Now where there are no parts, there can be neither extension nor form [figure] nor divisibility. These Monads are the real atoms of nature and, in a word, the elements of things.
Thus the final reason of things must be in a necessary substance, in which the variety of particular changes exists only eminently, as in its source; and this substance we call God.
Now, as in the Ideas of God there is an infinite number of possible
universes, and as only one of them can be actual, there must be a
sufficient reason for the choice of God, which leads Him to decide
upon one rather than another....Thus the actual existence of the best
that wisdom makes known to God is due to this, that His goodness makes
Him choose it, and His power makes Him produce it.
1. Biographical Information
Leibniz was born in Leipzig in 1646, the son of a professor of moral philosophy.
In 1661 he began to attend the University of Leipzig as a student of philosophy
and law, and in 1667 obtained the degree of Doctor of Law at Altdorf,
where he was offered a professorship, which he declined. From 1672
to 1676 he worked as diplomatic representative of Mainz at the Court of
Louis XIV in France. In 1675-76, his final years of diplomatic service,
he discovered infinitesimal calculus, unaware that Newton had already
done so. Returning to Germany, he accepted the position of librarian,
archivist, and court councilor to the Duke of Brunswick in 1680; he was
commissioned to write a history of the house of Brunswick. He founded
learned societies during this time, and exerted much effort in attempting
to re-unite Protestant and Catholic faiths. He died at Hanover in
2. Introduction to Leibniz's Philosophy Based on Monadology
Leibniz wrote many philosophical works, some of which were published and some that remained unpublished. What was published of Leibniz's works during his lifetime or immediately after his death include Theodicy, Discourse on Metaphysics, Monadology and New Essays Concerning Human Understanding. None of these publications, however, gives a complete account Leibniz's philosophy. To appreciate fully Leibniz's philosophical system one needs to take into account all of his many writings, including the fifteen thousand letters and unedited fragments of Leibniz's works discovered as late as 1903 in Hanover. A careful reading of his work Monadology, however, serves as a good introduction to Leibniz's philosophy. Because of its brevity, Monadology tends to be obscure at points, so that it is necessary to provide clarification at times. Methodologically Leibniz is a rationalist, which means that he believes that there are necessary truths of reason from which one can deduce other truths.
2.2. Monads as Simple Substances
Leibniz reasons that for there to be anything there must be basic units of reality, which he calls monads or simple substances: "And there must be simple substances, since there are compounds" (2). He implicitly appeals to the axiom that changing, composite things must have unchanging component parts. By substance, Leibniz means an entity, or subject to which predicates may be attributed, which is the usual definition of it. The word monad is a Greek word meaning a single thing (monas); in Greek philosophy it is usually applied to God. For Leibniz, monads are the fundamental existing things, the "building blocks" of everything else. Leibniz assumes that it is rationally undeniable that things are composed of parts. Monads are simple, which means that they are irreducible, having no component parts; rather all composites things are composed of monads: "These Monads are the real atoms of nature and, in a word, the elements of things" (3). True substances are the monads, not those things composed of monads. Composite things, as aggregates of monads, are substances or entities in a secondary and derivative sense.
not interpret Leibniz's monads as fundamental units of matter; rather,
these monads have "neither extension nor form [figure]
nor divisibility" (3). In other words, monads are unextended in
the sense of existing in space, and, therefore, they have no shape and
cannot be divided. For Leibniz, it is a truth of reason that simplicity
and extension are logically incompatible, for whatever is extended is
also divisible and therefore must be a plurality, being composed of parts
that can be separated from one another. Yet all things that are identifiable
as material existents are composed of monads, being "the
elements of things" (3). Exactly why it is a truth of reason that
only a composite thing is extended is not explained.
