When we last encountered this category of SUBSTANCE, it was when considering "movement of the infinite" as the truth holding between thinking and being: "...movement is not the image of thought without being also the substance of being."

So, perhaps we should begin defining the nature of conceptual personae through an analysis of the linguistic category of SUBSTANCE.

In our first derivation based upon these linguistic categories, we identified the SUBSTANCE OF CONTENT as PROXIMITY; and the SUBSTANCE OF EXPRESSION as IMMANENCE.

	MATTER	SUBSTANCE	FORM
CONTENT	metrical	proximity	assemblage
EXPRESSION	non-metrical	immanence	composition

In our second derivation, we associated PROXIMITY with FEATURES and IMMANENCE with RE-MARKINGS. However, at this point, we can substitute two terms used by Guattari and Deleuze: with PROXIMITY being associated with DIAGRAMMATIC FEATURES, and IMMANENCE being associated with INTENSIVE ORDINATES.

	MATTER	SUBSTANCE	FORM
CONTENT	sensory contrasts	diagrammatic features	meta-stabilities
EXPRESSION	singularities	intensive ordinates	meta-narratives

As important as these considerations are to our definition of conceptual personae, of even more use to us will be the observation noted from the second derivation - that the category of substance is bracketed by VIRTUAL POINTS and PARTIAL OBJECTS.

Thus, whenever we can find any virtual points directly associated with partial objects, we will have found a position which brackets the linguistic category of substance - and which is thus characteristic of 'substance of being', and of conceptual personae.

Points of View

But, what exactly do we mean by 'points of view constituted by conceptual personae'? It is tempting to say that conceptual personae create points of view; that is the obvious answer.

But, it is not necessarily the answer that we need:

"Each one, each subject, for each individual notion, each notion of subject has to encompass this totality of the world, express this total world, but from a certain point of view. And there begins a perspectivist philosophy. And it's not inconsiderable. You will tell me: what is more banal than the expression "a point of view"? If philosophy means creating concepts, what does create concepts mean? Generally speaking, these are banal formulae. Great philosophers each have banal formulae that they wink at. A wink from a philosopher is, at the outside limit, taking a banal formula and having a ball, you have no idea what I'm going to put inside it. To create a theory of point of view, what does that imply? Could that be done at any time at all? Is it by chance that it's Leibniz who created the first great theory at a particular moment? At the moment in which the same Leibniz created a particularly fruitful chapter in geometry, called projective geometry. Is it by chance that it's out of an era in which are elaborated, in architecture as in painting, all sorts of techniques of perspective? We retain simply these two domains that symbolize that: architecture-painting and perspective in painting on one hand, and on the other hand, projective geometry. Understand what Leibniz wants to develop from them. He is going to say that each individual notion expresses the totality of the world, yes, but from a certain point of view.

What does that mean? Of so little import is it, banally, pre-philosophically, that it is henceforth as equally impossible for him to stop. That commits him to showing that what constitutes the individual notion as individual is point of view. And that therefore point of view is deeper that whosoever places himself there.

At the basis of each individual notion, it will indeed be necessary for there to be a point of view that defines the individual notion. If you prefer, the subject is second in relation to the point of view. And after all, to say that is not a piece of cake, it's not inconsiderable.

He established a philosophy that will find its name in the works of another philosopher who stretches out his hand to Leibniz across the centuries, to wit Nietzsche. Nietzsche will say: my philosophy is a perspectivism. You understand that it becomes idiotic or banal to whine about whether perspectivism consists in saying that everything is relative to the subject; or simply that everything is relative. Everyone says it, it belongs to propositions that hurt no one since it is meaningless. So long as I take the formula as signifying everything depends on the subject, that means nothing, I caused, as one says ... (end of the tape)

. . . What makes me = me is a point of view on the world. Leibniz cannot stop. He has to go all the way to a theory of point of view such that the subject is constituted by the point of view and not the point of view constituted by the subject. Fully into the nineteenth century, when Henry James renews the techniques of the novel through a perspectivism, through a mobilization of points of view, there too in James's works, it's not points of view that are explained by the subjects, it's the opposite, subjects that are explained through points of view. An analysis of points of view as sufficient reason of subjects, that's the sufficient reason of the subject. The individual notion is the point of view under which the individual expresses the world. It's beautiful and it's even poetic. James has sufficient techniques in order for there to be no subject; what becomes one subject or another is the one who is determined to be in a particular point of view. It's the point of view that explains the subject and not the opposite.

For Leibniz, every individual substance is like an entire world and like a mirror of God or of the whole universe that each substance expresses in its own way: kind of like an entire city is diversely represented depending on the different situations of the one who looks at it. Thus, the universe is seemingly multiplied as many times as there are substances, and the glory of God is redoubled equally by as many completely different representations of his/her/its (word missing from transcript). He speaks like a cardinal. One can even say that every substance bears in some ways the characteristic of infinite wisdom and of all of God's power, and limits as much as it is able to.

In all this, I maintain that the new concept of point of view is deeper than the concept of individual and individual substance. It is point of view which will define essence. Individual essence. One must believe that to each individual notion corresponds a point of view. But that gets complicated because this point of view would be in effect from birth to death for an individual. What would define us is a certain point of view on the world.

I said that Nietzsche will rediscover this idea. He didn't like him (Leibniz), but that's what he took from him. The theory of point of view is an idea from the Renaissance. The Cardinal de Cuse (spelling uncertain), a very great Renaissance philosopher, referred to portraiture changing according to point of view. From the era of Italian fascism, one notices a very odd portrait almost everywhere: face on, it represented Mussolini, from the right side it represented his son-in-law, and if one stood to the left, it represented the king.

