proposition that has been fully analysed the elements are names. Their meaning (Bedeutung) is identical with the objects they stand for (vertreten). The proposition says something because the elements that are combined within it are correlated with objects in the world. Part of the significance of this for what Wittgenstein is interested in dealing with in the Tractatus has to do with the determinacy of sense. He writes in 2.0211 and 2.0212: ‘If the world had no substance, then whether or not a proposition had sense would depend on whether another proposition was true. In that case we could not sketch any picture of the world (true or false)’. If in the analysis of a proposition we could not finally reach rock-bottom, that is, symbols whose meaning is determined by their immediate relation to reality, the analysis would be interminable. Meaning would under these conditions be indeterminable, unfixed. As Wittgenstein puts it in 3.23: ‘The requirement that simple signs be possible is the requirement that sense be determinate’. What this approach seems to be presupposing is, then, according to Brian McGuinness, ‘a magazine of objects which form, in one sense, the realm of Bedeutung’ [see: ‘The So-called Realism of the Tractatus’, in I. Block, ed., Perspectives on the Philosophy of Wittgenstein (Oxford: Blackwell, 1981), pp. 61-62]. The objects being thus presupposed are described as being simple, in the sense that they cannot be further analysed. They belong to all possible worlds: they are, so to speak, the possibilities of the world. They form the substance of the world or the form of the world. McGuinness writes: ‘They are what is unalterable and persistent (bestehend), while the configuration of objects, the states of affairs, are what varies from one possible world to another. These configurations of objects, these states of affairs, give objects what material or external properties they have. Naturally, there is only one set of configurations that is actually realised, and this is what we call reality or the world. The internal properties of objects are their possibilities of combination with one another, and the possession of these properties is necessary, not a mere matter of fact’ [p. 62].

McGuinness then raises the question of what is meant by assuming a magazine of objects of this kind. It is not that something exists which might not have done: ‘All unrealised possibilities are simply dispositions of objects different from that which actually obtains’ [p. 62]. The objects themselves are, so to speak, prior to the possibilities within which they are disposed. This means that all questions of existence are questions about what dispositions of objects actually obtain. When Wittgenstein writes: ‘The world is a totality of facts, not of things’ (1.1), he is expressing this view. All existence is a matter of fact, a matter of what is in the world. This seems to result in an ontology. As McGuinness puts it, ‘the world or reality consists of facts, that is to say in the Bestehen (in one sense), the obtaining, of states of affairs. States of affairs themselves, on the other hand, are combinations of objects, which bestehen or exist (subsist) in another sense. Existence as normally spoken of is equivalent to the Bestehen in the first sense of a certain state of affairs’ [p. 62]. Now the attraction of these opening pages of the Tractatus seems to be that they derive certain metaphysical results on the basis of some simple and natural assumptions about propositions being true or false. Nonetheless, it is essential to see that Wittgenstein had no intention of building a system of metaphysics or ontology on logic or the nature of language. As with his later work, so here: he rejected the idea that there is something by which our grammar is determined, and he did not, at any juncture, attempt to infer features of the external world from that grammar. It may seem as though he argued that ‘propositions with sense are possible only because some more primitive operations are possible — notably the correlation of names with simple objects, and it may seem that he goes on to argue that these more primitive operations are possible only because the world possesses certain characteristics’ [pp. 62-63]. However, these are the kinds of idea to which Wittgenstein applies the term ‘nonsense’ (Unsinn).

So how are we to approach the ontological parts of the Tractatus? McGuinness cites 2.0121 as an example: ‘Logic deals with every possibility and all possibilities are its facts’. What we have here is a transferred and illegitimate use of the word ‘fact’, and one might say that the whole seeming enterprise of ontology in the Tractatus is a similarly illegitimate and transferred use of words like bestehen. In using language in this way, Wittgenstein is showing us the nature of language and its limits, and it is this that constitutes philosophy as a critique of language—it is the activity of making clear the limits of language, which are identical with the limits of thought. What philosophy is concerned with, then, cannot be said, stated directly, but it can be shown: ‘What philosophy tries to make clear is not sayable, but it is shown by ordinary propositions that can be true or false’ [p. 64]. Philosophy goes wrong when it tries to say what can only be shown. This indicates what the importance of logic is for this undertaking. Logical propositions say nothing but they do show something: they show ‘the formal – logical – properties of language and the world’ (6.12). Wittgenstein’s aim in the Tractatus is to bring out that ‘philosophy and logic have to do not with a special realm of objects but with the necessary features of language – that is to say of any language whatsoever. This happens most clearly in the case of logic. The propositions of logic, the tautologies, are by various devices shown to be inevitable offshoots or by-products of saying something true or false. As such they show us something about what it is to say something true or false’ [p. 64]. Tautologies and contradictions say nothing, being true or false in all circumstances, and as such are described by Wittgenstein as senseless (sinnlos), a condition he differentiates from the nonsensical (unsinnig) (4.461-4.4611). ‘They do not represent any possible situations’ the way propositions with sense (those of science, for instance) do (4.462). ‘Tautology and contradiction are the limiting cases—indeed the disintegration—of the combination of signs’ (4.466). They are not nonsense, however, for they are revelatory of the logical form that does allow intelligible propositions to picture possible situations in the world (4.611). Gordon Bearn has made the point clear: ‘“p or not-p” is a tautology that is clearly related to the law of the excluded middle [i.e. that any statement is either true or false], but it says nothing. Rather it is a condition of making sense at all that all sensible propositions say nothing when put into this schema. It is not the pure foundation of sense. It is the first glimpse of the opposite: senselessness. And that the opposite of sense is first glimpsed in this way makes manifest the limits of any world we might know or imagine, dream, or dread.’ [See: Gordon F.C. Bearn, Waking to Wonder: Wittgenstein’s Existential Investigations (Albany: SUNY, 1995), p. 58.]

Fundamental to this approach is Wittgenstein’s idea that, as McGuinness has it, ‘in order for there to be propositions that may be either true or false, but must be one of the two, there will have to be a possibility of expressing those propositions by means of signs which of themselves will serve to express a proposition independently of what is the case. A state of affairs cannot be designated independently of whether it exists or not unless signs can be used whose significance could be given and understood and determined without reference to the obtaining or non-obtaining of that state of affairs’ [McGuinness, ‘The So-called Realism of the Tractatus’, p. 64]. This means that, for Wittgenstein, as McGuinness reads him, it is possible to make statements knowing them to be either true or false whatever the state of the world is.

He therefore thought that we were committed to the possibility of those propositions being expressed in such a form that all the constituent signs used could function in that particular combination whatever the case in the world was. [McGuinness, p.65]

These signs (these supposedly possible signs, reached only by analysis) would therefore be ‘possible constituents in propositions or possible contributors to producing a true or false proposition, regardless of what was the case in the world’ [p. 65]. Here, then, we have reached what in Blanchot’s idiom might be called the impossible conditions of possibility, the impossible origin anterior to writing. Wittgenstein attempted to rephrase language in just such terms, using what he called the simple signs or names alone. These are names that could not lack a bearer, and, although no actual example can be given of such a name, McGuinness cites a hypothetic example from Hidé Ishiguro that suggests what Wittgenstein may have had in mind: ‘Let a be the centre of a circle . . .’. In the discussion that follows, the question of whether a exists cannot arise. The point, then, is to consider what it would be like for names of this sort to form the whole substructure of a language.

