Delfold

These represent stable, unstable,neutral and metastable equilibria respectively. There is also reference to a 'caternary' curve -- that formed when a chain (caternaria) is suspsended from either end -- could be stable equilibrium as above but with a different curve.The point is that this notion leads on to all sorts of modern stuff about vectors and attractors, and the terminiology used in DeLanda, like states of systemts etc.

We are going to 'solve' the problem of linking the two levels or floors using dogmatism or incoherence as ever. There will be God or a magic substance -- vinculum subtantiale -- as well as the usual slippery and ambiguous definitions etc].

We start with Leibniz arguing that totalities are not just collectives, not just names. There is the notion of the collectivity which depends on shared or distributed individual qualities. Monads, for example, are a collective in that they share the same relation to the world. They are 'each, or every one for itself, while [other, external, material] bodies are one, some, or any' (114). Totalities of this kind are distributive, with relations of parts and wholes, as opposed to bodies which are merely aggregates, where one relates to the others [at the same level). The upper floor of the monad, the soul, belongs to the distributive totality.

In the material universe of bodies, we find movement, propagating waves and interactions. Whereas monads express the world, bodies are impressed by other bodies. This gives us two different regimes and two different sorts of cause. Souls are in 'vertical immanent causality' with the world, while bodies are in 'transitive horizontal causality'. In the first case, we find notions of liberty or grace, final causes and moral necessity, in the second one, we find efficient causes, physical laws and only hypothetical necessity '(if one is…, so then the other…)'(115). Yet these two must still be seen as connected, as two halves, We have already noticed that there is primal matter or primal force, arising between the minute perceptions of the monad, differentially related. In this way, the object becomes something 'perceived or the world as expression'. However, we need a different understanding of the other parts, the material part, which is not affected by the pure relations, but by those that produce efficient causes, producing bodies which can only resemble perceptions. Here we are talking about 'empirical laws of second Nature'.

Here we find empirical singularities, like the extremum. Curves are now finite, with definite coordinates, minimum and maximum, not just 'vectors of concavity' that defined inflection and inclusion. We can now determine the position of objects on such curves as effects of efficient causes [the forces at work, like gravity and other extrinsic vectors]. We can calculate particular curves, or contours, measure actual areas, determine movements, including vibrations affected by specific frequencies, and the interactions of 'all kinds of derivative forces, elastic and plastic alike'(116). So there are two equations of the world, one in minds and conceptions, and one in nature itself. How are they related?

For Leibniz they have to be 'concatenated 'or continuous [arising from the monistic and universal nature of God again?], so a calculus applies to both, and so do differential relations, although they do different things—producing 'a maximum of quantity of being' in the first cases, and concrete relations in an equation in the second. The dominant singularity in the material world is the extremum, but the other 3 are also connected, and presuppose it [the other singularities relate to more general properties of curves and have developed the mathematics of curves first?]. In this way, the two floors are related but also different. The upper floor of the baroque house displays weightlessness, the lower floor the 'gravity of mass', and they are connected by vertical transitions 'spiritual elevation and physical gravity'.

Others have talked about the differences between structures and figures [the latter being empirical shapes, as it were, while structures refer to relative positions]. A disciple, Ruyer, insists on the connection, however, in 'substantial or individual forms', although we can work with figures as having an autonomy of their own. The vertical dimension explains the soul of the monad, its ability to survey itself [and reflect], its quality as a superject. [Usual anti positivist sentiments, denying the complete sufficiency of the empirical world and accounting for our ability to vary it in thought -- essential to a critical position says Zizek].

We are not just talking about autonomous objects grasped by conventional subjects, but a notion of self presence, an absolute interiority, that displays self fulfilment and self enjoyment [developing perceptions regardless of material influences from organs or extrinsic forces]. Absolute forms can oversee the whole operation of perception, unconstrained by local linkages, and not just functioning to understand the empirical, but forming themselves. These processes affect not just living organisms but even inorganic particles and molecules, although in different varieties. These forms are the primary forces, or primary unities, and they are 'actualize a virtuality or a potential'. They also have a relation of harmony with each other.

[Then an aside on gestalt theory 117 – 18, explaining the structure of perceived figures and physical structures. A connection is established with a dispute between Leibniz and Newton, which partly turned on the 'critique of vacuum' and notions of attraction. If I recall accurately the discussion in Kuhn (Structure of Scientific Revolutions) , Newton was at odds with those who held a more mechanistic view of the universe—he actually specifies Descartes—who saw a mysterious ether filling the spaces between objects like planets, with forces traversing the ether literally by vibrating adjacent molecules of it. Newton's originally bizarre idea was that the planets actually attracted each other with a mysterious new force, gravity, that operated even across vacuums, without having to transmit vibrations. How it did actually work was clearly a philosophical problem, but physicists cheerfully ignored the problem, eventually anyway. Maybe, Leibniz is on the side of the mechanists here? Deleuze is arguing that, at the time anyway, his notion of thrusts and impulsions instead of attractions works just as well. He says more contemporary uses of 'the laws of extremum' to explain organic phenomena still work with assumptions about preformed paths and abstract forms generally, and if we abandon those, we end with 'linkages without sufficient reason'. However, do we want to preserve the notion of sufficient reason? The whole use of the term 'vibration' in Deleuze, to explain the ways in which one series can affect another, or one point another for that matter, has always struck me as anachronistic. Is Deleuze still using the preNewtonian understanding? If so, why? Does it explain chaosmos better than Newtonian physics? He wold want to go beyond Newton, no doubt -- but why back to mechanicism? He seems evasive here, so we never know if he is giving his opinions, or paraphrasing those of Leibniz, in the famous indirect free discourse].

