Philosophy 22 Lecture Notes: Leibniz

Stanford Encyclopedia of Philosophy Entries Problem of Evil, Philosophy of Mind
Human Freedom

There are many ways into the philosophy of Leibniz, just as there are many papers in which Leibniz enunciated his views. One of his earliest concerns was to salvage the possibility of human freedom, which was denied by his contemporary Spinoza. Recall that Spinoza had claimed that whatever exists, and whatever state an existing thing is in, follows from necessity from the essence of God. As a consequence, there is no distinction between possibility and actuality: whatever can be, will be. (This view was shared by Hobbes as well.)

In an early work, Leibniz attacked the conclusion of the argument, stating that we can conceive of things being differently, and that the different ways of being cannot co-exist. "One must certiainly hold that not all possibles attain existence, otherwise one could imagine no novel that did not exist in some place and at some time. Indeed, it does not seem possible for all possible things to exist, since they get in one another's way" ("On Contingency"). Spinoza could easily counter that if an alternative state of affairs were to get into the way of existing things, then they are not possible. Clearly, more needs to be said about possibility.

Leibniz's conception of possibility was logical: what is possible is what is self-consistent, containing no contradiction. For example, a married bachelor is impossible, because a bachelor is an unmarried male. So a married bachelor would be married and not-married -- a contradiction. Now consider a state of affairs that would "get in the way" of the existing state of affairs, say that George Bush was still President in 1995. There is no contradiction in the conception of Bush as having won re-election, so that state is possible. From this it follows that not all that is possible exists.

Not every contradiction is so apparent as that lurking in the conception of a married bachelor. If a square circle is impossible due to its contradictory nature, the presence of such a contradiction was not discovered by the legions of mathematicians who tried to square the circle. For that matter, there may even be a contradiction lurking in the conception we have of God. Thus Leibniz held that any attempt to prove that God exists must first establish God's possibility.

God's existence was affirmed by Leibinz, who also held that it of the nature of God to will the best of all possibilities. Thus it is incompatible with the nature of God that a possible world other than the existing world would have been created. This created a problem for Leibniz, since it seems as if the existing world exists of necessity, that it follows from the necessity of God's nature, just as Spinoza had stated!

Before considering this objection further, we may step back and look at Leibniz's ontology in a systematic way. Like Descartes and Spinoza before him, Leibniz distinguished between essence (the nature of a thing) and existence. For example, there may be natures such as "most perfect being," "perfect circle," "Julius Caesar," and we can ask whether something existing corresponds to each of them.

The principle of governing essences is that of possibility or non-contradiction. We must ask of any alleged essence whether or not it is a possibility. A possibility is that which contains nothing contradictory in its notion. For example, the notion of a "fastest motion" contains a contradiction. For consider a nail on a wheel which has the fastest motion. If the wheel is extended, a nail on the extended circumference moves faster than that which had the purportedly fastest motion.

In some cases, a notion is simple enough that one can analyze it into its elements and show that no contradiction is found in it. Thus the notion of a perfect circle, a plane figure all of whose parts are equally distant from a single center, is non-contradictory and hence a perfect circle is possible. Julius Caesar is possible because he actually existed. In general, one can infer "ab esse" (from existence) "ad posse" (to possibility). But is God possible? To show God's possibility, one would have to provide an analysis of the notion of God and prove that the analysis contains no contradiction. Leibniz asserted that God is possible , but we have yet to see on what basis he could make this assertion.

The principle of possibility can also be used to demonstrate necessity. Thus if the absence of a property is inconsistent with the notion of a thing, the thing has that property necessarily. For example, square is necessarily four-sided. Leibniz also held with Descartes and Spinoza that (given that God is possible), God necessarily exists To deny existence of a most perfect being is to allow that a being could be more perfect, which is a contradiction. (This is a version of the ontological argument.)