Every proposition we utter is either true or false, whatever the case may be in the world. This requires that every proposition be capable of analysis in just one form, irrespective of whether or not any such analysis has been reached. In Wittgenstein’s vision of things, at least as McGuinness presents it, ‘if we imagine the totality of all propositions, true and false, in their fully articulated, fully analysed form (a form that is possible in principle), then we know that every element in this articulation, every sign, every name, has meaning in the sense that it contributes to the truth-value (whatever it is) of any proposition in which it occurs’ [p. 69]. To understand these elements does not require any experience of what is the case, since the proposition is (by definition) fully analysed, and hence the objects exist independently of what is the case. In that case, how do we understand a proposition? To have in mind a structure conforming to that of a possible state of affairs is to understand the proposition. As McGuinness sums it up: ‘It will be seen at once that this amounts to saying that there is no proposition to be understood until there is an understanding of a proposition’ [p. 69]. Thus the question is: how do we understand a propositional sign?

We use the perceptible sign of a proposition (spoken or written, etc.) as a projection of a possible situation.
Thinking the sense of the proposition is the method of projection. (3.11)

For McGuinness, this means that ‘Thinking the sense into the proposition is nothing other than so using the words of the proposition that their logical behaviour is that of the desired proposition’ [p. 70]. He argues that for Wittgenstein the realm of reference is thus not some mysterious, infinitely extended magazine of things. There is already contained in language, as the Tractatus presents it, the possibility of all objects that are possible. Language is the site of its own (impossible) possibility. All logical forms are logically possible within language, within thought, or so McGuinness contends. ‘No separate investigation or exploration of ‘reality’ is conceivable’ [p. 70]. This leads him to insist that when the learner, the child, learns language he learns complete propositions or thoughts. He has to grasp these as a whole, and when he has done so he will have an understanding of the primitive signs contained within those propositions. The primitive element, the name, has its place in the proposition. ‘Only propositions have sense; only in the nexus of a proposition does a name have meaning’ (3.3). This remark follows another one (3.263), which prepares the way for it: ‘The meanings of primitive signs can be explained by means of elucidations. Elucidations are propositions that contain the primitive signs. So they can only be understood if the meanings of the signs are already known’. The point of this remark is made clear by Peter Winch: ‘one cannot learn the meanings of names separately from each other; to learn their meaning is to learn how they combine in sentences. In order to distinguish that, one has to be presented with sentences and learn to distinguish them from senseless strings of words. To have come to grasp the sense of a sentence is to have come to grasp the meanings of the names of which it is composed’ [Peter Winch, Trying to Make Sense (Oxford: Blackwell, 1987), p. 10]. Not only that, but grasping the sense of the one sentence also involves grasping the endless other combinations into which the name might enter: in other words, grasping something that comes only with the mastery of a whole calculus, a calculus it is one of the main concerns of the Tractatus to describe. (Logic exists only in its application. If there were no such thing as the application of logic there would be no such thing as logic. Another logic would be required to determine the correct application of the original logic.) Given this point of view, it becomes clear why McGuinness wants also to say that the processes of explaining the truth-conditions of a proposition and of determining the truth-value of a proposition cannot be broken down into any simpler operation than that of grasping the proposition or expressing the proposition. All these are operations possessed of the same degree of multiplicity or complexity. These considerations lead, finally, to the question as to what kind of object Wittgenstein’s simple objects are. The answer must be that they are not concrete objects at all, and that there is nothing intelligible to be said concerning their existence or non-existence. We can grasp only concatenations of objects, facts in the world. Hence, no example of such an object can, or could, logically speaking, be given.

Certainly our propositions in the last analysis are not about the workings of our own mind. What Wittgenstein is trying to convey is a point of view according to which what they are about is not in the world any more than it is in thought or in language. Objects are the form of all these realms, and our acquaintance with objects (our contact with them, to borrow a metaphor from Aristotle) is not an experience or knowledge of something over against which we stand. Thus it is not properly experience or knowledge at all. Objects are eti epekeina tes ousias (beyond being), and it is therefore misleading to regard Wittgenstein is a realist in respect of them. [McGuinness, ‘The So-called Realism of the Tractatus’, pp. 72-73]

The objects are beyond being and beyond non-being. The objects are outside of the world, and outside of the world there is nothing to be said. Bearn comes to the same conclusion:

So although the elementary propositions are introduced as pictures of simple objects, this is not something that—if we get the point of the Tractatus—we will find understandable, at all. . . . The book is metaphysical poison (nonsense/Unsinn) to end the explanatory metaphysical impulse. [Bearn, p.58]

The ‘metaphysical poison’ of which he speaks is that which Derrida has called the pharmakon, a drug that is both fatal and a cure. From this point of view, what Wittgenstein has brought to light is an object without object, a pure object where no object is and which no one could or ever will encounter. This strange quasi-object is what is to inaugurate language and to determine meaning, and yet it seems to resemble a fiction, something called up by the writing of the Tractatus and in the same gesture annulled, and it is to this impossible and undecidable object that the origin of meaning and language are to be referred.

There is a curious and uncanny logic at work here, one which it would seem to be a major purpose of the Tractatus to make clear: the things, the simple objects which the text appears to offer as the ultimate and originary foundations of sense, are in effect produced retroactively by the very process of symbolisation itself, by the process of making sense. The simple objects emerge only as a consequence of their loss. What the Tractatus brings us to see is that any attempt to conceive of the objects as having substantial being, or to think of them as ontologically prior to the states of affairs into which they enter, is to succumb to an illusion: the objects are a mirage of metaphysics, retroactively invoked by the propositions of the text, propositions which are nonsensical, and which are to be recognised as nonsensical. The significance of this for an understanding of language based on naming, or ostensive definition, has been made clear by McGuinness, in a second essay on the matter. As he argues, ‘TLP does not rest understanding of propositions on a process of ostensive definition. It does not suppose that the elementary propositions in which use is made of certain names are connected with reality by the correlation of those names with objects independently identifiable. This is because the notion of independent identification of objects in the TLP sense is an incoherent one. Only in a proposition does a name have meaning, so that there cannot be a pre-propositional act of giving meaning to a name by, for example, pointing to an object’ [McGuinness, ‘Language and Reality in the Tractatus’, Teoria 2 (1985): 136]. One can get at this another way, by saying that whereas in the ordinary world one can point to an object and give it a name this cannot be done for the objects of the Tractatus. To name an object requires the existence of that object as a matter of fact, but the objects of the Tractatus exist independently of what is the case in the world. As McGuinness points out, it is a crucial insistence of the book that the ‘experience’ necessary to understand language (the experience that there is a world) is very different from the experience of what there is in the world. ‘The former is not an experience of facts and confrontation with a concrete object is an experience of fact’ [‘Language and Reality’, 136]. What Wittgenstein is saying is thus to be seen as nonsensical. No meaning has been ascribed here to ‘object’ or to ‘experience’: language is, so to speak, outside or beyond itself, and to that extent beyond sense also.

