Mathesis and Analysis: Finitude and the Infinite in the Monadology of Leibniz

(This is the original version of an essay published in Heythrop Journal, Volume 47, Number 3, 2006, pp. 519-543)

Mathesis and Analysis
Finitude and the Infinite in the Monadology of Leibniz
James Luchte

There is an infinity of figures and of movements, present and past, which enter into the efficient cause of my present writing, and in its final cause, there are an infinity of slight tendencies and dispositions of my soul, present and past.[1]

Two years before his death in 1716, Leibniz finished his Monadology, which was to be the last, complete exposition of his philosophy.  In its ninety numbered sections, he seeks to disclose, in a succinct narrative, the ultimate unity of finitude and the infinite.[2] Despite the appearance of this radical differentiation, Leibniz contends that a necessary and sufficient ground for existence subsists in a divine unity – or, that there is a syndotic[3] intimacy between these “realms.”  We may suggest, provisionally, as a metaphor, that it is Leibniz’s task, as with his precursor Democritus,[4] to trace Ariadne’s thread out of the labyrinth[5] – along a continuum betwixt finitude and its mirror in the infinite.  His narrative unfolds as an exploration of a pathway from the latter toward the former.  As we will see, his unduly abstract starting point in the monad, and his subsequent revisions of each point of departure, lead us ever more closely to the concrete individuality of the finite being.  From a concrete perspective he begins with finitude seeking the infinite, but in the ideal perspective, finite existence has already been reflected, however abstractly, in the mirror of the infinite.  As the narrative unfolds, the concrete striving for the infinite, or power, is reflected and repeatedly overcome, sublated, amid the ideal transcendens of the concrete living individual.  Yet, with the realisation of concrete individuality, the self abides the infinite, but as it is with body, and will ever remain so, any sense or meaning of the infinite will remain tentative, precarious, makeshift.[6]

Such a trajectory is given a specific meaning in that each finite being abides in itself the potentiality for a disclosure of the sufficient reason for not only its own existence, but also for that of the “whole.”[7] In other words, and to put it again metaphorically, as did Leibniz, each being is a mirror of the entire cosmos, and thus contains within itself the resources for an interpretation of the/its world.  Significantly, this is a repetition of his principle of individuation (principium individuum), which he sketched in his first published work, Disputatio metaphysica de principio individui (Metaphysical Disputation on the Principle of Individuation).[8] Mates, in his The Philosophy of Leibniz, summarises this principle as the contention that “things are individuated by their ‘whole being’ (entitas tota); that is, every property or accident of a thing is essential to its identity.”[9] This “whole being” intimates Leibniz’s interpretation of substance as a monadic body,[10] which (from the “perspective” of the divine) contains all of its aspects (necessary and contingent), past, present, and future.[11]

In this way, the ontology of Leibniz is deeply wedded to a temporal problematic and must be distinguished from any merely de-temporalised, logical rationalism.  From Leibniz’s own indications, we must attempt to unearth the root for the “unity” of concrete existence entailed in the principle of individuation as we traverse the tapestry of being as a whole.  This principle and its operative corollary, the principle of sufficient reason, enact their drama upon the topos where we can discern the phenomena, and the originary connection (syndosis), of finitude and the infinite.  It is the task of this essay to follow this clue of “place” so as to set forth a hermeneutical interpretation of the Monadology.[12]

Leibniz seeks most of all to save the phenomena (as contingency is perfectly analysable or present in the intuition of the divine) and to disclose, through an analysis/exploration[13] of his own finite existence and monadic horisons,[14] a deeper plane of philosophical meanings and “reasons”.  All contingent truths/beings have sufficient conditions, even if it is beyond the powers and the desirability of the finite being to fulfill a total analysis of contingent existence.  Yet, this sense of analysis, as it is coordinated amidst the principle/pathway of individuation, will not seek to purify ‘truth’ from the contingent flux of existence or reduce ‘truth’ to a set of deductive, axiomatic “reasons” or premises.  On the contrary, that which is ‘analysed’ for Leibniz is to be acknowledged, described and sufficient reasons for its existence are to be sought.  That which is essential is that his notion of truth must be attuned to the principle of individuation, and thus, to contingent existence as the reciprocal mirror of the divine.[15]

If we are to provide an appropriate interpretation of Leibniz, we must explore Mates’ and others’ contentions that logic, as with Heidegger, is rooted in existence, and thus, for good or evil, can be articulated as the simultaneous ideality and reality of metaphysics.  The principle of individuation forbids any severance of logic and metaphysics.  In this way, a mathematical or logical reduction of the philosophy of Leibniz is not only aesthetically restrictive,[16] but also, philosophically violent.  At the same time, this does not reduce Leibniz to the descriptivism and aestheticism of Strawson[17] as the former is seeking to retrieve a metaphysical grounding for logic itself – and not to annihilate it.  In this way, we are attempting to transcend the dichotomy of rationalist and empiricist interpretations of Leibniz, toward a hermeneutic interpretation which discloses the intimate relation of metaphysics and logic.

Mates gives us a hint of a different portrayal of Leibniz, an indication which we will explore in the following essay:

… Leibniz’s attitude is that of a philosophical explorer, who reports what he finds to be the case and who notices that there are important logical interconnections among his discoveries.[18]

What can be gained from Mates description, and as I will outline in the main body of this essay, is a differing notion of analysis operative in the Monadology of Leibniz.  For while the latter is seeking the sufficient ground of existence, such an analysis is neither regressive, nor decompositional, in that it does not seek primarily to break down phenomena into schemas or logical forms.  As a philosophical explorer, on the contrary, Leibniz seeks the sufficient ground amidst an expansive and prospective unfolding of existence amidst ever higher unities, one which seeks an ultimate unity in the divine.  The logical interconnections, as Mates writes, are interesting, but remain parasitic upon and/or expressive of the factical situation surrounding the “discoveries” – the truths.  But that which is significant is the recurrence of unity which grounds these truths.  In this way, a merely formal logic, because of its arbitrary character and its up-rooted status, cannot disclose the truths of existence and being.  In other words, any authentic logos must be rooted in these scandalous origins.  In this context, analysis must acquire a topos from which to comprehend the philosophy of Leibniz in its specificity.

With Mates, Heidegger, and others, we must finally discard the haunting image inaugurated by Russell’s reduction and restriction of the significance of Leibniz’s philosophy to his own (retrospectively conceived) logical and mathematical protocols.[19] Such a reduction includes as to exclude – that which is excluded is the so-called metaphysical or that which does not include the “consistency” and “rigor” demanded of a coherent logical philosophy.  What is lost is the power of philosophy to speak to us and allow for a self-expression of existence.

An indication of a topos for our interpretation of Leibniz comes from a consideration of the deeper sense of unity in mathesis.  As a site of individuation, mathesis, as a primal distancing, opens up a qualitative place for an exploration of finite existence.[20] Amidst this opening, there are many perspectives, in that mathesis is a place of interpretation and analysis, or in the language of Schürmann,[21] a topology amidst an epochal economy of being.  In this light, amidst this multiplicity there already resides an intentional unity, one that is disclosed amidst the event and process of individuation.  Mates characterizes the difficult and far from straightforward task of interpreting Leibniz.  He writes,

The first and foremost difficulty is that in setting forth the philosophy of Leibniz, one does not know where to begin.  Some advice on this problem is found in a well-known passage in Alice in Wonderland:

The White Rabbit put on his spectacles.  “Where shall I begin, please your Majesty?  He asked.

“Begin at the beginning,” the King said, very gravely, “and go on till you come to the end: then stop.”

But unfortunately we cannot follow this good advice, for Leibniz’s philosophy has no “beginning,” that is, no unique, logically primitive set of axioms.  Contrary to what many commentators seem to have supposed, he does not treat his philosophical principles as a deductive system in which certain propositions are to be accepted without proof and the rest are to be deduced from these.  Instead, it is clear that he regards his doctrine simply as a network of important truths that have many interesting logical interrelationships.  He deduces the various principles from one another in different orders and combinations.  Often he gives alternative definitions of the same concept, sometimes even showing how to derive these from one another.  It is obvious that he had no particular order of theorems and definitions in mind.[22]

It seems clear that the true target of this text is the “commentator” himself.  Indeed, these “many commentators”[23] are merely echoes of an interpretation which Russell had set out – and refused to alter in any essential respect – in 1900.[24] What is interesting however is that the real violence of Russell’s interpretation resulted from his attempt to show that Leibniz’s metaphysics derive from his logic.  Yet, even though this is the ostensible programme for Russell, he remained skeptical of its complete success, so much so that he found it necessary to re-write the philosophy of Leibniz in order to demonstrate his case.  This is again very different from the position of Heinrich Scholz who argued that Leibniz’s system had a secure and complete logical foundation.  Of course there is disagreement here, but not on the level of the relevance of logic.  These two, while in disagreement, would surely become quick allies in another interpretive context, say for instance in one which sought to disclose the metaphysical foundations of logic.[25] And despite the belated criticisms of Russell in recent years, there is still a propensity to seek out the “logically consistent” aspects of Leibniz, for there is little taste for his more fantastical tendencies.[26]

