THE PRIMAL MIRACLE AND THE EXISTENCE
AS TOTALITY IN LEIBNIZ

Ioan Lucian MUNTEAN*

RESUME

Nous tentons d'approcher la raison pour laquelle les miracles engagent, chez Leibniz, l'existence dans sa totalité. On sait qu'il veut adapter la doctrine chrétienne des miracles à son système métaphysique. Pour ce faire, Leibniz utilise trois voies: 1) le miracle comme transgression des lois de la nature, conçues en tant qu'instances de la Loi de l'Univers (λ). Ici, la difficulté est de démontrer comment il est possible qu'un événement qui enfreint les instances particulières de λ (lois de la nature) peut se soumettre aux λ elles-mêmes. 2) Un critère épistémologique pour distinguer les miracles des événements ordinaires, fondé sur les limitations de notre faculté de comprendre les raisons supérieures de Dieu. 3) Le mi racle "primigène" de la Création qui ne se réduit pas au langage de 1) ou 2) et qui est lié à la question fondamentale de la métaphysique: "pourquoi donc y a-t-il quelque chose plutôt que rien?" Les premières explications se retrouvent dans plusieurs textes de Leibniz (et largement discutées dans l'exégèse), alors que la troisième est mentionnée brièvement dans quelques textes moins connus. Nous voulons démontre r que la troisième est indépendante d'un langage des lois ou d'un langage de l'épistémologie et qu'elle est premièrement ontologique. Nous considérons cette troisième explication comme fondamentale pour le système de Leibniz.


In this paper I investigate the connection between miracles and existence in Leibniz's philosophy. Following a Scholastic tradition, miracles have been  related to laws of nature because many authors since 17th century have conceived miracles as infringements of laws of nature or in a weaker sense as irregularities in the world order, i. e. something that commonly had no natural realisation by causation. Miracles as violations of natural laws are not simply events that nature  would not alone produce, but those that nature could not have produced on its own. Such an event would then always be incompatible with the relevant natural laws. Miracles are ev ents, although they belong to an uncommon kind of events.

In the first two sections I take into account the connection between miracles, laws of nature and knowledge as it can be found in Leibniz. 1 I sketch here two criteria for miracles in Leibniz's philosophy of nature presented by Robert McRae. 2 The first one is linked to the concept of law, the second is related to our power of understanding. The first criterion (A) implies the distinction between law (loi) and rule (règle), the second (B) depends on our capability of understanding higher reasons.

In the third section I discuss miracles as being linked to existence. I proof that Leibniz's theory of miracles involves an extensive ontological scheme containing also creation and the reason of existence, not only disconnected events and laws of nature. This can be interpreted as an attempt to bring forth a metaphysics of miracles, independent of the Christ ian dogma. For Leibniz miracles cannot be represented in a pure event-language of laws and orde r of nature. Hence in order to define miracles one needs to inquire into existence and to bring out more clearly the ontology of miracles. I hold that Leibniz pursues the idea of a miracle of existence as totality in a paramount question concerning the ground of all metaphysics: "why is there something rather than  nothing?" even if he doesn't mention explicitly miracles.3

Principally, our analysis is internal to Leibniz's philosophy and does not involve fundamentally the Christian dogma of miracle.

1. LAWS, RULES AND COMPREHENDING MIRACLES

It can be noticed that in Leibniz's metaphy sics there are at least three types of laws. 4 The first is the general law of Universe, 5 the second is identified with some architectonic principles as the law of continuity and the law of maxima-minima determination. And thirdly there are laws of nature.6 Individuals obey particular laws that are only variations of  the general law ruling the Universe. Monads are themselves under the same law even if their different aspects could seem opposite. 7 An infringement of such a peculiar law will be only a local deviation from a token of the general law of Universe, yet not an encroachment on the law itself. These types of laws are fully employed in  Discourse on Metaphysics and Essays on Theodicy where Leibniz attempts to explain that appa rent irregularities are finally conceivable and regular. 8 Discontinuities are simply logically impossible so a continuous Universe is not simply a matter of Divine choice. And finally the phenomenal Universe is governed by laws of motion which are best explained by the science of mechanics.