The analysis of points of view in mathematics -- and it's again Leibniz who caused this chapter of mathematics to make considerable progress under the name of analysis situs --, and it is evident that it is connected to projective geometry. There is a kind of essentiality, of objectity of the subject, and the objectity is the point of view. Concretely were everyone to express the world in his own point of view, what does that mean? Leibniz did not retreat from the strangest concepts. I can no longer say "from his own point of view." If I said "from his own point of view," I would make the point of view depend on a preceding subject (sujet prÈalable), but it's the opposite. But what determines this point of view? Leibniz (says): understand, each of us expresses the totality of the world, only he expresses it in an obscure and confused way. Obscurely and confused means what in Leibniz's vocabulary? That means that the totality of the world is really in the individual, but in the form of minute perception. Minute perceptions. Is it by chance that Leibniz is one of the inventors of differential calculus? These are infinitely tiny perceptions, in other words, unconscious perceptions. I express everyone, but obscurely, confusedly, like a clamor.

Later we will see why this is linked to differential calculus, but notice that the minute perceptions of the unconscious are like differentials of consciousness, it's minute perceptions without consciousness. For conscious perceptions, Leibniz uses another word: apperception.

Apperception, to perceive, is conscious perception, and minute perception is the differential of consciousness which is not given in consciousness. All individuals express the totality of the world obscurely and confusedly. So what distinguishes a point of view from another point of view? On the other hand, there is a small portion of the world that I express clearly and distinctly, and each subject, each individual has his/her own portion, but in what sense? In this very precise sense that this portion of the world that I express clearly and distinctly, all other subjects express it as well, but confusedly and obscurely.

What defines my point of view is like a kind of projector that, in the buzz of the obscure and confused world, keeps a limited zone of clear and distinct expression. However stupid you may be, however insignificant we all may be, we have our own little thing, even the pure vermin has its little world: it does not express much clearly and distinctly, but it has its little portion. Beckett's characters are individuals: everything is confused, an uproar, they understand nothing, they are in tatters; there is the great uproar of the world. However pathetic they may be in their garbage can, they have their very own little zone. What the great Molloy calls "my properties." He no longer moves, he has his little hook and, in a strip of one meter, with his hook, he grabs things, his properties. It's a clear and distinct zone that he expresses. We are all the same. But our zone is more or less sizable, and even then it's not certain, but it is never the same. What is it that determines the point of view?

It's the proportion of the region of the world expressed clearly and distinctly by an individual in relation to the totality of the world expressed obscurely and confusedly. That's what point of view is.

Leibniz has a metaphor that he likes: you are near the sea and you listen to waves. You listen to the sea and you hear the sound of a wave. I hear the sound of a wave, that is, I have an apperception: I distinguish a wave. And Leibniz says: you would not hear the wave if you did not have a minute unconscious perception of the sound of each drop of water that slides over and through another, and that makes up the object of minute perceptions. There is the roaring of all the drops of water, and you have your little zone of clarity, you clearly and distinctly grasp one partial result from this infinity of drops, from this infinity of roaring, and from it, you make your own little world, your own property.

Each individual notion has its point of view, that is from this point of view, it extracts from the aggregate of the world that it expresses a determined portion of clear and distinct expression. Given two individuals, you have two cases: either their zones do not communicate in the least, and create no symbols with one another -- there aren't merely direct communications, one can conceive of there being analogies -- and in that moment, they have nothing to say to each other; or it's like two circles that overlap: there is a little common zone, there we can do something together. Leibniz thus can say quite forcefully that no two individual substances have the same point of view or exactly the same clear and distinct zone of expression. And finally, Leibniz's stroke of genius: what will define the clear and distinct zone of expression that I have? I express the totality of the world, but I only express clearly and distinctly a reduced portion of it, a finite portion. What I express clearly and distinctly, Leibniz tells us, is what relates to my body. We will see what this body means, but what I express clearly and distinctly is that which affects my body.

Thus I obviously do not express clearly and distinctly the passage of the Rubicon, since that concerned Caesar's body. There is something that concerns my body and that only I express clearly and distinctly, in relation to this buzz that covers the entire universe.

In this story of the city, there is a problem. OK, there are different points of view. These points of view preexist the subject who is placed there, good. In this event, the secret of point of view is mathematical, geometrical, and not psychological. It's at the least psycho-geometrical. Leibniz is a man of notions, not a man of psychology. But everything urges me to say that the city exists outside points of view. But in my story of expressed world, in the way we started off, the world has no existence outside the point of view that expresses it; the world does not exist in itself. The world is uniquely the common expressed of all individual substances, but the expressed does not exist outside that which expresses it. The world does not exist in itself, the world is uniquely the expressed.

The entire world is contained in each individual notion, but it exists only in this inclusion. It has no existence outside. It's in this sense that Leibniz will be, and not incorrectly, on the side of the idealists: there is no world in itself, the world exists only in the individual substances that express it. It's the common expressed of all individual substances. It's the expressed of all individual substances, but the expressed does not exist outside the substances that express it. It's a real problem!

What distinguishes these substances is that they all express the same world, but they don't express the same clear and distinct portion. It's like chess. The world does not exist. It's the complication of the concept of expression. Which is going to provide this final difficulty. Still it is necessary that all individual notions express the same world. So it's curious -- it's curious because by virtue of the principle of identity that permits us to determine what is contradictory, that is, what is impossible, it's A is not A. It's contradictory: example: the squared circle. A squared circle is a circle that is not a circle. So starting from the principle of identity, I can have a criterion of contradiction. According to Leibniz, I can demonstrate that 2 + 2 cannot make 5, I can demonstrate that a circle cannot be squared. Whereas, on the level of sufficient reason, it's much more complicated, why? Because Adam the non-sinner, Caesar not crossing the Rubicon, is not like the squared circle. Adam the non-sinner is not contradictory. Understand how he's going to try to save freedom, once he has placed himself in a bad situation for saving it. This is not at all impossible: Caesar could have not crossed the Rubicon, whereas a circle cannot be squared; here, there is no freedom.
(From: Charles J. Stivale's translation of Richard Pinhas' transcription of Gilles Deleuze's lecture series on Leibniz; Lecture One, 15/04/1980).