[For Leibniz] empirical laws relate to collections, masses and organisms, not individual beings and the primary forces that constitute them. They explain the distribution of 'derivative forces', and the distinction is really what is at stake when distinguishing the organic from the inorganic. It is a matter of distinguishing the individual from a collective phenomenon, an absolute form from [empirical] 'massive, molar figures or structures'. Again, these phenomena live on different floors. However, it is individual beings that operate sufficient reason through their forms and primal forces, and it is these that make up collections as secondary. This is not to say that the lower floor is in some way merely secondary and composite, since 'Clearly [!] , one level is folded over the other' (119). The levels have different sorts of folds, creases or 'bends of matter'. The difference between organic and inorganic can be explained in terms of different folds as well. The bends of matter manage to hide their influence on the boundary between the floors, however, while the folds of form on the upper surface are open to self examination, revealing the details 'of an absolute surface that is copresent with all its modifications'. {Shows the limit of 17th century philosophy that had not developed any empirical analysis of social influences on thought?]

We can see this in terms of a virtuality being actualized in the monads. The only way the world can be actualized is in monads, even though this is conveyed through each monad 's point of view. But there is another process at work as well, involving the possible and the real. Once God has chosen the best world, the other worlds are still being actualized in their own monads. In other words, a number of actuals can be possible, without being 'forcibly real'. There is a further stage, where the actual is realised. There is only a possibility of being realized. The issue is still related to the monads and their perceptions, since perceiving, which 'requires a resemblance of the perceived to something' is itself a form of realization [here we go with ambiguous terminology]. Realization arises from something that happens in bodies, that makes bodies themselves real or substantial [another ambiguity is about to be introduced through the notion of substance].

So we have actualization in monads and realization in bodies, but how does the world manage to produce both? What is it that is being actualized and realized? We can perceive and experience events, like a physical blow which my body receives and my soul feels as pain, but what about the other part of the event, the bit that is not realised and actualized? There must be another secret part, 'a neutral singularity, incorporeal as much as impassable', something which originates in all expression and all realizations, the eventum tantum 'a pure virtualityy and possibility...the pure predicate' (120)

[According to Kirkeby (2004) the eventum tantum is 'a concept used by both Heidegger and Deleuze... [Meaning]… "The great events" or "so much of the event"… This concept transcends both ontology and epistemology… [It is] the prototype of the event… that which is beyond Sameness, and hence beyond both the concept of identity, and beyond its negation [similar to the term non-aliud] a term in language, which defines any representational structure. It denotes that it can neither be defined by affirmation and nor by negation… [It] could be a way to grasp the concept of an absolute immanence, a mode of existence, which implies no distinction between "outside" and "inside", between thinking and thought, and between subject and object in a process of time. {Pretty magic substance then, and quite handy in the circumstances} The genuine event is the shape, which absorbs knowing into the known… [Leading to the definition] "that it has everything outside itself, except the knowledge of having everything outside itself. The event is totally dependent and totally autonomous, at the same time'(291 - 2).

One implication seems to be that philosophy should not domesticate this original event with schemas derived from ontology or epistemology, with names, by attempting to make sense—that would not be worthy of the event. Deleuze's example, apparently, makes every event like death, both double and impersonal, almost the negation of the present, offering no form of human relation, so that it becomes impossible to talk about me actually dying, while recognizing that others die [apparently in Logic of Sense]. It is allied to the stoic notion of ascending to fate {which does seem more recognisable in L of S}. Ultimately, at the level of the virtual, there is a relation between the 'sense of the event, the proto events, and the event of sense'(294)].

The world can be seen as 'the "pure" reserve of events that are actualized and realized'. Leibniz requires this preexisting world, this element of the event [since those bits of the events which are expressed and implemented are not the totality— nor do they just add up to the totality], and that there is 'a potential that exceeds the souls that direct it and the bodies that execute it'(121). It is the material universe that is expressive, [Reality 2 as opposed to the normal Reality 1] both to the world and to the soul.

Actualization and realization are different regimes of expression: 'one is distributive where the other is collective'. Actualization by monads is internal and independent of others, while realization at the level of bodies involves relations with other bodies, ultimately, the totality of bodies, the whole material universe. The first process goes from whole to part, from the entire world to a zone of it; the second one relates parts and parts, near to far, from the expression of its related monad, to the zones of expression of others. However, luckily, there is an accord between these regimes, or harmony, between the soul and its body, and therefore between other souls and other bodies in its surroundings.

However, we still have a problem because the soul is an 'each or every,' while the body is a 'one'. What forms the connection between one body and each monad [and here, Deleuze is is going to use the phrase 'appurtenance', which implies possessions]? Leibniz here is engaging in an old debate about the union of the soul and the body, about incarnation. However, harmony might explain the correspondence between each soul and the universe [because this has already been defined as a relation between parts and wholes], but there are still problems explaining the correspondence between the soul and the body. The relation cannot just be an aspect of the body [I'm not sure why, you can define it however the hell you like --maybe this would introduce a hierarchy?]. Instead we need 'a theory of appurtenance', or belonging (122).

Husserl gives us an example of a theory of appurtenance, in the fifth of the Cartesian Meditations [discussing how we know about others] and this refers to Leibniz. For H, the monad is replaced by the ego, the self has a sphere of its possessions, and in that sphere of appurtenance, I can find something that I do not possess, something foreign to me, something objective, an other. Leibniz has a similar strategy, and asks what belongs to me, with the answer that it is all the thoughts of the self, the cogito, and because thoughts are so diverse and changing, the predicates include the entire world as perceived -- or rather the entire world that I express clearly. This is still my world, and I own the primary matter in it, especially my body which I can use and coordinate what is perceived. This body is uniquely extrinsic, however, foreign and objective as above. The difference is that Husserl was to go on to argue that we can apperceive the other as another monad [through the assumption of reciprocal perceptions and so on], but Leibniz had already assumed that there are other monads, and seeing everything outside my clear zone as indicating their existence, as 'a community of monads' [sic]. Together, they express all their clear zones to make up 'a first Nature': there is no need for bodies. Monads do not contain others, but those others can be assumed because we can see their mark in the obscure zones within me. For Leibniz, actully meeting others means encountering a second Nature [something that really does contain unexpected elements?].