Some “good advice” may come from the perspective of a newer resident in our Leibnizian City.   Although he is “new”, and might be deemed suspect as he is not really a “Leibniz scholar”, Foucault, in his The Order of Things, portrays Leibniz as an initiator of the 17th century mathesis, an order of identity and difference in the Classical, pre-Kantian episteme – the site of perspective, orientation and self-interpretation.[27] Foucault respects the principle of individuation as he seeks to disclose the genealogical “whole” amid an indigenous history of the present.  He describes mathesis as a “universal science of measurement and order” but, in another way, as an ‘order of simple natures’, or as the place of these simples which are bestowed via their situation amidst this “order.”  Foucault writes, tracing the genealogy of mathesis as a pursuit of the “whole”:

… the fundamental element of the Classical episteme is neither the success or failure of mechanism, nor the right to mathematicize or the impossibility of a mathematicization of nature, but rather a link with the mathesis which, until the end of the Eighteenth Century, remains constant and unaltered.[28]

Foucault, from his perspective, seeks to unfold the philosophy of the Classical era, and thus, that of Leibniz, within the context of its own limits and horisons.  He is also disclosing a situation in which one metaphysic, episteme, can exist and then be displaced.  The primal differentiation of the mathesis is also a fracture in the “unity” of knowledge.  Amidst these displacements, new metaphysical possibilities can emerge, but it is not possible to see these various displacements in a linear fashion as older forms are constantly re-immerging amidst the newer forms.[29]

It is from this indigenous topos that we can perhaps begin to understand the meaning of philosophical analysis in Leibniz.  Foucault writes,

In this sense, analysis was very quickly to acquire the value of a universal method and the Leibnizian project of establishing a mathematics of qualitative orders is situated at the heart of Classical thought; its gravitational centre.  But, on the other hand, this relation to the mathesis as a general science of order does not signify that knowledge is absorbed into mathematics, or that the latter becomes the foundation for all possible knowledge.[30]

Foucault, with his genealogical/archeological methodology, on the contrary, traces/excavates mathesis (and taxonomy and genesis) out from underneath the archive of mathematical and logical reductions/transformations.  Indeed, mathematics and logic cannot be conceived as autonomous and independent “realms”, in Leibniz’s view, as they cannot establish themselves as pure relations except as those severed from the qualitative order of substance, or from vis primitva.  On the contrary, mathesis is the orientational horison for the disclosure of sufficiency with respect to the phenomena of existence.  In this way, analysis would be the act of disclosing the sufficient unity of existence and being within the limits of mathesis.  In the neighborhood of Foucault, Russell et al. is not justified in his elimination of the rich sense of mathesis from the early modern philosophy of Leibniz, in favour of his latter-day and violent reduction and re-construction.  Indeed, his mockery of these aspects of Leibniz is indicative of the great distance that separates these two philosophers both in method and intention.[31]

From this perspective, Leibniz, in the Monadology, can be seen as laying out a hermeneutical situation which is inclusive and variegated in itself, and open to the beyond.  In this way, we are confronted by the question of the indivisible forms which are the ’causes of the appearances,’[32] an uncertain question which seeks to navigate upon a sea of ‘perplexing cases.’[33] For Leibniz, analysis of finitude toward its sufficient grounds could be conceived an exploration of the unfolding of existence and being amid the finite perspectives of created beings.  These considerations intimate that there is ‘more’ to Leibniz than his common portrayal as a mathematical, logical scholar, and discoverer (independent of Newton) of Calculus.  This ‘more’ is rarely mentioned, despite its prominence in his writings.  The theodicy[34] of Leibniz had been put to sleep by the now tottering ethos of scientific and logical hegemony.[35]

In the following pages, I will trace a thread from the topos of the created monad and its insularity amid proximate perception to that of the uncreated Monad of an infinite divine being.  This thread will consist of a series of provisional points of departure, in which each starting point will be makeshift, a temporary shelter, so as to engage a philosophy which contests that there is no beginning and that “everything is in everything.”  I will begin in The Monad with the abstract concept of the monad as a first point of departure upon our pathway between finitude and the infinite.  In Monad and Perception, a second, revised point of departure will emerge in the appetitive monad indicating the changing manifoldness within each monad.  In Monad and Entelechy, as a third point of departure, I will disclose the sufficient condition for the aspiration of finitude for the infinite in the entelechy, actuality, which strives for a ‘certain perfection’ amid the radical diversity of perceptive existence.  In The Principle of Rational Soul (Mind), I will describe a fourth point of departure as the principle of rational soul, which, Leibniz asserts, emerges ambivalently amid the striving of actuality for self-consciousness (apperception).  In light of these limitations of mind, I will reflect, in Monad and the Body, upon the ‘body’ as a fifth, revised point of departure, as the existence of a self-conscious living being.  The monadic body is a mirror of the physical cosmos and is an index of the relative state of perfection of the soul vis-a-vis the absolute perfection of the divinity.  In God as Supreme Monad, I will set forth Leibniz’s designation of divinity as the necessary and sufficient ground for essence and existence.  But, as we are finite, we can neither unfold our perception to rival a god, nor can we interpret our own existence from the ‘perspective’ of infinity.  In this way, “God” cannot become, within the limits of this analysis currently at play, a sixth, revised point of departure.  In The Meaning of the Monad, I will attempt to decipher the significance of the monad in light of Leibniz’s metaphors of the city and of the windowless monad.  I will suggest that these metaphors complement and remain linked as each discloses a perspective desired by the other.  I will close in the Epilogue with an alternative possibility, from Leibniz’s correspondence with Arnauld, which suggests that our desire for transcendence is in truth an intimation of a vague but true remembrance of our emergence in the world via the self-expression of the divine will.  In this way, amidst the simultaneity and identity of mortal existence and the divine, the need to escape from finitude becomes the wrong question/solution.  There must instead be a comprehension that each soul is a recurring truth, moment, amid the life of the All.  Yet, the reason for our desire for transcendence remains unknown to us.  Heidegger would call this our basic state, transcending.  Indeed, as it emerges amidst the mirror of finitude, it must have, for Leibniz, a sufficient ground for its existence in the understanding of the divine.

The Monad

The first point of departure for our analysis is the monad.  Of course, this is only a provisional starting point, as we embark in the spirit of Mates.  Considered as such for the moment (although no monad ever ‘lives’ in this way), a monad is a simple substance.  In this state of abstraction, the monad can only be defined in the negative.  Simplicity entails a be-ing “without partition,” with ‘neither extension, nor form, nor diversity.’[36] Moreover, as a simple substance, or as a soul, the monad cannot be destroyed or created ‘through natural means,’[37] since it does not operate according to the laws of composition.  Unlike composites which ‘begin or end gradually’, monads can only be created or annihilated ‘all at once.’[38] In this light, Leibniz deems the monad a first principle, and describes it as free with respect to other substances, including God.[39]

Yet, despite their simplicity and transcendental significance, monads must have for Leibniz ‘some qualities, otherwise they would not even be existences.’[40] Indeed, in light of his principle of individuation, monads must subsist in the very heart of contingency as the very constituents and limits of things themselves.  It is this apparent paradox that we must attempt to fathom.  For although Leibniz contends that simple substances ‘make up’ composites, the monad remains strangely distant from the topography of finite contingency where living beings appear to exist.  This strangeness is echoed in a metaphor, where Leibniz writes, ‘The Monads have no windows through which anything may come in or go out.’[41] As simple, a monad can neither be effected by another created being, nor can change be effected by an external source.  Indeed, in the context of the monad, a question-mark is placed over the very actuality of an ‘external’, a “mere prejudice” for Leibniz, as Russell asserts.[42] The dogmatic object, for Leibniz, as Fichte would later echo, does not exist.  Instead, any authentic outside, as suggested by the principle of sufficient reason, subsists just beyond the limits of the contingent world, as the necessary condition for the existence of states of affairs, situations… existence.

The paradox is alleviated with a displacement of metaphors with respect to the possible readings of “windowless.”  Windowless is not meant to indicate an entitive plane of intereacting things.  This is just an image, a way of conceiving Leibniz’s metaphor.  Another reading of the metaphor conjures a differing image of a self which is intimate amidst its world – one not enslaved within the ideal architecture of the house and its windows (cf. Descartes).  Not only does each monad mirror the universe from its own perspective, but each also strives for the whole perception.  Yet, it is the finitude of each monad as a created, living being which forbids the disclosure of a perception of the universe, of an authentic outside or totality.  The created monad must always inhabit a body as a being in and beyond the world.  It ceaselessly strives to perceive the whole, it harbors a hidden secret to be a god or to be with one.  It is in this way that the first point of departure in the abstract monad becomes insufficient as it does not adequately account for its striving for the “whole” amidst a topography (mathesis) of perception.  Indeed the negative connotations of an abstract monad in itself leads us astray into an ambivalent image of a mere geography of things which conceals this topos of existence.  Moreover, as a hypothesis, it does not adequately account for the temporality of the monad, in its rich, concrete sense, as a being which contains within itself the entire potentiality (and eventual actuality) of its substance, its being.  In this way, we must move beyond the abstract starting point to a second point of departure in a monad with perception.