The translation of this series can be found at:

GILLES DELEUZES' LECTURE SERIES ON LEIBNIZ;

Gilles Deleuze. "Sur Leibniz. April 15, 1980."

Gilles Deleuze. "Sur Leibniz. April 22, 1980."

Gilles Deleuze. "Sur Leibniz. April 29, 1980."

Gilles Deleuze. "Sur Leibniz. May 6, 1980."

Gilles Deleuze. "Sur Leibniz. May 20, 1980."

(I recommend this entire series to anyone interested in non-metrical image writing; there are many useful concepts here, and they are brilliantly explained).

So for Leibniz, points of view define the observer. Can we use this definition? Certainly. To say that a conceptual persona constitutes a point of view does not preclude what Leibniz wants to say; we are simply saying here that planes of immanence are defined by points of view, and that this act of definition takes place through conceptual personae. “Planes of immanence and conceptual personae presuppose each other”…a presupposition which implies point of view. To be precise: planes of immanence are co-extensive with conceptual personae; and such co-extension can be characterized through points of view.

One can object that Leibniz is describing an idealist philosophy, which does not include a real, objective world. However, that isn't much of a drawback for us here because, non-metrical image writing presents a world that no longer exists; and, in some cases, a world that hasn't existed for tens of thousands of years. So, in this respect, Leibniz's description of a perspectivalist philosophy works perfectly well for what we want to use it for. Again, we will not be thinking here in terms of ‘subject’ and ‘object’, but in terms of territory and earth. In other words, we will be considering territory and earth as co-extensive, with territory being intended and the earth being extended.

For our purposes here, it makes a lot of sense to say that perspectivalistic points of view create positions in which we can localize conceptual personae. Specifically, points of view allow us to define the intensive ordinates through which concepts are defined. Using intensive ordinates to define concepts then allows us to move from durations to event horizons, which are territorial aspects co-extensive with the earth.

Certainly, it isn't difficult to see how the perspectivalism of a point of view would first be implicit in the production of diagrammatic features. Or, that every perspective utilizes a virtual point, the vanishing point of its relativizing horizon. This isn't the event horizon where we define concepts; but then, we are not yet working with concepts when we are dealing with diagrammatic features. That comes later. Virtual points are essential to relativizing horizons, and so the points of view that constitute the truths of essence which characterize the earth are always relativizing. Event horizons can be considered to be absolute in that, as with points of view, they are implicit in and define all truths of existence. From this point of view, we might say that conceptual personae are absolutely free relative to the earth (but we would be making a philosophic joke).

(In that human consciousness is co-extensive with itself, people can be said to be self-conscious. It is self-consciousness which distinguishes that separation found between humans and the rest of the animals; but it is human intersubjectivity that truly defines that which distinguishes humans from all other animals.

Animals, for their part, maintain an existential immediacy in their experience of the world that humans have, to a certain extent, abandoned. Ironically, those endeavors which humans value most highly - science, art, philosophy, etc. - are the very devices whereby we seek to regain something of a direct access to the fundamental nature of reality.

Of course, as well as any aspect of these greatest of human accomplishments successfully functions in grasping consistencies and connectivities from the chaos of the real...well, such insights are always produced and established (by necessity) before they become intersubjective.

Intersubjectivity isn't just the co-extensive field of social forces where the consistencies and connectivities of the real are made conjunctive with those co-extensions of human consciousness which initially discern them; it is also the field of forces where social power is expressed. The nature of self-consciousness, as co-extension, also becomes the intersubjectivity of social organization; and this can be seen in the organizational functions of everything from politics to religion (instead of holding your consciousness as co-extensive with itself, you can make it co-extensive with Jesus, or Buddha, or the leader of any political party you desire to identify and associate with): from the singular gods and religious leaders of world-wide systems of moral dictates, to the psychotic demands of small cult leaders...and from large political parties, to petty back-room egoists.

SO: to say that humans are "absolutely free relative to the earth" is, at this stage of our development, more to say that "we are quite capable of self and mass delusion" than it is to say, that "we are capable of sustaining ourselves irregardless of the earth's condition".

This is why post-structural philosophy places such an emphasis upon the creation of new concepts...as well as the deconstruction of existing concepts: because the ONLY way to be aware of political manipulations in the intersubjective field of social forces is by becoming aware of how the co-extensive nature of human consciousness grasps its connectivities of consistency from the chaos of the real.

Oh; and, need I point out here that the fact that my research has been politically suppressed in Canada, in order to prevent it from becoming intersubjectively known, in no way challenges or discounts the validity of my findings?)

Such virtual points aren't actually there, as distinct and distinguishable points of sensory contrast; but we are free to think of them as if they were.

Similarly, we can also find great variance in points of view as they are related to truths of existence. Here, this variance is most adequately expressed in terms of partiality: in terms of the relativized existence which characterizes absolute differences in kind (between kinds of things, beings, and events). In so thinking such virtual points and partial objects, we are fulfilling one function of a conceptual personae as a 'distinct operator'...as did those people who produced the non-metrical images we are considering. What we are doing here is no less than defining the co-extensive nature of thought itself; and in doing so we are seeking to reconstruct the resonant consistencies that formed of the co-extensions between existential territoriality, and an earth which is essential to any concept of territory.

A "distinct operator", as a conceptual persona, is precisely localized in those conceptual functions which associate the virtual points of diagrammatic features with the partial objects that define intensive ordinates.

Toward Geophilosophy

Thus, whenever we can find any virtual points functionally linked (in a grammatological sense, within non-metrical image writing) with partial objects, we will have found a position characteristic of conceptual personae.