Do you agree that, if there are compounds, there must be simple substances
or monads? Why cannot a thing be infinitely divisible? Since
it is unextended, can a monad be part of a composite thing that is extended?
are simple, monads are indestructible. Destruction is decomposition
into component parts, but, since they are simple, the decomposition of
monads is impossible: "No dissolution of these
elements need be feared, and there is no conceivable way in which a simple
substance can be destroyed by natural means." Likewise, monads
cannot come into being, since, something new comes into being as the result
of new aggregates of monads; monads are the fundamental units of being,
and do not come into existence in the same that new combinations, or aggregates,
of monads do: "For the same reason there is
no conceivable way in which a simple substance can come into being by
natural means, since it cannot be formed by the combination of parts [composition]." That
which is composed of monads can neither create nor destroy that of which
it is composed; only a Being that is ontologically prior to the monads
can create or destroy them, which is why Leibniz writes,
"Thus it may be said that a Monad can only come into being or come to
an end all at once; that is to say, it can come into being only by creation
and come to an end only by annihilation, while that which is compound
comes into being or comes to an end by parts."
2.2. Monads as Diverse and
As existing things, monads must have qualities, since to exist is to be something that is described in terms of qualities (8). Leibniz reasons that it is necessary that the differences that one observes among phenomenal things, those things that are compounds of monads, requires that monads differ in their qualities one from another: "And if simple substances did not differ in quality, there would be absolutely no means of perceiving any change in things" (8). Otherwise, if everything were alike, there would be no way of ever perceiving change. In fact, since, according to Leibniz, no two things are alike, it follows that no two monads are alike; if some monads were alike, then one would find identical compounds of monads, but this does not happen. He writes, "Indeed, each Monad must be different from every other. For in nature there are never two beings which are perfectly alike and in which it is not possible to find an internal difference" (9). (Leibniz coins the phrase "identity of indiscernibles" to express the truth that two things cannot be two substances indiscernible from each other, for otherwise they would be indistinguishable from each other.) In addition, Leibniz reasons that monads change because that which is composed of monads changes continuously: "I assume also as admitted that every created being, and consequently the created Monad, is subject to change, and further that this change is continuous in each." (10). Change in composite things requires change in the simple monads. Leibniz's conclusions implicitly appeal to the axiom of sufficient causation: that a cause must be commensurate with its effect.
Monads differ from one another in the totality of their predicates, but their predicates, it seems, are their relations to other monads. Since they are simple and unextended, a monad cannot differ from another with respect to what it is in itself; their differences is their relations to other monads: the relations are a monad's qualities. (As already stated, however, since monads are unextended, a quality that a monad cannot have, unlike composite things, is form or figure, since only something existing as extended can have a shape.) Rather, it differs from another with respect to the totality of its relations to other monads. Moreover, they change according to an "internal principle," which means that the cause of their change is from within as opposed to being caused from without by other monads or compounds of monads. Leibniz holds that there are no true cause and effect relations between monads (and their compounds); rather, a monad changes in relation to other monads according to its own concept or nature. A monad's relational predicates are internal predicates of some perfect (in the sense of complete or all-inclusive) concept, so that the perfect concept of a monad includes all of its "relations" at every time of its existence to every other monad in the universe.
A monad is self-sufficient. Having all these properties within itself, there is no need for a monad to be causally related to other monads. Even without the alleged influence of other monads, a monad will still change relationally as if it is being so influenced. This is consistent with Leibniz's view of truth. For him, a true proposition is one in which the predicate is contained in the concept of the subject. But by a true proposition, Leibniz means more than what is normally called an analytical proposition or tautology, because he holds that every subject, or every monad, which is the fundamental subject or substance, is distinguishable from other monads and so definable by all of its predicates. Whatever can be predicated of a monad, its changing relations with other monads, is part of the perfect concept of that subject. (The same applies to compounds of monads, taken to be subjects; see Discourse on Metaphysics 13: "It is the nature of such a perfect concept of a substance to involve everything." In Leibniz's view, a substance is defined as a subject in which all of the predicates that it will ever have are contained; these predicates would be knowable to an infinite mind, God's mind.) Expressed differently, the change of a monad is self-caused or teleological, according to a goal inherent in the monad. Leibniz draws an analogy from ordinary experience to demonstrate the possibility of multiplicity in a simple substance; the human mind, being simple in the sense of being a unity, can have as its object that which is more than one: "We have in ourselves experience of a multiplicity in simple substance, when we find that the least thought of which we are conscious involves variety in its object. " (16). The simple mind is defined by its predicates (what it is thinking about) in the same that a monad is defined by the totality of its predicates, or history of its relations with other monads.
