SOURCE: "God and the Mind of God," in The Philosophy of Leibniz, Prentice-Hall, Inc., 1967, pp. 11-21.

God

Leibniz, more than any other modern philosopher, took seriously the idea of a creation of the universe, giving it a centrally important place in his system. Like the theories of the medievals for whom he had such great respect, his system put God as the author of creation at the focal position in metaphysics. The concept of God provides the theoretical foundation upon which the structure of the Leibniz metaphysic is built.

God, for Leibniz, may be defined as "the perfect being."¹ His existence is not a seriously problematic issue; it follows directly from the idea (or essence) of his perfection, by reasonings along the lines of the Ontological Argument of Anselm as refurbished by Descartes, and also by other, related arguments—a topic to which we will return at some length. Indeed, all characteristics of God must inhere in and derive from His attribute as "the perfect being." Three of these characteristics are of primary importance for Leibniz: omniscience, omnipotence, and (omni-) benevolence.² These are the operative theological concepts in terms of which the drama of creation unfolds itself.

Substance

In the philosophy of Leibniz, as in that of Descartes and Spinoza, the conception of substance plays a fundamental role. Leibniz defines a substance as "a being capable of action."³ God, of course, is a substance—the primordial substance, the only substance that exists in its own right. All other substances are in the first instance mere possibilities whose actualization hinges upon God, upon the creation. The prime characteristics of Leibniz' substance are: 1) a given individual substance is a simple, perduring existent, not in the sense of logical simplicity, but in the absence of spatial parts; 2) a given individual substance is capable of functioning as the subject of propositions, the predicates of true propositions concerning the substance standing for attributes of the substance. One can loosely describe Leibniz' individual substance as a spatio-temporal existent (God apart) without spatial parts, but not without attributes, and with a perduring individuality. One of Leibniz' own characterizations, helpful but incomplete unless interpreted in the context of many variant characterizations, reads as follows:

There are only atoms of substance, that is to say, real unities, that are absolutely devoid of parts, which are the sources of action and the absolute first principles of the composition of all things and, as it were, are the ultimate elements in the analysis of substantial things. One could call them metaphysical points. They have something vital, a kind of perception; and mathematical points are their points of view, from which they express the universe.⁴

In a cognate passage we read that the individual substances, the monads,

cannot have shapes, otherwise they would have parts. And consequently a monad, in itself, and at a given moment, cannot be distinguished from another except by its internal qualities and actions which cannot be otherwise than its perceptions (i.e., representations of the compound, or of what is outside, in the simple) and its appetitions (i.e., its tendencies to pass from one perception to another), which are the principles of change…. It [viz. a monad] is as a center or a point where, simple though it is, an infinity of angles are found made by the lines that come together there.⁵

The identification of the simple (primitive) predicates entering into the defining notions of substances with the simple perfections of God is a point repeatedly insisted upon by Leibniz.⁶ This aspect of substances draws together several strands of thought in Leibniz' system, such as his thesis of the varying degrees of perfection (and correlatively their imperfection or finitude), and his penchant for the Ontological Argument for the existence of God. Moreover, it accounts for his conception of the immanence of God in monadic life, a conception which led some writers to class Leibniz among the medieval and Renaissance mystics in whose ideas he displayed great interest.

Against the Cartesian notion of physical substance as pure extension, Leibniz cast three objections of a fundamentally conceptual character: extension cannot comprise the essence of material substance because 1) it is an incomplete notion; 2) it is a complex and not a simple concept, since it can be analyzed further into plurality, continuity, and coexistence;⁷ 3) the very conception of extension is in its genesis imaginary and phenomenal, since size, figure, and so on, are not distinct self-subsisting things, but are relative to our perceptions.⁸

Substance Sub Ratione Possibilitatis

Prior to the creation⁹ (and we think here not of literal and temporal but of figurative and conceptual priority) all substances aside from God existed, or rather subsisted—since ex hypothesi they did not exist—only as ideas in the mind of God:

in God is found not only the source of existence, but also that of essences, insofar as they are real. In other words, He is the ground of what is real in the possible. For the Understanding of God is the region of the eternal truths and of the ideas on which they depend; and without Him there would be nothing real in the possibilities of things, and not only would there be nothing in existence, but nothing would even be possible.¹⁰

It should be stressed, however, that although presence in God's thoughts gives to unexistent possibles whatever "existence" they possess, the nature of such possibilities is wholly self-determined and in no way subject to God's will.