(This would, of course, work PARTICULARLY well if one were able to define the virtual points associated with the diagrammatic features presented through a system used in the [First Nations' traditional] mapping of territory; and if one were then to correlate such virtual points with the partial objects associated with the intensive ordinates that are co-presented through an event-language such as non-metrical image writing. Then, we would not only be able to define relevant conceptual personae; we would also be able to construct the geophilosophy which these conceptual personae held in relation to the territories in which they lived. And that, for a post-structural philosopher, would be quite a bit of fun! I think that this would also be of interest to the First Nations, as it would help to explain to non-Aboriginals the traditional role of Hereditary Chiefs).

We should also note that for Leibniz, there are two types of truth: truths of essence, which can only be so (as they are); and truths of existence, which might always be otherwise (than how they actually occur). Leibniz is primarily concerned with truths of essence, as they apply to mathematical determinations: and to invariate rules of logical definition as they apply to identity (A=A). Truths of existence, as they apply to contingent situations which are not necessarily as they came to become, are another case altogether.

This distinction by Leibniz corresponds to a distinction that we noted earlier, in relation to shifts between event horizons. So, we can say that the inherent nature of temporality, which is common to different event horizons, is of the nature of a truth of essence. Truths of existence, on the other hand, can indeed be contradictory; and this is what (in part) distinguishes between different event horizons. In order for occurrences to be common to an event horizon, Leibniz would say that as truths of existence, they must be compossible. It is not enough for an event to be possible, it must also be possible with other occurrences upon the same event horizon.

Thus, with the constructs we have termed meta-stabilities, we often find that the concepts which are co-expressed within a non-metrical assemblage are non-compossible. One pattern of grouping might present a smiling face; another, a frowning face. This demonstrates to us how shifts between event horizons can produce meta-narratives in ways that are more easily determinable than (but subject to the same grammatological rules as) those produced by partial indeterminacies within sensory contrasts. Shifts in event horizons caused by the partial indeterminacies of sensory contrasts are essential, and so relativize conceptual personae by way of points of view; and points of view can be common to absolutely differing event horizons. An indeterminacy of sensory contrasts produces essentially meta-stable assemblages which relativize event horizons; but the absolute differences of separable event horizons express the existential truths of temporal existence. Meta-stabilities present endoconsistencies characteristic to variances in kind, as truths of essence. Event horizons present exoconsistencies characteristic to variances of kind, as truths of existence. Meta-stabilities are assemblages which present the variant structures of event horizons; meta-narratives are differential compositions. Meta-narratives, as compositional, are inclusive of all possible linkages and disjunctions.

Thus, the functional effects of partiality are also evident within event horizon shifts localized to meta-stabilities; here, the partiality of objects defines such shifts. It is this partiality which, when expressed as variance of (within) kind, provides the differential shifts found within specifically identifiable event horizons. Partial indeterminacy, however, tends to provide the essential differentiation between event horizons within meta-narratives. Event horizons are the differential variance of transitional phase found in shifts between meta-stabilities and meta-narratives.

As a quick review of what we are referring to when talking about partial objects, let's return for a moment to the section entitled "About Schizo-Analysis", which is appended to the second section entitled "What Is Non-Metrical Image Writing?"...
(Full text located at: About Schizo-Analysis).

"So, there is no desire, says Deleuze, that does not flow into an assemblage, and for him, desire has always been a constructivism, constructing an assemblage (agencement), an aggregate: the aggregate of the skirt, of a sun ray, of a street, of a woman, of a vista, of a color... constructing an assemblage, constructing a region, assembling. Deleuze emphasizes that desire is constructivism. Parnet asks if it's because desire is an assemblage that Deleuze needed to be two, with Guattari, in order to create. Deleuze agrees that with Felix, they created an assemblage, but that there can be assemblages all alone as well as with two, or something passing between two. All of this, he continues, concerns physical phenomena, and for an event to occur, some differences of potential must arise, like a flash or a stream, so that the domain of desire is constructed. So every time someone says, I desire this or that, that person is in the process of constructing an assemblage, nothing else, desire is nothing else...

So, Deleuze continues, on the level of theory, these misunderstandings -- spontaneity or la fête -- were not the so-called philosophy of desire, which was rather: don't go get psychoanalyzed, stop interpreting, go construct and experience/ experiment with assemblages, search out the assemblages that suit you. What is an assemblage, he asks? It's not what they thought it was, but for Deleuze, an assemblage has four components or dimensions:

1) Assemblages referred to "states of things", so that each of us might find the "state of things" that suit us (he gives the example of drinking, even just drinking coffee, and that we find that "coffee drinking" that suits us as a "state of thing").

2) "Les énoncés", little statements, as kinds of style, each of us finding a kind of style of enunciation (he refers again to the Russian revolution's aftermath, with again finding a style of cinema; or new types or styles of enunciation following of May '68).

3) An assemblage implicates territories, each of us chooses or creates a territory, even just walking into a room.

4) An assemblage also implicates processes of deterritorialization, movements of deterritorialization.

It's within these components that desire flows, says Deleuze."
[L'Abécédaire de Gilles Deleuze, avec Claire Parnet
(Gilles Deleuze's ABC Primer, with Claire Parnet)
Directed by Pierre-André Boutang (1996]).

Overview prepared by: Charles J. Stivale,
Romance Languages & Literatures,
Wayne State University.

...which can be viewed here.

Since desire is always an assemblage, its components are always partial. This is to say that any 'object' (or 'conceptualization') of desire is in fact a composite, formed of partial objects. This partiality of objects is an integral aspect of the functional nature of meta-stabilities, and helps to define the compossibility of the event horizons which might shift between various stable compositions within a meta-narrative.

