UC Davis Philosophy 22N

Leibniz Lecture Notes

G. J. Mattey

Revision of January 29, 2007

The published works of Leibniz were overt attempts to reconcile philosophy with Christian doctrine. His most famous published book, Theodicy, promised an explanation of the existence of evil in a world created by a being who is perfectly good. In it, he advanced the thesis that ours is the best of all possible worlds--a thesis ridiculed by Voltaire in Candide.

But there was another side to Leibniz. He was a great innovator in logic, though he published little of his results. As can be seen in his correspondence with Arnauld, Leibniz regarded the theory of truth, not religion, as the starting-point of philosophy. Bertrand Russell, writing nearly 200 years after Leibniz's death, claimed that Leibniz had two philosophies: one genuine and based primarily on logic, and one intended to garner fame and fortune, which required avoiding the shocking consequences of the genuine system. (A Critical Exposition of the Philosophy of Leibniz, p. 3). Here we will have a look at the unpublished Discourse on Metaphysics and some letters Leibniz wrote to Arnauld regarding issues raised therein. These works bring out the relation between the two tendencies in Leibniz.

It is important to understand that our texts represent the views Leibniz held relatively early in his philosophical career. While many of the positions advanced in the Discourse and Arnauld correspondence remained in Leibniz's later work, they took on different forms there. And many new positions and arguments sprang from Leibniz's fertile mind in the ensuing years. The reader may wish to contrast the present texts with the rather succinct "Monadology," which was written 28 years after the Discourse.

God's Will and Intellect

We begin our examination of Leibniz with the assumption that God, a supremely perfect being, exists. (Leibniz thought this could be proved by the ontological argument and other arguments, but we will not examine them here.) It is also assumed, contrary to Spinoza, that God's mind consists in a will and intellect, like the human mind.

Descartes had claimed that it would be contradiction to suppose that God's will is determined to act in one way or another (Reply to Sixth Objections, Objection 6). God does not act out of a prior conception of what is good or bad, but rather God's acts of will determine what is good or bad. This allowed Descartes to explain God's freedom in terms of the indifference of God's will. Leibniz considered this view to be dangerous, in that it threatened to make values relative, as Spinoza had claimed they are. If what is good or bad depends on God's arbitrary whim, the same things that we now call bad could just as well be good.

Leibniz proposed instead that God does that which he sees to be the best. A positive reason in favor of this claim is that "all acts of will presuppose a reason for willing and . . . this reason is naturally proper to the act of will" (Discourse on Metaphysics, 2). To act on the basis of a reason is no diminution of God's power, because what is best is the consequence of God's understanding and not something external to God. This description of God's action is embodied in one of Leibniz's most basic general metaphysical principles, the "principle of sufficient reason." Anything that exists is due to the activity of God, and God always acts for the reason that it is the best. So there is, for anything that exists, a reason sufficient to determine God's will to bring it about, i.e., the reason that its existence would be for the best. The corresponding principle for human action is that we will that which appears to us to be the best, because unlike God, we frequently do not know what is the best.

Ontological Economy

Exactly how is it that God brings about what is for the best? Leibniz claimed that God's actions follow what can be called a "principle of economy": God acts according to the most economical means to bring about the most abundant ends. To support this claim, Leibinz appealed to many analogies. An architect, for example, will use "his location and the funds set aside for a building in the most advantageous manner, allowing nothing improper or lacking in the beauty of which it is capable" (Discourse on Metaphysics, 5). God's economy is carried out through the use of general rules governing creation. Some of these rules are discoverable by us humans, and we call them laws of nature. Others are hidden. These are in play when there is a miracle which violates a law of nature. Miracles are not irregular events but conform to more general regularities. (For this reason, Leibniz called laws of nature "subordinate maxims").