As indicated, when it changes, a monad changes relationally. As a simple substance, a monad cannot change in the same way that compounds of monads change, i.e., by changing the quantity and configuration of its component parts. Rather, monads change the relations that they to other monads to form the compound things of which they are a part. A monad in its present state with respect to its relations is a consequence of its previous states, and at the same time has potentiality to enter into future because of its present state: "And as every present state of a simple substance is naturally a consequence of its preceding state, in such a way that its present is pregnant with its future" (22). A monad is also "pregnant" with the future just as much as it is "laden" with the past. The complete past and future relational history of monad is the perfect concept of the monad, its nature. What defines the essence of each monad, its perfect concept, is its history and future history of its relations with other monads, which is what Leibniz means when he writes, "But, besides the principle of the change, there must be a particular series of changes, which constitutes, so to speak, the specific nature and variety of the simple substances" (12). At the beginning of time, therefore, each monad differed from the others, not in its shape, size, weight etc., which are qualities of extension, but in its potentiality to enter into relation with other monads.
Can one explain the diversity of things and their changes by recourse
to the theory of monads? How
can monads as simple and unextended be different from one another by means
of their relations to other monads?
2.3. Monads as without "Windows" and as Entelechies
Individual monads cannot be causally influenced by other monads. As Leibniz expresses it, "Monads have no windows, through which anything could come in or go out." He means that monads are such that they are closed off from the influences of other monads, so that a monad cannot be changed either substantially or accidentally by causal agents from without. It can neither cause nor be caused to be what it is or what it becomes. If one takes the metaphor of being without a window seriously, it seems that Leibniz believes that causal interaction between two beings requires the transposition of the parts of a substance into another. Another term used by Leibniz for monads is "entelechies," so chosen because all simple substances have within themselves a certain perfection (enteles) or goal towards which they move as they change, which makes them the cause of their own change. (The term entelechy is Aristotelian, and refers to a thing fully realized in act.) This gives a monad a self-sufficiency, in the sense that it is not dependent on another monad to reach its goal or perfection. Monads are automata in the sense that they change automatically without requiring an external influence.
2.4. Perception and the Impossibility
Leibniz asserts that a monad is aware of its changing relations with other monads, its multiplicity, and this awareness he calls perception. This is what he means by the difficult phrase"the passing condition, which involves and represents a multiplicity in the unit or in the simple substance," which defines perception. The passing condition is the change of a monad's relations with other monads; this history of its multiciplicty is represented to the monad. In other words, all monads in all things have perception, or are aware of their changing relations with other monads to some degree. Perception, however, is not self-awareness ("apperception") or consciousness as normally defined as a human property. Rather it is lower level of awareness. Not all monads are self-aware although all have perception defined in this way. This leads Leibniz to take exception to Descartes view that only minds (unextended or intellectual substances) have "perception," which, in Leibniz's terms, means that only they would be monads, whereas material substances are purely inert. Even animals, according to Descartes, are machines, without a "soul," by which it may have perception.
Leibniz rejects the idea that perception can be caused mechanistically, by which is meant that perception could arise out of that which does not perceive, such as the sense organs operating in conjunction with the brain. Rather composite things are capable of perception because monads, their component parts, already perceive: "Thus it is in a simple substance, and not in a compound or in a machine, that perception must be sought for." (17). For this reason he opposes the reductionistic explanation of perception as being caused by that which does not perceive. He adds that monads consist of changes and their perceptions of their changing relations to other monads: "Further, nothing but this (namely, perceptions and their changes) can be found in a simple substance. It is also in this alone that all the internal activities of simple substances can consist" (17). One monad is what it is because of the history of its relations with other monads (and its future relations); these changes are perceived by the monad.