But there is no other essence whose non-existence involves a contradiction. That is, the existence of something with an essence other than God's is contingent. To account for the existence of such a thing, another principle is needed. This principle is that of sufficient reason, according to which whatever contingent thing exists does so by virtue of a reason sufficient to bring it about.

One way in which Leibniz stated the principle of sufficient reason was as a principle of perfection. That is, what exists is that which is more perfect than that which does not exist. This principle is based on the nature of God as the most perfect being. Such a being would not will to exist anything which is not the best possible. So among the essences which are, as it were, contending for existence, God picks the "world" of things which together is better than any other "world." The created world is the best of all possible worlds.

But what is the best world? Leibniz claimed that in the comparison of one complex of objects to another, two considerations come to the fore: variety of objects and economy of the principles which govern them. The best world, on this scheme, is that which provides the greatest variety with the most economical use of principles (i.e., laws of nature which govern the created world). Thus laws of nature are based on final causes, which is a break from Descartes's mechanical view of natural laws. It is important to note that the basis of comparison of worlds is truly global: individuals are significant only insofar as they are related to the world as a whole. Thus Leibniz from the start regards the created world "holistically." We will see later how extreme his holism really is.

The principle of sufficient reason and consequently the choice of the best world are consequences of God's nature. Leibniz made it very clear, however, that they flow from God's intellect, rather than God's will. Descartes had held that God's will is absolutely free, in the sense that it is subject to no constraints at all: it could be willed that 2 = 1 + 3. But Leibniz countered that if the will of God were arbitrary, there would be no more reason to praise God for what was actually created than there would be to praise God if God had created what God chose not to create. (Here Leibniz follows the general line of Plato in the Euthyphro.)

Leibniz, in fact, accused Descartes of holding a doctrine that leads to fatalism. Descartes had (rather innocently, it would seem), held that all combinations of material things will eventually be realized, given enough time. Leibniz thought that this inspired Spinoza to his doctrine according to which everything possible is eventually actualize, and hence to his hard determinism. The doctrine of other possible worlds is intended to give Leibniz a way of saying that not all that is possible is actual.

If he existence of contingent things depends on the existence of a reason sufficient to bring them about, it can fairly be insisted that things in the world exist of necessity. This necessity is "hypothetical," based on the existence of the sufficient reason. This is in contrast to the "absolute" necessity with which God exists. There is no contradiction in the notion of the non-existence of a contingent thing (this is what makes it contingent), though there is a contradiction between its non-existence and the existence of its sufficient reason (this is what makes it hypothetically necessary).

Although the distinction between the two types of necessity is intelligible, with the exception of Leibniz's immediate followers, it has not been well-received by philosophers. The German philosopher Crusius (1715-1775), for example, raised the following objection, which was cited by Kant ("A New Elucidation of the First Principles of Metaphysical Cognition," 1755). To conceive of the non-existence of an existing thing as possible, one must consider the thing in isolation from its sufficient reason. But this "absolute possibility" is of no import to the real world. As Kant put it, the distinction between absolute and hypothetical "obviously has no power at all to break the force and effective power of necessity. For what avail is it if the opposite of an event, which is precisely determined by antecedent grounds, can be conceived when it is regard in itself, since the opposite still cannot occur in reality?"

For example, if Caius has defrauded someone, he is now dishonest. By the principle of sufficient reason, his dishonesty now is the consequence of reasons which were adequate to bring it about. On a global level, Caius's dishonesty now is the result of God's "free" decree to create the world as it exists: a decree which brings with it all states of the world from its beginning. So given this decree, Caius must be dishonest.

It might be responded that the freedom of God's decree makes the existence of this world, and hence of Caius's dishonest, merely contingent. But we must be very clear about what the freedom of God's decree amounts to. Does it mean that God created the actual world arbitrarily? Leibniz attacked Descartes' doctrine that God's acts of will are not determined by what is antecdently the best. It is part of God's perfection that all his acts be done for a reason, the reason in each case being that it is for be best. Leibniz believed that there are created beings, distinct from God, and that the world of them comprises the best possible world. His criterion for the best was economic: the greatest variety with the fewest number of forms (laws of nature).