Leibniz further [bullshits] by saying that body and soul are both distinct and inseparable. It is a particular kind of harmony and union that produces real distinctions together with inseparability [I am reminded of Durkheim and the hope that organic solidarity would provide a social bond between separate and autonomous individuals]. There is some notion of a general connection with other bodies, because the monad knows them only through resemblance—so its own body must be organic, resembling the body of another man or another animal. Leibniz drags in God to further argue that the body must be organic, that is provided with organs. [Delirium awaits]: the body is made up of an infinite number of material parts collected together, but also able to form organs, as a result of 'crowds of little monads, monads of heart, liver, knee' (123), according to their special zone. These monads belong to parts of my body, and are requisites of it. It then seems to follow that since these little monads are capable of perception, so must my body be [could be wrong here—certainly matter itself is seen as inseparable 'from these little souls capable of perception'].

Overall, Leibniz's theory of appurtenance produces an endless inversion [infinite regression] — monads that have a body are different from monads that are specific requisites of this body, or parts of it, and they in turn possess a body, other than a collection of requisites for another body, and their body 'possesses crowds of tertiary monads' -- and so on. In this way, soul and body are different, but they're always undergoing 'the coming and going between one level and the other', and this defines their inseparability [physical inseparability as opposed to logical inseparability—slippery concepts again].

My body is a collection of smaller monads which are always in flux. Those that once belonged and now depart are only '"pro tempore" prerequisites', nonsymmetrical or temporary ones. The latter produce 'the revelation of a half-other'(124), 'the animal in me as a concrete being'[good Leibnizian grounds for becoming-animal, then]. By contrast, Husserl never sees the human body as decomposable like this, and the animal part of ourselves is only an anomaly [a weird echo of this in volume five of Proust, which I have been reading, where our hero sees illness as reflecting some independent animal-like qualities of the body]. For Leibniz, we have already assumed that there are other human bodies, but it is the animal that now 'springs forth amid my effects'[the organs are seen as animal like], and it follows that our body contains '"an infinity of creatures that are also worthy of life"'[with a reference to a Leibniz letter].

Actual animals are only an enlargement of the smaller ones, producing an animal psychology and an animal monadology, and Leibniz needs this argument. It is difficult for us to know what does belong to us and what does not, and phenomenology is no help here [the example is Beckett's Malone, who apparently has trouble listing his possessions]. However, the notion of possessions becomes important for philosophy, which can now put 'the element of Having in place of that of Being' (125). A list of what things possess helps us classify and develops the notion of Being [apparently, Tarde was on to this, 125]. Leibniz had already been talking about the diverse thoughts of the monad rather than just the act of thinking, and we have already seen how perceptions of predicates, as properties [geddit?] have replaced the notion of attributes. Working out how bodies act involved all sorts of relations among the possessions, including 'inversion, turnaround, precariousness, and temporalization'. This in turn emphasizes continually changing relations among the monads, despite their [spiritual] harmony and union. The final implication is that monads have as their properties not abstract attributes such as 'movements or plasticity', but relations to other monads, some of which they possess [subjugate, dominate, or appropriate], so these are also power relations, and include the power to fold or to contain something. Again, the baroque generally featured 'the crisis of property' (126), with the emergence of new machines or new living beings in the organism.

Appurtenance requires domination, to make little monads cohere to produce my body, and to be able to renew it with new little monads. In spelling out what this domination means, Leibniz envelops the term substantial vinculum, 'a strange linkage, a bracket, a yoke, a knot, a complex relation that comprises variable terms and one constant term' (126). The constant term is the dominant monad, and this vincular relation belongs to it.

This produces problems, however. Other monads are its variable terms, the ones that are dominated, but the dominant monad cannot actually own or contain the others, as predicates of its subject [because no monad can contain the other monads by definition]. Here, we have a relation not of subject and predicate, but one that is substantial. However, every relation must have a subject, so the dominant monad must still be the subject of the substantial vinculum [otherwise, the substantial vinculum must have no subject, and therefore just appear in some free floating way]. We have to get round this by arguing that in this case, the dominant monad is an unusual subject, 'a "subject of adhesion", not of inherent or of inhesion'. This looks like a real problem for Leibniz, 'an almost insufferable paradox', because so far, the notion of a preestablished harmony between the monads has implied no outer relation, 'but only ties regulated on the inside'. The substantial vinculum looks like an extrinsic possession, 'the relation that clearly has the subject, but that is not in its subject, and that is not a predicate' (127). How can the monad, as an absolute interiority, suddenly possess another side, the one that seems important, 'strictly complementary'?

[My notes on Look's article reveals the extent of the apparent contradiction or paradox. Deleuze proposes to resolve it, through magic]. We can think of it in topological terms. The monad is unilateral, closed off by a particular 'torsion of the world, an infinite fold, that can be unwrapped in conformity with the condition [of closure of the monad] only by recovering the other side, not as exterior to the monad, but as the exterior or outside of its own interiority; a partition, a supple and adherent of membrane coextensive with everything inside'[so a magic fold solves the problem, with a magic outside that is also an inside]. This makes the vinculum 'the unlocalisable primary link that borders the absolute interior. [A diagram on page 127 doesn't help, but I reproduce it].