The impossibility of reductionism is the reason that Leibniz concludes that monads have perception. Even considering the possibility of perception as an emergent property, one would still violate the principle of sufficient reason by explaining perception as resulting from a non-perceptive cause. Implicitly, he accepts as a necessary truth that a thing cannot derive from its opposite, in this case, the perceiving from cannot derive from the non-perceiving (ex nihilo nihil fit). Given this necessary truth, it follows that the fundamental units of reality, monads, must have perception, for otherwise compounds of monads could not have perception, but they do.
Does it make sense to speak of monads as perceiving?
2.5. Appetition and Souls
Somewhat obscurely, Leibniz calls "appetition" the internal principle or cause by which the perception of a monad changes insofar as it changes in relation to other monads: "The activity of the internal principle which produces change or passage from one perception to another may be called Appetition" (15). A monad "desires" and so changes itself, which produces a new perception, or awareness of its new relation to other monads. (For Leibniz, change is a passage from one perception to another because of a change of relation.) But a monad cannot be said to be caused to perceive by the new object of perception, for then a monad would not be an entelechy, as explained above; this means that a monad must cause its own perceptions to change as it itself changes its relations with other monads. (Now what is true of monads is also true of compounds of monads.)
Since monads have perception, Leibniz states that it is appropriate to call them "souls"; he decides, however, to only calls "souls" those monads that have both perception and memory. This means that monads differ from one another in another respect: their capacity for perception. Although they are simple and unextended and therefore do not differ from one another except in their relations, monads do differ in their capacity for perception. Some monads are what human beings normally call souls, whereas other are the component parts of material things, even though they have perception.
2.6. Degrees of Perception
Monads differ from one another in degree of perception and appetition. Leibniz distinguishes the soul from what he calls "a bare monad," insofar as the latter has perceptions without consciousness: "It thus appears that if we had in our perceptions nothing marked and, so to speak, striking and highly-flavored, we should always be in a state of stupor. And this is the state in which the bare Monads are." (24). Memory provides monads with the possibility of connecting several perceptions together, which, Leibniz says, resembles reason; in fact it is a kind if inductive reasoning (arguing from particulars to the general) that even animals have (26). Those compound things that lack consciousness are composed of these "bare monads." By contrast, it seems that what human beings normally call souls are monads with consciousness. The difference between the two extremes in the monad perception continuum is, however, quantitative (degree) and not qualitative (kind).
2.7. Two Types of Truth
Leibniz holds that human beings differ from animals with memory (and who can "reason" inductively thereby) by the fact that the former have "the knowledge of necessary and eternal truths," which gives them "Reason." He means that human beings alone can reason deductively, beginning with necessary propositions and deducing other necessary truths from them. The ability to know necessary truths presupposes the capacity for abstraction (since necessary truths are abstract truths; this capacity for abstraction leads to being able to distinguish the "I" from its predicates, and this then leads to the abstract notions "of being, of substance, of the simple and the compound, of the immaterial, and of God Himself, conceiving that what is limited in us is in Him without limits" (30). This is because the "I" is an immaterial subject or substance that, as a soul, is simple, but which is compound in its predicates; the notion of God derives from the negation of the finitude of the "I" as a simple substance.
All reasoning is based on two principles: "that of contradiction" (31) and "that of sufficient reason" (32). In other words, all reasoning is based on the principle that something cannot be true and false at the same time in the same manner, so that whatever is not false is true, and the principle "that there can be no fact real or existing, no statement true, unless there be a sufficient reason, why it should be so and not otherwise, although these reasons usually cannot be known by us." (32). There are also two types of truth "those of reasoning and those of fact." The second principle simply affirms that there must a adequate cause for whatever is. A truth of reasoning is a necessary truth or a proposition the denial of which is impossible; its consists of "simple ideas, of which no definition can be given" and has the nature of an axiom, a self-evidently true proposition: "in a word, primary principles, which cannot be proved, and indeed have no need of proof; and these are identical propositions, whose opposite involves an express contradiction" (35). A contingent truth is a truth of fact, meaning that its opposite is not contradictory. But the principle of sufficient reason always applies to contingent truths, so that every "fact" must be fully explained in terms of its antecedent causation. In other words, for every predicate that is true of a subject, there will be a set of other true predicates that together constitute a sufficient reason for its being true. This seems to imply that each predicate of a subject is necessarily true, since it has sufficient reason for being true. But its necessity is not of the same type as a truth of reasoning.