Monad and Perception

The simple and windowless character of the monad precludes internal change from an ‘external’ source.  Yet, as the monad must be constitutive of the composite, it must also be capable of a type of change which is ‘continuous in each.’[43] This change comes from an internal principle of change, appetition, which, indigenous to the monad, ceaselessly ‘brings about the change or the passing from one perception to another.’[44] In this way, the appetitive monad becomes a second point of departure for our analysis.  It is this desire, or drive (Drang), as Heidegger thematises in his Metaphysical Foundations of Logic,[45] which throws the monad beyond its state of abstraction.  Amid the finite disclosure of its world, the perception of the monad is a ‘passing condition which involves and represents a multiplicity in the unity,’ in the simple substance.[46] Monadic perception indicates a phenomenology of any living unity of monad and manifold.

As we cannot conceive of the effectation of the monad by an external object, there must be, within the monad, not only a principle of change, but also, a changing manifoldness which ‘constitutes, so to speak, the specific nature and the variety of the simple substances.’[47] The manifoldness is a ‘multiplicity in unity’, a myriadity of changes in the unchanged, a ‘plurality of conditions and relations’ in the simple.  As it is to be a constituent of apparent ‘actuality’, perception, each monad will be different from every other, not only due to its own principle of change, but also due to the perspectival character of its existence, its proximate perspectives and expressions of truth.

Appetition or desire seeks the whole of the perception, but cannot obtain it.  Yet, its drive for transcendence and its striving for the whole, though a necessary failure, does open up a topos of new perceptions, and through this contrast, a chance for a primeval reflection upon the truths of existence.  But, we must not begin to form the picture of a monad as an entity standing outside – in relation to a series of perceptions – conceived as an external entity, or, as a spectator.  Neither can we credit any longer any explication of the monad from the standpoint of abstraction.  Leibniz is not rehearsing the Platonic myth of the descent of a disembodied soul into the world.  Indeed, the soul or monad is active amidst its “world” and discovers its own “self” amidst the durable contingency of its perception.  It is thus never without proximate, finite perceptions, even if these are only vague or unconscious.  Leibniz does write that there is only perception in the monad.  In this way, contrary to Plato, and Plotinus, the body is not the prison house of the soul.  The body is instead the phenomenal life of the soul, and the latter, the monad, in that it is the vita activa of unity, is the sufficient ground condition for life, body, and world.

Each monad abides a potentiality, a toti-potency,[48] to perceive and express the whole – of itself and the All.  Yet, such an unobtainable perception is dispersed amidst a perceptual topography of extension, shape and virtual effectation (without itself being effected).  That which drives it toward transcendence is at once that which forbids the actualization of its intent, its desire for the whole – its ultimate double bind.  Indeed, since the composite (body) is itself composed of monads, of simple substances, it could be said that the very fate of the monad as having to be the constitutive substance of the world is that which renders it finite.  It is in its own sacrifice that a perception of the whole is forbidden to the created monad.  Yet, its sacrifice enacts the gift of its own freedom, or liberty, as it is not swallowed, as with Spinoza, in the homogeneity of an enlightening substance which seeks to assimilate every alterity.

To understand Leibniz’s meaning with respect to the apparent opposition of soul and body, I would suggest that we look not to Plato or Descartes, but instead to Democritus, as I have mentioned, and to Heraclitus’ indications of a ‘unity of opposites’ and of logos (“The thunderbolt (i.e., Fire) steers the universe.”)[49] In this light, the contingency of the world is not mere flux, but is instead steered by a higher unity, which, in these references, is Zeus, the wielder of the thunderbolt and the patron god of the oak tree.[50] It is the logos which unfolds existence and its tacit self-interpretation.  The steering of the thunderbolt (logos) occurs as the unified aspiration of a pathway of life in its germination, cultivation, growth, harvest, decay, and rebirth.  The created monad persists, in this way, as the eternal ground of living beings to the extent that it emulates the perfection of a still higher unity.  In this way, as Foucault has indicated, the finite monad orients itself amidst the horisons of the mathesis, in the prospective search for such a higher horizon of meaning and order.

From our second revised point of departure in the finite perception of the appetitive monad, as opposed to that of the prior abstract definition, we can see that the monad gives ‘unity’ to living beings and that each has a perception which is intimate to itself – and constitutes the phenomenology of its life.  This is an active or immanent perception, however, as the latter is not an objective series which the monad, conceived as a subject, merely observes, passively and at a distance.  On the contrary, for Leibniz, perception is born amidst the pregnancy of the present moment, from the appetition and striving of the monad for transcendence, for an orientation among, and perception of, the whole.  Moreover, due to the differentiation of monads, there will also be a variance with respect to the extent and depth of their respective perceptions.  In this way, we can trace a pathway from the primordial monadology of silent material beings, bare monads, without feeling or soul, to beings which properly have soul, and to those which have soul and spirit, and finally to the divine as the necessary and sufficient reason or condition for all existence and being.  In this way, we must move toward our third point of departure in the monad as entelechy.

Monad and Entelechy

The possibility of a pathway from a bare monad to a substance that is divine finds its operative ground in Leibniz’s indication of the monad as entelechy.  He deploys this Aristotelian word as he seeks to give shape and direction to the flux of perceptions that are indigenous to the monad.  The monad as entelechy, as actuality, will thus be the third point of departure for our analysis.  Yet, it will benefit our analysis, before we move along upon our pathway, if we take a brief detour into Aristotle’s De Anima[51] so as to more fully disclose the significance of the monad as entelechy.

Russell mentions the notion of entelechy in his “commentary” on Leibniz.  Indeed, it is in this section of his interpretation where he most distinctly attempts to provide a ‘true’ commentary on the philosophy of Leibniz.  Yet, it is precisely these aspects of Leibniz that Russell has already warned us are irretrievably problematic.  And, having rejected them, he seems to be merely “going through” these ideas as a simple matter of historical interest or completeness.  However, it seems that this is a slight of hand on his part as we are already aware that Russell is seeking to quarantine these ideas into a state of diminishment, when, it could be argued, these notions are the primary truths of the philosophy of Leibniz.  He cautions us most suspiciously, and all-too-briefly, that the notion of entelechy should only be regarded as a stand-in for “form” as that which is distinct from “matter.”[52] This description gives us the immediate sense of a crude dualism in which an abstract form sets against an incoherent chaos of matter.  In the setting-against, the form can decide not to mix with matter, as Russell would seem to prefer.  Yet, it is quite clear, as we will more fully comprehend, that the reference to Aristotle cannot denote, in any way, an abstract pseudo-Platonic form.  There is no suggestion in Leibniz of a Cartesian dualism.  The entelechy is something else besides.   We must turn to Aristotle to disclose this fact.

In radical contrast to its designation as an abstract “form” in Russell, Aristotle writes in De Anima that “soul is the actuality of the body.”[53] Soul as entelechy – actuality – is neither an abstract, de-sensualised form, nor the “idea”, “look” (eidos) of a thing.  It pertains instead to the operational[54] features of the existent, to the ‘how,’ as in the Four Causes in his Physics.  For the latter, and for Leibniz, it is the ‘how’ which must be the topos of disclosure for the ‘what’.  In this way, eidos (beyond mere form) becomes not only the interstitial configuration of the being, but also its morphology and physiology, as for instance, in Goethe’s An Attempt to Interpret the Metamorphosis of Plants.[55] In this way, entelechy, as distinct from an abstract form or a vulgar notion of substance, would point instead to energeia, the vital force of life amidst its actualization from bare potentiality.  In this light, there can be no dualism or atomism, as the soul is the actualization of the body; it is this “unity” which travels a trajectory toward an animate actuality.  Indeed, Aristotle simply dismisses the possibility of dualism, when he writes:

We should not enquire whether the soul and body are one thing, any more than whether the wax and its imprint are or in general whether that matter of each thing is one with that of which it is the matter.  For although unity and being are spoken of in a number of ways, it is of the actuality that they are most properly said.[56]

For Aristotle, at the same time, the soul has pre-eminence in its relationship to ‘phenomena’ as it is the seed of life, that which distinguishes one being from the next, and sets forth the telos toward its “appropriate kind.”[57] The latter reference intimates a “psychic hierarchy” in which actuality, the entelechy, strives for the fulfillment of its potentiality.  The soul for Aristotle, which unlike Leibniz, pertains to only living beings, is the logos of human actuality.  Following Aristotle, Leibniz writes that the entelechy, actuality, abides ‘a certain perfection,’ and thus, unfolds according to a trajectory which is not merely random.  The sufficiency of an entelechy, described strangely by Leibniz as an ‘incorporeal automaton’, maintains and augments itself in its striving towards its own perfection.  In this way, the sufficiency of energetic substance is the source and ground for appetition and desire.  It is a primordial desire and longing which differentiates each monad and living being in itself.  Its own desire for perfection invokes a topos of perception amidst which it strives and lives.