The dominated monads appear in the relation as objects, but they can exist without the relation and vice versa, because the relation belongs to the constant monad and not to them. The relation can actually acquire an infinity of dominated monads. If they escape submission to this vinculum, they are grounded by another one attached to another dominant monad, although they can also be completely free [below] . The vinculum works by first acquiring its variables [the dominated monads] as a mass, although each monad keeps its own individuality, and must do. Then the vinculum 'extracts a "common modification"' (128) [the metaphor is that they form an echo when they are reflected on the surface of a wall. The vinculum itself is the reflecting wall, as a kind of outside of the dominant or constant monad]. In this way, the vinculum produces a mass effect from individual variable monads, producing a collective echo, an amplification of individual whispers [and, particularly mysteriously, 'the passage from optics to acoustics']. This mass acquisition produces an inversion of the normal relations of appurtenance when we consider the relation of the monad to its body. Normally, the body belongs to the monad, but when they are acquired as a mass by a vinculum, they are the ones belonging 'a infinity's material parts that are inseparable from them' [the parts that make up the dominant body?]. The parts are both homogenous, so they can be replaced, and heterogeneous because they play different roles for the dominant body and have to be coordinated.

As a membrane, the vinculum acts as a grid filtering available monads in order to make up organic parts. As parts, the bodies of the variable monads are not the same as the [original, primary, defined] body of a constant monad. This composite organic body possesses the dominant, as 'a body that here finds the determination of its specific unity' [some general body? An actual or real organic body, as opposed to a simpler, predefined one?]. Something else emerges. The vinculum is attached first of all to an individual dominant monad, and helps determine the individual unity of the body that belongs to it—my own specific body. We can presuppose this as a function of the vinculum [by pursuing classic tautological philosophical reasoning]: 'there would be no specific unity if individual unity were not already presupposed'. The organic body must persist as a unified one despite the coming and going of the bits which make up its parts. So we have 'a cycle of the body and the soul', beginning with 'Every and One'[the soul and the body as above, and then returning to 'Every' [probably a different kind of every, though, not the definitional one that we started with, but something more like any individual every?]. To sum up, each individual monad possesses a body inseparable from it; each one [also] possesses an [organic] body because it is the subject of its vinculum; the vinculum assembles a mass of variable monads; these masses become infinity's of material parts, which make up the organic composition of an [organic] body, under the control of the vinculum; this organic body is the one that belongs to the individual monad, produced as an individual unity by the vinculum. [I still think this is not just a circular relation, because the body means different things at each stage—that's why I have insisted that the second kind of body is qualified by my adding the term organic. This could be wrong? It certainly looks more profound and mysterious if you don't do this!]

We have to remember that we can classify monads, according to their clear zones of expression: reasonable monads have a wide and intense zone which means they can reflect and deepen their insights, so they can 'tend towards God' (129). However animal monads also have their own clear zone, even ticks, or monads of the liver etc.. We can therefore consider each monad to be 'a simple substance, a primary active force, and inner unity of action or of change'. The monad has a body and is inseparable from it [which explains its ability to act in the clear zone], but the monad does not contain the body, and is 'distinguished from it' [monads are always souls AND bodies]. However, a monad needs a body because its power to act is limited considered as primary matter [here rendered as 'initial matter ("moles")']. All reasonable monads are dominant, but to a lesser degree, so are all monads, all have requirements, and dominance even survives death [described here and elsewhere as a kind of dispersion of little monads]. Monads are 'immediately present in the body, but only through projection'[this seems a bit of a leap, and I'll have to go back and check the argument]: this projection enables the projection of active primary force at a point in the body.

Reasonable monads are never dominated, animal monads are always dominated, although they also dominate in their turn. Domination by reasonable ones takes the form of being acquired as a mass, in clusters, not in terms of the bodies they possess, but in terms of the material parts of which they are aggregated, so the body of dominated monads get incorporated into the bodies of dominant ones. The vinculum attached to an individual dominant monad does this, acting as 'a knot'[I still don't see the significance of this metaphor—something interwoven?]. We can reserve particular terms for particular stages of this process, using aggregates to refer to material elements, clusters to monads. Aggregates of material parts are the things that make organisms—they are active but also collective and derivative, '("plastic forces")' (130), and in their mass state, they can generate and corrupt organic materials, 'through envelopment, development, and fluxion of material parts'. They are no longer projected, but collectively related to material parts, 'they are themselves said to be material' [as 'second matter'], corporal or composite substances [by magic, they have been realized in material forms!]. However, this requires a dominant body itself to have a living organic body.

This applies to all secondary matter. Primary matter requires a body, a secondary matter, an organism emerging from a crowd of monads. Yet we have seen that monads organize inorganic aggregates. There must be some derivative forces on secondary matter, structures and figures in the material aggregates themselves, produced by forces that tend towards equilibrium, the extrema. We are not just talking about any external forces, but special ones that produce these phenomena. They are 'effectively those of dominated monads' (131), and are connected deeply with their individuality [as usefulness for a dominant monad], as projected on to the dominant monad ['exist only in the pure individuality of the dominant as a primary force of surveillance'].

The derivative forces occupy a special place between mere statistical collections and individual distributions. We can use them to understand the behaviour of crowds. They describe not purely collective behaviour but something 'more interindividual and interactive'. This is what makes them organic [secondary matter here is also called 'clothed matter']. They affect aggregates, 'but belong to the organisms'. They produce figures, structures and also textures in matter. This was understood in baroque conceptions as texture being underst/l ood and produced by 'a generalized organicism, or… a ubiquitous presence of organisms'[and the example is Caravaggio's paintings!]. Secondary matter is clothed, meaning that 'matter is a buoyant surface, a structure endowed with an organic fabric, or that it is the very fabric or clothing, the texture enveloping the abstract structure'.