So in what sense is God's decree free? The sufficient reason for the existence of the world (i.e. the totality of existing things) is the fact that it is better than any other possible world, and that God wills the existence of the best world. But it seems that the act of creation is absolutely necessary, since the creation of an inferior world would be inconsistent with the nature of God. In "On Freedom and Possibility," Leibniz stated of a non-existent thing that it is possible "even though its coexistence with God can in some way be said to imply a contradiction." If this is so, Crusius's argument can be applied to the creative act of God: its non-occurence is of no consequence. God can no more decree another world than could Caius as he exists be honest.

Let us, nonetheless, explore a bit the question of the possibility of other worlds. It might be suggested that it is possible for dishonest Caius to be honest. Had God created another world, in which Caius was raised in different circumstances, Caius might be as honest as the day is long. But as Arnauld pointed out, it does not seem that there can be several Caiuses, if we take Caius as "a particular nature," any more than that there can be several versions of myself. Thus if there is another "Caius" in another world, it is not a particular Caius but a "vague" Caius, one who is undetermined, lacking in some specific properties.

Leibniz's response is that individuals are "world-bound" or confined to a single possible world. At best, there could only be a "counterpart" of an individual in another world. Corresponding to this view is Leibniz's "hyper-essentialism," according to which all the properties of an individual are essential to it, as being contained in its notion. Thus each individual has its own essence (or "haecceity, as the medievals called it), which contains every determination of that individual.

This doctrine was alarming to Arnauld, who thought that it leads to "a necessity more than fatal." [Click here for a synopsis of Leibniz's correspondence with Arnauld.] It does pose a severe problem for Leibniz's view of contingency. Caius's honesty is incompatible with his essence, just as God's creation of less than the best possible world is incompatible with the divine essence. So the problem of the possibility of alternatives is reduplicated on the level of created things.

There is a second way to understand contingency, which might seem less problematic. With what is absolutely necessary, a finite process of analysis will reveal that a contradiction is implied in its denial, whereas with what is contingent, the analysis would be infinite, and thus unattainable by a human being. The existence of anything in the actual world, or the occurrence of any event in the actual world, is contingent, in that it would require an infinite analysis to uncover its sufficient reason, which really involves the entire world. We would have to demonstrate that it is the best possible world, but this cannot be done. So even if God can (absolutely) create only the best possible world, the fact that this world is the best cannot be discovered by analysis.

The problem for this view lies in the fact that it seems to make contingency a matter of knowledge, rather than anything metaphysical. In this way, Leibniz seems to echo the views of Hobbes and Spinoza, both of whom asserted directly that the assertion of contingency is only an admission of ignorance.

Indeed, it is difficult to see how Leibniz can accommodate freedom on the basis of contingency. Leibniz says that, "Absolutely speaking, the will is in a state of indifference, as opposed to one of necessity, and it has the power to do otherwise or even to suspend its action completely; these two alternatives are possible ard remain so" ("Discourse on Metaphysics, Section 30). But at best, this contingency reflects a bare possibility which cannot be actualized given God's nature and our own. Perhaps it would be better to settle for Spinoza's account of a free cause, namely, one which acts from the necessity of its own nature (Ethics, Part I, Definition 7.) (Compare Descartes's declaration that, "The more I am inclined toward one direction . . . the more I choose that direction more freely" (Fourth Meditation).

In fact, Leibniz suggested such an account in some notes he had written on a meeting with Michel Angelo Fardella in Venice (1690, text p. 102). After making his usual claim that God's foreknowledge does not abolish freedom, Leibniz made the following observation.

Furthermore, we must understand that the mind is not determined by something else, but by itself, and that there is no other hypothesis which favors human freedom more than ours does. This is because . . . one created substance does not influence another, and, therefore, the mind derives all its operations from within itself, even though its nature is so ordered from the beginning that its operations harmonize with the operations of other things.
Note that this appeal to the pre-established harmony does not at all depend on the contingency of events, so that even Spinoza could embrace it (except for the reference to "created substance").