Since we are in the middle, in between the bare monad and the divine, it is perhaps beyond our finite perceptive horisons to comprehend the situations and actualities of other existent perspectives, of other monads, amidst our pathway.  Yet, although he cannot obtain the “perception” of the divine, Leibniz can excavate other regions of existence which depart from our ‘normal consciousness’ so as to provide the necessary contrast for a disclosure of a pathway toward perfection.  He offers intimations of perceptions of the bare monad in syncope[58] and dreamless sleep – or, when we turn around and around (as with the Islamic Sufi Dervishes) and swoon and are able to distinguish ‘nothing’.  Leibniz writes,

In such a state the soul does not sensibly differ at all from a simple Monad.  As this state, however, is not permanent and the soul can recover from it, the soul is something more.[59]

In this light, even in this ‘nothing’, there still persists perception in the monad.  Its present, even if characterized by a sudden ‘recovery’, is the ‘natural consequence of its preceding state, in such a way that its present is big with its future.’[60] This continuum of perception suggests an indigenous continuity between monads which are wholly bare and those with a ‘higher flavour’ of perception.  Indeed, for Leibniz, such a continuum could be extended still further, and by analogy, even to the divine itself, as if finitude were merely another syncopic state from which we could recover.[61]

It is in this way that the entelechy sets forth a directionality amid the changing manifold of perception, from lower and higher states of existence and being.  Those living beings which Leibniz deems of a ‘higher flavour’ are animals which have a perceptive soul and a memory which allows them the capacity for the expectation of an effect from a habitual cause. The consecutiveness and coherence of its perception, grounded in memory, ‘imitates reason’, but is not identical to Rational Soul (Mind).  Indeed, even man acts according to the manner of the animals in so far as the ‘sequence of their perceptions is determined by the law of memory…’[62] But, just as there is a continuum and thus differentiation betwixt monads, there is also a identity and difference between living beings and within each living being.  Man does act as the animals if his perception is determined by memory, truths of fact.[63] Yet, with respect to the “striving for a certain perfection” indigenous to the entelechy, the perceptions of man are also determined by other grounds, truths of reason.[64] In this way, we could speak of higher and lower perceptions of the soul, but not of higher and lower souls.  Indeed, there can be no radical breach as each exists amidst a continuum of existence and being – from the bare monad to the divine.  In this way, the point of departure in the entelechy throws us still further to our fourth, provisional point of departure in the Rational Soul or Mind.

The Principle of Rational Soul (Mind)

That which is purported to distinguish men from ‘mere animals’ is, for Leibniz, the existence of rational Soul.  The evidence for the existence of this principle is the alleged knowledge within man of eternal and necessary truths.  This knowledge allows us to comprehend ourselves and have intimations of the divine.  But, just as perception and existence are in flux, so knowledge must be characterized by movement, it must shift amidst the flux of present perceptions, memories, and desires, each of which is pregnant with a future.  In this way, a fourth point of departure for our analysis has presented itself in the life of a being with a rational soul.  The higher perception of this knowing activity can conceptually “express” the flux of existence.  Leibniz writes that knowing occurs through reflective acts which occur as abstractions from eternal and necessary truths.  It is from these reflective acts that there emerge objects of reasoning, such as the ‘I’, and, as he delineates: being, substance, simple, composite, material thing and the divine.[65] These objects become the sufficient grounds for perception and are a provisional fulfillment of the striving entelechy for a “certain perfection.”  As we traverse the continuum and ascent of perception, it seems that the differentiation of concept and perception is only apparent as each exists as an aspect of our new point of departure.

While this differentiation between objects of reasoning and perception does not return us to our initial situation of abstraction and apparent severance between substance and life, it neither abides merely in the natural harmony of the living being – nor only upon the ladder of the entelechy which sends us to the phase of Mind.  The rational soul is a principle which influences the array of perspectives through its greater powers of perception.  As the monad strives for an ever greater perception of the whole, it exhibits its augmentation of power as Mind as it begins to direct the sequence of perception to an ever greater extent and depth, on its way to a promised perception of the whole.

Yet, in the wake of its augmentation of power in its direction of the flux of perception, the mind becomes confused amid a movement along the continuum in which it increasingly seeks to emulate, in the convention of our epoch, a bodiless “God.”  In its striving for a perception of the whole, the monad as merely a rational soul, begins to tear, however ill-advisedly, at the limits of its own bodily existence.  In the wake of finitude, such limits stand before it as taboos.  In this light, there remains the temptation to transgress these limitations, a desire born of a metaphysics which seduces Mind into the presumption that it is also bodiless and could either therefore commune with a divine beyond existence or could set itself up as highest principle (in place of God).  Yet, the non-simplicity of rational soul, with reference to its ideas, is forgotten as is its rootedness in soul and body.  It forgets it containment in individualised substance as actuality, and thus, in the metaphysical “foundations” of existence.  Mind, in this way, is not that which truly transcends the series of contingency, beyond existence.  Any such attempt would lead, to borrow a phrase from Hegel, to a “bad infinity.” Yet, we cannot easily move to the divine as a fifth point of departure, but must, strangely, return to the body as the next topos amidst our pathway toward the “good” infinite.

Monad and the Body

Since the created monad and living being is finite, its potential perception of the universe is limited within the horizons of its own perspective, its ‘body’.  In this way, the monad as perception, entelechy, and rational soul expresses an aspiration for the whole amid the horisons of its finitude.  But, the mind cannot be our final point of departure as it fails to comprehend its own embeddedness in the substantial monadic topos.  It seeks  the bodiless state of the divine and seeks to direct the all, yet it cannot succeed as it is merely another perspective amid the actuality of the finite monad.  In this light, rational soul must be seen as another aspect within a fifth point of departure in the monad as body.  For Leibniz, “body” abides a myriadity of basic aspects that stand in relation within a single monad.  Body is the virtual expression of the monad and its site of self-interpretation.  Substance or the individual being conceived as body is thus the unifying topos of existence.  It is such an organic totality which can be described as body in its richest sense.  It is the body conceived in this way which most radically indicates the “whole being” that is the microcosm for the macrocosm of the divine totality of existence and being.

Contrary to Descartes’ dualism and his judgment of dissolution upon the body, we must instead regard the body not only as a multiplicity in the unity of perception, as an indication of the finitude of the created monad, but as the “great reason”[66] which, for Leibniz, intimates the divine ground of being.  The body abides a soul which is its own actuality – their unity is that of an organic, living being, one which is a ‘mirror of the universe according to its own fashion.’[67] Moreover, it is by virtue of the fundamental diversity of the aspects and the plurality of substances that Leibniz is able to avoid the homogeneity of Spinoza.  And, while the body is the mirror of the divine, we cannot conceive of this as a pantheistic identification, in the latter’s sense.[68] For the divine, the infinite, as we will investigate in detail in the next section, is bodiless, ideal.  It is in this sense that the metaphor of the mirror becomes revealing.  The reciprocal mirroring contains within itself the provision that the image in the mirror is the reverse of the extant original.  There is thus not only a difference in the “positions” of the mirrors but also in what is revealed in the mirrorings.  In a distinct antipode to the monad conceived as windowless, Leibniz writes,

… all bodies are in a state of perpetual flux like rivers, and the parts are continually entering in and passing out.[69]

Indeed, the makeshift character of “bodies” stands in contrast to the monadic body, which as the place of “entry” and “exit,” remains a site for the interaction of bodies, which in light of the windowless character of the monad, must be conceived as phenomena.  It is not only a mirror of the cosmos ‘within’ the finite monad but also intimates upon its own microcosmic level the ideal interaction of monads in the divine.  The monadic body, as a higher actuality, a higher unity, emerges amid its own drive toward transcendence.  This unity of aspects, of souls, bodies and minds, in the original substance conceived as a living being, as the inseparable body, can be seen as the metaphysical corollary of the principle of individuation.  It is in the body, conceived in this way, that the whole being (entitas tota) is emphatically disclosed as a harmony of diverse aspects.  And, it is in this way that the body serves as the exemplar of the divine in our world.

Leibniz describes the organic living being as a ‘natural automaton’,[70] a divine artwork even in its smallest parts.  It is this infinite continuity of divinity in the art of nature which distinguishes it from the art of the finite being.  In this sense, nature is not to be considered as a raw standing reserve of material for the art of man, but as the artwork of the divine.  In this way, Leibniz contends, ‘There is, therefore, nothing uncultivated, or sterile or dead in the universe, no chaos, no confusion, save in appearance.’[71] The apparent chaos of souls and bodies does not amount to discordance, as each created monad, is ‘fitted to each other in virtue of the pre-established harmony between all substances, since they are representations of one and the same universe.’[72] This ‘fitting’ operates according to a principle of the ‘conservation of the same total direction in the motion of matter.’[73] In a rather Neoplatonist formulation, Leibniz writes that the body mirrors the soul just as the latter mirrors the created universe.  It is animated body, in this metaphor, which mirrors the mirror of the cosmos and thus, though distinct, intimates most nearly the ideal harmony of the divine.