Substance

Now that we have some idea of how God acts, we should investigate the products of God's creation. Like Descartes, Leibniz held that created things are individual substances. But his conception of substance was closer to the Aristotelian than to the Cartesian (see Aristotle's Categories, Chapter 5). An individual substance is a subject to which predicates are attributed, but which itself is not a attributed to anything else. Leibniz accepted this "nominal" definition but took it further, by examining how correct attribution works. "We must consider what it is to be attributed truly to a certain subject" (Discourse, 8).

Attributions to a subject are made in a proposition by connecting the concept of the subject ("haecceity") with a predicate. Although Leibniz is not clear on this point, we may take a predicate to be a representation of a property or quality that a thing might have. An example of a subject is Alexander the Great, and a quality that may be truly predicated of him is that of being a king, or that of defeating the Persian king Darius.

A proposition attributing a predicate to a subject is true just in case the predicate is contained in the concept of the subject. The predicate may be contained in the subject-concept in two ways: expressly and virtually. It is contained expressly when the relation between subject and predicate is one of identity, as in the proposition that King Alexander was a king. It is contained virtually when "anyone who understands perfectly the concept of the subject will also know that the predicate pertains to it" (Discourse, 8). Leibniz adopts the standard description of this relation as "being-in" or in-esse.

This description of the truth of attributions has very far-reaching consequences. Anyone who understands perfectly the concept of Alexander can find in it a "basis or reason" from which can be deduced all the predicates that can be truly attributed to him. No human being has such perfect knowledge, and only God is capable of deducing every fact about a substance by considering its concept alone. The rest of us will have to resort to experience to discover most of the properties of a substance. We humans can only know "from natural history" whether Alexander died a natural death or was poisoned.

Because every predicate of a substance is at least in principle deducible from its knowledge of its concept, there is no room for the traditional distinction between essential and accidental properties. Two subject-concepts differing even in the most trivial predicate could not represent the same subject. Given that Alexander died a natural death, a subject who resembled Alexander in every respect except that he died from poisoning would not be Alexander himself. The metaphysical thesis that identical subjects must share all the same predicates is generally known as "Leibniz's Law," which Leibniz himself described as an "important paradox" (Discourse on Metaphyics, 9).

Holism

The consequence of Leibniz's account of true attribution do not stop at the properties of the subject. Alexander does not exist alone in the created world. He is connected to all other created substances by laws of nature. His connections with other things are also contained in his concept.

Thus when we consider carefully the connection of things, we can say that from all time in Alexander's soul there are vestiges of everything that has happened to him and marks of everything that will happen to him and even traces of everything that happens in the universe, even though God alone could recognize them all. (Discourse, 8)
Leibniz's metaphysics of created substances is "holistic," in the sense that "traces" of all the predicates of everything in the universe are contained in each indvidual concept. Leibniz illustrates his holism with an analogy. If a pebble is thrown into a pond, waves will ripple out to the shore, and no part of the pond is unaffected by the event. This holds more generally throughout the universe, Leibniz believed. Now suppose that one were at one point on the shore. With enough knowledge of the wave that laps up on it, one could deduce the event of the pebble that was thrown into the pond some distance away, and all the effects of that event.

We must not take this analogy too literally, however. As will be seen below, although Leibniz believed that there are natural laws relating all things, these laws do not involve causal connections between substances. Each substance unfolds its history according to its own concept, while reflecting the history of all the others. "Every substance is like a complete world and like a mirror of God or of the whole universe, which each one expresses in its own way, somewhat as the same city is variously represented depending upon the different positions from which it is viewed" (Discourse, 9).

In Section 15, Leibniz claims that view follows from his account of the relation of God to created substances. Individual substances exist only due to God's preservation of them. Leibniz adds that God "even produces them continually by a kind of emanation, just as we produce our thoughts." What God produces is a substance that conforms to the individual concept God has of it. The predicates of this subject are already found in the individual concept, so when they exist, it is due directly to God's production of them. Given that this is the case, the predicates do not belong to the substance due to the interaction of the created substances with one another.