This has the further consequence that, as McGuinness argues, mentalist accounts of meaning simply dissolve. We do not think sense into propositions by mentally associating the words (and so the elementary names that would occur if the proposition were to be fully analysed) with objects. To argue in this way is simply to return to notions of ostensive definition, but performed this time privately or internally. Wittgenstein makes the point explicitly in 3.11: Thinking the sense of a proposition is identical with the method of projection: ‘the use of the proposition is what gives meaning to its names, not some additional act of mental dubbing or intending’ [‘Language and Reality’, 137]. This is the point that the so-called picture theory of meaning is meant to elucidate. The picture-theory and the account of language associated with it is less a theory than an account of mental phenomena: no further mental power, the power of thinking, is required. One cannot explain what pictures are by introducing human agency. ‘Rather, you explain human agency by the notion of picturing. It is not man that makes pictures, so to speak, but pictures that make a man’ [‘Language and Reality’, 137]. Someone who learns a language is confronted by a whole language in use, a language consisting of propositional facts or pictures. Each one of these possesses a complexity, which, so the learner comes to understand, can have only one meaning, can only indicate or affirm one state of affairs. The point at issue here is clarified, McGuinness believes, by reference to one of Wittgenstein’s most subtle and important distinctions, that between showing and saying. According to 4.022, a proposition shows its sense, shows how things stand if it is true, and it says that they do so stand. The thought here is that the complexity or organisation of the proposition, once fully understood, shows what state of affairs is involved, what state of affairs either exists or does not exist: at the same time, a further function of sense must be understood within the proposition. In other words, sense here is to be understood as something like direction (a proposition is like an arrow, not a point): we have to understand what way the proposition is to be taken, in what direction it is aimed. Is it to say that p or that not-p? It must be determined which is the p that it states, and which is the not-p. Wittgenstein argues that, if we think only in terms of complexity or structure, p and not-p are equivalent. It is possible for p and not-p to say the same thing, so that what they each show is the same thing. For example, suppose a situation in which we communicate with one another by means of pictures. In that case, if we wish to say that the book is on the table, we hold up a picture of this state of affairs. But how do we communicate that the book is not on the table? We can hold up the same picture and then, say, turn it back to front. The picture and the same picture turned back to front have opposite senses, opposite directions, but which sense is which is given by the use of the proposition. If one has understood a proposition one has already discriminated all the facts necessary to understand its negation. McGuinness concludes from this that reference is a function of fact-stating, and not vice-versa. Reference is given retroactively, in the very act of formulation. The proposition itself shows us what fact it refers to (that is, what fact it states or misstates). There is no separate act of correlation between the language and reality: there is only the act of acquiring the language, i.e. of using pictures as they are used in the language. That facts are taken in such and such a way is thus something manifest within language. ‘The use of language shows that something is taken as a true elementary proposition, in that the other things that are then unhesitatingly said reflect its being so taken’ [‘Language and Reality’, 137]. For one thing, inferences are based on it.

But if this is so, facts drop out of the account. There are instead verification procedures, which correspond to the analysis of a proposition into elementary propositions, for which no examples can be given. This is to assert both the principle of bivalence, namely, that a proposition is either true or false, and that no grounds can be given for the principle. One might say that the principle and its lack of foundation are what is shown in the logical form of the proposition, a form which is both interior to the proposition (inasmuch as analysis leads back from the given proposition to the elementary propositions contained with in it and of which it is a truth function), and exterior to it (inasmuch as the proposition is connected to propositions outside or beyond it by similar relations of inference.) Every proposition contains, and is contained by, the whole of logical space, which is given immediately, in our grasping of the proposition. There is therefore an excess of syntax over semantics, in that logical form is always already beyond the proposition: the senseless, because tautological, propositions of logic do not coincide with the positions of sense, propositions that are either true or false, nor can the propositions of sense be reduced to, or expressed in terms of, the logical system. This is evident from the use Wittgenstein makes of the Sheffer stroke, and of recursion, in what he calls an operation, in order to show the general form of the proposition. At the time of writing the Tractatus, it had been shown that all the logical constants (negation, disjunction, implication, and so on) could be replaced by a single constant, the so-called Sheffer stroke, whereby p|q, for example, is equivalent to ‘neither p nor q’. Using this notation, one can eliminate all the constants, used in Principia Mathematica, for example, and bring them under a single form. Wittgenstein describes this at 5.1311: ‘When we infer q from p v q and ~p, the relation between the propositional forms of “p v q” and “~p” is masked, in this case, by our mode of signifying. But if instead of “p v q” we write, for example, “p|q.|.p|q” and instead of “~p”, “p|p” (p|q = neither p nor q) then the inner connection becomes obvious’. Further clarification is given by H.O. Mounce:

p v q’ and ‘~(~p.~q)’ can now be written in the form ‘p|q.|.p|q’. This means: neither, neither p nor q, nor, neither p nor q. It has to be written in this somewhat artificial way to preserve the neither . . . nor form. But all that is in fact happening is that one is ruling out the possibility of neither p nor q, which can be seen on reflection to be equivalent to asserting ‘p or q’ or ‘It is not the case that not p and not q’.

Since the logical constants can all be defined in terms of one another, there is one fundamental operation that underlies them all, an operation of iterated negation. It is the fundamental operation by which all propositions are produced out of elementary propositions and Wittgenstein calls it the general form of the proposition. To see exactly what Wittgenstein has in mind, we need to see more clearly just what he means by an operation:

5.2 The structures of propositions stand in internal relations to one another.
5.21 In order to give prominence to those internal relations we can adopt the following mode of expression: we can represent a proposition as a result of an operation that produces it out of other propositions (which are the bases of the operation).
5.22 An operation is the expression of a relation between the structure of its result and its bases.
5.23 The operation is what has to be done to the one proposition in order to make the other out of it.
As Mounce points out, an operation is performed on base proposition to produce a different proposition as a result. But what Wittgenstein has in mind is a particular model of the way this done. At 5.2521 he writes: ‘If an operation is applied repeatedly to its own results, I speak of successive applications of it (‘O’O’O’a’ is the result of three successive applications of the operation ‘O’ζ’ to ‘a’)’. And at 5.2523 he says ‘The concept of successive applications of an operation is equivalent to the concept “and so on”’. To apply O to a one gets Oa; repeat the operation, applying O to Oa, and one gets OOa; and so on. In other words, an operation, as it concerns Wittgenstein here, is a procedure that takes its own results as a base. An example is doubling: 2 doubled is 4; take the result and double again [H.O. Mounce, Wittgenstein’s Tractatus: An Introduction (Oxford: Blackwell, 1990), p. 50]. The fundamental operation by which all propositions are generated from elementary propositions is an operation of this type. At proposition 6 and onwards, the general form of the proposition is represented in a way such that every proposition is to be seen as the result of successive applications to elementary propositions of an operation of negation (N). Any proposition whatever will be the result of the iterated application of this procedure. The negation in question is the operation of joint negation (neither . . . nor) represented by the Sheffer stroke. The successive applications of this operation of joint negation to the elementary propositions will produce all other propositions [Mounce, pp. 52-53]. As Mounce makes clear, this, then, is how the complex propositions of ordinary discourse are produced, and he gives as an example the way ‘p v q’ is produced from p, q, two elementary propositions. If we apply the operation of joint negation to p, q, we get N(p,q) – i.e. neither p nor q. Apply the operation that, and we get N(N(p,q)) – i.e. neither, neither p nor q, nor, neither p nor q, which is equivalent to ‘p v q’. Wittgenstein goes on to show how this same operation of joint negation can account, not only for the propositional calculus, but also the predicate calculus, the logic of generalisation, thereby opposing the accounts given of these matters by Frege and Russell, by proposing a logical operation that does not rely for its articulation on the use of metalanguage.