How can miracles be understood if there are thr ee types of laws? For Leibniz miracles infringe laws of nature but they don't encroach on the general law of Universe λ, as "the most general of the laws of God which rule on the whole sequence of the universe has no exceptions." 9 An exception to a law of nature (e.g. the "conservation of force") would be a miracle, but it would not infringe the law of Universe. It seems that Leibniz faces here a difficulty. To allow miracles in his system he has to reject an argument involving infringement of "the law of  Universe" by miracles. One can render this in a quasi-formal language of classical logic, but let us clarify firstly the concepts involved.

Let λ be the unique law of Universe. One can assume 10 that λ is a composite "metaphysical" law, a logical conjunction containing law of non-contradiction (NC), law of sufficient reason (SR), law of identity of indiscernibles (II) and law of maximal compossibility (MC).11 Let λk be one of λ's instances (or a set of such instances considered as one). As a token of λ, λk is a law of nature and metaphysically obeys any component of Λ.

Let ek be an individual event (or a set of events  considered as one). Tacitly Leibniz assumes that to every ek corresponds a (or a set of) λk which it "normally" obeys. That "ek infringes λk" means ek is incompatible with some other events that naturally follow from a) the causal history of ek and b) λk itself. One can admit that by infringing λk, ek obeys all components of λ but MC, as it represents a state incompatible with other states in the same Universe (or possible world). Compossibility does not re- quire law-governed. One can imagine a Universe (U0) made up by compossible states without obeying any peculiar λk and another Universe (U1), instantiating some λk, made up by states which are not altogether compossible because of λk. In this case U1 presupposes only NC, SR, II and a pre-established harmony, but not MC. In U1 there are no miracles, as there are no incompatibilities. By consequence, MC is the "weaker" component of λ.12

One can improve the account of miracles if  one insists upon Leibniz theory of natural order of things, i.e. compossibility and compatibility. The subset of the set of all possible existences partitioned by the relation of compossibility (COMP) is an equivalence class that can be used to define a possible world as a collection of states that are recipr ocally compatible (i.e. not incompatible, ¬INC). A complete set of compossible monads is a "universe" where every monad reflects any predicates of every other monad.13 A miracle can be described by a state being incompatible (INC) with some states of the same world, even if it is not incompatible with the pre-established harmony which contains the set of all COMP relations of all possible worlds.14

But there is another difference between the type Λ and its tokens λk. Unlike Λ, laws of nature (λk) involve abstract concepts that are only "full", but not "complete". 15 A complete concept reflects everything that could and will happen, but an abstract concept is only full in the sense that it cannot grasp the infinite complexity of individual subs tances. Containing only "full" concepts, laws of nature cannot "bind" miracles in this metaphysics.

Now let us go back to the argument about  infringement. It can be formalized as follows:

(1) λk is an instance of Λ
(2) ek should obey λk ("normally")
(3) ek infringes λk (it has INC with some λk's consequences)
(4) Therefore, ek infringes also Λ

Leibniz has to explain why this argument is invalid, i. e. to refute the inference to (4) from (1)-(3) and to explain why the infringement of a peculiar instance of Λ (i.e. a λk) would not infringe Λ itself. For this he has to employ firstly two further theoretical devices: the distinction between rule and law and the definition of miracles as the limitation over the power of understanding God's creation. My claim is that his refutation of 1)-4) is not possible without invoking the existence as a whole and its metaphysical ground. I present this ontological analysis in the third section.

A) Laws and rules . I switch now to the difference betw een general rules and laws of nature, as exposed by Leibniz. 16 In his response to the occasionalist  Fr. Lamy, he bestows attention on a sharp distinction between a general rule and a law of  nature. Usually, his examples concern motion, and especially the force to continue the movement in a st raight line, i. e. the inertia. These are not simply rules, but laws according to the nature of bodie s. Had God force a general rule upon nature as a curve-path for a freely moving object, then this woul d be followed by a continual series of miracles. And this rule would not be a law of nature, due to its non-conformity with the nature of bodies. Had by such a rule God impose a circular movement even after the body has been released from constraints (sling, rope, etc.), then this would be a continual mira cle in respect of the nature of the motion of a body.17 A law of nature is linked to the nature of  objects complying it, not only to sets of events, while rules refer exclusively to events or sets of events. The trend of a body to move in a straight line is a law, as it implies the nature of the body, where as the non-rectilinear free movement would be only a rule that would demand continual miracles an d would not conform to the nature of bodies. 18 The tendency of all bodies to move freely in circle s would be a miracle in all possible worlds, as such motions are not consequences of the natures that God gives things and they cannot be understood. 19 Elsewhere Leibniz explains that the criterion for a mi racle is not its character of being unusual (as it is the case for a rule), but the surpassing of creatures' forces and natures. 20 Clarke uses a "regular" definition of a miracle, as "something that God seldom does" and by this He is breaking a rule. Miracles do not imply the nature of things.21