QUESTION: Do you agree with Leibniz that there are two types of truth? Do you agree with the two principles: "that of contradiction" and "that of sufficient reason"?
Leibniz argues for the existence of God from the necessity of a first term in the sequence of sufficient causes, which he calls an a posteriori argument: "The sufficient or final reason must be outside of the sequence or series of particular contingent things" (37). His point is that, however vast the totality of the sequences of contingent things is, the ultimate cause of this sequence must be outside of it, and not a part of that sequence. The universe, or the total aggregate of monads and their compounds in all time is contingent, meaning that it is not necessary but could be other than it is. As contingent, all things that constitute the universe do not explain themselves, because they did not cause themselves. For this reason, there must be something outside the totality of contingent things that explains them by causing them. Leibniz's position does not necessarily presuppose that the universe had a beginning, because even an eternal universe would still be contingent and therefore require an explanation. Leibniz further concludes that "the final reason of things" or the first cause must be necessary, presumably because it is by definition not contingent. That is to say, only the necessary can be the ultimate cause of the contingent, since a contingent cause would itself need a cause. Insofar as God is the first cause, God is all change, or one could say that "the series of particular contingent things" exist eminently in God, meaning that they are caused by God. But God is different from them as effects, being their cause. In other words, God is nothing like the effects that he produces as their cause and cannot be identified with the effects. Leibniz also concludes that, since only one God is necessary as the first cause, then there is only one God: "Now as this substance is a sufficient reason of all this variety of particulars, which are also connected together throughout; there is only one God, and this God is sufficient." (39). In addition, since all particular, contingent things are interconnected and so exist as a unity there could only be one sufficient cause, not more than one.
Leibniz says that God is a substance that is "a pure sequence of possible being" and that "must be illimitable and must contain as much reality as is possible" (40). What he means is that God is the necessary substance that makes all contingent substances possible. To say that God is the sequence of possible being is to say that all causal sequences depend on God for their existence. God must also be illimitable, by which is meant that God cannot have limits, presumably because nothing can be or even be conceived as independent of God. For God to be the cause of all reality, to use a metaphor, all possible reality is contained in God, so that all things are dependent on God. This leads Lebniz to say that God is perfect, defined as containing the total amount of "positive reality"; to be perfect in fact is to be without limits or infinite, since God as containing the total amount of "positive reality" is by definition without limits. By contrast, all created or contingent beings are perfect within limits, which is to say that they are also imperfect because they are not all "positive reality": they are what they are determined to be by God, but they are not everything, as God is everything in the sense of being the source and container of all possible being (42).
Leibniz also proposes an a priori argument for the existence of God. God is said to be both the source of existences and essences or eternal truths: whatever is and whatever can be originates with God. By essence or eternal truth he means those basic ontological components of all reality, something like Plato's Ideas, without which there could not be particular substances, or composites formed from monads. He says that the possible cannot exist except as dependent upon the actual: "For if there is a reality in essences or possibilities, or rather in eternal truths, this reality must needs be founded in something existing and actual, and consequently in the existence of the necessary Being, in whom essence involves existence, or in whom to be possible is to be actual" (44). Leibniz defines God as necessary, which means that God is a being whose mere possibility implies his actual existence. What he means is that if the existence of God is possible in the sense of not being logically contradictory, then God exists necessarily, because the idea of God is that of a necessary Being. God's existence is possible, since, by definition, "Nothing can interfere with the possibility of that which involves no limits, no negation and consequently no contradiction, this [His possibility] is sufficient of itself to make known the existence of God a priori" (45).
Has Leibniz proved the existence of God? Do you agree with Leibniz's
definition of God as a substance or monad?