This brings us to an issue crucial to Wittgenstein’s enterprise in the Tractatus, the nature of the text of the Tractatus itself. As we have seen, the operation must always be able to be applied to its own result. The iterability of this application to its own result is the principle of recursion, by which succession is presupposed. This is what operates the series, as we have seen, the ‘And so on’. To say, therefore, that one proposition is first or elementary (primordial) is to presuppose the temporal series of propositions of which this proposition presents itself as first. The implications of this are spelt out by Vincent Descombes, writing, not of Wittgenstein, but Derrida:

[I]t must be said that the first is not the first unless there is a second to follow. Consequently, the second is not that which merely arrives, like a latecomer, after the first, but that which permits the first to be the first. The first cannot be the first unaided, by its own properties alone: the second, with all the power of its delay, must come to the assistance of the first. It is through the second that the first is the first. The ‘second time’ thus has priority of a kind over the ‘first time’: it is present from the first time onwards as the prerequisite of the first’s priority without itself being a more primitive ‘first time’, of course; it follows that the ‘first time’ is in reality the ‘third time’. [Modern French Philosophy (Cambridge: Cambridge University Press, 1980), p. 145]

Derrida’s ‘non-concept’ of différance, based on the iterability of the trait, has certain features in common with Wittgenstein’s account of the repeated operation of joint negation. One such point of comparison can be seen to emerge here: Descombes’ account of the ‘logic’ of originary delay, an idea of fundamental significance at least for Derrida’s earlier thought, also provides a way of drawing out the consequences of a tenet central to the Tractatus, that only in a proposition does a name have meaning. As the Tractatus presents logical form, the ineluctable temporality internal to that form and so to language means that no sense can be given to the idea of a primordial relation between language and reality, between names and simple objects, which language may be thought to originate from. For reasons such as those Descombes lays out, and those we have already seen McGuinness demonstrate in some detail, it is nonsensical to think to look outside language in order to give for language or for the truth and falsity of propositions any account (any theory) that depends on describable features of the world. The temporality of discourse, on Wittgenstein’s showing, means that the propositions formulating the general form of passage from one proposition to another are themselves subject to that same operation of passage, as is clear not only from the general form of the proposition but also from the following series: ‘the world is the totality of facts’ (1.1), ‘a picture is a fact’ (2.141), and ‘logical pictures can depict the world’ (2.19). To think of language as somehow able to reach outside itself and so to ground sense in anything other than the movement of its own operations is nonsensical (unsinnig). Not only this, but to pose the question of the logical form of the proposition is, at the same time, to pose the question of the status and meaning of the very text, the Tractatus, whose propositions we are in the process of trying to comprehend.

What Wittgenstein shows in the Tractatus is that sense does not need to be validated by logical theory. The intelligibility of the proposition is rather the primary datum on which the logical theory grows, by analysis. The network of necessary relationships between meaningful propositions is also the logical framework of the world. There are no intermediaries between the proposition and the represented state of affairs. As Alberto Emiliani has argued, in a commentary on McGuinness’s two articles, this is the crucial insight of what might be called the immediacy of semantic agreement. [See: Alberto Emiliani, ‘What Nonsense Might Be: The Metaphysical Eye Opens’, Philosophical Investigations 26:3 (July 2003): 205-229]. Language is fundamentally intentional: the proposition reaches right up to reality. In order to be able to represent a state of affairs a proposition must have something in common with it and that something is form—that is, the possibility that their elements combine in just that way. To make the point again, we don’t start in the Tractatus from features that symbols must have in order to combine with one another in meaningful propositions: we start from the propositions and proceed to the properties of the constituents. ‘An object can only be designated qua part of a state of affairs; a symbol only has meaning qua part of a proposition’, a point Emiliani makes in order to emphasise that the meanings a symbol can be assigned in such and such a combinatorial context are necessary and show a logical feature of the world [216]. If ‘a is red’ and ‘b is green’ are meaningful, then so is the combination ‘a is green’ meaningful. According to this view of the Tractatus, the articulation exhibited by a proposition is not reducibility to simpler and independent elements (the simple objects); it resides in the interchangeability without loss of meaning of its parts or constituents with the part of constituents of other propositions [216]. It is the network of these relations of interchangeability that is given by the general form of the proposition, the recursive operation of the iterated neither . . . nor. As Emiliani makes clear, similar remarks apply to the form of the world: objects, as presented by the Tractatus, are not determinate entities that, in addition to their peculiar or individual features, also possess combinatorial possibility (perhaps engendered by their individual features). ‘They are instead interchangeable parts of possibilities states of affairs, and so, their possibilities of occurring in states of affairs constitute them as objects’ [216-7]. The form of world of the world thus exhibits a mirror image of the form of the proposition, of the context principle mentioned earlier. A proposition is internally related to a (possible) state of affairs; it is this relation that makes it into a determinate proposition and thought. The radical nature of this thought is made explicit by Emiliani: ‘the possibility of a state of affairs is the possibility that the elements of a proposition meaningfully combine with one another. The form of language and the form of reality do not merely “match”, but they are one and the same. It is the form of reality that is present in language, by being mirrored in it (4.121). Logical form is shared by language and the world (it is what they have “in common”: cf. 4.12, 2.18)’ [220]. Emiliani concludes that, for the Tractatus, pictorial form just is the possibility that things are related to one another in the same way as the elements of the picture. A picture contains the possibility of the situation that it represents and so it contains the form of the very situation that is represented.

The possibility that a combines with b is not different from the fact that the proposition ‘ab’ is meaningful; the meaning of the proposition is not some other fact of a special kind. As Emiliani points out, the root of the issue is that the nexus between a and b cannot itself be a third constituent of the state of affairs: ‘the nexus, the combination, can only be presented by means of a nexus of symbols: this is the kernel of the insight that a proposition is a picture. Proposition and state of affairs share their connective structure, and this is why their relation is internal’ [221]. The nexus between a and b is shown by the proposition ‘ab’ having a sense, by the way the symbols hold together into a whole. There is no other ‘fact’ to be described. Emiliani again: ‘The possibility of the nexus of things is given in the meaningfulness of the nexus of symbols: there is not anything else which the nexus of things is in addition to that which is given in the meaningfulness of the nexus of symbols’ [221]. At this juncture it becomes possible to clarify the role of nonsense in the workings of the text of the Tractatus. So far as the text is concerned, there is no such thing as nonsensical propositions that can be used to aim at ineffable qualities of reality or language. There are no sentences that are nonsense on account of the peculiarly illegitimate kind of thing they try, but fail, to say. That is, there are no metaphysical truths that though they may not be stated may nonetheless be shown. There is no such thing as ‘expressive nonsense’. From the point of view of their construction, according to the Tractatus, all nonsensical propositions are equivalent. One or more expressions have not been assigned any meaning in a certain context (or any context). Emiliani gives as an example ‘ this notion is yellow’. In this case, ‘x is yellow’ only has a sense when a material object is substituted for x. Here, then, no meaning has been assigned to ‘notion’. Nonsense is nonsense; there is nothing it says. And yet, as Emiliani insists, this is not quite the end of the matter. It is true that ‘this notion is yellow’ does not communicate the true nature of colour in some hidden or mysterious way. However, we recognise it as nonsensical only insofar as we have a commanding view of the way the words are actually used. If we don’t have such a view, it may be that the nonsense ‘proposition’ will lead us to see things aright, and so in its effects be significant. To recognise nonsense requires more than the withdrawal of the incriminated sentences. ‘Whether a nonsensical proposition is plain, trivial nonsense or significant nonsense depends on us, on what we see clearly and what we do not. What is qualified as significant or trivial is not so much the nonsensical proposition itself – this distinction is not based upon any properties that are intrinsic to it. Such a qualification instead applies to our appraisal of it’ [224-225].