I conclude that miracles are occurrences of unexpected events and they presuppose God's intervention not only in world's regular system of  rules. This means that mira cles break natural laws and not only natural regularities. Consequently, they  are events contradicting somehow the nature of real objets. But this doesn't mean that miracles infringe Λ, as neither they nor λk reflect necessarily the essence of God or the essence of matter. Albeit laws of nature, unlike rules, operate with the natures of objects as full concepts, they cannot capture their essences which are necessarily complete concepts.

B) Miracles as epistemic entanglements . For the theology and philosophy of the 17 th and 18 th centuries the definition of miracles supervenes on our power of understanding: Locke (and eventually Hume) has stated that a "miracle criterion" depends entirely on our power to grasp events and not on an ontological difference among them. Accordingly,  the miracle criterion is the converse of the law criterion; that means that all events are either  law-governed or miraculous. Leibniz acknowledged partially such a weak epistemological criterion: s ubsequently miracles are somehow in relation to our understanding, more precisely in relation to an understandable order laid down between created things.22 Concerning universal law Λ, all things must conform to it, even miracles, as it is logically impossible to admit a Universe without Λ. Miracles aren't essentially different to other events, although God performs them by higher reasons compared to natural agencies. Even if Leibniz is has been drawn into temptation to use here a theological difference between Divine works of nature and Divine works of Grace23, the difference between miracles and natural ev ents is epistemological and "actional": firstly they cannot be explained by the natures of created things and second they cannot be performed by creatures.24 It worth noticing that Clarke and Leibniz agreed apparently on this point, even if eventually Clarke would happily take heed of some  of Leibniz's self-contradictions. 25 Elsewhere Leibniz had provided a well-known geometrical analogy: if  one draws a complicated line it appears irregular to human eyes, although a mathematician can understan d it as a perfect rational object geometric by means of its equation. When a rule is very complicated, what obeys it seems irregular 26 — the same is true about laws. Even if in this context complexi ty has arguably a strong epistemical meaning, complexity of miracles is not their essential part.

Despite his confidence in the power of human  understanding, Leibniz states an epistemical difference between natural events and miracles: a  creatural mind can forecast no miracles or extraordinary interventions of God, as the unders tanding of general order  and law surpasses all creatures.27 This can be linked to the difference between tr uths of facts and truths of reason, all being truths of reason for God.

In a contemporary key one can read Leibniz's  epistemical account of miracles as follows: we humans can not translate the descriptions of miracle s in descriptions of natural events, even they are not essentially different. But one should not ov erestimate this epistemological difference between miracles and natural events. It is clear that this epist emical criterion is second for him to the fact that miracles do not infringe Λ because they are conformal to essence of mater and God. Contrary to other thinkers, he haven't engaged an exclusive epistemol ogical criterion for miracles (B), therefore the infringement of natural laws (A) is much more  important as he needs "an internal difference" between miracles and natural events.

2. DEGREES AND NUMBERS OF MIRACLES IN POSSIBLE WORLDS; MIRACULOUS STATES OF MONADS

For Leibniz some miracles described in  the Bible are not miracles of the first  degree, as God could change entirely the "flow" (le cours) of the Universe and this would not be in accordance with his explanation of change and becoming.28 God's intervention in this case would imply more than we could imagine.29 As it manifest in his correspondence with  Clarke, an overflow of miracles would have infringed the pre-established Harmony. As miracles  can be performed by angels without breaking the laws of nature and not necessary by God Himself, one  can admit again that miracles certify our finite faculty of understanding "higher reasons". Even if we cannot understand it entirely, the angels' ingenuity differs from ours only by a degree of perfection, as neither they nor us are capable of surpassing God's direction (dispensation)30, in other words cannot surpass Λ and the pre-established harmony. This means that in some ways miracles are truths of God's Reason.

