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.