Presented on 24 February 1965, approximately one month after Yves Duroux’s introduction, “Psychology and Logic”.
Miller begins by noting that only those who have gone through personal analysis and gained the “precise conceptions of analysis” should concern themselves with “it”. He does not state what “it” is, but I presume that “it” is the “logic of the signifier”.
Miller asks himself a question from the perspective of the audience: if he does not have the credentials to speak about it, what is he doing here?
He then redirects the question: why are analysts here, listening to somebody without credentials, without practice. Miller seems quite amazed, almost dumb-founded, that he has an audience of analysts listening to him speak.
“The Freudian field is not representable as a closed surface” – this is what Miller claims gives him the authority to speak to an audience of analysts.
If you are situated on the inside, and Miller is outside, and the two are here speaking, then, this is because the two surfaces join up and the periphery or outer edge crosses over the circumscription.
Interested in the logic of the signifier. It is a general logic – it governs all fields of knowledge. It is a minimal logic – there is a movement, a progression, along a linear sequence.
The logic of the signifier is not only a logic for linguistic study. It can be imported into other discourses. And we should import it into psychoanalysis.
There is a relationship between the signifier’s logic and the “logician’s logic.” The signifier’s logic treats the emergence of the logician’s logic. The signifier’s logic is the logic of the origin of logic. This means that the signifier’s logic does not follow its own laws – it itself falls outside of the jurisdiction of its logic.
There is something similar being done in our method as Derrida did in his phenomenology [Edmund Husserl’s Origin of Geometry: An Introduction, by Derrida).
Miscognition finds its point of departure in the production of meaning. It is constituted on repression. To designate all of this Miller uses the name “suture”.
Suture names the relation of the subject to the chain of its discourse; it figures there as the element which is lacking, in the form of a stand-in [holding in place of, substitute]. Just because something is lacking doesn’t mean that it is purely and simply absent. Suture – which is a relation of lack to structure – is a taking the place of.
Suture is not named explicitly by Lacan, but it is there in his system.
Miller is not speaking as a philosopher, Freud, quoting Heinrich Heine, claimed that philosophers “with his nightcaps and the tatters of his dressing-gown, patching up the gaps in the structure of the universe.” Suturation is not peculiar to the philosopher. Philosophers suture universal structures. And the logician, like the linguist, also sutures at his particular level. And so does anybody who says “I”.
We must focus on the letter of a discourse and not its meaning. We are concerned with a dead letter – the meaning dies.
We are concerned with Gottlob Frege’s argument in The Foundations of Arithmetic (1953). Frege’s system puts into question natural numbers taken as primary, (1) zero, (2) number, and (3) succession.
What is it [a question of being] which functions in the series of whole natural numbers and to which we can assign their progression/succession?
Miller provides the answer up front. At this point we’ve already taken a step beyond Duroux’s short text: “in the process of the constitution of the [numeric] series, in the genesis of progression, the function of the subject, miscognized, is operative.”
Frege’s logical discourse begins with an exclusion which makes possible the passage of the thing to the unit and to the set/collection of units to the unit of number. Frege excludes the subject as the basis for this passage. The function of the subject is the support of the operations of abstraction and unification.
The unity of individual [unit?] and set only holds if we presume that the number functions as its name.
A subject – the other side of the subject is politics – is a faculty of memory necessary to close the set without any loss of any of the interchangable elements, and a faculty of repetition which operates inductively. Deciphering this: the subject is what makes possible the faculty of repetition, and the memory of that which preceded number, the passage from one number to another, for example.
But Frege excludes the subject from the start, excludes it from the field in which the concept of the number is to appear.
The subject is not reducible to the psychological – the exclusion of the subject from the field of number is assimilable to repetition.
Frege’s discourse begins with three concepts: the concept, the object, and the number. It also includes two relations: subsumption [relation of concept to object], and assignation [relation of concept to number]. A number is assigned to a concept which subsumes objects.