The soul (and thus the Mind, as rational soul) cannot ‘live’ without body.  Nor, can it be severed from its perceptions and perspectives, though these may be temporarily eclipsed in the syncopic state betwixt instantiations.  And, it is only in light of this original unity that it is at all possible to conceptually distinguish monad and body, the sufficient limit from the changing perspectives of the soul.  For Leibniz, conceived in this manner, each follows its own laws.  The soul follows final causes, while bodies act in respect to efficient causes.  Yet, despite this apparent disunity, Leibniz argues, ‘The two realms, that of efficient causes and that of final causes, are in harmony, each with the other.’[74] This harmony is not an afterthought, but an original syndotical unity, and it thus could be described as the monadic body in its richest sense.  As the soul cannot be without body, Leibniz writes, significantly, that death – usually fathomed as the separation of the soul from the body – is instead an ‘envelopment and diminution’ back into the bare monad.

Indeed, Leibniz intimates the necessity of the monad entering into another awakened state, just as syncope is still entwined within the continuum of perception, as the spirit of the unconscious.  In this way, we could perhaps infer a reference to transmigration in this inseparability of monad and body.  Such a possibility would allow for an unfolding of our pathway beyond the body, to a sixth point of departure in the divine.[75] Yet, such a possibility is disallowed by Leibniz since it is precisely in such a unity of opposites, of finitude in the unity of the infinite, that existence and the divine are at all possible.  From this perspective, there can be no bridge across the pathos between finitude and the infinite.  Leibniz expresses this distance in another metaphor, as God, the monarch of the city and architect of the universe, who is the father to his children.  His children, the totality of spirits, inhabit the city of God, a moral world within the natural world, and gain access to grace ‘along natural lines.’[76] God unites in himself efficiency and finality.   It is our inseparability from body – even at death – which keep us in the never-ending state of childhood.  I will return to this theme in my Epilogue below.

God as Supreme Monad[77]

That which accounts for the differentiation between finitude and the infinite is, for Leibniz, the contention that the sufficient reason for existence must subsist outside the inexplicable series of contingency.  Unlike Kant who forbade knowledge of things-in-themselves, of the noumena, Leibniz contends that that which stands outside as the sufficient reason for contingent existence must be a necessary substance, still a monad, but without an intimate entanglement in ‘body’[78] – the divine as a pure sequence of possible being – unique, universal and necessary.

Since the divine is without body, the specific ideas of contingency are present in it ‘merely potentially, as in the fountain-head…’[79] For Leibniz, the divine is the source of ‘the real in the possible’[80] the necessary being ‘in whom essence includes existence, or in whom possibility is sufficient to produce actuality.’[81] Moreover, the divine is perfect, where perfection indicates the ‘magnitude of positive reality in the strict sense.’[82] Without limits, perfection is absolutely infinite and contains ‘as much reality as possible.’[83] Leibniz contends, with respect to the bodiless god,

… nothing is able to prevent the possibility of that which involves no bounds, no negation, and consequently, no contradiction, this alone is sufficient to establish a priori his existence.[84]

Divinity is characterized by power, knowledge and will.  In other words, for Leibniz, it is the source of everything, possesses the details of the All in potentiality, and effects changes ‘in accordance with the principle of the greatest good.’[85] For Leibniz, an infinity of possible universes exists in the ideas of “God”, and any of these could be made to exist by him.  Yet, as this singular cosmos exists, there must be a sufficient reason for it.  This reason is to be found in the fitness or degree of perfection of each possible world, in its desire and claim to ‘godliness’[86] in proportion to its own perfection, and in the arbitration of each and all of these desires and claims in the consideration of the divine.  Leibniz writes,

This is the cause of the greatest good; that the wisdom of God permits him to know it, his goodness to cause him to choose it, and his power enables him to produce it.[87]

Created beings are distinguished from the divine by their own specific finite natures, by their bodily perspectives and by the peculiarity of their perceptions.  The perfection of monads and of living beings, as entelechy, can be traced, for Leibniz, to the ‘influence of God.’[88] The trace of the divine is sketched upon the monads as they spring forth amid the ‘continual outflashings of the divinity from moment to moment, limited by the receptivity of the creature to whom limitation is essential.’[89] It is this specification that created monad is essentially characterized by receptivity, which gives us a clue to distinguish finitude from the infinite, or the divine.  It is only a god in whom spontaneity is infinite or perfect.[90]

The divine is the sufficient reason for existence as he is irretrievably more perfect than, and thus is able to give an a priori reason for, the created being.  It is in this way that it can act upon the created being.  He does not need to come through windows as he is already inside each monad as the root of its created being.  A monad is perfectible only in the wake of its own approach to the perfection of God, the uncreated.  As the divine can have an impact upon the windowless monads, and as there is nothing else with this power, it becomes the topos and logos amidst which created monads interact.  The interaction of Monads is ideal – ’causes’ and ‘effects’ (logos) occur upon the topos of the divine.  It is through such a ‘primal regulation that one can have dependence upon another.’[91] Moreover, as the divine is oriented by the principles of rational soul and the ideal of the greatest good, it ‘finds in each one reasons obliging him to adapt the other to it; and consequently that which is active in certain respects is passive from another point of view.’[92] The ‘regulation’ of each and all – as each strives for the whole perception – sets forth a picture of a situation in which each monad or simple substance comports itself to ‘all the others’, and is thus ‘a perpetual living mirror of the universe.’[93] Each mirrors the All, but cannot “witness” or become the All in light of its condition of receptivity and finitude.  Each ‘lives’ its perspective amid this existence.  This primal regulation of the divine is the spontaneous event that facilitates the reciprocal interactions of the monads.   This reliance upon the divine is rooted in the finitude of the created monad whose perception remains confused amid proximity and receptivity.  If the monad had a ‘clear and distinct’ perception of the world, it would itself be a deity.  At the end of the day, its perspective must be limited amid its ‘distinct perceptions.’[94] As Leibniz describes, ‘It cannot all at once open up all its folds, because they extend to infinity.’[95]

Yet, that which incites us still is the impossible perception of the whole – of the lingering possibility of a transcendence of our contingent perspective and series of perceptions – to the infinite.  In wake of the “psychic hierarchy”, we seem to resist our own finite status and resent the body which we mistakenly consider the obstacle to the divine.  But, as we are embedded within the present moment, our perspective cannot witness existence in its totality, in its past, present and future.[96] The created monad, in the wake of the valourisation of a divinity without body, must remain content with its status as a mirror of the cosmos.  Leibniz gives us a rough sketch of our predicament:

And as the same city regarded from different sides appears entirely different, and is, as it were, multiplied perspectivally, so because of the infinite number of simple substances, there are a similar infinite number of universes which are, nevertheless, only the aspects of a single one, as seen from the special point of view of the monad.[97]

This perspectivism, a precursor to Nietzsche, allows for the greatest variety amid unity, the greatest possible perfection and, for Leibniz, the greatest articulation of the topos and logos of the divine.[98] And in its access to each and all, the divinity can arrange the best of all possible worlds – though not a perfect world.  This best of all possible worlds is articulated in the metaphor of the city and leads us into a hermeneutics of the monad in the metaphors of Leibniz.  Indeed, our basic state, that of transcending, is characterized by the necessity of interpretation amid the individuation of the finite substance across its existential and temporal continuum of perspectives.

The Meaning of the Monad

Just as there are no higher and lower souls, but only higher and lower perceptions of Soul, of perspectives amid a totality of souls, a diversity of monads does not indicate an atomistic fragmentation of the world.  Neither should the principle of individuation be feared.  Instead, as with the metaphor of the city, there exists a topography of myriad perspectives, each of which, though limited by proximity and power, expresses the totality of the city in its own pregnant moment. This metaphor unfolds a positive phenomenology of perspective in the totality of the divine.    In the quotation at the head of this essay, Leibniz portrays his own writing in light of the perspectives of efficient and final causes.  Yet, he does not see these causes as distinct and in need of some external mediation.  Indeed, these causes are not two different things, but are differing indications in an ‘account’ of one and the same existence which unfolds across a continuum of bare monad, animality, rational soul, and the divine.  This continuum entails an infinity of causes, which are practically unanalysable in the context of a finite perspective.  In this way, Leibniz places absolute emphasis upon a prior unity of existence and being, as a knot which ties together the myriad threads of perspective.  The ground for such a unity is for him the infinite perfection of a supreme being, one that is prior to the differentiation of a monad and its ever-changing manifold of perception.  There is only perception in the striving monad, and, as we fathom from the metaphor of the city, only perspective amidst perspective in the totality of the divine.  To repeat – for Leibniz, divine unity is the necessary and sufficient ground for existence, and existence is the topos or place for phenomenality, expression, and action.