We could therefore say in some way and properly speaking, though not in accordance with common usage, that one particular substance never acts upon another particular substance nor is acted upon by it, if we consider that what happens to each is solely a consequence of its complete idea or notion alone, since this idea alreadly contains all its predicates or events and expresses the whole universe. (Discourse on Metaphysics,, 14).
Each substance is "like a world apart, independent of all other things, except for God" (Discourse on Metaphysics, 14).

Despite the lack of causal interaction with one another, substances stand in a weaker relation of "expression." A substance expresses another substance when it represents it in some way or other. Different substances represent what they do with different levels of clarity. God represents all things with perfect clarity, while humans represent some things with great clarity, due to their ability to know what is true.

In the Discourse on Metaphysics, Leibniz was willing to concede at least the possibility that animals have souls (34), which Descartes had denied in the Discourse on Method, Part V. What distinguishes human souls (which he calls "minds") from other souls is that they are self-conscious and are capable of grasping necessary truths such as are found in mathematics and metaphysics. Thus, human beings are the only souls capable of knowing God and their own place in God's scheme for the world. Thus Leibniz claimed that human minds express God, while all other souls would express only the world (36). The most important consequence of human knowledge is that it enables us to be subjects of morality and to enter into a moral community with God.

The substances which express the universe with the knowledge of what they are doing and which are capable of great truths about God and the universe, express it incomparably better than do those nature, which are either brutish and incapable of knowing truths or completely destitute of sensation and knowledge. (Discourse on Metaphysics, 35)
Leibniz uses the notion of relative perfection of expression to give a correct metaphysical account of the truth underlying the false common belief in causal interaction. If there is a change involving more than one substance, the cause is that whose perfection of expression immediately afterwards is increased, and the effect is that in which it is decreased. An increase in the perfection of expression is an exercise of power, while a decrease is a sign of weakness (Discourse on Metaphysics, 15).

Pre-Established Harmony

Given that substances do not interact with one another, Leibniz must explain why the world appears in the orderly way it does. The most fundamental reason is that all substances conform the the same laws of nature. These laws do not govern causal interactions, as Descartes had maintained, but instead govern the histories of each of the individual substances.

The precise manner in which the laws of nature operate on a given individual substance is contained in its complete concept. Each substance is governed by the same set of laws. (For example, human beings must act on the basis of what appears to them to be the best.) In creating substances, God takes into account the consequences of the laws of nature on their histories and insures that there is a general harmony, pre-established by God, in the way they unfold. As Leibniz puts it in the Discourse, the situation is like that when several people arrive at a single location based on their previous agreement to meet there.

The general harmony is used by Leibniz to solve the problem of the relation of mind and body that had been raised by Descartes. Like Spinoza, Leibniz held that there is no causal relation between mind and body. Rather, the way we express bodies in the universe is by expressing their relation to a single body, which we call our own. So our perceptions, though they flow from our individual concept in accordance with the laws of nature, correspond to states of our body. The relation of a class of our perceptions to our body also explains why those perceptions are not fully clear. For we express all other bodies through our expression of our own body, and the attendant perceptions merge with one another the way drops of water make up a wave (Discourse on Metaphysics, 33).

Nature

Leibniz was highly critical of the Cartesian account of nature. Descartes thought that substantial forms and final causes have no place in our understanding of the natural world, while Leibniz tried to show that these metaphysical notions can be useful for natural philosophy. This attempt raises a number of difficult questions that cannot be pursued here.

Instead, we will look at Leibniz's criticism Descartes's account of motion. In the Principles of Philosophy, Descartes had laid down three laws of motion and seven rules predicting the outcome of the collision of bodies with one another. The only two variables in the rules are the size and the speed of the bodies. Force could only be understood as "quantity of motion," a which is the size multiplied by the speed.

Leibniz thought he could refute Descartes through a single thought-experiment. Consider a body A and a body B four times the size of A. When A and B are in free-fall, their speed increases. Now suppose that body A has fallen four units of distance and body B has fallen one unit of distance. Galileo had shown that the speed of A at the end of its fall would be twice that of B at the end of its fall. Now we can calculate the Cartesian "quantity of motion" in the two bodies, which is the size times the distance. So body A would have a quantity of motion of 2 (1 x 2), while body B would have a quantity of motion of 4 (4 x 1).