Subsumption [concept <> object]
Assignation [concept <> number]
Logic of Frege’s system: a concept is defined and exists solely through the relation which it maintains as subsumer with that which it subsumes [concept relation to object]. Also: object only exists insofar as it falls under a concept – the object takes its meaning from its difference to the thing integrated, to the real. Does this not imply a new concept, then? What is a thing? Miller does not say. Object is related to something which is not a concept and which is not a number – it is a thing, and it is in the real.
Miller picks this up immediately: the thing disappears from Frege’s system, it must disappear for the object to appear. The object then:
Object is thing insofar as it is One.
The thing is counted as One, it is elevated to the status of One.
So there is a redoubling: the concept is formed through the determination of subsumption [concept <> object]: the concept of identity to a concept. [concept <> object, 1 <> 1 is taken where there should be object <> thing, 1 <> 0].
So this redoubling, Miller seems to call “identity”. The concept is redoubled, induced in the concept by identity – and it effects the disappearance of the thing it gives rise to the emergence of the numerable. The thing, as 0, is erased, to give the 1.
Identity as a logic, is similar to what Duroux named equivalence – there is a correspondence, presumed, between thing and object, or, if not presumed, avoided or repressed, in favour of redoubling of the concept – in favour of the concept referring only to the concept.
Assignation of number [concept <> number]: ‘the number assigned to the concept F is the extension of the concept ‘identical to the concept F’”. All that is left to the Thing, in Frege’s system, is the support of its identity with itself. This is the support for the numerable.
Distinctive unit supports the number, unifying unit is assigned by the number.
A distinctive unit’s foundation is situated in the function of identity. The function of identity confers on each thing in the world the property of being One, whole – a unit. It also transforms the unit into an object of the logical concept. Miller therefore insists that we call this logic “identity” rather than “equality”.
Frege takes his definition from Leibniz: ‘Those things are identical of which one can be substituted for the other salva veritate, without loss of truth.’ Here is the emergence of the function of truth. What the function assumes is more important than what is expresses: that is, identity-with-itself.
A thing can not be substituted for itself – where does this therefore leave truth?
If a thing can not be substituted for itself then this subverts the field of truth, ruins it, abolishes it.
But identity-with-itself is essential if truth is to be saved – and identity-with-itself is what we connote when we pass from the thing to the object, according to Frege.
Truth is. Each thing is identical with itself.
Let: Thing, X, be in the world
Let: There is an empirical Concept of Thing X
But: Empirical Concept of Thing X is a redoubled Concept
Therefore: Concept of Thing X is identical with the Concept of Thing X.
Let: Object X fall under Concept X as a Unit.
Let: Number Assigned to Concept X be “1”
This means: The number 1, as function, is repetitive for all things of the world.
Thus: Number 1 is only the unit which constitutes the number as such, and not the 1 in its personal identity as a number with its own particular place and a proper name in a series of numbers.
The construction of the Number 1 demands that we call upon the thing in the world and yet this, according to Frege, can not be done. What is logical can therefore only be sustained through what is logical itself.
For Number 1 to pass from the repetition of 1 of the identical that of its ordered succession [eg., 2], in order for the number to gain autonomy definitively, without any reference to the real, the zero has to appear.
Zero is the number assigned to not-identical-with-itself.
So: there is a Concept, “Not identical with itself” This concept must subsume an Object – but it doesn’t, it does not subsume an Object.
Zero is supported by the proposition: truth is.
If no Object falls under the Concept “not identical with itself” then this is because truth must be saved.
The concept of not-identical-with-itself is assigned by the number zero, and it sutures logical discourse.
It has been necessary in Frege’s system, in order to exclude any reference to the real, to evoke on the level of the concept an object not-identical-with-itself which is subsequently rejected from the dimension of truth.
The zero assigned as number consummates the exclusion of this object. [an object is missing here]. The object is missing, it is lacking, and so nothing can be written there – if a 0 must be traced, it is merely in order to figure a blank, to render visible the lack.