Since God is omniscient, His concept of the substance is not approximate and incomplete but descends to every detail of its (possible) career, and includes every single one of its properties. With respect to possibles, the principle obtains that alternative "descriptions" of the same thing must, unlike actual existents, be logically equivalent. In God's plan for ontological possibilities there is no room for the sort of incompleteness that figures in recipes for cooking or plans of architects ("Take 1 pint of milk." But from which cow? "Use such-and-such a piece of lumber." But from which tree?). Thus every possible substance, not only the ones actually singled out for creation, is represented in the mind of God by what Leibniz calls its complete individual notion (notio completa seu perfecta substantiae singular is), in which every detail of the substance at every stage of its (potential) career is fixed.¹¹ For simplicity and convenience we shall call this complete individual notion of the (possible) substance its program. The history of a substance is merely the continuous unfolding of its program with the same inexorable inevitability with which a mathematical series is generated in the successive development of its defining law. This lawfulness comprises the essence of the substance and is the source of its continuing self-identity: "That there is a certain persisting law which involves the future states of that which we conceive as the same—this itself is what I say constitutes the same substance."¹² In view of its specifications through its complete individual notion, every substance "contains in its nature a law of the continuation of the series of its own operations and [thus] of everything that has happened or will happen to it."¹³ The complete individual notion of a substance is, of course, known only to God, not to mortals:

The notion of myself, and of any other individual substance, is infinitely more extensive and more difficult to understand than is a generic concept like that of a sphere, which is only incomplete…. Therefore, although it is easy to determine that the number of feet in the diameter is not involved in the concept of a sphere in general, it is not so easy to decide if the journey which I intend to make is involved in my notion; otherwise it would be as easy for us to become prophets as to be Geometers.¹⁴

The contemplation of substances—not as existent actualities but as subsistent possibilities—forms in God's mind a "realm of possibles" (pays des possibles) in which every conceivable substance is presented "under the aspect of possibility" (sub ratione possibilitatis).¹⁵ In God's mind we find the entire gamut of cosmological possibilities. (Note here the echo of Nicholas of Cusa's idea of the world as explicatio dei, its history being the unfolding of the divine plan, the "reading off in nature of the book of God.) This part of the contents of the divine mind, the possible worlds, we must study, for it is an essential preliminary to a discussion of Leibniz' theory of creation.

Any actual state of affairs could, conceivably, have been different, for such an assumption involves no contradictory consequences. But if any actual state of affairs were different, then, since it is but the outcome of a natural course of development,¹⁶ the entire universe would have to have a different history of development. In fact, we should have to resort to a world different from ours, involving another possible development of things: our hypothetical investigation would lead us to another, altogether different possible world. Anterior to the existence of our world there was recorded in the divine mind entire infinities of notions of possible individual substances, whose only being at this point is that sub ratione possibilitatis in God's mind.

Compossibility and Order

Since the program of a substance involves the specification of literally every facet of its career, it involves all details of the relation of this substance to others. But now suppose that:

1. Possible substance #1 has the property P and also has the property that there is no substance having property Q to which it (#1) stands in the relationship R.

2. Possible substance #2 has the property Q and also has the property that every substance having the property P stands in the relationship R to it (#2).

These two substances are patently incompatible (on logical grounds). God might realize #1 or He might realize #2, but He cannot possibly realize both of them. (It is a fundamental tenet of Leibniz' philosophy that even omnipotence cannot accomplish the impossible.) Substances which do not clash in this way are characterized by Leibniz as compossible.

Thus the very concept (i.e., the defining program) of a possible substance marks it as either compossible or incompossible with any other given substance, and the fact that a given substance is compossible with such and such others must be incorporated in its concept. Since each of these possible substances involves one possible history of the development of the universe, only those involving the same history are compatible with each other. Because the actualization of some possibilities is incompatible with that of others, the manifold of possible substances splits into mutually exclusive systems of "compossibles." God's choice of creation is not of selection among individual substances, but among entire possible worlds; His will thus being always general "God never has a particular will."¹⁷

Possible Worlds

There is an important difference between the compossibility of (possible) substances and the compatibility of propositions. One proposition can be mutually compatible with each of two others which are, in turn, incompatible with one another. This can happen only when the first proposition is "incomplete," i.e., simply fails to embody any information that commits it one way or another as regards the other two incompatible ones. Since this sort of incompleteness is excluded from the realm of the "complete individual concepts" of possible substances, it follows that whenever one substance is compossible with each of two others, they in turn must be compossible with one another. This is a consequence of the descriptive completeness with which every possible substance is identified in terms of its complete individual notion.