The propositions of the Tractatus are more complex than the example just considered, and yet there are some features that they have in common. One can see what is involved by returning to the basic insight of the immediacy of semantic agreement. Emiliani formulates the issue as follows: ‘the meaningful proposition is internally related to a state of affairs: it directly agrees with it, as a mask fits a face and does not fit another. The fitting is a matter of form – in order to be able to fit a determinate state of affairs, the proposition must have a form in common with it’ [225]. However, it must be noted that this form is not a physical form. It has to do with the way constituents of propositions link with each other in a certain structure (like the links of chain) and with the meaningful recombination and interchange between such constituents. But at this point the notion of form becomes questionable. No property of a material object is being referred to. The use of ‘form’ is not even metaphorical, since metaphors can be paraphrased. The same consideration applies to other notions in the Tractatus: ‘nexus, ‘links in the chain’, object’, and so on. One might call this use of words false metaphor: words are being used in contexts where they have been given no meaning. One might also say, in the idiom of Philosophical Investigations II, xi, that ‘form’ and words like it are being used in a secondary sense. To say, for example, that the vowel ‘e’ is yellow, or that the world is unreal, is to use ‘yellow’ and ‘unreal’ in secondary senses. The use of words in this way is closely allied to seeing aspects, as when one says that one sees the cruelty in a person’s smile, or a triangle as a wedge or an arrow. Transferred into the new context, where no meaning has been assigned to them, they are used as expressions of how things strike us, of how they appear to us. Something of this kind is at work here, in the way the text of the Tractatus leads us on: as we move from one formulation to another, it eventually becomes clear that any formulation is misleading, since they all presuppose that there is some thing we are talking about. Both the propositions of the Tractatus and the formulations of commentaries on it use constituents to refer to form, whereas the basic point is that form is not a constituent at all, but a nexus, a way of connection into a meaningful whole. To treat the nexus as a constituent of a state of affairs is to misrecognise the fact that it is a connection between elements: it is not an element, or what Emiliani calls ‘a mythological object’. And yet this very use of the word ‘connection’ is also misplaced: ‘if you have understood me, you recognise my use of “connection”, “form”, “internal relation between proposition and state of affairs”, “possibility of combination” etc. as nonsensical’ [226]. To recognise the nonsensical use of words such as ‘form’ in this context, and to be shown, to see, the ineffable nature of logical form, of the logical connection into a whole, are not, in the end, separate acts. It is one of the ways a proposition may illuminate by being recognised as nonsensical. Part of what is being shown here derives from what was referred to above as the temporality of discourse, whereby the propositions formulating the general form of passage from one proposition to another are themselves subject to that same operation of passage. Logical form structures the very propositions which are trying to give its nature. When employed in this way, words like ‘form’ and ‘connection’ are nonsensical, though when used within a proposition or set of propositions to describe some feature of the world, they are fully intelligible. This means that, for Emiliani, there are no dubious assumptions being made about how nonsense may communicate ineffable truth: nonsense communicates nothing. Nonetheless, the showing is in fact accomplished, though not by describing something that is not describable but by recognising a proposition as genuinely nonsensical. As Emiliani has it, ‘the mythological object disappears when form shows itself – form shows itself when the mythological object disappears’ [226].

What we can say, then, is that the Tractatus itself, as a whole, offers itself to be recognised as an expression of the urge to metaphysics. In that recognition the metaphysical idea, the idea that a complete analysis of logical form is possible, and that logical form so understood determines the limits of the application of signs, fades away. And as it fades away, so too does the similarly metaphysical requirement that sense be determinate. Statements about simple objects are nonsensical in exactly the way that statements about logical form are nonsensical. In effect, the work of the Tractatus is to bring about a change of aspect, so that how we see the text itself, and how we seek to understand the way language operates, undergo alteration. At 5.5423, Wittgenstein presents a clear instance of aspect change in relation to the complex form of a proposition: ‘To perceive a complex means to perceive that its constituents are related to one another in such and such a way’. He then draws a comparison between the complex form of a proposition and the form of a schematic cube: when one looks at such a figure, the front face seems to change places with the back face, and front and back flip flop back and forth, each replacing the other. This shifting of aspect, like that of the famous duck-rabbit of Philosophical Investigations, points to what occurs in the structure of the text of the Tractatus itself as we, its readers, engage with it. Under one aspect, the text makes sense, so that it is perfectly intelligible to argue that in the body of the Tractatus Wittgenstein elaborates a critique of, amongst other things, Russell’s theory of types and logical objects. On the other hand, this critique, deriving from and so dependent on the notion that logical form is what determines the limit of the application of signs, is nonsensical. The text is thus many-layered, and operates in different modes at different levels, and part of what it requires of its readers is that they be alert to the shifts of level possible at any point. This, it should be said, avoids the obvious absurdity that every line of the Tractatus is simply nonsense. It is clear that the account of the truth tables, of succession and recursion, as well as of the Sheffer stroke, is wholly intelligible. However, these reflections do not justify the belief that it makes to imagine there could be such a thing as a perspective from which one can survey how language represents the world: whether one takes language ‘internally’, with respect to the form of the proposition, or ‘externally’, with respect to language ‘as a whole’, the possibility of either an ‘internal’ or ‘external’ point of view on how language represents states of affairs is unintelligible.