The notion of interindividual and interactive clustering implies temporary appurtenances, 'provisional possessions', as parts come and go from aggregates. This hints at an explanation for the transformation of species, although Leibniz referred to mutations, or associations and dissociations, 'metamorphosis' (132). This involves a capacity to envelop and develop parts, and a 'fluxion' that affects parts as they enter and leave different aggregates. There can be 'free unlinked monads without a vinculum', however. They are aggregated like the particles of felt, pressed together. They comprise inorganic bodies or elements of bodies, [not proper bodies, not like those that belong to monads], 'substantial components, semisubstances'. The bodies are purely mechanical, following mechanical linkages. They are actualized phenomena, but must have monads after all, or they would not follow natural laws: the forces they exert are not plastic ones [what a lot of convoluted and backwards pointing argument! All necessary only to preserve consistency].

So organic and inorganic bodies obey laws because their 'inner nature' enables them to do so—hence the universal application of something like the law of gravitation. The preestablished harmony between monads works in every case, not just occasionally [and apparently there were 'occasionalists' at the time]. We can also not rely on miracles or any divine mechanisms to explain general laws. There therefore must [!] be in inorganic bodies 'a third species of monad'(133).

These are neither dominant nor dominated, with some weaker kind of the inner unity. Dominant monads 'are unities of the inner change', dominated ones 'units of organic generation and corruption'. The third species, 'degenerated or defective monads' are 'units of outer movement', concerned with determination, or mechanical linkage—all only possible because of the 'inner unity' of these monads. In this sense, Leibniz agrees with Bergson [and other philosophers briefly mentioned above], that extrinsic determination requires some 'inner unity of the trajectory', with the determination as a means, or sometimes an obstacle. The inner trajectory is produced by 'an active elastic force', pervading the universe, energized by aggregates, or 'defective monads without a vinculum', and appearing as tendencies.

Leibniz argues that force and action are the same thing, operating in different ways according to the types of monads. Dominant monads actualize, as a kind of power in action. Dominated ones are not passively collected under a vinculum without developing their own kind of power as 'dispositions or habitus' [a sort of background power to influence?]. The third kind develop tendencies [they seem to be dynamic on their own, so the extrinsic force that animates them does so by removing impediments to action]: these tendencies only last a split second, but they are future -oriented and their energy passes along to the next instant to produce an 'inner unity of movement' (134), so they are 'flashing, twinkling in a way', illuminating matter.

We have to clarify derivative forces and how they are linked to different types of monad. Derivative forces seem to be 'material, accidental, modal, "states of a substance" that are exerted on bodies'. But we should not understand term 'state' as referring to a predicate contained in a subject. Instead, the term refers to 'status or a (public) aspect'. Derivative forces are primary forces except in terms of their status, which arises from their being organized by a vinculum, taken as multitudes and turned into either plastic or elastic forces. Derivative forces are therefore the result of several substances in a crowd or mass. They still belong to a body 'are present to a body', constituting their '"material souls"'. They are requisites for a body constituted by a multitude which is itself a primary force, produced by projection [the combined force of lots of the smaller monads?]. It is possible to think of the composite producing derivative forces as a public status [and apparently, this is how Whitehead used the term].

Leibniz uses 'public' to mean the derivative state of the monad, and private as referring to what they are in and of themselves, 'their primitive condition'. As public, they belong to a composite body which is not their own, even though they constitute it. Reasonable monads are private in another sense, because they have no public status as defined above, and nothing that can be derived from them. [They seem to be like private individuals in civil society, subjects of God].

The three classes of monads also refers to their entelechies [roughly, self defining organisms, or the vital force that actualizes organisms]. Some only have perceptions, animal souls have 'memory, feeling and attention', reasonable ones have minds. It might be that being reasonable explains their domination, and animals are placed in the relation of both domination and dominance according to their capacity for reason. It is also a matter of the state of the entelechies, however—some can be 'tied to a body, in a heap' (135), a kind of degeneration, and this explains variations within the overall categories.

Souls and matter or bodies are distinct, and 'each operates according to its own laws, one by inner spontaneity or action, the other by outer determination or action', but there is no direct interaction between the two. However, we can specify 'an "ideal action"' (136), where something bodily is the cause of what happens in the soul, as in suffering, or than something in the soul causes something to happen in a body '(a movement taken as voluntary)'. In the normal state of affairs, the world is expressed as two distinct expressions, actualization and realization, but we can use the notion of an ideal action to suggest that there are occasions when the two might be combined as 'an "ideal cause"', 'the best expressant'. There is only one world, and it is both actualized by souls, and realised by bodies: we can think of this with the metaphor of heavenly and earthly cities, or the two floors of the house. We can further subdivide the house into private apartments on top, and public or common ones below, [primary and derivatives respectively] , the individual, and the collectives or totalities.

Unlike Kant, for Leibniz the two floors are inseparable although distinct, with 'the presence of the upper in the lower. The upper floor is folded over the lower floor'. It is not a matter of the one acting on the other, but rather one belonging to the other [so folds supplant {and incorporate} causes]. The soul becomes the principle of life 'through its presence and not through its action', and, in general, all 'force is presence and not action'[I thought we had agreed the two were identical, or at least always found together]. Bodies project into souls and vice versa [this sort of projection is well discussed, in the beginning, I have just remembered], bodies are requisites of souls. Possessions replace the notion of action, and souls do not act upon bodies even when they possess them. This belonging involves 'a strangely intermediate, or rather, original zone', which helps bodies acquire individuality even as a possessive, if they belong to a private soul, or, when souls become public, to a crowd or some other collective body. This produces a material fabric linking the two levels, with the upper folded over the lower, so that 'we can no longer tell where one ends and the other begins, or where the sensible [material] ends and the intelligible [cognitive] begins' (137).