By means of this principle the possible substances sort themselves out into possible worlds. The possible world of any substance is the totality of all substances compossible with it. Each possible world consists of a family of possible substances, every one of which is compossible with all the rest, and the individual characteristics (and therefore, as we shall see, the mutual relations) of which are determined in every conceivable respect by their individual defining concepts. The substances of each possible world are thus reciprocally adjusted to one another in a thoroughgoing, total way. To use one of Leibniz' favorite metaphors, the substances of a possible world "mirror" one another in their mutual accommodation.¹⁸ Since the entire history of each possible world is determined in every possible detail in terms of the complete individual notions of its constituent substances, there is no question of God's direct, immediate intervention in the course of natural events. (The possibility of divine action within the course of history is denied by Leibniz, so he rejects on this score both occasionalism and the interventionalism of Newton's divine clock-readjustor. Leibniz does, in the Theodicy, admit the possibility of continuous "creation," but this is not a matter of the introduction of new substances but of the temporal continuation of existing ones in accordance with a pre-established program.)¹⁹

Creation and the Actual World

If the concept of creation is to be introduced into the ontological framework just outlined in a viable way, the question of the existence of a possible substance must not be pre-empted by its complete individual notion. Thus Leibniz must either 1) adopt (i.e., anticipate) the Kantian course of denying that existence is a predicate, or else, 2) granting that existence is a predicate, rule existence out from the sphere of predicates that can feasibly enter into the defining notion of individual substances. Although in view of the paucity of evidence one cannot speak very firmly, it does appear that Leibniz took the second course, being willing to regard existence as a predicate,²⁰ albeit one of a sort that cannot enter into the essence of a substance (other than God), being inevitably consequent upon a pre-specified essence.²¹

The question can be raised: Is there anything to a Leibnizian substance over and above the attributes that belong to it by virtue of the predicates loaded into its complete individual notion? From the human standpoint the answer is yes—we actually do not ever know the complete individual notion of a substance, but encounter that substance only in experience (in fact, in confused perception). Even from God's standpoint an affirmative answer must be given, for an existing substance is, ex hypothesi, or existent, i.e., an entity or a thing, and its existence is never a matter of the attributes overtly guaranteed by its complete individual notion.

Suppose that God, contemplating a conceivable world sub ratione possibilitatis, finds it meritorious and chooses to create it, i.e., advance it from the status of a possible to that of an actual substance. Since He is omniscient, He knows the relationship of this substance to all the others that are compossible or incompossible with it. Being beneficent He wishes to maximize existence, to create as much as possible,²² and thus would not choose to actualize a certain possible substance without actualizing other substances compossible with it—i.e., its entire possible world. But which of the possible worlds is God to choose for actualization? Clearly, the answer must be the best.²³ But what criterion of merit does God employ to determine whether one possible world is more or less perfect than another?

The Criterion of Goodness

The criterion of goodness for possible worlds is plainly set forth by Leibniz in the following terms:

God has chosen [to create] that world which is the most perfect, that is to say, which is at the same time the simplest in its hypotheses [i.e., its laws] and the richest in phenomena.²⁴

The characteristic properties of each substance change from one juncture to another in accordance with its program. The properties of substance #1 at one juncture may be more or less in accordance with and thus reflected or mirrored in those of substance #2 at this juncture. Out of these mirroring relationships grow the regularities which represent the "hypotheses," the natural laws of the possible worlds. The "best," most perfect possible world is that which exhibits the greatest variety of its contents (richness of phenomena) consonant with the greatest simplicity of its laws.

Our world—the actual world—is the "best possible world" in this rarified metaphysical sense of greatest variety of phenomena consonant with greatest simplicity of laws. Its being the best has (at bottom) little to do with how men (or men and animals) fare in it. The facile optimism of Dr. Pangloss, the butt of Voltaire's parody Candide—Si c'est ici le meilleur des mondes possibles, que sont donc les autres?²⁵—misses the mark if Leibniz (and not some naive and simple-minded Leibnizian) is intended as its target.

There is, to be sure, a genuine difficulty in the Leibnizian criterion of which he himself was unquestionably aware, but which he did not resolve with the sharpness we might wish for. If merit of a possible world is determined by macro-considerations that operate in the large ("variety," "simplicity"), what assurance is there that the outcome is as we would wish it to be on the basis of micro-considerations that operate in the small (specifically, enumeration of the individual perfections of the several substances that comprise the possible worlds)? Leibniz adduces considerations which may mitigate, but do not wholly remove, doubt:

The ways of God are those most simple and uniform … [being] the most productive in relation to the simplicity of ways and means. It is as if one said that a certain house was the best that could have been constructed at the same cost…. If the effect were assumed to be greater, but the process less simple, I think one might say when all is said and done, that the effect itself would be less great, taking into account not only the final effect but also the mediate effect. For the wisest mind so acts, as far as is possible, that the means are also ends of a sort, i.e., are desirable not only on account of what they do, but on account of what they are.²⁶

This line of approach glosses over the genuine difficulty of a possibility of conflict between the components of Leibniz' two-factor criterion: What is to be chosen when we confront, for example, a sacrifice in "simplicity of means" for the sake of a greater "variety of phenomena"?