In 6.54, when Wittgenstein writes: ‘My propositions serve as elucidations in the following way: anyone who understands me eventually recognises them as [nonsense]’, it would seem that he is insisting that ‘thinking cannot be completely reduced to and be fully expressed by anything we are likely to be content to call a “logical system”. What is as a consequence nonsense is the assumption of logical analysis that all thinking, in order to be thought, must be captured by a propositional sign that on examination is found to be either sensical, senseless or nonsense’. [Rupert Read and Rob Deans, ‘“Nothing is Shown”: A “Resolute” Response to Mounce, Emiliani, Koethe and Vilhauer’, Philosophical Investigations 62:3 (July 2003): 254.] That is, the very distinction, between propositions that make sense, the senseless propositions of logic (the tautologies), and the nonsense propositions of the Tractatus, is itself a nonsensical distinction, based as it is on the desire to express thought in terms of the structures of a logical system (the general form of the proposition). What logical form shows is the impossibility of making fully explicit the nature of sense, of meaning. Always beyond itself, and always lacking the objects on which the determinacy of sense depends, the syntactical (the senseless) and the semantic (the sensical) cannot be brought into a one-to-one relation. The reader begins with the idea that a limit has to be established to thinking and to the expression of thought, and a distinction set up between sense and nonsense. It is here that the analysis of simple objects and logical form is addressed, but ‘[w]hat the reader is left with is the realisation that there is thinking going on as the propositions of the Tractatus are engaged with, but without thought in anything like the Fregean-Russellian sense. Logical analysis can neither fully capture nor fully specify just what it is to think. Thought and language cannot be “pinned-down” and the attempt to give a complete analysis breaks down; but not because it is impossible, for this suggests there is something here that cannot be done, but because the very idea of giving a complete analysis is unintelligible’ [Read and Deans: 258]. No sense can be given to the idea of a vantage-point from which we can survey language as a whole, or of getting beyond it and seeing it as it were laid out before us, open to inspection. This does not mean that there is no role for logical analysis, in showing how language is actually used, in inference or other forms of argument. It does mean that logical analysis cannot justify or found meaning: logic is derived from our use of words to say what we mean, and not the other way round. In 6.1203, Wittgenstein gives a procedure for producing a picture, a physical depiction or image, of a tautology (~(p.~p)). Given that a proposition with sense is a picture of a possible state of affairs, a tautology is a picture of nothing. A tautology has no truth conditions, since it is unconditionally true, and a contradiction is true under no conditions (4.461). Since all the propositions of logic are tautologies (6.126, 6.22), logic says nothing: it lacks sense. The tautology, then, is both a part of logic (e.g. p implies p) and logic as such. When Wittgenstein presents an image of a tautology, what he is giving is a representation of a representation of nothing. To make an image or picture of a certain tautology may, on the one hand, be merely a novel and clearer way of laying out the truth table for that tautology. But if, on the other hand, it is taken as an image of tautology as such, that is, of logic as such, of the sinnlos in itself, the image is nonsense. Removed from any context of use, it stands on its own, above logic and above sense. We are, so to speak, taken beyond the limits of the text into an image of language qua language, into a material depiction that in depicting the absence of depiction asserts its own material presence beyond the opposition between meaning and non-meaning. In representing its own failure to represent, the text produces a nonsensical image, the seeing of which is seeing the distinction between sense, the senseless and the nonsensical as itself nonsensical. The image of the doubling of the doubled brackets in 6.1203, the typographical reduplication within the text, effects a kind of folding back of the Tractatus on itself, in which the physical inscription of the writing interrupts and inhibits the distinction between meaning and non-meaning. When Wittgenstein insists (in 6.54) that whoever understands him will eventually recognise his propositions as nonsensical, the point is that the aspect of the text that will eventually force itself onto the reader will be that aspect which has already forced itself onto Wittgenstein himself, the text’s author. It is not man makes images, but rather images that make a man, and so with the text as a whole: it is the Tractatus that creates both its author and its reader. Wittgenstein and his reader stand on the hither side of the propositions that constitute it. The image the propositions create is that of a language spoken by no one.

In using words here like ‘text’ and ‘writing’ I have wished to evoke something of the idiom of Blanchot and Derrida. My purpose is not to assimilate ‘continental’ thought to that of Wittgenstein, or vice versa, but to suggest points of comparison. I have argued that, whereas Blanchot in particular bases his thought on a concept of naming that is untenable, in order to reach the impossible conditions that are the possibility of writing as such, Wittgenstein begins from the meaningful proposition. The Tractatus is thus not an attempt to establish how meaning is possible. Whereas Blanchot, and others in the tradition to which he belongs, use language in way that implies that there is a sense in talk about the impossibility of possibility, Wittgenstein’s approach would characterise such talk as nonsense. No meaning has been given to the words like ‘impossibility’ in the context in which Blanchot seeks to use them. Nonetheless, I want now to propose that, despite the unsatisfactory foundations of Blanchot’s thought, its final direction, towards an understanding of the language of literature, is pertinent to a reading of the Tractatus. When Wittgenstein writes, in the Tractatus (6.4311), that death is not an event in life, since we do not live to experience death, one cannot but be put in mind of Blanchot’s reflections on the impossibility of dying, a comparison that may be further reinforced by reference to Wittgenstein’s remark (also in 6.4311) that our life has no end in just the way in which our visual field has no limits. We are being taken by remarks of this order beyond the expressible, towards what Wittgenstein calls the mystical: ‘There is indeed the inexpressible. This shows itself; it is the mystical’ (6.522). So far as the Tractatus is concerned, the notion of the mystical has its source in the discussion we have already looked at, that concerning simple objects: ‘Objects can only be named. Signs are their representatives. I can only speak about them: I cannot put them into words. Propositions can only say how things are, not what they are’ (3.221). Mysticism is motivated, in part, by the fact that if we are to understand anything we have to be related to objects, things. But, as Gordon Bearn indicates [Waking to Wonder, p. 60], objects are the unchanging structures of logical space: this means that, since whatever we experience could be otherwise (5.634), there can be no experience of objects, a conclusion reached also by McGuinness, from the different starting point of the meaningful proposition. How then are we to understand the givenness of objects, the givenness of the world? It is an experience not of HOW the world is but THAT it is, at all (6.44).

The ‘experience’ that we need in order to understand logic is not that something or other is the case, but that something is: that, however, is not an experience.
Logic is prior to every experience—that something is so.
It is prior to the question ‘How?’, not prior to the question ‘What?’. (5.552)

Here again the language can be seen in the process of shifting its status, as the word ‘experience’ undergoes a self-cancelling alteration, from a primary to a secondary sense. Logic is before the how, not before the what. But how the world is, is what is the case. So the experience we need, as Bearn puts it, ‘if we are to understand logic is not an experience of what is the case, of what has happened in the world’ [p. 60].

To view the world sub specie aeterni is to view it as a whole—a limited whole.
Feeling the world as a limited whole—it is this that that is mystical. (6.45)

Mystical wonder is not wonder at the way things are, but wonder at the bare existence of things, that they are—the what not the how. This returns us to the point I have emphasised before: when we understand logic we understand that it is senseless. Other than world there is nothing, and it is nothing that logic treats of. Bearn has said that, for Wittgenstein, understanding something is to understand that something against the background of logic, against the background of nothing. Bearn here compares Wittgenstein with Heidegger:

In July 1929, Heidegger had tried to understand the deepest form of anxiety in terms of his belief that ‘human existence can relate to things only if it holds itself out into the nothing’. In December of that year Wittgenstein said, ‘To be sure, I can imagine what Heidegger means by being and anxiety’. [Bearn, p. 61]

A comparison with Levinas and the notion of the il y a is also pertinent. This line of argument also brings something to the fore, the structure of the Tractatus itself. It exhibits exactly the torsion, the twisting turn, which is not exactly a circle but more like a Moebius strip, whereby what is anterior reappears in what succeeds. We move from an ‘experience’ of what is prior to the world, an experience that is not an experience, to an experience that is also not an experience, the experience of the ‘there is’ of things. Torn from our everyday existence, from the world of how things are, it is as though existence emerged from behind the world. I am no longer related to this or that possibility, but to existence itself, an experience that (according to the Tractatus, as well as to Levinas and Blanchot) is internally related to the experience of nothing. In coming face to face with the bare existence of things, that they exist at all, we come face to face with ‘no-thing’ at all: ‘There are, indeed, things that cannot be put into words. They make themselves manifest. They are what is mystical’ (6.522).