Where is the fold moving [found]? It moves between essences and existences, between the body and the soul, between the inorganic and the organic for bodies, and between the species of monads for souls. It is a 'sinuous fold, a zigzag, a primal tie that cannot be located'. There are also different looser types of linkage, not just vincula: they only binds souls to souls, producing the 'double [two way] belonging' which connects them [again, I thought the substantial vinculum also linked to material parts of bodies—there must be different sorts of vincula, no doubt]. The looser connection arises because the soul possesses a body which might be possessed in common by other souls as well, hence the 'perpetual overlappings of the two floors'. This sort of connection enables us to posit ideal causes, working both ways [between actualization and realization]. This sort of connection also permits us to insist that souls can also be material, and forces mechanical [depending on what sort of connection between the two we are talking about, and at what stage in the sequence?]. We have a variety of syntheses, in matter itself, produced by 'laws of exteriority', and in souls, under the action of the vinculum, or through the tendencies which flash, as above. Bodies are animated by souls because they belong to them: in practice, only souls have an inner action, with specific laws, which bodies realize, according to their own laws.

Actualization and realization are folded together, both in souls and in bodies, and affected by the two regimes of laws. This double fold is a zweifelt, as above, producing a crease or seam [but not a split]. Bodies are not themselves real, but become real only after something has been actualized in the soul: it is then completed by being realized in the body. The soul has to perceive something first, so realization in the body is 'the realization of phenomena' (138). The fold itself is a product of realization [so, in the strange backwards terminology of philosophy, 'what is realized is the fold of the two levels']. So is the vinculum as another fold ['the fold of the two levels… [is]... the vinculum itself or its replacement']. What we have in Leibniz is a 'transcendental philosophy of the event', which features 'the double operation of transcendental actualization and realization (animism and materialism)'[I have often thought that Deleuze's universe is an animist one].

Chapter nine. The new harmony.

We can think of folds in simple terms as in textiles. When we clothe human bodies, the fabric is not just subordinated to the body, especially in baroque costume, as in the rhingrave-canon [below].

The effect of baroque clothing is to overwhelm the wearer, freedom from conventional space [with lots of examples of painting and sculpture to follow, 139-140]. The style alludes to something 'placed between clothing and the body'(140), 'the Elements'[the classic four elements]. We see in painting, and above all in sculpture the effects of these elements, of the breeze that makes the ribbon below, or flattens the cloak, the far older us, the effects of water as in Goujon's bas reliefs [below].

Clothing is autonomous, and not just decorative, expressing 'intensity of a spiritual force exerted on the body', to alter it, but also 'to turn it inside out and to mould its inner surfaces'. In this way, the Elements can be seen as derivative forces 'that materialize an infinite spiritual force'

The fold appears in 'everyday recipes or modes of fashion as well' (141), in still life, with its drapery, 'jewelry that burns with folds of fire', vegetables 'caught in their earthy folds'. These paintings are packed with folds, which could never be unravelled except by going to infinity, where we will encounter the spiritual. Since 'the law of extremum of matter entails the maximum of matter for a minimum of extension', we get an overflowing, sometimes even when matter flows out of the frame as in trompe l'oeuil. Sometimes this is an unfolding upward, into airiness, but more often it is in terms of length and extension, width, the depiction of extensive masses. There is also extension by prolonging one art into the next, from painting extending into sculpture, then into architecture, and then eventually into city planning: one art form provides the 'frame' which can be detached and extended into the next. Overall, the arts combine to form 'a universal theatre', that includes the elements as well, and where the city becomes 'a decor' (142). The whole of public space, the Socius, becomes 'the sum of the arts'. This anticipated current collapsing of boundaries between the arts, again with its forms of 'folding and unfolding, wrapping and unwrapping'.

Frames open out on to unlimited space, heading only towards a new form of unity, both 'comprehensive and spiritual, punctual… conceptual'. This is the notion of the world as a pyramid or cone, with a material basis, and the luminous apex as origin or point of view [the latter provides a form of individuality that is easily 'reconciled' with 'full continuity', just as in the discussion of the point of view earlier]. The cupola is the 'baroque figure par excellence', sometimes with an apex that has a concave surface instead of a point, extending the notion of infinite folding. Sculptures of the human body also incorporate this notion of massive base and upper unity, derivative forces and primal force respectively. Unity cannot exist without broad extension, and the universe is seen as centred, still something produced by a summit or point of view [the current view is to see the world as a theatre or a dream or illusion, says Deleuze]. A spiritual presence is somehow realizing itself and unifying space with 'hallucination'.

We also need to understand the baroque as offering allegory. Benjamin argued that allegory is not the same as a symbol, which 'combines the eternal and the momentary', because it 'uncovers nature and history according to the order of time' (143). Both symbol and allegory link concepts to objects, sometimes not single objects but rather an idea that develops the concept, and sometimes not single objects, but a series of them. Allegories appear in 'devices and emblems' [the example is the porcupine standing for "from near and afar", because it was thought to erect its spines when year, but also showed them from afar]. These devices have 'images or figurations, inscriptions or maxims, and personal signatures or proper names of owners', permitting 'seeing, reading, dedicating (or signing)' (144).

Considered as basic images, these devices break out of their frames as allegories to 'form a continuous fresco' or cycle, not just refer to an essence or an attribute. They refer to events which have histories or series, antecedents and sequels. Inscriptions are also propositions which point to 'an inner concept', not just the subject and an attribute ['from near and afar' is itself a predicate], and they also relate to an individual subject, appearing as the owner, who possesses individual virtues or qualities. Together, we get to the particular baroque notion of the concept, 'a "concetto" or an apex', a kind of unity of different propositions and images of cycles and series folded in the individual subject, or the universe imposed in the baroque world. The notion of a cone is important, and sometimes even this is depicted as an allegory.