And, since partial objects are also characteristic of desire, they can be defined in terms of their inherent intentionalities. This means that partial objects are indeed indicative of intensive ordinates; and this is why they can be used, along with diagrammatic features, in the co-definition of conceptual personae.

We can further define shifts in the event horizons found within a meta-narrative, when such shifts are the effect of the partiality of objects, as characteristic of truths of existence. This means that such shifts can be differentiated through the principle of compossibility; and that this principle can be used to define the nature of distinct compositions within the meta-narratives which are produced from meta-stabilities in the formation of differential textures.

Shifts in event horizons that are the result of partial indeterminacies within sensory contrasts are characterized by truths of essence. This means that such shifts are defined by logical (necessary) consequence; and as necessary truths, the expressive effects of such shifts are not limited to any particular event horizon. Thus, the differentiations within both meta-stabilities and meta-narratives that are a result of partial indeterminacy within sensory contrasts are held in common throughout meta-stabilities and meta-narratives. They are consistent aspects associated with singularity itself, and structurally apparent through the virtuality of any point which expresses a differentiation within meta-stability or meta-narrative (and thus can be seen to be relativizing).

Such a structurally essential virtuality can occur in many ways:
- as an animal's form which, as a differentiation in kind, is always associated with essential characteristics that are in turn expressed through the contingent truths of existence found within specific events involving specific animals (partial indeterminacy of a specific animal's essential kind is always apparent in non-metrical image writing: a nice, plump bunny rabbit seen sitting on its haunches from a distance might prove, upon closer examination, to be the head of a saber tooth tiger that is lying on its back);
- as the necessary geometric properties of a specific shape, the virtual points common to partially indeterminate (not fully defined) geometric forms (in perspectivism, circularity, image-areas, etc.);
- and, some very interesting variations upon such essential virtualities of structure that I won't go into here.

Instead, I will again refer to Deleuze's lecture series on Leibniz, and a very instructive description of the relationship between singularities and sensory contrasts found therein:

"All this together consists in saying: look at the kind of relationship between singular and ordinary, such that you are going to define the singular as a function of curvilinear problems in relation to differential calculus, and in this tension or opposition between singular point and ordinary point, or singular point and regular point. This is what mathematicians provide us with as basic material, and yet again if it is true that in the simplest cases, the singular is the extremity, in other simple cases, it’s the maximum or the minimum or even both at once. Singularities there develop more and more complex relations on the level of more and more complex curves.

I hold onto the following formula: a singularity is a distinct or determined point on a curve, it’s a point in the neighborhood of which the differential relation changes its sign, and the singular point’s characteristic is to extend itself into the whole series of ordinary points that depend on it all the way to the neighborhood of subsequent singularities. So I maintain that the theory of singularities is inseparable from a theory or an activity of extension.

Wouldn’t these be elements for a possible definition of continuity? I’d say that continuity or the continuous is the extension of a remarkable point onto an ordinary series all the way into the neighborhood of the subsequent singularity. With this, I’m very pleased because at last, I have an initial hypothetical definition of what the continuous is. It’s all the more bizarre since, in order to reach this definition of the continuous, I used what apparently introduces a discontinuity, notably a singularity in which something changes. And rather than being the opposite, it’s the discontinuity that provides me with this approximate definition.

Leibniz tells us that we all know that we have perceptions, that for example, I see red, I hear the sea. These are perceptions; moreover, we should reserve a special word for them because they are conscious. It’s perception endowed with consciousness, that is, perception perceived as such by an "I", we call it apperception, as a-perceiving. For, indeed, it’s perception that I perceive. Leibniz tells us that consequently there really have to be unconscious perceptions that we don’t perceive. These are called minute perceptions, that is, unconscious perception. Why is this necessary? Why necessary? Leibniz gives us two reasons: it’s that our a-perceptions, our conscious perceptions are always global. What we perceive is always a whole. What we grasp through conscious perception is relative totalities. And it is really necessary that parts exist since there is a whole. That’s a line of reasoning that Leibniz constantly follows: there has to be something simple if there is something composite, he builds this into a grand principle; and it doesn’t go without saying, do you understand what he means? He means that there is no indefinite, and that goes so little without saying that it implies the actual infinite. There has to be something simple since there is something composite. There are people who will think that everything is composite to infinity, and they will be partisans of the indefinite, but for other reasons, Leibniz thinks that the infinite is actual. Thus, there has to be something (word missing in transcript, probably ‘simple’). Henceforth, since we perceive the global noise of the sea when we are seated on the beach, we have to have minute perceptions of each wave, as he says in summary form, and moreover, of each drop of water. Why? It’s a kind of logical requirement, and we shall see what he means.

He pursues the same reasoning on the level of the whole and the parts yet again as well, not by invoking a principle of totality, but a principle of causality: what we perceive is always an effect, so there have to be causes. These causes themselves have to be perceived, otherwise the effect would not be perceived. In this case, the tiny drops are no longer the parts that make up the wave, nor the waves the parts that make up the sea, but they intervene as causes that produce an effect. You will tell me that there is no great difference here, but let me point out simply that in all of Leibniz’s texts, there are always two distinct arguments that he is perpetually trying to make coexist: an argument based on causality and an argument based on parts. Cause-effect relationship and part-whole relationship. So this is how our conscious perceptions bathe in a flow of unconscious minute perceptions.