The encounter with the il y a is an encounter with horror, as when for the insomniac things take on the terrible and dreadful aspect of the ‘other night’. To experience the ‘there is’ is to experience the void or absence in which the things of the everyday world, the world of ‘how’ things are, dissolve and disappear. In a classic essay first published in 1991, Cora Diamond has brought out something similar in the way Wittgenstein’s understanding of the mystical (and of nonsense) relates to his discussion of ethics and treatment of the question of evil. A crucial matter for her is the manner of reading the Tractatus requires of us: ‘if I understand Wittgenstein in the way that he asks to be understood, then I read the sentences in question twice: first, entering (wittingly or not) into the nonsense that they are about ethics; secondly, entering into the nonsense of the book as argument to a conclusion that those remarks are not “about ethics”, for nothing is a “remark about ethics”. There are no “ethical propositions”, and sentences in question have no more to with “ethics” than “piggly wiggly tiggle”. If I understand Wittgenstein, I enter the nonsense of reading the book as ethics and of reading the book in such a way that it leads me to self-consciousness about the activity of such reading’ [Cora Diamond, ‘Ethics, Imagination and the Tractatus’, in Alice Crary and Rupert Read, eds., The New Wittgenstein (London and New York: Routledge, 2000), p. 164]. The Tractatus requires a reading that at first takes us in, requiring us to take its propositions as making sense, as being about logic and so on, despite not being so. This is to take what Diamond calls the ‘austere view’ of nonsense, the view that all nonsense is just nonsense, that there is no such thing as articulating the meaning of a particular bit of nonsense, while at the same time acknowledging that there is such a thing as an imaginative activity of understanding someone who utters nonsense, of ‘letting oneself be taken in by the appearance of sense that some nonsense presents to us’ [Diamond, p. 165]. When I ascribe a belief or thought to someone, I must use an intelligible sentence of a language I understand. If I am to understand someone who utters nonsense, I have to participate imaginatively in what is said and see nonsense as sense. I become, as it were, the person who thinks he thinks it: ‘I treat that person’s nonsense in imagination as if I took it to be an intelligible sentence of a language I understand, something I find in myself the possibility of meaning’ [p. 165]. In other words, I am a participant in a change of aspect. Diamond’s point is similar to one I made above: when Wittgenstein says that whoever understands him will come to recognise his propositions as nonsensical, the point is that the aspect of the text that will eventually force itself onto the reader will be that aspect which has already forced itself onto Wittgenstein himself. Sense is seen as nonsense, nonsense as sense. This to see the Tractatus as uncanny.

There is a close connection in Wittgenstein’s thought, both in the earlier work and later, between logic and ethics. As we have seen above, logic is not for Wittgenstein a particular subject, with its own special truths, requiring some kind of scientific treatment, but something internal to all thought. Logic permeates our whole use of intelligible propositions in the course of our lives with language. Likewise, an ethical spirit, an attitude to the world and life, penetrates a whole way of living, and is manifest in how we talk and think. It is not the abstraction of a moral code, or a distinct set of rules. Ethics is a discourse turned towards everything there is or can be, the world as a whole. There is an important sense in which the ethical spirit for Wittgenstein involves an attitude towards the world ‘in terms of an acceptance of the independence of the world from one’s own will’ [Diamond, p. 154]. The ethical spirit, for him, Diamond believes, ‘is tied to living in acceptance of the fact that what happens, happens, that one’s willing this rather than that is merely another thing that happens and that one is in a sense “powerless” [p. 154]. It is in this connection that Wittgenstein speaks of two different attitudes to the world: the world of the happy man and the world of the unhappy man, though it is by no means clear how far these two attitudes can be kept separate. [Cf. Brian McGuinness, ‘The Mysticism of the Tractatus’, Philosophical Review 75 (1966): 316-317.] The happy man achieves a kind of piety in life, looking at the happenings of the world with clear eyes, whatever those happenings may be. Wittgenstein contrasts this with the state of mind of the suicide, for whom going on with life is made conditional on things being this way and not that. It is as though I were to reject the powerlessness fundamental to life, by willing to leave life if things do not go the way I want them. Diamond finds an example of such a refusal of powerlessness in Nathaniel Hawthorne’s story, 'The Birthmark', the main character of which, Aylmer, is ‘unhappy’ in Wittgenstein’s sense; the world does not meet the conditions he lays down. This spirit is evident in his response to the birthmark on his beautiful wife, and is further seen in his destructiveness of her life, goodness and beauty. There is, then, an analogy between the idea of understanding someone who utters nonsense and someone, whether oneself or someone else, to whom one ascribes an evil will, in the sense that one would be willing to ascribe such a will to a figure like Aylmer. A further example occurs in Wittgenstein’s remarks on Frazer’s account of the Beltane Fire Festival in eighteenth century Scotland. Wittgenstein says he has a sense of something terrible and sinister about the ritual games enacted in the festival, but what the source of that sense of the terrible is remains unspecified. On the surface there is nothing terrible, and even if one knows that there is a distant connection with human sacrifice this still does not account for the sense of the terrible that lies at the heart of the practices here, something terrible in the human heart itself. There is thus a tie here between something evil in a person’s will or in what people do, and an understanding of the person in which one sees him or her as willing something, but one specifies what is willed in words that have no content. In ascribing an evil will to someone, as with understanding someone who is the grip of an illusion—believing that what one utters is sense when it is nonsense—one must engage in a similar act of imaginative participation, giving ‘content’ where there is no content to give. Neither logical illusion nor the case of evil will is understandable. When one engages with what a person says who is in the grip of logical illusion (such as the illusion of the general form of the proposition) one is not inside that person’s thought as one is when he makes sense, because there is no thought to understand, there is no ‘inside’.

You are not inside, because there is as it were no inside; you cannot remain outside, because outside all you can see is someone inclined to put together words, to come out with them in certain circumstances, to associate them with images, feelings and so on; from the outside, there is nothing to be seen that could be called his being in the grip of an illusion that so-and-so, as opposed to his being inclined to come out with certain word-constructions. There is, as I said, no inside. But what it is to understand a person who utters nonsense is to go as far as one can with the idea that there is. [Diamond, art. cit., p. 157]

Diamond finds what she has in mind well put by Wilhelm Grimm, when he speaks of the evil in the tales he and his brother edited, not as something very bad which one could get accustomed to, but as something terrible, black and wholly alien that cannot even be approached. In Rumpelstiltskin, the miller who brags about his daughter and endangers her, and the avaricious king who sets the girl an impossible task, and threatens to kill her if she does not accomplish it, are far from being decent folk. But what is bad about these two is not of the order of the evil of which Grimm speaks, and to which what is dark and sinister in the human heart is able to respond, evil as terrible and unapproachable as that of Rumpelstiltskin. Unapproachable evil would once have been called supernatural or demonic, beyond the world, transcending it and irreducible to the deliverances of psychology or natural law. Rumpelstiltskin’s strength derives from his name being unknown to humans, and just as his name is unknown so his mode of being is ungraspable, and because of this the very eagerness of his demand for the girl’s first child brings it with a sense of horror inseparable from what he embodies of the dark and unappeased, a horror confirmed and augmented by the appalling death he undergoes at the tale’s end. The Tractatus succeeds, just as surely as the tales of the Brothers Grimm, in placing us outside the world, beyond the expressible, beyond the true and the false, an achievement whose power and profundity are for Wittgenstein inseparable from ‘ethics’.