Another of Leibniz’s major metaphors in this work, that of a windowless monad, reminds us however that, although our perspectives subsist in the divine, that we are not ourselves God.  Since it is windowless and thus contains within itself the potentiality of its entire existence, the created monad, while its lives, remains embedded within the intentionality of the phenomenal world.  For while its character as windowless intimates a separation of the monad from external effectation, there still remains a tacit acknowledgement of an ‘outside’ – the remainder of which is the perception of the body.  The metaphor can be linked to Descartes who, as he confessed in his Meditations,[99] often gazed from the safety of his window at those who were passing and wondered if these were in fact ‘automatons’.  Descartes diminishes perception in favour of judgment, as he judges that they are men.  Leibniz however does not look at an external world from the safe distance of a window as he abides in the intimacy of perception – a perception only limited by the finitude of the created monad.  Such intimacy displaces the prohibiting edifice of the subject and object.  Yet, the metaphor still suggests a place where windowless monads, whether these be turrets or tombs, stand in some blind relation to the others.  Amid this ‘geography’ of simple substances, where there is only perception in the monad, other monads disclose themselves to me within the horisons of my perspective – facilitated by the divine.  In this way, other simple substances and perspectives must exist independently of my mind and will.  It is this otherness as such to which I must remain blind however as I am cast adrift amid my own perspective and perception.  In this sense, each monad is windowless since it is finite.  It is the divine which is the supreme simple substance and who is the conduit for this array of perspectives.  This metaphor of the windowless monad serves as an index of our finitude and thus has a different, negative, role than the metaphor of the city.  It has a distinct ontological significance as it intimates the temporal meaning of finitude for the finite creature.  Yet, these metaphors complement each other and remain linked together.  Each discloses a perspective desired by the other in its own striving for a perception of the whole.  They are mirrors of each other, one positive, the other, negative.

The very act of reading the Monadology, as it is divided into sections, each of which expresses the “whole”, allows us to see the monad as a migrating ground of unity in the multiplicity of existence.  The sense of the monad therefore lies in its location in-between the radical diversity of perception and the ultimate unity of divinity.  It stands at the “gateway of the moment,”[100] and as an entelechy indicates a philosophy of finitude on its way to the infinite. Yet, despite the trace of its genealogy in the divine monad, the created monad is forbidden any communion with the infinite.  Any transgression towards the infinite will always already be interdicted.  We remain in-between since we are existentially forbidden to transcend the primordial antithesis of existence and the divine.  Yet, as entelechies, we remain compelled, for unknown reasons, to strive after transcendence and seek out proscribed pathways towards that perfection.  Since each expression is an eternal truth, such striving must also have its sufficient reason and truth.

Epilogue

In closing, I will set forth another possibility – perhaps as a metaboleoverturning – of the preceding narrative.  It could be argued, on the basis of another text, that Leibniz holds that it is an illusion that finitude must seem to have the character of deprivation or negativity – or that it cannot obtain the radical other.  Perhaps we are not seeking Ariadne’s thread after all, but are instead seeking to understand the monadic body as the expression of the divine spirit in the world.  In his letter to Arnauld of April 30, 1687, to return to an earlier suggestion, Leibniz rejects the doctrine of metempsychosis as it implies a continuous revolution of bodies to which the soul is subject – until it can somehow transcend the cycle.  This would be unacceptable for Leibniz as the soul, as windowless and self-organizing, is already always free.  He sets forth instead metaschematismi as an alternative narrative, which he describes as a ‘transformation of the same animal which always preserves the same soul’.[101] In other words, he seems to suggest that individual souls return as emanations from the divine, as instantiations of the same kind.  For Leibniz, spirits can never be conceived as being subjected to revolutions of bodies, but instead, this revolution ‘must serve the divine economy for the sake of spirits.’[102] From this perspective, he may not be seeking the thread out of the cycle of finitude, but seems to suggest, on the contrary, that finitude is the self-expression of the divine in its constant placement of souls into living beings.  In this way, Leibniz attempts to reconcile finitude and the infinite in the creative being of the divine.  In light of this scenario, the question of a pathway from finitude to the infinite is transfigured into that of an eternal recurrence, which, however, eludes the question of an escape from finitude per se, as this state is not conceived as a prison of the soul, but as the self-expression of the divine will.

In this light, we could perhaps trace a conditional sixth point of departure in the creative will of the divine, of which we are, for Leibniz, its expressions.  It is conditional as we gain no intimacy with the divine in the syncopic state of the monad, bare between instantiations.  Diminished in body at death, the monad, soul, sleeps with the others in the city of god and waits for the latter to send it into another awakened state.  There is neither transmigration nor mystical transcendence of the body, but a decided and continuous outflashing from the divine source.

In this way, finitude must not be disclosed as a negation of the divine, as a state from which one would seek to escape, but as a moment within the being of an infinite that ceaselessly regulates all and deploys and re-deploys monads, souls, and spirits for the sake of the greatest good.  In this way, we can ascertain a theodicy of a non-linear cosmos in which each monad must recur as a living being amidst an incessant and eternal creation of harmony.  Its instantiated life in which it sleeps and awakens is thus a microcosm of its great life in which it oscillates between a recurrent envelopment in death and outflashing into new awakened states.  This alternative possibility is thus not a metabole of the original narrative of a pathway, as the latter is re-inscribed into the narrative of recurrence which is operative as a still higher unity.


[1] Leibniz, G. W. Monadology in Discourse on Metaphysics, Correspondence with Arnauld and Monadology, Translated by George Montgomery, (Open Court, 1990), No. 36, p. 259.

[2] From a historical perspective, it might be suggested that Leibniz had become increasingly concerned with the topics of finitude and the infinite, and, under the heavy burden of his continuing project, the History of Brunswick, desired to express his system in a succinct formulation, not only due to his own failing health, but also due to the recent deaths of his confidant and correspondent, Sophie Charlotte (1705), a philosopher in her own right, and her mother, Duchess Sophie (1714), a patron and friend, and the departure of, and his abandonment by, George Ludwig (George 1 of England) in 1714. (For a broader consideration of Leibniz’s biography, see Benson Mates’s excellent work, The Philosophy of Leibniz, Oxford University Press, 1986).

[3] Heidegger, M.  Phenomenological Interpretation of Kant’s Critique of Pure Reason, Indiana University Press, 1998.  Heidegger writes (p. 93):

Pure intuition is an advance unifying giving together of the pure manifold of space and time.  There is in this intuition an original togetherness whose unity is not the connecting of what is scattered, is not a synthesis.  But even the expression “synopsis” is misleading, as if the manifold of pure space and time is only given in their one wholeness when I intuit this manifold together sequentially.  Hence we need here another expression, namely syndosis.  The verb συνδιδωμι means to give along with, give together, give something along with something else.  Thus σύdoσιV means connection.  We say that space and time as pure intuitions are syndotical, meaning thereby that they give the manifold as an original togetherness from unity as wholeness. (We should compare the expression “syndotical” with the word-image άνέκδοτος, which comes from έκδιδωμι and means anecdotal.

A syndosis indicates the originary topos of identity and difference which becomes doubled in the analytic and synthetic transformation and reconstruction of being into reality.  In this way, syndosis, as an original unity ironically signifies for the system of representative consciousness a discontinuity, as does metaphor, as the spacing (Spacings, John Sallis) betwixt the chain of logical and mathematical reasonings.  Indeed, the reference to anecdote is significant in light of the narrative topography of the Monadology.

[4] Patôcka writes in his Plato and Europe (Stanford, 2002):

Democritus’ thirst is a thirst for the divine, for the divine – that is, the eternal, the permanent, άει (eternal) – and for this reason, Democritus says: “Who takes care of knowing, for matters of the soul, he takes care of the divine: and who takes care of other things, practical, primarily body, then he takes care solely for the human. (p. 68)

[5] This is a reference to chapter nine, “The Labyrinth of the Continuum”, in Russell’s A Critical Exposition of the Philosophy of Leibniz: With an Appendix of Leading Passages, George Allen & Unwin Ltd., 1975.  Russell writes (p. 111):

Only space and time are continuous in Leibniz’s sense, and these are purely ideal.  In actuals, he says, the simple is prior to the aggregate; in ideals, the whole is prior to the part (G. II. 379).  Again he says that the continuum is ideal, because it involves indeterminate parts, whereas in the actual everything is determinate.  The labyrinth of the continuum, he continues – and this is one of his favourite remarks – comes from looking for actual parts in the order of possibles, and indeterminate parts in the aggregate of actuals. (G. II. 282).

This notion of a labyrinth as a finite topos of interpretation will be significant for the discussion that follows, beginning with Mates.

[6] It can be suggested in this connection that the perspective of the Monadology differs from that of the Discourse on Metaphysics, since the latter sets out a point of departure in God as relatively unproblematic, while the former projects God as a rather speculative ending along a exploratory pathway.

[7] Leibniz also makes this point in his Discourse on Metaphysics, IX:

It can indeed be said that every substance bears in some sort the character of God’s infinite wisdom and omnipotence, and imitates him much as it is able to; for it expresses, although confusedly, all that happens in the universe, past, present and future, deriving thus a certain resemblance to an infinite perception ofor power of knowing.

[8] It may be considered problematic to attribute the principle of individuation to Leibniz on the strength of his thesis due to the specific practices of German universities of the era.  Yet, it will be shown in the following that the principle of individuation is necessary for Leibniz’s philosophy and is reflected in his basic logical analyses of necessary and contingent truth.  Moreover, a statement from his Discourse on Metaphysics clearly shows that the principle of individuation, in relation to the concept to substantial forms, was a longstanding concern for him:

This is why these latter qualities are unable to constitute “substance” and if there is no other principle of identity in bodies than that which has just been referred to a body would not subsist more than for a moment. (XII)

[9] Mates, B. The Philosophy of Leibniz, Oxford University Press, 1986, p. 18.