Leibniz provides the philosophy for this conception, transforming perceptible objects into figures or aspects, subject to a law of continuity, and working out the relation between events and these figures, inscribed in propositions. He then goes on to relate these propositions to an individual subject, defined as an apex or point of view, and collects those individuals in terms of the principle of indiscernibles 'assuring the interiority of the concept and the individual'. A new relation of the one and the multiple emerges: 'the one must have a multiplicity "of" one and the unity "of" the multiple'(145). Others have suggested that ones must also be related to ones, and multiples to multiples more directly [I think the implication is to retain the different notions of the multiple as distributive where it relates to the one, and collective where it relates to aggregates]

Again we see the importance of appertaining or belonging to. This is also the key to allegory, so 'Leibniz's philosophy must be conceived as the allegory of the world… but no longer is the symbol of the cosmos'. The notion of the pyramid of possible worlds explored in the Theodicy [above], and this combines 'figures, inscriptions or propositions, individual subject or points of view with their propositional concepts [properties?]' (146). We get a new dynamic: 'description replaces the object, the concept becomes narrative, and the subject becomes points of view or subjective expression'.

We have already seen the link between horizontal extension and spiritual vertical unity, and there is no suggestion that one precedes the other. The process can be illustrated with baroque music, already recognized as an ambiguous combination of intellectual order and 'affective pleasure', from vibrations impacting on the senses. Melody operates horizontally, but harmony works vertically to establish unity. Harmony can be extracted from melody, constantly restoring higher unity to the dispersion of melodic lines, and this offers a general definition of baroque music. There is some doubt whether Leibniz meant musical harmony just as a synonym, or whether he actually meant it more literally [to describe the reality]. Certainly, preestablished harmony does have an important role in resisting occasionalism [above].

Harmony relates multiplicities to a definite unity with distinctive traits, later to be defined in terms of 'Existence, Number, and Beauty'(147). Harmonic unity is also a numerical unity, and this makes it possible to derive individual existents. Individual notes imply an existing harmony, so '("to exist means nothing other than to be harmonic")'. We perceive harmony only aesthetically, 'in confusion', but we can thinking out in terms of simple numbers [apparently, specifically, irrational numbers].

Leibniz was also to understand unity in terms of the inverse or reciprocal numbers—the 'denominator shares a relation with the numerical unity [1] as a numerator' (147), and the harmonic appears in other mathematical terms such as harmonic mean, harmonic division, and, eventually, 'the harmonics of a periodic movement' (148). We can see these examples as demonstrating the link between harmony and monads: 'monads are initially harmonic', initially, because they are designed like that by God, to express the world, to become an existent in harmony with the whole. We can also see the monad as a numerical unit, a number, a simple number, and, in Leibniz, 'the inverse, reciprocal, harmonic number'. We have already seen how the monad is the inverted image of God, one over infinity, not infinity over one. This is what is meant by preestablished harmony, and it also serves as 'an original proof of the existence of God', if we can infer this existence from the way in which the monad works [as we did, in a rather dodgy way, earlier].

The inverse number is infinite or infinitely small, a part of the natural number in the distributive sense. Inverse numbers are not identical with each other, implying that harmony is a reconciliation of individuals, not seen as parts of some universal spirit. This is 'pantheism'(149). [an account of the work of a more modern mathematician eventually refers back to the infinitesimal series as a further example—this series never entirely adds up to one, but does express a region or zone of one, 149].

The work of the monads is to establish differential relations and integrations upon the part of the series appearing in their clear zones. This can be seen as a matter of presenting 'accords' between the state and its infinitesimals, 'establishing differential relations among infinitely small units that are integrated into this state'. We can consider affective 'accords' as well, involving the calculus again, but this time in explaining things like the noise of the sea [as above, the synthesis of lots of little noises], or the [musical only?] chord. In this sense, the monads produce chords as well as accords [Jesus!].

At the human level, accords are produced from the constant state of disquiet mentioned above, integrating infinitely small perceptions to make one clear one. I am particularly able to do this if I am operating with my own own clear zone, while I cannot do this with everything else. However, monads are linked together to produce another type of accord. Leibniz might have borrowed this conception from the musical model, at least through analogy, but developed to a new level of rigour. Thus the monad can produce its own 'major and perfect accords', especially if this follows reflection. This is a particularly pleasurable form of harmony, detectable even in the middle of suffering, as when martyrs experience joy[and cf counteractualization in Stoic conceptions of death in Logic of Sense] . However, these accords can link with other accords, and combine with them in various ways, as 'mirror accords', for example, simple inversions. There can also be 'dissonant accords', where dissonance is resolved in acceptable ways, and this is like reconciling elements of pain which always accompany pleasure, displacing it to an acceptable level, suppressing 'resonance or resentment, by avoiding passivity, by pursuing the effort to suppress causes' (151). This is regarded as a 'good' way to manage dissonance, whereas the damned produced diabolical ways, through resentment or hate of god, getting pleasure from pain [somehow, they still 'make possible the infinite progression of perfect accords in the other souls' however — a note refers us to a French reference]. The whole process is 'spontaneity', the production and transformation of accords ending in a resolution or modulation, aspects of the expression undertaken by the monad. The monad can be seen as existing 'so as to extract accords from one part of the line of infinite inflection that makes up the world'. This is 'self enjoyment'. [Deleuze notes that this might be a contradiction with the earlier description of constructing differential relations, but says that Leibniz does not care!]

We return to the notion of harmony as vertical while the line of the world is horizontal, and remind ourselves that this has always been the case. This leads to a second kind of harmony, however, 'concertation'. [as when different instruments of an orchestra combine in a concert?]. Monads are linked to each other, and this can generate accord between their own spontaneous accords. It is another example of the effects of the fold passing through [linking] different entities—the floors, Nature and God, the material and the soul, and even different sorts of substance. All these effects are produced by the initial harmony between the souls. We also find harmony between the little monads and the dominant ones as above. However, spontaneous accords exist only on the inside of every monad. Luckily, they can join together in a choir, says Leibniz, singing in perfect accord without even being aware of the other.