The horror arising from this kind of exile is everywhere to be found in cinema. George Bailey’s expulsion from the world in It’s a Wonderful Life is an example whose effect is particularly shocking, given the context established by the film’s ease and comic precision of the importance of the quotidian to the progress and meaning of George’s life. The sudden access of darkness evoked at the moment of his mother’s repudiation of any knowledge of him, a repudiation by which he becomes as though he were no one, devoid of both identity and place, ruptures the film’s surface, and suspends us, for a moment, before the world even as it renders its reality unapproachable. While George Bailey is gathered back into the world, the protagonist of Witchfinder General, Matthew Hopkins, is a man whose evil excludes him from any relation to others except that of torture and sadism. Free of compassion or fellow feeling, driven by ambition and will to power, he seeks to mould the world to his own liking, by employing the theology of witchcraft and witch-hunting to place himself outside the world and subjugate it to his sovereignty. The ‘logic’ of ‘floating’, whereby witches are tested for guilt or innocence—if they drown they are innocent, if they float they are guilty—serves this purpose admirably. Whatever the result, death is the automatic consequence, and Hopkins’s judgement cannot be gainsaid. Hopkins’s sovereignty, dependent on a form of logical necessity over which he can have no control, is thus internally related to impotence, a fact made abundantly clear by the atrocious death he suffers, as the lover of the girl he has driven mad by torture quarters him and the witchfinder’s own excess devours both him and the man who dismembers him. In Day of Wrath Merete, the elderly mother of Absalon, an elderly priest, and the grandmother of Martin, is consumed with hatred for Anne, Absalon’s young wife, who is to fall in love with Martin, her stepson. The oppression and power of the church, represented by the keys that Merete carries with her wherever she goes, are finally turned against the girl, after Absalon’s death, when in a paroxysm of rage and loathing the old woman accuses her of witchcraft. It is easy to see in Anne a figure of life, of the natural expression of love and freedom, expelled from a world whose power and institutional terror base their legitimacy on the burning of witches. The film itself, however, does not permit this simple opposition: Merete is too powerful and impressive a figure to be reduced to what on that reading would be merely a representative role. Her hatred takes on a physical presence that goes beyond the demands of either narrative or psychology, and exceeds even the theological justifications that might be found for it. She is more than the world of the church and more than the world of love. She appears to serve a principle of expenditure and destruction that has no exact correlative in the film, and in relation to her Anne, who we might be initially inclined to think of as unambiguously sympathetic, takes on a demonic aspect. Dreyer films Anne, as she talks at night to Martin of her love, in a contrasting light that suggests the corruption and evil present in what she is doing, exactly as though we were being brought to see the relation between Anne and Martin as Merete would see it. Dreyer reveals here the cinema’s strange and unsettling relation to the power of the image, as Day of Wrath separates off from meaning only to re-inscribe itself in the anonymity of the text and choral rendition of the Dies Irae. The final image of the film is a cross not photographed but etched in white on a black ground, a cross with a sloping top to it reminiscent of the cross employed in the burning, under Absalon’s jurisdiction, of Marte, an old woman convicted of witchcraft, about halfway through the film. The cross, replete with the symbolism of Christianity, is at the same time an image of an image, an image of nothing.

The manifestation of which the Tractatus speaks, of what lies outside idealisation and the continued possibility of meaning, the manifestation of the ‘there is’, that things are, not how they are, is an irruption of otherness more radical than any that could be reached within language: ‘What we cannot speak about we must pass over in silence’ (7). Silence in this context is not only the negation of language seen as a totality from a place beyond language; it is also an interval or interruption that ruptures language and disturbs and displaces the self. Whatever one thinks such a feeling to be, it is, for Blanchot at least, even in its excess and affliction, affirmative. As the narrator of Madness of the Day puts it: ‘I saw that even on the worst days, when I thought I was utterly and completely miserable, I was nevertheless, and nearly all the time, extremely happy’ [Madness of the Day, trans. Lydia Davis (New York: Station Hill Press, 1981), p. 7]. The narrator adds that the discovery was not a pleasant one. The world of the ‘happy’ man and that of the ‘unhappy’ cannot be kept separate one from the other. The event to which the Tractatus, like the work of Blanchot, seeks to open us is an event of no fixity, no determination. Even though we never stop making sense, of dwelling in a world made up of everything that is the case and represented by propositions that are true or false, we are always already impotent before the fascination of what lies beyond world and sense. ‘It makes what is ungraspable inescapable; it never lets me cease reaching what I cannot attain’ [The Space of Literature, trans. Ann Smock (Lincoln, London: University of Nebraska Press, 1989), p. 31]. The fascination is that inherent in the condition of writing, a condition the Tractatus attains to and is recognised as having when we recognise the text as nonsense. In the act of such recognition we are precipitated into logical impossibility: ‘Just as the only necessity that exists is logical necessity, so too the only impossibility that exists is logical impossibility’ (6.375). We find ourselves in that place whose existence is ruled out by the logical structure of language, just as the simultaneous presence of two colours at the same place in the visual field is logically impossible, ruled out by the logical structure of colour (6.3751). For Blanchot, to enter this nowhere, which he calls the ‘essence of solitude’, is to surrender to the fascination of time’s absence. Time’s absence is not purely negative: it is ‘a time without negation, without decision, when here is nowhere as well, and each thing sinks into its image while the “I” that we are recognizes itself by sinking into the neutrality of a featureless third person’ [The Space of Literature, trans. Ann Smock (Lincoln, London: University of Nebraska Press, 1989), p. 30]. The time of time’s absence has no present, no presence. Having no present, it has neither past nor future. What has no present has never happened, not even for a first time, and yet it starts again, over and over, forever re-begun, without beginning, without end. Wittgenstein writes: ‘If we take eternity to mean not infinite temporal duration, then eternal life belongs to those who live in the present’ (6.4311). An eternity lived in the present is a time that is neither eternity nor the present—a time that is not time, an impossible time, excluded by the logical structure of time and so existing only in impossibility. This is the time internal to art, where images reveal that they do not reveal, and we, seeing them, are driven by the passive compulsion that fascination is into intensified states of excitation, as when in the cinema we are seduced ‘by masochistically exacerbating erotic tension, in an orgy of unproductive expenditure’. [Steven Shaviro, The Cinematic Body (Minneapolis, London: University of Minnesota Press, 1994), p. 57.] For this reason, horror films are revelatory of the nature of cinema in itself and of what constitutes our relations to it, especially insofar as we are complicit with the victimisation and driven quality of the monsters who inhabit them. Not driven by power but compelled by his vulnerability, Michael Myers is both child and rapacious killer, forced at the end into the position of accepting his own death at the hands of Dr Loomis, a death that can never come. The masochism, the impotence, evidenced in the spectacle of his ‘killing’ creates a space of excess, which is given in the film in repeated shots of the places where Michael has been but is no longer present, places which he yet inhabits (there where the film’s theme music, associated with his presence, puts him, there where he is not). Throughout Carpenter’s film, Michael has striven to repeat the move that constitutes his situation in the opening sequence, from being behind the image, behind the mask, to being seen full face, a move from first to third person. No sooner does he close in on the centre of the image, in what is the penultimate sequence, than Loomis ‘kills’ him, by expelling him from the screen. Michael becomes subsumed into an image, but an image of nothing and nowhere. He is no one.