The Monads and God

An existing substance that is a member of the actual, and thus of the best possible, world, Leibniz calls a monad. He did not introduce the term monad until relatively late in his career. In the Discourse on Metaphysics of 1685, the first systematic presentation of his doctrine, he spoke simply of "individual substances." He continued to use this term, sometimes alternating it with substantial form and entelechy, or (when appropriate in context) soul or spirit. The term monad first began to be generally used by Leibniz in 1696.²⁷ Little else can be said about this definition apart from a question that has created something of a flurry of controversy among Leibniz scholars: Is God Himself a monad?

The answer to this must be in the affirmative. God is a monad, but a very special and unique one, for he is the supreme and the prime monad. The idea that God is a monad was called into question by Bertrand Russell,²⁸ who proposed to regard those passages where Leibniz explicitly speaks of God as one among the monads²⁹ as mere "slips." I think it unfortunate to charge an author with more mistakes than absolutely necessary, and see no reason why we must view Leibniz' declarations that God is a monad as errors from the standpoint of his system. That His status is fundamentally similar to that of the monads can be seen from the fact that He, like them, is an existing substance, indeed the supreme substance.³⁰ Leibniz explicitly assigns God a place in the scale of monads, holding Him to be the highest spirit.³¹ Moreover, if God were not a monad it would be a contrastless qualification and senseless redundancy for Leibniz to speak, as he does often, of created substances and monads, since God is the only noncreated existent in his ontology. In summary, we may regard it as certain that God has a place in Leibniz' system of monads, although this place is beyond any question a special and pre-eminent one.

Notes

¹Un estre absolument parfait. Phil., IV, p. 427.

² This is explicit in, e.g., the essay Causa Dei asserta per justitiam ejus cum caeteris ejus perfectionibus. Phil, VI, pp. 437 ff. Leibniz follows in the footsteps of the tradition of those who, like St. Thomas Aquinas, hold God to be perfect in being, knowledge, and wisdom. Cf. Monadology, § 4.

³ "Principles of Nature and of Grace," § 1. (This work is henceforth cited as PNG.)

⁴Phil, IV, pp. 482-83.

⁵Phil, VI, p. 598; PNG, § 2.

⁶ See, for example, Phil, V, p. 15 (bottom).

⁷Phil, II, pp. 169-70.

⁸Discourse on Metaphysics, § xii. (This essay is henceforth cited as DM.)

⁹Phil, VI, p. 614.

¹⁰ To speak of anything "prior" to the existent universe is to use the term in a purely logical, and by no means temporal, sense; and when one does so, one deals with the necessary being, the necessary truths, and the possible worlds, i.e., one enters the sphere of pure logic. It is hardly possible to find here a place for activity of any sort.

¹¹Monadology, § 43.

¹²Phil, II, p. 264.

¹³Phil, IV, pp. 432-33; Couturat, Opuscules, pp. 403, 520.

¹⁴Phil, II, p. 45.

¹⁵ This is the key idea of one of Leibniz' ways of establishing the existence of God, since not even possibles would exist without the existence of "a being who could produce the possible" (Phil, III, p. 572).

¹⁶ In Leibniz, one must remember, we are confronted with a strict mechanist.

¹⁷Theodicy, § 206.

¹⁸ It is derived from Nicholas of Cusa, according to whom the entire universe is a mirror of God.

¹⁹ Cf. DM, § xxx: "God in co-operating with our actions ordinarily does no more than to follow the laws He has established, which is to say that He continually preserves and produces our being in such a way that thoughts come to us spontaneously or freely in the order carried in the concept of our individual substance, in which it could have been foreseen through all eternity."

²⁰Phil, V, p. 339. Cf. Russell, Critical Exposition, pp. 77, 174, 185.

²¹Phil, VII, p. 195.

²² Leibniz is fundamentally committed to the idea that existence is preferable to nonexistence.

²³ We return to the topic of creation at greater length in Sec. 4 of Chap. 5.

²⁴ DM, § 6. Cf. ibid., § 5, and also PNG, § 10; Theodicy, 208.

²⁵ Voltaire, Candide, Chap. vi.

²⁶Theodicy, § 208.

²⁷ See A. G. Langley (tr.), G. W. Leibniz: New Essays Concerning Human Understanding (New York & London: Macmillan Co., 1896), p. 101, notes. Cf. also Gerhardt's observations in Phil, IV, pp. 417-18. Prof. L. E. Loemker informs me, however, that Leibniz employed the term monas (pl. monades)—albeit in a mathematical sense—as early as the Leipzig period.

²⁸ Russell, Critical Exposition, p. 187.

²⁹ For example, Phil, III, p. 636; Phil, VIII, p. 502.

³⁰Monadology, § 40.

³¹Phil, IV, p. 460.