How can one relate this to the metaphysical components of Λ? As I have already flagged out, Leibniz explained how a miracle felt under metaphysical constraints as NC, SR and II but how it might infringe MC (which is not a metaphysical constraint). This  remark brings us to the idea of miracles as indexicalized to possible worlds and having to do  with Leibniz's possibilism. It follows that the number of miracles in actual world has a reason. We  know that Leibniz maintains against Spinoza's or Descartes' necessitarianism that laws of nature (λk) are contingent and they don't follow necessary from the essence of matter or from the essence  of God: "These laws are not necessary and essential but contingent and existential... For since it is c ontingent and depends on the free decree of God that the series of things exists, the laws of  the series will also be contingent." 31 Likewise "it is possible that some laws of nature are entirely without rational founda tion and that their obtaining is the result of a raw exercise of divine power".32 Though for Leibniz God's power to create a real world is bounded to groups of compossibles (not necessarily maximal), it  does not preclude Him from creating a world which is not  strictly law-governed or (as a logical c onsequence) from creating a world  completely deprived of miracles. This means that laws of nature and rules cannot be necessitated like in Descartes or Spinoza, even he admits a hypothetical (or consequential) necessity stated only by Divine choice of future events.33 But even all events are certain in relation to God, their reciprocal connections are not always necessary.

Miracles are part of this world and from the  beginning they have been wrapped and represented internally to it. In order to conceive miracles  within the actual world, one is committed to take the world as a state of pure possibility 34 and not simply investigate it by the means of senses or empirical observations. That is why there is no empirical science of miracles. Miracles are as possible as actual events even through laws-limitations they are not  as probable as actual events. Although their description state is incompatible (INC) with other states from the same Universe, they can not be rejected on logical or metaphysical ground. MC can be a logical or a metaphysical constraint on the possible states of a world and on number of miracles, not on their possibility or existence.

For Leibniz each world has it s own peculiar laws (series of λk) and as the number of possible worlds is infinite, there are also infinitely many tokens of laws. Each individual of any world contains in the concept of itself the laws of its world. And  Leibniz adds that this can be stated equally about miracles, each world having its own miracles, even if  they remain in the concept of the Universe. Each substance mirrors the whole Universe and consequently all miracles, too. 35 So λks are indexed to possible worlds, whereas Λ is unique for all possible worlds. Usually Leibniz refers to possible worlds as containing monads, spirits, minds, but here he points to possible phenomenal worlds of moving bodies, not spirits and monads. 36 In his view we are living in the best possible world with a minimal set of laws of nature (series of λk) and also with a minimal numbers of miracles chosen by God, or more precisely "only miracles which were necessary". 37 On one hand the best of all  possible worlds is acquitted of being overflowed with miracles and on the other hand it has a minimal set of laws of nature.

Concerning monads, it is relevant to make here a  point on Leibniz's account of their miraculous states as opposed to miracles involving phenomena. There are at least two contradictory accounts of "miraculous states" of a monad. a) "Miraculous" st ates of monads are those produced externally by God, so they do not arise from the nature of  the monad itself. "Properly speaking, God performs a miracle when he does something that surpasses the forces he has given to creatures and conserves in them".38 This view of a Divine intervention in the state-series of a monad is quite opposed to Leibniz. I take it as being deviant in respect of his later metaphysics; b) Conceptual  ensemble of monads includes their states, both natural and miraculous. This view is consistent with the Leibnizian system as a whole. But here arises a difficulty: if we conceive concept s as causes, then Leibniz cannot draw the distinction between natural and miraculous states,  since on the conceptual unfolding view 39 all states of a monad have the same cause — its concept. Then there are no miraculous states. 40 But it is clear that Leibniz favours the distinction between the set of all states  of a monad and the set of its miraculous states. "[...] we can say equally that the extraordinary ac tion of God on this substance does not fail to be miraculous, despite the fact that it is packed in t he general order of Universe as it is revealed by the essence of this substance or its individual notion." 41 And this second view bolsters my argument for miracles as entailing the existence as a whole.