This follows from the links we have already explored, from overlapping clear zones. There is even 'a law of the inverse' at work, so that for every monad that conveys obscurely, another monad conveys clearly. We can also see this as a matter of cause and effect, with clear expression as the cause, and obscure expression as the affect [almost a notion of musical resonance here?]. This will only be one of those strange ideal causes though, 'without real action' (153). This suggests something more established than the law of the inverse: that is too simple because clear zones can expand and contract, and sometimes even overlap, so it is a matter of more or less clarity. There are also processes that augment or diminish clarity.

Back to causes at the level of bodies. Some statements of cause are ideal, while some take the form of clear propositions [the example is a bit odd—the ideal cause here is some initial statement that a movement of a boat causes the water to be displaced, while the clearer proposition specifies in more detail, for example that it is the prow that pushes the water aside]. So relations of cause can involve a movement from clear to obscure, as above, but also movements from the more to the less clear [also describable as the confused or the less stable]. There is this notion of diminution here in sufficient reason as well, where clear expression 'increases in the cause, but… diminishes in the effect'[and some connection with the ability to perceive immediate causes because they are more clear and stable, while we can only get the resemblance of the broader causes, say of pain]. Any road up, 'concertation is the sum of ideal relations of causality'(154), moving from the more clear to the less clear, and this is perfectly compatible with spontaneity, since spontaneity helps to clarify something in the monad.

So we get to linked aspects of harmony, spontaneous accords, on the one hand, following inner reason, and correspondence between them on the other, deployed through normal space and time. A further implication is that every major and perfect accord is [must be?] accompanied by a minor or dissonant record in another monad. Combinations are possible without identical accords. Monads can even relate to what the other one is producing, responding to concertation [while also remaining spontaneous, of course]. It follows that space and time are not empty but are vectored, by this 'order of coexistence' between the monads, and this explains why harmony is preestablished. In fact it is twice established, once by inner reason and spontaneous expression, then again through concert. Deleuze says that this suggests that communication in the world is constant and preestablished, still useful [for him] as a modern equivalent of sufficient reason.

Usually, vertical harmony is subordinated to horizontal melody, and here we can talk more about a specific vinculum rather than a preestablished harmony. We see this, for example in the way in which a continuous bass structures a tonality for the chords. However, any vinculum also gathers clusters of dominated monads producing material aggregates, and this provides 'a new freedom and unity, or a flux' for the melody, escaping the structure. There are other points of contact, for example counter point ['bi-univocal correspondences among points on diverse lines' (155)]. Melody can also introduce all sorts of other variations and foreign elements including delays and interweavings , even a unique motif across different tonalities. We can generalize from here to talk about the ways in which 'melodies of development' operate in the material universe producing 'Nature [as a] immense melody and flow of bodies', and none of it contradicts the other spiritual inner unity. Indeed, the former depends on the latter which provides it with a body just as with monads: the way in which melody appears to join together my senses helps me 'recognize harmony in the real'. Harmony and melody are themselves in harmony, and this is how the soul links to the body, the intelligible to the sensible, and the sensible to other elements of the sensible in extension. Everything fits together because of folds which fold these things together [fold=harmony now, or is harmony and additional force linking things?] .

This seems to be an exact analogy between philosophical and musical harmony in the baroque. Leibniz was even able to predict inexplicable melodies, an example of what we have already seen as 'excessive representation', produced by some direct connection to feeling. Other definitions of baroque music include vertical harmonies, in chords as well as other intervals, dissonant chords, concert involving contrast inner voices and instruments, melody encounter point, and continuous bass to consolidate tonality [what better example could you get than some of the famous organ works by JS Bach—follow the link here for one of my favourites. Too obvious and vulgar for Deleuze I expect ]. Leibniz continues with a musical analogy by examining different relations of body and soul, 'influx, chance and ...harmony', which can be compared to two different ages of music.

However, we must not think of binaries between text and music, but rather folds. Again, the baroque stressed the need for accords to structure affect, including the way that voices develop particular inflections, and to explain the pleasure of listening to the music and following the text. Here, the relation is one of '"fold - in" or… "fold according to fold"' (158).

Since the baroque, accords are no longer so important, but the baroque, and Leibniz, have evolved, and can be seen in terms of different points of view, different figures and grounds, with the new notion for the monad, not the closed chapel, but 'the sealed car speeding down the dark highway' [attributed to an unreferenced Tony Smith]. Things have changed because we no longer think in terms of possible but divergent worlds which have already been selected, and which already assures some consonance between the monads. Now there seems to be no underlying selection. Nor does harmony retain its privileged, permitting unresolved dissonances, divergences, no tonality at all. This makes the monad straddle several worlds [with a strange analogy about being half open like a pair of pliers, 157], unable to contain the entire world. As a result, it is no longer centred, but follows a spiral trajectory away from the centre. Vertical and horizontal harmonics are no longer distinguished, and this implies that spontaneous of vertical private harmony is no longer separated from public concerted melody. Instead, 'the two begin to fuse on a sort of diagonal' (157-8), monads penetrate and modify each other, and there are mobile groups of prehension that carry them along and offer only 'transitory captures'.

Stockhausen or Dubuffet [see below --he wanted to mix high and low aesthetics, apparently] have collapsed the boundaries between inside and outside, public and private, and replaced 'monadology with a "nomadology"'(158). However, 'we are all still Leibnizian, although accords no longer convey our world or our text. We are discovering new ways of folding, akin to new envelopments, but we all remain Leibnizian because what always matters is folding, unfolding, refolding'.

Thank the Lord!!

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