On the one hand, this has to be so logically, in accordance with the principles and their requirement, but the great moments occur when experience comes to confirm the requirement of great principles. When the very beautiful coincidence of principles and experience occurs, philosophy knows its moment of happiness, even if it’s personally the misfortune of the philosopher. And at that moment, the philosopher says: everything is fine, as it should be. So it is necessary for experience to show me that under certain conditions of disorganization in my consciousness, minute perceptions force open the door of my consciousness and invade me. When my consciousness relaxes, I am thus invaded by minute perceptions that do not become for all that conscious perceptions. They do not become apperceptions since I am (only) invaded in my consciousness when my consciousness is disorganized. At that moment, a flow of minute unconscious perceptions invades me. It’s not that these minute perceptions stop being unconscious, but it’s me who ceases being conscious. But I live them, there is an unconscious lived experience. I do not represent them, I do not perceive them, but they are there, they swarm in these cases. I receive a huge blow on the head: dizziness is an example that recurs constantly in Leibniz’s work. I get dizzy, I faint, and a flow of minute unconscious perceptions arrives: a buzz in my head. Rousseau knew Leibniz, he will undergo the cruel experience of fainting after having received a huge blow, and he relates his recovery and the swarming of minute perceptions. It’s a very famous text by Rousseau in the Reveries of a Solitary Stroller (Reveries d’un promeneur solitaire), which is the return to consciousness...

Do we have to say that only about perception? No. And there, once again, appears Leibniz’s genius. There is a psychology with Leibniz’s name on it, which was one of the first theories of the unconscious. I have already said almost enough about it for you to understand the extent to which it’s a conception of the unconscious that has absolutely nothing to do with Freud’s which is to say how much innovation one finds in Freud: it’s obviously not the hypothesis of an unconscious that has been proposed by numerous authors, but it’s the way in which Freud conceived the unconscious. And, in the lineage from Freud some very strange phenomena will be found, returning to a Leibnizian conception, but I will talk about that later.

But understand that he simply cannot say that about perception since, according to Leibniz, the soul has two fundamental faculties: conscious apperception which is therefore composed of minute unconscious perceptions, and what he calls "appetition", appetite, desire. And we are composed of desires and perceptions. Moreover, appetition is conscious appetite. If global perceptions are made up of an infinity of minute perceptions, appetitions or gross appetites are made up of an infinity of minute appetitions. You see that appetitions are vectors corresponding to minute perceptions, and that becomes a very strange unconscious. The drop of sea water to which the droplet corresponds, to which a minute appetition corresponds for someone who is thirsty. And when I say, "my God, I’m thirsty, I’m thirsty," what do I do? I grossly express a global outcome of thousands of minute perceptions working within me, and thousands of minute appetitions that crisscross me. What does that mean?

In the beginning of the twentieth century, a great Spanish biologist fell into oblivion; his name was Turro. He wrote a book entitled in French: The Origins of Knowledge (L’Origine de la Connaissance) (1914), and this book is extraordinary. Turro said that when we say "I am hungry" ? his background was entirely in biology -- and we might say that it’s Leibniz who has awakened-- and Turro said that when one says, "I am hungry," it’s really a global outcome, what he called a global sensation. He uses his concepts: global hunger and minute specific hungers. He said that hunger as a global phenomenon is a statistical effect. Of what is hunger composed as a global substance? Of thousands of minute hungers: salt hunger, protein substance hunger, grease hunger, mineral salts hunger, etc. . . . When I say, "I’m hungry," I am literally undertaking, says Turro, the integral or the integration of these thousands of minute specific hungers. The minute differentials are differentials of conscious perception; conscious perception is the integration of minute perceptions. Fine. You see that the thousand minute appetitions are the thousand specific hungers. And Turro continues since there is still something strange on the animal level: how does an animal know what it has to have? The animal sees sensible qualities, it leaps forward and eats it, they all eat minute qualities. The cow eats green, not grass, although it does not eat just any green since it recognizes the grass green and only eats grass green. The carnivore does not eat proteins, it eats something it saw, without seeing the proteins. The problem of instinct on the simplest level is: how does one explain that animals eat more or less anything that suits them? In fact, animals eat during a meal the quantity of fat, of salt, of proteins necessary for the balance of their internal milieu. And their internal milieu is what? It’s the milieu of all the minute perceptions and minute appetitions.

What a strange communication between consciousness and the unconscious. Each species eats more or less what it needs, except for tragic or comic errors that enemies of instinct always invoke: cats, for example, who go eat precisely what will poison them, but quite rarely. That’s what the problem of instinct is.

This Leibnizian psychology invokes minute appetitions that invest minute perceptions; the minute appetition makes the psychic investment of the minute perception, and what world does that create? We never cease passing from one minute perception to another, even without knowing it. Our consciousness remains there at global perceptions and gross appetites, "I am hungry," but when I say "I am hungry," there are all sorts of passages, metamorphoses. My minute salt hunger that passes into another hunger, a minute protein hunger; a minute protein hunger that passes into a minute fat hunger, or everything mixed up, quite heterogeneously. What causes children to be dirt eaters? By what miracle do they eat dirt when they need the vitamin that the earth contains? It has to be instinct! These are monsters! But God even made monsters in harmony...

So there is an unconscious defined by minute perceptions, and minute perceptions are at once infinitely small perceptions and the differentials of conscious perception. And minute appetites are at once unconscious appetites and differentials of conscious appetition. There is a genesis of psychic life starting from differentials of consciousness.

Following from this, the Leibnizian unconscious is the set of differentials of consciousness. It’s the infinite totality of differentials of consciousness. There is a genesis of consciousness.

The idea of differentials of consciousness is fundamental. The drop of water and the appetite for the drop of water, specific minute hungers, the world of fainting. All of that makes for a very funny world.

I am going to open a very quick parenthesis. That unconscious has a very long history in philosophy. Overall, we can say that in fact, it’s the discovery and the theorizing of a properly differential unconscious. You see that this unconscious has many links to infinitesimal analysis, and that’s why I said a psycho-mathematical domain. Just as there are differentials for a curve, there are differentials for consciousness. The two domains, the psychic domain and the mathematical domain, project symbols.If I look for the lineage, it’s Leibniz who proposed this great idea, the first great theory of this differential unconscious, and from there it never stopped. There is a very long tradition of this differential conception of the unconscious based on minute perceptions and minute appetitions. It culminates in a very great author who, strangely, has always been poorly understood in France, a German post-Romantic named Fechner. He’s a disciple of Leibniz who developed the conception of differential unconscious...