Although Leibniz holds that the creation of things is a miracle, he repels the idea that regularities in nature like harmony between mind and body, c onstitution of plants and animals, or movements of celestial bodies are not perpetual miracles. 42 He admits that some are wonders ( merveilles), but not miracles and provides no satisfactory explanation  on the difference between them. Although I suggest that wonders are a lower species of miracles which only impress us emotionally and can be performed by men, too. 43 Wonders are foreseeable by men, but miracles are foreseeable only by God. A miraculous state of a monad is compossible with all other states, so miraculous states of a monad does not infringe MC.

I conclude that Leibniz acknowledges that laws of nature λk can contradict some events (see argument above, premise (3) but this doesn't imply t he conclusion (4). If a miracle involves monads or real objects, it still occurs in the actual world or in a possible world under the reign of Λ.

3. MIRACLES AND PERFECTION OF EXISTENCE

As I have mentioned, miracles are discussed usuall y along with natural regularities, natural order and laws of nature which are best described in a la nguage of events. But I venture to claim that in Leibniz's system miracles involve also statements concerning existence as a totality, more precisely the beginning of existence or the process of "popping up" from nothing. In other words, even if laws of nature (A) are more important that our epistemological limitations (B), the law-language is not the final point Leibniz has made in dealing  with miracles. In order to fulfil  his explanation of miracles, Leibniz needs more than law, order and epistemic consider ations. He must complete his analysis with the creation and existence as a whole. For this, a third type of miracles which escapes the law-language and epistemological considerations has to be defined.  This add-on is the primal miracle of creation (PMC, miracle primigène de la Création). If (A) and (B) can be accommodated to Christian dogma of incarnation and Biblical miracles, this type of miracle is more  or less a philosophical explanation, involving possibilism, logic and metaphysics.

The "moment" of creation involves a miracle, but this cannot be thought as a simple event as it is not grounded (G) in or simultaneous with (SIM) other events44 and laws of nature (λk) are not at work in the creation itself, even if creation obeys Λ. But this is not the main reason to take creation as a miracle. Likewise, creation is not a miracle inasmuch  as we do not understand it. Creation is a miracle yet not in a language of laws, rules and/or epist emical suppositions. There is another reason to hold that creation is a miracle.

As early as the period of Theodicy, Leibniz has advocated a theory of conservation as a perpetual creation,45 which is aloof to later tenets of a law-governed world in which God seldom intervenes. Leibniz's debate with Clarke can be interpreted in a  more fundamental ontology, too. This special type of miracles (PMC) is incidentally en gaged in the debate with Clarke, 46 as Leibniz tries to exclude miracles from the world governed by laws, especially  perpetual miracles involved in motion. Leibniz recalls also PMC when he speaks of a miracle reserved only to God, the power to create and annihilate things.47 In setting off his position a gainst Clarke, Leibniz rejects God's intervention in the "flow" of Universe, except the moment of creation. I claim th at PMC is basically related to the so-called "most fundamental question of metaphysics" 48 and not directly to laws of nature or epistemological considerations.

This interrogation is announced in a text set up in the same period, i. e. "Principles of Nature and Grace founded in Reason" but more  explicitly enunciated in "De Rerum Originatione Radicali". Leibniz takes for granted his principle of sufficient reason according to which nothing happens without a sufficient reason and asks "a question which should rightly be asked: why there is something rather than nothing?".49