[10] It may be argued that the phrase “monadic body” does not allude to alleged shifts in Leibniz’s view of the body.  Yet, we must also heed Mates’ contention of a remarkable continuity and consistency across the entire range of Leibniz’s philosophy.  Indeed, the very conception of a “monadic body” as a term, emerged for myself, only in the present analysis from a hermeneutical reading of Leibniz’s Monadology.

[11] An excellent discussion of the historical background to Leibniz’s concern for the “whole” can be found in Leroy Loemker’s Struggle for Synthesis: The Seventeenth Century Background of Leibniz’s Synthesis of Order and Freedom, Harvard University Press, 1972.

[12] Such a desire and possibility of a differing interpretation of Leibniz was also expressed by Gottlob Frege, as Mates relates in his The Philosophy of Leibniz:

Leibniz, in his writings, spread out such an abundance of seminal thoughts that there is hardly another philosopher who can be compared with him in this respect.  A portion of these ideas were worked out even in his own day, and with his collaboration; another portion were forgotten but were later rediscovered and further developed.  This justifies the expectation that in his works there is still a great deal that now appears dead and buried but will eventually enjoy its resurrection.

[13] From Mates, The Philosophy of Leibniz, p. 4, as will be discussed below in more detail.

[14] This lateral orientation for a monadology is suggested by Gilles Deleuze in his The Fold: Leibniz and the Baroque, University of Minnesota Press, 1992.

[15] What is sought is the metaphysical background of the philosophy of Leibniz, a theme which was explored, for instance, in Heidegger’s Metaphysical Foundations of Logic,[15] where “Leibniz” is re-situated amidst a topography of existence in which temporality is disclosed as the primeval ground and condition of ‘logic’, its prerequisite logos and being (Sein).[15]  Moreover, from his interpretation of the principle of individuation and of the synergistic recognition that “everything is connected with everything”[15] we can comprehend Mates’ (and Heidegger’s) contention that Leibniz’s metaphysics cannot be severed from his logic or vice versa.[15]  In other words, Leibniz is not primarily concerned, in a philosophical sense, to merely mathematize existence or translate, with Frege, Russell, and Quine, all expression (via a transformative [interpretive] reduction) to logical form, as a regression to a set of analysable statements or axioms (propositions).[15]

[16] Aesthetics concerns the dimension of phenomena which is art, but more broadly unfolds the domain of space, time, and causality – and ultimately, existence and the divine.

[17] Wilson, Catherine.  Leibniz’s Metaphysics: A historical and comparative study, Manchester University Press, 1989, pp. 308-309.

[18] Mates, p. 4.

[19] Russell B. A Critical Exposition of the Philosophy of Leibniz: With an Appendix of Leading Passages, George Allen & Unwin Ltd., 1975. Russell, in his seminal “commentary” on Leibniz,[19] takes a hammer to him and tries to knock off that which he does not like, what does not cohere with his own preferences, his own logical protocols.  However, much is lost, not only the more interesting expressive possibilities of Leibniz (such as his use of metaphor), but also the integrity and grounding of Leibniz’s philosophy in the principle of individuation (and the divine).  The irony is that Russell rejects Leibniz’s notion of substance, and hence, the former principle on the ground that it is ‘empty’, that it is merely ‘logical.’[19]   Yet, Russell, unlike Kant, fails to comprehend that substance can at the very least be deployed as a heuristic (hypothetical) or regulative principle of unity not only for the disclosure of aspects, but also for the disclosure of their existential configurations.  The “whole being” is more than the sum of its parts and the true motivation for the notion of substance is ontological and existential – in which “formal” logic, as with Kant, plays only an ancillary role.

[20] Esposito, Joesph, Schellling’s Idealism and Philosophy of Nature, Bucknell University press, p. 143: “Mathesis is the condition of Schelling’s Absolute Identity, wherein the first differentiation occurs.  Abstractly considered, this is the separation of God and Nothing.”

[21] Schürmann, Reiner. Heidegger: Being and Acting, From Principles to Anarchy, Indiana University Press, 1987.  These indications are also related to Deleuze’s interpretation of Leibniz in his The Fold.

[22] Mates, p. 4.

[23] Those who perpetuate Russell’s approach, to name a few, are G.H.R. Parkinson, Logic and Reality in Leibniz’s Metaphysics, Oxford, 1965 and again in 1995 in The Cambridge Companion to Leibniz, Chapter 7 “Philosophy and Logic.”  Those who begin to dismantle this view are Martin, Gottfried.  Leibniz, Logic and Metaphysics, trans. K.J Northcott and P.G. Lucas, Manchester University Press, 1964. (suggests the view that there is disagreement over Russell’s ideas, at least in Germany and Catherine Wilson, Leibniz’s Metaphysics, 1989.

[24] Indeed, Russell had plenty of opportunities to change his positions.  Not only the 1937 preface, but as late as 1971, in his essay, “Recent Work on the Philosophy of Leibniz”, he, in a discussion of Couturat, restates the basic premise of his work of 1900: “Leibniz’s metaphysic rests solely upon the principles of his logic, and  proceeds entirely from them.”  (Leibniz: A Collection of Critical Essays, University of Notre Dame Press, 1976, pp. 366-400)

[25] Martin, Gottfried.  Leibniz, Logic and Metaphysics, trans. K.J Northcott and P.G. Lucas, Manchester University Press, 1964.

[26] This is very clear even if we merely read the Preface to the first edition of A Critical Exposition where Russell writes (p. xiii):

I felt — as many others have felt — that the Monadology was a kind of fantastic fairy tale, coherent perhaps, but wholly arbitrary. At this point I read the Discours de Metaphysique and the letters to Arnauld. Suddenly a flood of light was thrown on all the inmost recesses of Leibniz’s philosophical edifice. I saw how its foundations were laid, and how its superstructure rose out of them. It appeared that this seemingly fantastic system could be deduced from a few simple premisses, which, but for the conclusions which Leibniz had drawn from them, many, if not most, philosophers would have been willing to admit.

[27] It may be objected that Foucault is the last person to reference in an interpretation of Leibniz, especially as the former does not, allegedly, adhere to the principle of sufficient reason, a concept which is central to Leibniz.  However, it could easily be argued that not only does his notion of discourse meet this criteria, but also that his excellent analysis of the Classical episteme sheds much needed new light upon the philosophy of this era, and most specifically, upon Leibniz.  Indeed, I will admit that my interpretation does not require Foucault, but I think his mention opens up the possibility for differing readings of tired texts.

[28] Foucault, The Order of Things, p. 57.

[29] For instance, Foucault, in The Order of Things, p. 247, describes the fracture of mathesis and the endeavors which arose in wake of this breach:

Doubly fractured: first, along the line dividing the pure forms of analysis from the laws of synthesis, second, along the line that separates, when it is a matter of establishing syntheses, transcendental subjectivity and the mode of being of objects.  These two forms of fracture gave rise to two series of endeavors which a certain striving toward universality would seem to categorize as echoes of the Cartesian and Leibnizian undertakings.  But, if we look more closely, the unification of the field of knowledge does not and cannot have the same forms, the same claims, or the same foundations in the nineteenth century as in the Classical period.

The essential question is not if we can dispense with metaphysics, or, if, somehow, the Classical age will return, but instead, to ask after the possibility of creation amidst our present moment and its incommensurability with different epochs, differing forms, differing claims and differing foundations – even if it is not so different, after all.

[30] Ibid. p. 57.

[31] In this light, analysis need not be confined to a mathematical logic – in the sense of an a priori method of deduction from a set of axiomatic ‘truths’.  Indeed, many contemporary modalities of analysis, such as phenomenology, hermeneutics, and post-structuralism have little regard for formal logic and the mathematical character and aesthetic of its regressive method.  It could alternatively be stated that, for Leibniz, in the Monadology, a phenomenologically adequate analysis opens itself toward the whole, to existence and its prospective ground as the unfolding of the world in reference to an order of a substantial world of beings.

[32] Monadology, XVIII, p. 33.

[33] Leibniz obtained a Doctor of Law at Altdof in Nürnberg with the Dissertation De Casibus Perplexis (‘On Perplexing Cases’) in 1667.

[34] Leibniz, G.W. Theodicy: Essays on the Goodness of God, the Freedom of Man and the Origin of Evil, trs. by E.M. Huggard, Open Court, 1990.

[35] For Leibniz, there is no need to escape from the phenomena, from the body or from illusion.  Perception is indigenous to each monad and each monad is the creation, in the ‘first’ instance, of a god who is himself subject to his own operative principles.  It is this metaphysical and theological context which sheds light on the meaning of analysis in Leibniz.  This particular context evokes a heterodox Christianity in that the monad cannot ‘live’ without body, and will remain with body always.  For Leibniz, analysis is not, therefore, the purification of the soul from the taint of the body, but instead is a pathway which traces the cosmos itself from out of the perspective of the mirror.  The omission of the metaphysical and theological dimensions of Leibniz is a distortion of the meaning of his philosophy in general and his notion of analysis in particular.  Such omissions are quite contrary to a philosophy that holds that every finite expression is an eternal truth.

[36] Monadology, 3, 251.