Thus our conscious perception is composed of an infinity of minute perceptions. Our conscious appetite is composed of an infinity of minute appetites. Leibniz is in the process of preparing a strange operation, and were we not to restrain ourselves, we might want to protest immediately. We could say to him, fine, perception has causes, for example, my perception of green, or of any color, that implies all sorts of physical vibrations. And these physical vibrations are not themselves perceived. Even though there might be an infinity of elementary causes in a conscious perception, by what right does Leibniz conclude from this that these elementary causes are themselves objects of infinitely minute perceptions? Why? And what does he mean when he says that our conscious perception is composed of an infinity of minute perceptions, exactly like perception of the sound of the sea is composed of the perception of every drop of water?

If you look at his texts closely, it’s very odd because these texts say two different things, one of which is manifestly expressed by simplification and the other expresses Leibniz’s true thought. There are two headings: some are under the Part-Whole heading, and in that case, it means that conscious perception is always one of a whole, this perception of a whole assuming not only infinitely minute parts, but assuming that these infinitely small parts are perceived. Hence the formula: conscious perception is made of minute perceptions, and I say that, in this case, "is made of" is the same as "to be composed of." Leibniz expresses himself in this way quite often. I select a text: "Otherwise we would not sense the whole at all". . . if there were none of these minute perceptions, we would have no consciousness at all. The organs of sense operate a totalization of minute perceptions. The eye is what totalizes an infinity of minute vibrations, and henceforth composes with these minute vibrations a global quality that I call green, or that I call red, etc. . . . The text is clear, it’s a question of the Whole-Parts relationship. When Leibniz wants to move rapidly, he has every interest in speaking like that, but when he really wants to explain things, he says something else, he says that conscious perception is derived from minute perceptions. It’s not the same thing, "is composed of" and "is derived from". In one case, you have the Whole-Parts relationship, in the other, you have a relationship of a completely different nature. What different nature? The relation of derivation, what we call a derivative. That also brings us back to infinitesimal calculus: conscious perception derives from the infinity of minute perceptions. At that point, I would no longer say that the organs of sense totalize. Notice that the mathematical notion of integral links the two: the integral is what derives from and is also what operates an integration, a kind of totalization, but it’s a very special totalization, not a totalization through additions. We can say without risk of error that although Leibniz doesn’t indicate it, it’s even the second texts that have the final word. When Leibniz tells us that conscious perception is composed of minute perceptions, this is not his true thinking. On the contrary, his true thinking is that conscious perception derives from minute perceptions. What does "derive from" mean?

Here is another of Leibniz’s texts: "Perception of light or of color that we perceive, that is, conscious perception ? is composed of a quantity of minute perceptions that we do not perceive, and a noise that we do not perceive, and a noise that we do perceive but to which we give no attention becomes a-perceptible, i.e. passes into the state of conscious perception, through a minute addition or augmentation."

We no longer pass minute perceptions into conscious perception via totalization as the first version of the text suggested; we pass minute perceptions into global conscious perception via a minute addition. We thought we understood, and suddenly, we no longer understand a thing. A minute addition is the addition of a minute perception; so we pass minute perceptions into global conscious perception via a minute perception? We tell ourselves that this isn’t right. Suddenly, we tend to fall back on the other version of the text, at least that was more clear. More clear, but insufficient. Sufficient texts are sufficient, but we no longer understand anything in them. A wonderful situation, except if we chance to encounter an adjoining text in which Leibniz tells us: "We must consider that we think a quantity of things all at once. But we pay attention only to thoughts that are the most distinct . . ."

For what is "remarkable" must be composed of parts that are not remarkable ? there, Leibniz is in the process of mixing up everything, but on purpose. We who are no longer innocent can situate the word "remarkable," and we know that each time that he uses "notable", "remarkable", "distinct", it’s in a very technical sense, and at the same time, he creates a muddle everywhere. For the idea that there is something clear and distinct, since Descartes, was an idea that circulated all over. Leibniz slides in his little "distinct", the most distinct thoughts. Understand "the distinct," "the remarkable," "the singular." So what does that mean? We pass from minute unconscious perception to global conscious perception through a minute addition. So obviously, this is not just any minute addition. This is neither another conscious perception, nor one more minute unconscious perception. So what does it mean? It means that your minute perceptions form a series of ordinaries, a series called regular: all the minute drops of water, elementary perceptions, infinitesimal perceptions. How do you pass into the global perception of the sound of the sea?

First answer: via globalization-totalization. Commentators answer: Fine, it’s easy to say. One would never thinking of raising an objection. You have to like an author just enough to know that he’s not mistaken, that he speaks this way in order to proceed quickly.

Second answer: I pass via a minute addition. This cannot be the addition of a minute ordinary or regular perception, nor can it be the addition of a conscious perception since at that point, consciousness would be presupposed. The answer is that I reach a neighborhood of a remarkable point, so I do not operate a totalization, but rather a singularization. It’s when the series of minute perceived drops of water approaches or enters into the neighborhood of a singular point, a remarkable point, that perception becomes conscious.

It’s a completely different vision because at that moment, a great part of the objections made to the idea of a differential unconscious falls away. What does that mean? Here appear the texts by Leibniz that seem the most complete. From the start, we have dragged along the idea that with minute elements, it’s a manner of speaking because what is differential are not elements, not dx in relation to an x, because dx in relation to an x is nothing. What is differential is not a dy in relation to a y because dy in relation to a y is nothing.

What is differential is dy/dx, this is the relation.

That’s what is at work in the infinitely minute.

You recall that on the level of singular points, the differential relation changes its sign.