This question is justified by an  a priori argument from simplicity: "nothing is simpler and easier than something" a principle that should  be called "Spontaneity of Nothingness" (SoN).50 So it is necessary that there should be a reason why things must exist so and not otherwise. In this respect, the world's most natural state of affairs according to  should be to not exist at all. As a consequence, the non-existence state of the world is conceptually the simplest and ontologically the most stable, the lesss complex so in other words epistemologically the most accessible. This means that the non-existence state of affairs is coherent and natural. It is the most natural one as it infringes neither the λks laws nor Λ and it does not involve any epistemical entanglements. As the most natural one, the non-existent state of world is also free of miracles as well as free of any laws of nature. 51 Needless to say, the moment of creation is also free of instances of λk to be encroached. All possible things have an equal right toward existence according to their degree of perfection. In possible things there is an exigency to existence, a reaching out for existence (praetensionem ad existendum) and a tendency toward existence. This is strictly speaking beyond a language of  laws of nature and explanation of understanding. Regarding Leibniz's argument against premundial t ime deployed in the third letter to Clarke, he mentions again PMC. It entails also the transformation from ideal  time to real or concrete time. Ideal time is perfectly homogenous, and concrete time is related to events it contains. Only elements of concrete time can be distinguished one from the other, so "ordinary" miracles can be located only "after" the PMC. Creation makes possible the criterion  of individuality of events by their place in time order. Laws of nature are invariant to a translation of the origin of time. PMC is a miracle beyond laws of nature in this respect, too: it them possible.

Neither nothingness nor existence after creation presuppose  stricto sensu miracles in this full sense, i.e. beyond MC and a law-governed Universe, but only the popping up of matter from nothing is a "true" miracle in the sense of  PMC. In other words, only the transience from nothingness governed by SoN to a series of law-governed states is an "existence type" miracle. The third type of miracles fulfils Leibniz's doctrine of miracles and generally  is coherent with his metaphysical system, while the other two criteria raise some difficulties of interpretations.

REFERENCES
G: Die philosophischen Schriften von G. W. Leibniz, edited by C. I. Gerhardt, 7 vols., Berlin, 1875-90.
E: God. Guil. Leibnitii, Opera Philosophica  Omnia quae exstant Latina Gallica Germanica , ed. by J. E. Erdmann, 2 vols., Berlin, 1840.
C: Opuscules et fragments inedits de Leibniz, edited by L. Couturat, Paris, 1903.
Richard Arthur, [1985], "Leibniz's Theory of Time", in Kathleen Okruhlik; Brown James, Robert, (eds.), The Natural Philosophy of Leibniz, Reidel, Dordrecht Lancaster, 263-313.
Kenneth Clatterbaugh; Marc Bobro, [1996 (July) ], "Unpacking the Monad: Leibniz's Theory of Causality", in Monist, 79 (3), 408-425.
Adolf Grünbaum, [2000], "A New Cr itique of Theological Interpretations of Physical Cosmology",  in British Journal for the Philosophy of Science, 51 (2000), 1-45.
Robert McRae, [1985], "Miracles and Laws", in Ka thleen Okruhlik; Brown James, Robert, (eds.),  The Natural Philosophy of Leibniz, Reidel, Dordrecht Lancaster, 171-183.
Kathleen Okrulik, [1985], "The Status of Scientific Laws in the Leibnizian System", in Kathleen Okruhlik; Brown James, Robert, (eds.),  The Natural Philosophy of Leibniz,  Reidel, Dordrecht Lancaster, 183-206.
Christina Schneider, [1998], "Leibniz's Theory of Sp ace-Time: An Approach from His Metaphysics", in Monist, 81 (4), 612-632.
Richard Swinburne (ed.), [1989], Miracles, New York, Macmillan.