2.9. The Nature of God
Leibniz rejects the notion that eternal truths, by which he means necessary truths, are arbitrarily created by God; rather, "necessary truths depend solely on his understanding and are its inner object" (46). What he means is that the eternal truths recognized as such by human beings are the necessary objects of the mind of God. He adds that God is the original simple substance, whereas derivative or created monads come into existence through God's "fulgurations," i.e., God's emissions of light, insofar as God is the all-inclusive potentiality containing all "positive reality" (see 41). The image is that of a substance, whom Leibniz calls "the primary unity,"that projects its potentiality outward, thereby bringing into existence finite or imperfect monads. The derivative monads, being finite, are only partial actualizations of this total potentiality.
Leibniz identifies three "attributes" of God: power, knowledge and will. The three attributes of God correspond in derivative monads to "the ground or basis, to the faculty of Perception and to the faculty of Appetition," which are manifested in varying degrees according to the perfection of the monad. In other words, the power of God is the reason that a monad exists. A monad's perception corresponds to God's knowledge and a monad's appetition, or its awareness of its changes from one perception to another, is a type of volotional activity, corresponding to the will of God. He also says that God creates according to the principle of the best, which implies that the whole in all its diversity is not arbitrary, but as perfect as possible.
2.10. Monads as Active and Passive
Leibniz distinguishes between
a monad as active and as passive. Although his manner of expression
tends to be obscure, he seems to mean that, insofar as it changes according
to an internal principle, which is reflected clearly in its perception
of itself in relation to other monads, a monad can be said to be active
and perfect. But a monad can be said to be passive insofar as its perceptions
are confused, by which Leibniz seems to mean that it is not self-caused
and therefore not an entelechy; rather it is acted upon, in a sense, by
that which is self-caused, another monad. Its perceptions would be clear
if they were correlated with the realization its own potentiality, as
self-directed. Yet, Leibniz makes it clear that monads do not really
act upon another as efficient causes, but merely appear to, according
to the design of God; this is what he means when he says that the influence
of one monad on another is "ideal," as opposed to existing in
reality: "But in simple substances the influence
of one Monad upon another is only ideal, and it can have its effect only
through the mediation of God, in so far as in the ideas of God any Monad
rightly claims that God, in regulating the others from the beginning of
things, should have regard to it" (51). One created monad is more
perfect than another, insofar as it is "that which
serves to explain a priori what takes place in the less perfect, and it
is on this account that the former is said to act upon the latter."
(50) When one monad appears to act upon another monad, the true relationship
between these is one of logical priority: that monad is prior by which
the other is explained. Monads exist is a hierarchy of relationship of
logical priority and posteriority (52).
2.11. The Universe as the Best Possible
Leibniz asserts that the eternal truths or "the Ideas of God" give rise to numberless (i.e. infinite) possible contingent universes; but only one universe can be actual, and in accordance with the principle of sufficient reason this one actual universe must have a reason to be. That reason is that the one actual universe has the highest degree of perfection; each monad and compounds of monads rightly seeks to become what it is potentiality, which is "to aspire to existence in proportion to the amount of perfection it contains in germ" (54). Of all the possible universes that could exist, this one is the most perfect that it could be, given its inherent limitations. God creates a universe that is the most perfect, for this is an expression of the infinity of God as an infinite being. Leibniz concludes, "Thus the actual existence of the best that wisdom makes known to God is due to this, that His goodness makes Him choose it, and His power makes Him produce it." (55)
Is it a "truth of reason" that the universe must be the best possible?