You recall that on the level of singular points, the differential relation changes its sign. Leibniz is in the process of impregnating (engrosser) Freud without knowing it. On the level of the singularity of increases or decreases, the differential relation changes it sign, that is, the sign is inverted. In this case of perception, which is the differential relation? Why is it that these are not elements, but indeed relations? What determines a relation is precisely a relationship between physical elements and my body. So you have dy and dx. It’s the relation of physical excitation to my biological body. You understand that on this level, we can no longer speak exactly of minute perceptions. We will speak of the differential relation between physical excitation and the physical state by assimilating it frankly to dy/dx, it matters little.

And perception becomes conscious when the differential relation corresponds to a singularity, that is, changes its sign.

For example, when excitation gets sufficiently closer.

It’s the molecule of water closest to my body that is going to define the minute increase through which the infinity of minute perceptions becomes conscious perception. It’s no longer a relation of parts at all, it’s a relation of derivation. It’s the differential relation between that which excites and my biological body that is going to permit the definition of the singularity’s neighborhood. Notice in which sense Leibniz could say that inversions of signs, that is, passages from consciousness to the unconscious and from the unconscious to consciousness, the inversions of signs refer to a differential unconscious and not to an unconscious of opposition.

When I alluded to Freud’s posterity, in Jung, for example, there is an entire Leibnizian side, and what he reintroduces, to Freud’s greatest anger, and it’s in this that Freud judges that Jung absolutely betrayed psychoanalysis, is an unconscious of the differential type. And he owes that to the tradition of German Romanticism which is closely linked also to the unconscious of Leibniz.

So we pass from minute perceptions to unconscious perception via addition of something notable, that is, when the series of ordinaries reaches the neighborhood of the following singularity, such that psychic life, just like the mathematical curve, will be subject to a law which is that of the composition of the continuous.

There is composition of the continuous since the continuous is a product: the product of the act by which a singularity is extended into the neighborhood of another singularity. And that this (product) works not only upon the universe of the mathematical symbol, but also upon the universe of perception, of consciousness, and of the unconscious.

From this point onward, we have but one question: what are the compossible and incompossible? These derive directly from the former. We possess the formula for compossibility. I return to my example of the square with its four singularities. You take a singularity, it’s a point; you take it as the center of a circle. Which circle? All the way into the neighborhood of the other singularity. In other words, in the square abcd, you take *a* as center of a circle that stops or whose periphery is in the neighborhood of singularity *b*. You do the same thing with *b*: you trace a circle that stops in the neighborhood of the singularity *a* and you trace another circle that stops in the neighborhood of singularity *c*. These circles intersect. You go on like that constructing, from one singularity to the next, what you will be able to call a continuity. The simplest case of a continuity is a straight line, but there is also precisely a continuity of non-straight lines. With your system of circles that intersect, you will say that there is continuity when the values of two ordinary series, those of *a* to *b*, those of *b* to *a*, coincide. When there is a coincidence of values of two ordinary series encompassed in the two circles, you have a continuity. Thus you can construct a continuity made from continuity. You can construct a continuity of continuity, for example, the square. If the series of ordinaries that derive from singularities diverge, then you have a discontinuity.
(From: Charles J. Stivale's translation of Richard Pinhas' transcription of Gilles Deleuze's lecture series on Leibniz; Lecture Three, 15/04/1980).

GILLES DELEUZES' LECTURE SERIES ON LEIBNIZ;

Located at:

Gilles Deleuze. "Sur Leibniz. April 15, 1980."

Gilles Deleuze. "Sur Leibniz. April 22, 1980."

Gilles Deleuze. "Sur Leibniz. April 29, 1980."

Gilles Deleuze. "Sur Leibniz. May 6, 1980."

We noted briefly in our passing considerations of Husserl and intentionality that the neuro-mechanical parameters of sensory perception functionally structure our conscious expression of desire, as intentionality. So too, truths of essence are structurally implicated in the expression given to truths of existence. Thus virtual points, although distinct from partial objects, co-define conceptual personae; with the virtuality of points being associated with truths of essence, and partial objects with truths of existence.

This relationship can further be defined, by expressing matters pertaining to the earth as truths of essence; and matters pertaining to any territory defined upon the earth, as truths of existence. Transitions of territoriality (deterritorialization, as well as reterritorialization) can be either relative, or absolute.

Simply put, then, conceptual personae functionally operate within non-metrical image writing as geophilosophers who link the virtual points of diagrammatic features (as truths of essence) with the partial objects of intensive ordinates (as truths of existence). Through this function, they think the linkages that form within their lives between the earth they live upon (as truth of essence), and the territory they define by living within (as truth of existence).

As it so happens, this could also serve as a functional description of the traditional role played by the Hereditary Chiefs within First Nations culture.

It is not the role played by archaeologists and anthropologists.

I should also add here that, by conceptual personae, we are not referring to anything like a Jungian "archetype" or a "Tarot card": conceptual personae are all about DIFFERENCE, not identity; there are no limits to the number of conceptual personae, for they are as infinite as the concepts they are associated with.

TO SUMMARIZE: in reading non-metrical image writing, we will be experiencing how the co-extensive nature of consciousness (as expressed through the conceptual personae of those who produced this form of writing) grasped, from the chaos of the real, resonant consistencies holding as co-extensive between the earth on which they lived, and the territorializations through which they lived.

"Subject and object give a poor approximation of thought. Thinking is neither a line drawn between subject and object nor a revolving of one around the other. Rather, thinking takes place in the relationship of territory and earth..."
Gilles Deleuze and Felix Guattari, in the section "Geophilosophy",
pages 85-86 of WHAT IS PHILOSOPHY,
translation copyright 1994 by Columbia University Press.

An Interpretive Application of Post Structural, Grammatological Analysis, With Reference to an Actual Example of Non-Metrical Image Writing.