“From the zero lack to the zero number, the non-conceptualizable is conceptualized.”
If through subsumption [concept <> object] we move from 0 to 1:
Thing = 0
Concept = Concept of 0
Object = Unit of Concept 0
Number = 1
Circulation: number 0 -> concept of 0 -> object of 0 -> number 1
The entire system is constituted with the 0 counting as 1.
The concept 0 subsumes nothing in the real but a blank. This is the support of the series of numbers – of succession.
Successor is obtained by obtaining the number following n by adding a unit to it, n’. Thus, n+1.
n … (n+1) … = n’
Frege opens n+1 to discover what is involved in the passage from n to its successor.
Successor, for Frege: the Number assigned to the Concept member of the series of natural numbers ending with n is what follows in the series of natural numbers ending after n.
For example: …member of a series ending with 3. The number assigned to this Concept is 4. The number here functions as a unifying name of a set.
The 3 subsumes 3 objects in the order of the real. In the order of number, which is that of discourse bound by truth, it is numbers which are counted: before the 3 there are 3 numbers, but with the 3 there is a fourth, the 0.
In the order of number there is the additional 0, and the 0 counts for 1.
That which in the real is pure is simple – finds itself in number noted as 0 and counted for 1.
Something is rejected by truth – an object not-identical with itself – and is sutured by discourse or annulled.
The emergence of a lack as 0, and of 0 as counted as 1, is what determines the successor.
Let: n be.
Let: 0 lack.
Let: 0 be fixed as 1
Let: n+1 absorb the 1
The 1 of n+1 counts the 0 as 1. Subsumption is this process.
The sign of “+” is somewhat unneeded then.
The 1 is the primary symbol of the emergence of lack in the field of truth. The sign “+” indicates the crossing, the transgression through which the 0 lack comes to be represented as 1 … and this allows for the name of a number to come into being, succession.
This opens up the new logic, the logic which comes before the logician’s logic.
The fact that zero is a number assures the logical dimension of its closure.
The zero is a number which sutures and stands-in for the lack.
The zero cancels out the meaning of each of the names caught up in the metonymic chain of successional progression.
0 (as lack of contradictory object) must be distinguished from that which sutures this absence in the series of numbers
1 (as the proper name of a number) must be distinguished from that which comes to fix in a trait the zero of the not-identical with itself sutured by the identity with itself. It is the law of discourse in the field of truth.
The paradox: the trait of the identical represents the non-identical, whence is deduced the impossibility of its redoubling, and from that impossibility the structure of repetition as the process of differentiation of the identical.
0 is represented and excluded in the chain of succession.
The 0 summons and rejects in order to constitute itself. The succession wants to know nothing of it, rejects it. We name this object which is rejected and which the chain wants to know nothing of, the subject.
It is excluded from the discourse is suture.
Number = signified
trait = signifier
logic of signifier = relation of lack to the trait.
relation of subject to the Other (the locus of truth) = relation the zero entertains with the identit6 of the unique as the support of truth.
Zero = not identical with itself.
The subject is excluded by the field of the Other and is represented in that field (Subject <> Other) in the form of the unit, the trait – the unit-trait. The exclusion is marked by Lacan as $<>A.
This exteriority of the subject to the Other institutes the unconscious.
Repetition is produced by the vanishing of the subject and its passage as lack. Only the unconscious can name the progression which constitutes the chain in the order of thought.
A definition of the subject: the possibility of one signifier more.
This explains the possibility of an enumerable infinity.
Lacan: sign is that which represents something for someone – signifier is that which represents the subject for another signifier. The insertion of the subject into the chain is representation. It is not necessarily an exclusion as a vanishing.
Once we have a signifier: the subject is both before and after the signifier. The subject is the effect of the signifier and the signifier is the representative of the subject.
Suture = 0
The subject flickers – a movement open and closes for the subject, in succession. It delivers up the lack in the form of 1 in order to abolish it in the successor itself.