* I would like to thank especially Rom Harré (Linacre College, Oxford) and Don Rutherford (University of California, San Diego) for revising previous drafts of this paper. I also greatly appreciate the seminal discussions and exchange of ideas I have had on the occasion of the meetings at New Europe College (Bucharest, Romania, 1999-2002) and during the summer school "Spaces of freedom in modern thought. Individuals, reformation projects, multiple societies" (Tescani, Romania, 2-15 September 2001) with Vlad Alexandrescu (University of Bucharest), Katherine Brading, (University of Notre Dame, USA), Sorin Costreie (University of Western Ontario, Canada), Dana Jalobeanu ("Vasile Goldi" Western University, Arad, Romania) and Horia-Roman Patapievici (New Europe College, Bucharest) on laws of nature, causation and miracles in the 17th century which have helped me to write this paper. Version date: November 04.
1 Although this is a topic undertook in his correspondence  with Clarke and it had been announced already in the first letter, we rely in our analysis on other less known texts.
2 [McRae, 1985].
3 We follow here especially two texts "De rerum originatione radicali" (1697, E 147-150) and "Principes de la nature et de la grâce, fondés en raison" (1714, E 714-718).
4 [McRae, 1985, 171].
5 As explained in Monadologie, the Universe is taken to contain monads, spirits and minds.
6 Another classification of laws in Leibniz's philosophy can be established if the division between Realm of Grace and Realm of Nature is considered primary, as in  Essais de Théodicée, Monadologie and "Principes de la nature et de la grâce, fondés en raison". Consequently there are three types of laws: logical, physical and moral, but I don't emphasise here this distinction. See S. Costreie, "Leibniz on Miracles" (this volume issue) for further details.
7 See (G IV, 553).
8 E. g. Essais de Théodicée, §242.
9 "[...] car la plus generale des loix de Dieu qui regle la suite de l'univers est sans exception",  Discours de Métaphysique, s. VII.
10 As Rom Harré has indicated in a private communication.
11 A possible world is a maximal set of compossible individuals. Two individuals fail to belong to the same possible world if they are logically in contradiction with one anot her or if they do not harmonize with one another by a pre-established harmony. We will discuss later the metaphysical status of MC.
12 [Okruhlik, 1985, 188].
13 [Okruhlik, 1985, 189], [Arthur, 1985, 304].
14 We can recall here Arthur's formalisation of these relations [Arthur, 1985, 304]: aINCb — state a is incompatible with state b; SiCOMPSj — where Si, Sj are two monadic series of all possible monads: (∀Si, Sj ∈ U) SiCOMPSj =df. (∀ai ∈ Si)[(∃aj ∈ Sj) (¬ajINCai) & (∀bj ∈ Sj) (¬bjINCai → bj = aj).
15 [Okruhlik, 1985, 196].
16 "Réponse aux Objections que l'auteur du livre «De la C onnaisance de soi-même» a faites contre le système de l'harmonie préetablie" published in Journal des Sçavans, suppl. 1709, June, p. 275-279, where Leibniz provided an ans- wer to Fr. Lamy (E 458-460).
17 Letter to Arnauld, 30 April 1687 (G II, 93).
18 See "Réponse..." to Father Lamy, "Une telle loi de mouvement circulaire ne seroit donc point naturelle [...] Ainsi il ne suffit pas pour éviter les miracles, que Dieu fasse une  certaine loi, s'il ne donne point aux créatures une nature capable d'exécuter ses ordres" (E 460). Also third letter to  Clarke, §17: "Si Dieu vouloit faire en sorte qu'un corps libre se promenât dans l'Ether en rond [...] cela ne se pourroit que par miracle, n'étant pas explicable par les natures des corps" and §45: "Car ces effets [que les corps s'attirent de loin, sans aucun moyen et qu'un corps aille en rond, sans s'écarter par la tangente, quoique rien ne l'empêchât de s'écarter ainsi] ne sont point explicables par les natures des choses".
19 "Replique aux reflexions de Bayle" (1702), (E 185).
20 Fifth letter to Clarke, §107.
21 Fifth reply, §107.
22 Discours de Métaphysique, s. VI. Leibniz uses here "ordre" to design ate the Universal order. We conjecture that given the monadological context of subsequent sections what he means is that the Universal order obeys   and not only a general rule or a peculiar set of λk.
23 "When God works miracles he does not do so in order to supply the wants of nature, but of grace", first letter to Clarke, §4. As we have already noticed, this distinction is not essentially to Leibniz metaphysics as a whole but only to Essais de Théodicée and eventually Monadologie.
24 The nature inherent to created things is the capacity  of act and to be acted on: "natura insitam nondiffere a vi agendi et patiendi", De ipsa natura, §9 (E 157).