[37] Ibid.,5, 251.

[38] Ibid. 6, 251.

[39] It is important to keep in mind the significance of Leibniz’s deployment of the free monad in the context of the raging debate about “Spinozism” which even plagued Kant sixty-seven years later.

[40] Monadology, 8, 252.

[41] Ibid. 7, 251-252.

[42] Russell, p. 115.  Russell also writes in his Critical Exploration (p. 72):

He proceeds, however, to a radically unphilosophical remark on the first question.  “Although the whole of this life were said to be nothing but a dream, and the visible world nothing but a phantasm, I should call this dream or phantasm real enough, if, using reason well, we were never deceived by it” (N. E. 718 -9; G. VII. 320).  In this passage, the unduly practical nature of Leibniz’s interest in philosophy very plainly appears.  He confesses, both here, and in many other passages, that there is no “exact demonstration” that the objects of sense are outside us, and that the existence of the external world has only a moral certainty.  To obtain even this, he requires first the existence of God, which has absolute certainty.

[43] Monadology, 10, 252-253.

[44] Ibid., 15, 253.

[45] Heidegger, p. 82.

[46] Perception is quite broad and deep in this definition, as is substance, and must be distinguished at this juncture from consciousness or apperception.

[47] Monadology 12, 253.

[48] Ibid., 66, 266.

[49] Freeman, Kathleen.  Ancilla to the Pre-Socratic Philosophers, Harvard University Press, p. 29.

[50] Aristotle’s Physics could also be suggested with respect to the Four Causes and the metaphor of the Oak if it were not for Leibniz’s lifelong struggle to free himself from Aristotle.  Yet, it must be stated, as will become obvious in the next section, that Leibniz remains tied to Aristotle, despite his attempt at escape.

[51] Aristotle. De Anima (On the Soul), trs. Hugh Lawson-Tancred, Penguin, 1986.

[52] Russell, p. 104.

[53] Aristotle, p. 157.

[54] Ibid., p. 157.  Aristotle writes: “In the same way, if some tool, say an axe, were a natural body, its substance would be being an axe, and this then would be its soul.”

[55] Goethe, J.W. ‘An Attempt to Interpret the Metamorphosis of Plants,’ Chronica Botanica, Vol. 10, No. 2, 1946, pp. 89-115.

[56] Aristotle, p. 157.

[57] Ibid., p. 162.

[58] Clement, Catherine.  Syncope: The Philosophy of Rapture, Trs. by Sally O’Driscoll and Deirdre Mahoney, University of Minnesota Press, 1994.  In this text, syncope is precisely the state which is described by Leibniz as dreamless sleep or swooning in the Monadology.

[59] Monadology, 20, 255.

[60] Ibid. 22, 256.

[61] In a letter to Arnauld of April 30, 1687, Leibniz seems to suggest, on the contrary, that it is our suspension in-between instantiations which is the syncopic state of the bare monad.

[62] Monadology, 28, 257.

[63] Ibid. 33, 258.

[64] Ibid. 33, 258.

[65] Ibid. 30, 258.  Leibniz qualifies his Promethean rhetoric with the proviso that we can know God to the extent that what is limited in us is unlimited in him.  Yet, this does not remove the striving of the Monad to obtain the whole perception, or in other words, to become God or be with him.  Yet, this would seem to be impossible as the monad cannot be without body.  And, God is without body, unless that is, we can conceive of the cosmos itself as his body, in which the longing of the finite Monad could be satisfied.

[66] Nietzsche, Friedrich.  “On the Despisers of the Body,” Thus Spoke Zarathustra, Trs. by Walter Kaufmann, The Portable Nietzsche, p. 146:

The body is a great reason, a plurality with one sense, a war and a peace, a herd and a shepherd.  An instrument of your body is also your little reason, my brother, which you call “spirit” – a little instrument and toy of your great reason.

[67] Monadology, 63, 265.

[68] It is interesting that it is in this context that Russell writes that Leibniz is at his most unoriginal.  His problem seems to be with the use of the body as a metaphorical place for the interaction of monads in relations of activity and passivity.  Russell writes:

By this relation, both activity and passivity acquire new meanings.  From this point onwards, Leibniz’s philosophy is less original than heretofore.  Indeed he is chiefly engaged in adapting to the doctrine of monads previous theories (notably that of Spinoza), which, by means of the relation of activity and passivity, become available for him in spite of the denial of transeunt action.  Thus a sharp line should, I think, be drawn between those part’s of Leibniz’s philosophy which we have thitherto discussed, and those which, through passivity, depend upon the apparent interaction of monads. (Critical Exposition, p. 139)

It could be argued on the contrary that it is precisely in his reference to passivity that we can not only begin to ask the question concerning the relation of finitude to the infinite, but also, to begin to construct a topos in which an organic harmony in the realm of perception and the body can be found which adequately mirrors the ideal unity of the divine.  We should recall Mates suggestion that the Monadology is a “heuristically useful fairy story”.  As we will see below in The Meaning of the Monad, it is Leibniz’s use of metaphor which allows him to approach the contingent aspects of existence which must still, in the context of the principle of individuation, be accounted for in the “whole being.”  In this way, we may agree with Russell that a line must be drawn, but we may just as well remain on the other side.

[69] Monadology, 71, 267.

[70] Ibid., 64, 265.

[71] Ibid., 69, 266-267.

[72] Ibid., 78, 269.

[73] Ibid., 80, 269.

[74] Ibid., 79, 269.

[75] I will return to this possibility in the next section, The Meaning of the Monad.

[76] Monadology, 88, 271.

[77] Foucault writes in The Order of Things, p. 298:

God is perhaps not so much a region beyond knowledge as something prior to the sentences we speak; and if Western man is inseparable from him, it is not because of some invincible propensity to go beyond the frontiers of experience, but because his language ceaselessly foments him in the shadow of his laws: ‘I fear indeed that we shall never rid ourselves of God, since we still believe in grammar.’ (from Nietzsche, Twilight of the Idols)

[78] Once again, the severance of God and body can be seen as a divergence from “Spinozism.”

[79] Monadology, 38, 259.

[80] Ibid., 43, 260.

[81] Ibid., 44, 260.

[82] Ibid., 41, 259-260.

[83] Ibid., 38, 259.

[84] Ibid., 45, 260-261.

[85] Ibid., 48, 261.

[86] As we have intimated, this emulation of the divine cannot be interpreted as one that seeks a resemblance with the bodiless character of God.  In its stead, the continuity of emulation must subsist as the respective harmonies of existence and the divine.

[87] Monadology, 55, 263.

[88] Ibid., 42, 260.

[89] Ibid., 47, 261.

[90] This does not mean, however, that all reality is subject to the will of God, but only to his understanding, for even God’s will is subject to the principles of Mind and the Good.  In this way, both the created thing and God are monads, but are distinguished by their respective activity and passivity, spontaneity and receptivity.

[91] Monadology, 51, 262.

[92] Ibid., 52, 262.

[93] Ibid., 56, 263.

[94] Ibid., 60, 264.

[95] Ibid., 61, 265.

[96] Foucault writes in The Order of Things:

As an inadequation extending to infinity, man’s limitation accounted both for the existence of the empirical contents and for the impossibility of knowing them immediately.  And thus the negative relation to infinity – whether conceived of as creation, of fall, of conjunction of body and soul, or determination within the infinite being, or individual point of view of the totality, or link between representation and impression – was posited as anterior to man’s empiricity and to the knowledge he may gain from it.  In a single movement, but without reciprocal return or circularity, it provided the foundation for the existence of bodies, needs, and words, and for the impossibility of subjugating them within an absolute knowledge. (p. 316)

[97] Monadology, 57, 263.

[98] It may seem strange to make a reference to Nietzsche in the context of a discussion of the divine.  Yet, there are some very interesting correspondences between Leibniz and Nietzsche, as well as questions of a nature which would send us beyond the confines of the present essay.  Suffice it to indicate that both of these thinkers were not only adherents of the principle of individuation, but were also committed to a perspectivism which remained oriented to a “whole” and a “continuum” – even if their respective conceptions of this whole are distinguished by the event of the death of God.

[99] Descartes, Rene.  Meditations on First Philosophy, translated by John Cottingham, Cambridge University Press, 1994, p. 21: ‘But then if I look out of the window and see men crossing the square, as I just happen to have done, I normally say that they are men themselves, just as I say that I see the wax.  Yet, do I see any more than hats and coats which could conceal automatons?  I judge that they are men.’

[100] “The Vision and the Riddle,” Thus Spoke Zarathustra,   p. 267-271.

[101] Leibniz, G.W. Correspondence with Arnauld, in Discourse on Metaphysics, Correspondance with Arnauld and Monadology, Translated by George Montgomery, (Open Court, 1990), p. 195.

[102] Ibid., p. 195.

1 Comment

  1. greentymer1 said,

    October 15, 2013 at 12:58 pm

    Wonderful paper.

    That said, as I great admired your philosophical instincts and expertise, I am hoping that you will give me some thoughts about the “union of finitude with infinity” metaphor diagram found at http://TrueTyme.org/WholenessAndOnenessSeenAnew.pdf .

    Warm regards


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