2.12. Monad as Mirror of the Universe
The universe is a system of monads, each changing in unison with the other monads; this means that each monad is in relation to all the others and is part of a larger unity. As a result, insofar as it is a part of the whole, each monad reflects the whole, since the whole defines the individual monad and the one monad stands in relation to a nexus consisting of all the other monads. This is what he means when he says that a monad is a "perpetual living mirror of the universe" (56). It reflects the universe, because the whole is contained in it, the part, since it is part of the whole. The reflection of the whole by a monad, however, is relative to its relationship to the whole, so that it reflects the whole from a limited point of view, with the result that "This representation is merely confused as regards the variety of particular things [le detail] in the whole universe, and can be distinct only as regards a small part of things, namely, those which are either nearest or greatest in relation to each of the Monads" (60). Each monad reflects the whole in proportion to its nearness to other monads that constitute the whole. Otherwise, each particular monad would be God, reflecting the whole at once without limit. Perfection in the universe is defined as maximum diversity in maximum unity or order. It follows that all compounds of monads (bodies) are analogous to the monads as simple substances insofar as all bodies influence all other bodies, but not in the sense of being efficient causes, but being in coordination with them: "Every body feels the effect of all that takes place in the universe" (61).
2.13. Body and Soul
According to Leibniz, although it reflects the universe, each monad more distinctly reflects the body to which it belongs as part of a compound. He seems to be thinking of the relationship between a human soul (entelechy) and the body to which it belongs. Because the body represents the whole universe through its connection with the plenum, i.e., the totality of created monads, the soul likewise represents the whole because of its relation to the body. He defines a "living being" as the combination of an entelechy (in the case of a human being) or a soul (in the case of an animal), both of which are monads, with a body. A "living being" is said to be organic, by which he means that each monad in this compound reflects the universe through the body, and, in so reflecting, is as orderly as that which it reflects, a unity in diversity. He adds that "a living body" is a natural automaton, in the sense that "the machines of nature, namely, living bodies, are still machines in their smallest parts ad infinitum" (64). He seems to mean by this that, although compounds are composed of monads, this is not to say that monads are the "atoms" or the smallest extended parts of the compound; rather every monad is in a sense the whole and whole is in every monad.
2.14. Infinite Divisibility of Matter
Leibniz concludes that, because
each part of the universe expresses the whole, it follows that what we
call "matter" is infinitely divisible and that each part has some "motion,"
by which he means that each part has its own self-directed activity, the
impulse to realize its potentiality. The result is that there are infinite
universes in infinite universes: "Whence it appears
that in the smallest particle of matter there is a world of creatures,
living beings, animals, entelechies, souls" (66). To use modern
terminology, he understands the whole as having a fractal nature: it is
infinitely self-similar. It seems that, because monads have no extension,
then there is no limit on their number. Thus, the universe is living and
orderly through and through; there is no "dead" matter or basis inert
stuff out of which living matter is formed.
If monads are immaterial, then does it follow that "matter" is infinitely
divisible? Or is this notion simply rationalist nonsense?
2.15. Dominant Entelechy
Each (human) body has what Leibniz calls a "dominant entelechy," by which he means what is normally called a soul. Each part of the body—infinitely divisible, it would seem—contains the whole universe, so that, "The members of this living body are full of other living beings, plants, animals, each of which has also its dominant entelechy or soul" (70). Perhaps he means that a part that is infinitely divisible is infinite, which means that each part is actually the whole. The body to which a soul belongs changes slowly and there is never any beginning or end of the body. It is not clear what Leibniz means by this in light of the facts of birth and death.
2.16. Final and Efficient Causation
According to Leibniz, souls and bodies do not interact; this is impossible because the laws operative in the physical world do not allow for the addition to "the quantity of force" in matter. (There is also the "law of nature which affirms also the conservation of the same total direction in matter.") Souls "act according to the laws of final causes" (79), which means that souls choose ends and then means to accomplish those ends; bodies, on the other hand, "act according to the laws of efficient causes or motions" (79), which means that their actions are determined by causal antecedents or efficient causes. (But this is true only on the phenomenal level, because metaphysically monads do not influence one another.) Yet because of the pre-established harmony, souls and bodies appear to interact: God has pre-determined that volitional activity would be correlated with the change in the physical world (e.g., moving parts of body): "According to this system bodies act as if (to suppose the impossible) there were no souls, and souls act as if there were no bodies, and both act as if each influenced the other." (81)
Is it true that there is no interaction between mind or soul and matter,
as Leibniz suggests?
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