25 Clarke's third reply, §17: "si tout ce qui n'est pas l'effe t des forces naturelles des corps [...] est un miracle; il s'ensuivra que tous les mouvemens des animaux sont des miracles."
26 Discours de Métaphysique, s. VI.
27 Discours de Métaphysique, s. XVI.
28 Essais de Théodicée, §249. Leibniz's example is the Wedding in Cana of Galilee.
29 "Ainsi ce miracle demandoit plus qu'il ne paroît", idem.
30 "Discours de la conformité de la Foi avec la Raison", §3.
31 (C, 20).
32 [Okrulik, 1985, 185].
33 (G, II, 400).
34 "...les miracles qui arrivent dans le monde, étoient  aussi enveloppés et representés comme possibles dans ce même monde, considéré dans l'état de pure possibilité", Essais de Théodicée, §54.
35 "Observations sur une lettre [...] de M. Arnauld", 1687, (G, II, 40).
36 [McRae, 1985, 178].
37 "...puisqu'il [Dieu] en a choisi le meilleur [Univers], et n'a employé que les miracles qui y étoient néccesaires.", Essais de Théodicée, §248 (E 579).
38 Letter to Arnauld, 30 April 1687 (G, II, 92); see also Discours de Métaphysique, s. XVI (all quoted above).
39 According to this doctrine, the cause of each perception of a monad is to be found in its individual concept, [Clatterbaugh&Bobro, 1996, 409].
40 [Clatterbaugh&Bobro, 1996, 415].
41 "[...] on peut dire de même que cette action extraordinai re de Dieu sur cette substance ne laisse pas d'estre miraculeuse, quyqu'elle soit comprise dans l'ordre general de l'Univers entant qu'il est exprimé par l'essence ou notion individuelle de cette substance", Discours de Métaphysique, s. XVI.
42 Fifth letter to Clarke, §89 quoted above. See also §11 5, same letter: "Quant aux mouvemens des corps célestes, et, plus encore, quant à la formation des plantes et des anim aux, il n'y a rien qui tienne du miracle, excepté le com- mencement de ces choses."
43 Clarke eventually would not miss the occasion to take ad vantage of some shortcomings in Leibniz's argument. Fifth Reply of Clarke, §107.
44 No possible events could occur before the beginning of the world because they would then be the beginning of the world. See fourth letter to Clarke, §15.
45 §382-390.
46 Fifth letter to Clarke: "L'Harmonie ou Correspondance ent re l'ame et le corps, n'est pas un miracle perpetuel, mais l'effet ou la suite d'un miracle primigène fait dans la  création des choses, comme sont toutes les choses natu- relles", §89.
47 Fourth letter to Clarke, "mais il y a des miracles réservés  à Dieu, et qui surpassent toutes forces naturelles; telle est celui de créer ou d'anihiler", §44.
48 Qualification used by some theist and atheist philosophers e. g. M. Heidegger,  Einführung in die Metaphysik, 1953, Tübingen, Niemeyer, p. 1; see also R. Nozick,  Philosophical Explanations, Harvard Univ. Press, 1981. The thesis that a question on the state of nothingness can bear a sense was  strongly denounced by L. Wittgenstein, R. Carnap, or more recently by P. Quinn and A. Grünbaum, although on completely different grounds.
49 "Principes...", (E 716). This question has an Aristotelian bias: "[...] our original inquiries, i. e. all men begin, as we said, by wondering that things are as they are" (Met. 983a13), although Leibniz raises it here on different grounds.
50 Statement uttered by many theist philosophers: Aquinas, Descartes, Leibniz and more recently R. Swinburne,  The Existence of God, (1979), see [Grünbaum, 2000, 5].
51 At least for Leibniz, SoN together with the principle of sufficient reason can provide an ontological argument, as the answer to this question isn't to be found in the series ( suite) of contingent things, but in a substance that carries in itself its own reason, i. e. the necessary Being, God. Arguments in §10-12 are all together proofs for the existence of God based mainly on theodicy and perfection of God. No matter how far we may have gone back to earlier states of things, we will never discover in them a full reason wh y there should be a world at all, and moreover no reason why it would be such as it is. Even if we were to imagin e the world to be eternal, the reason for it would clearly have to be sought elsewhere. The reason for its existence cannot be found in existing things. See "Rerum..." (E 147): "itaque utcunque regressus fueris in status anteri ores, nunquam in statibus rationem plenam repereris, cur scilicet aliquis sit potius mundus, et cur talis. Licet  ergo mundum aeternum fingeres, cum tanem nihil ponas nisi statuum succesionem, [...] patet alibi rationem quaerendam esse." and "Principes...", §8.