Leibniz argued that the force of body A and body B are in fact equal. This requires two assumptions. The first assumption is that the force of a body at the end of its free-fall is equal to the force that would be required to lift it back to its original position. This is illustrated by the motion of a pendulum, which returns nearly to its original height when it reaches the bottom of its arc, the diminuition being due to the "the air and some other small obstacles" (Discourse on Metaphysics, 17). The second assumption is that the same force is needed to raise a body of one pound to the height of four units as is needed to raise a body of four points to the height of one unit. "All this is admitted by our new philosophers." Based on these two assumptions, the force acquired by the two bodies at the end of their falls is exactly the same.

The key point here is that force is a function of the work that it can do. To acquire the force to lift it to a height of four units, the speed of body A would have to be much greater than double the speed of body B. Leibniz ends his discussion by claiming that force is something real, over and above the attributes assigned to body by Descartes, "and one can therefore judge that not everything conceived in body consists soly in extension and its modifications, as our moderns have persuaded themselves" (Discourse on Metaphysics, 18).

Determinism

At this point, we leave the Discourse and consider some issues surrounding it that were raised by Arnauld in his correspondence with Leibniz. Arnauld expressed shock at what he took to be one of the consequences of that work. His knowledge of the Discourse was incomplete, given that Leibniz had sent him only the section headings.

As Leibniz himself notes in the body of Section 13, given that the entire history of a substance is contained in its concept, it would appear that a "great difficulty" arises. "It seems that this would eliminate the difference between contingent and necessary truths, that there would be no place for human freedom, and an absolute fatalism would rule our actions as well as all the other events of the world" (Discourse on Method, 13).

Leibniz understood the contingency of any event as requiring the possibility of another outcome. As explained in the notes on Spinoza, an event is contingent when it depends on some other event which is not determined beforehand. If all events in the history of the world are contained in the notion of each substance, it seems that there is no room for any conditions that are not themselves already determined. Whatever occurs, occurs necessarily. This can be called "fatalism" in the sense that whatever events occur will do so come what may. Every event is "fated" to occur due to its being contained in the notion of each individual substance. Leibniz refused to describe events as fated. Instead, they are "certain" to occur.

Necessity

The solution begins with Leibniz's account of necessary truths. Some truths are necessary because their denial involves a contradiction. These truths Leibniz called "absolutely necessary." Other truths are necessary because they are incompatible with some condition or hypothesis. These truths are called "hypothetically necessary." So, for example, the truths of logic and mathematics were counted by Leibniz as absolutely necessary. And one truth about existence is absolutely necessary as well: the fact that God exists. All other necessary truths about which things exist are hypothetically necessary. That is, whether a thing exists or not depends on whether God decrees its existence. If God does decree that it exist, its existence is hypothetically necessary. It is inconsistent with the decree and God's power that the object not exist. On the other hand, if God does not decree the existence of a thing, there is no way that it can exist.

The distinction between absolute and hypothetical necessity is the first step in dealing with the problem of determinism. We can say that every event is absolutely contingent, because it depends on God's decree that the substance involved in the event exist in the first place. For example, God could have decreed not to create Alexander. But given that he did, it is hypothetically necessary that Alexander become king of Macedon. This is still an absolutely contingent truth: it depends on the fact that God decrees that Alexander exist, which is something God is free not to do.

Leibniz's distinction between absolute and hypothetical necessity and contingency was not enough to satisfy Arnauld, who raised a number of issues. First, he thought that the doctrine that a substance always has all its properties is "strange." But Leibniz apparently satisfied him on this point by claiming that it is a matter of logic, concerning the nature of truth, as discussed above. Second, he wondered about what we now call "unactualized possibilities." If God's decree that creates the world is to be free, there must be other alternatives, possible worlds which God does not create. Arnauld objected that these possibilities seem to be figments of the human imagination. This point of dispute was never resolved.

God's Freedom

What really made Leibniz scramble for an answer was the question of whether Leibniz's system allows for God's freedom. Suppose God decrees that Adam be created. Given Leibniz's holism, it follows from the notion of Adam that "Isaac, Sampson, Samuel and so many others" will come into existence as offspring of Adam (Arnauld to Leibniz, May 13, 1686). In that case, God does not decree independently that they exist. God is forced, so to speak, to create them through his creation of Adam. One ready response to this objection is that it seems to portray God as reacting to events that take place by making new decrees. (This is a heretical doctrine of Faustus Socinus (1539-1604). Leibniz in second paper of the correspondence with Clarke held that Newton's doctrines come close to this view.) Arnauld explicitly disavowed this unorthodox view. But even if God's decrees take place "all at once," the decree to create the descendents of Adam should be separate from the decree to create Adam himself.

So Arnauld recognized that for Leibniz, God does not have certain knowledge of the future course of events simply by knowing his own decrees. In some sense, God knows what will take place through his knowledge of the notion of Adam, which is "intrinsic and necessary." The best response to this objection would seem to be to appeal to holism. Leibniz could counter that there is only a single decree of God to create the whole universe, which includes all the individuals mentioned. The notion of Adam is no less included in the notion of Sampson than the notion of Sampson is included in the notion of Adam. They are all in it together. God does not know that Sampson will exist on the basis of a particular decree, "Let there be Sampson!" Instead, the decree is, "Let there be a world that includes Sampson!"

There still remains a problem, though. God's creation decree is that a world exist, but not that it exist in a certain way. God's free decree to create the world is based on his knowledge that this would be for the best. It seems as if God's choice is between infinitely many possible worlds, each of which has a nature of its own, independent of God's decrees. To use an analogy suggested by Arnauld, the creation of circular objects would be based on God's knowledge of the eternal and immutable nature of a circle. God would not, on this picture, be free to craft a world of his own choosing.

Leibniz's response was to deny that worlds and the things making them up have natures that are independent of God's decrees. What makes a world the world that it is depends on some general decrees that govern the way the world will operate. Such decrees include the "laws of nature" that are discovered through scientific investigation. Leibniz did not give any examples, but we can concoct one for him. The basic law of human action, according to Leibniz, is that we do what is apparently the best. All the decisions Alexander makes, and all the events that flow from those decisions, are based on that law. Now what if the law were different? What if he acted so as to do what appeared worst to him. Different events would follow. In this way, the course of the world really is contingent on more than just God's selection of the best world.

Of course, God actually decrees a set of laws governing the created world, but there are other, merely possible, free decrees that God does not make. And herein lies the contingency of events in the world. Arnauld rather abruptly conceded that what Leibniz had said about the truth of propositions was enough to persuade him of the doctrine that substances have complete notions containing all their properties. Russell has conjectured, though, that the encounter with Arnauld frightened Leibniz from ever again making his true views known beyond himself.

World-Bound Individuals

At least part of God's freedom lies in the ability to choose which possible world among infinitely many to create. According to Leibniz, no individual inhabits (so to speak) more than one possible world. If we say that there is a world in which Alexander becomes king and a world in which he did not, we are not referring to a complete individual, but are only using a vague notion. There is only one Alexander, the one who lived in this world, no matter how much an individual in another world resembles our Alexander, he is not the same individual. Every individual substance is "world-bound."

This doctrine seems to pose a problem for human freedom. Leibniz wanted to be able to say that human actions are contingent, not necessary. One way to understand this is in terms of which world God chooses to create. Whether Alexander becomes king depends on whether God chooses to create a a world where this event occurs. Because Alexander is world-bound, if God were to create a world in which Alexander does not become king, God would not create Alexander at all. So there is no alternative for Alexander to any of his actions. We are left to ask how this can be compatible with his freedom. It seems that again we must have recourse to a Spinozistic conception of freedom, i.e., that there is nothing external to Alexander that determines his actions.


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