It is time to move on to other metaphysical issues in Leibniz. Closely related to his hyper-essentialism is his principle of the "identity of indiscernibles." No two things, A and B, can differ solely numerically, but must differ with respect to some property or other. Thus no two snowflakes can be exactly alike in every respect. Perfect similarity could only occur at the level of abstraction, which yields "vague" individuals. Each fully determined individual is essentially different from each other one, constituting, as it were, a species to itself.

Pre-Established Harmony

Another central doctrine associated with hyper-essentialism is that no two individuals in the world interact with each other. Since all the properties of an individual follow from its nature, there is no active role for any other thing to play. The individual objects which make up a world are synchornized to unfold their natures harmoniously with one another, as if they interacted. A bat does not move a baseball toward the fence, but changes in the bat are echoed in changes in the ball.

At times Leibniz described the harmony as an hypothesis which was better than its rivals, Cartesian interactionism and Malebranchean occasionalism. The problem with interactionism is that it has no explanation for the causal efficacy of mind on body, and vice-versa. Leibniz saw Descartes as having given up trying to explain how it is possible for mind and body to interact, and Descartes's followers even thought body/body interaction is inexplicable. Hence Malebranche's thesis that God is the sole cause of bodily movement and is the source of perceptions in the mind.

Malebranche's occasionalism was seen by Leibniz as an improvement over the Cartesian view. There is no question that God is capable of causing the requisite changes in the appropriate circumstances. The problem is that God's constant intervention in the world would be a perpetual miracle. To be sure, God constantly preserves the existence of all created things, but otherwise, God operates through laws of nature ("secondary causes") which operate on their own. A miracle, properly speaking, is an event which occurs as an exception to a law of nature, though it too has its place in the larger scheme of a world. (This point would be used later against Newton.) So if laws of nature are bypassed altogether, all events in the created world are miraculous. The only viable alternative to occasionalism is the hypothesis of the harmony.

There are further reasons adduced for the superiority of the harmony hypothesis, but they cannot be understood without a much more detailed look at the minds and bodies which make up the created world. Leibniz's description of finite things departs greatly from that of Descartes, so we will begin with a look at how he rejected the Cartesian picture, starting with the notion of corpreal bodies as extended substance.

Extended Things

Descartes had described extension as the essence of body. All other properties, including figure, size, motion and rest, are modes of extension. Leibniz pointed out that extension is always extension of something. An extension is a repetition: an extra few days to finish the paper, another few feet on the ladder, etc. When we say that a body is extended, then, what is it that is repeated through its length, width and depth? On Descartes's scheme, there can be no answer to this question, because the essence of body is extension itself.

Moreover, if extension is the essence of bodies, then the properties of bodies are purely geometrical. The only changes in bodies can be changes in size, shape, motion and rest. Descartes held that change is purely passive: motion is transferred by contact from one object to another. The only active beings are minds endowed with will: God is a prime mover who set the universe in motion, and humans have limited control over their own bodies. But all other motion is merely passed on.


Leibniz maintained that there is an active element in the material world, that changes are brought about by things themselves. (Of course, this is the only description compatible with his hypothesis of harmony.) Descartes was right that extension cannot be a source of activity, so Leibniz claimed there is an active element, force, in bodies. Laws of nature would have to be understood dynamically, as governing the force of acting and resistance. It is these forces which are extended: "The notion of extension presupposes the substance of body, which involves the power of acting and resisting, and exists everywhere as corporeal mass, and . . . the diffusion of this substance is contained in extension" ("A Specimen of Dynamics").

Now we have a better idea of the nature of physical change. A body has a source of activity, force, within itself. But it changes according to its own notion. So when a body changes, e.g. when a racquetball becomes compressed when it hits a wall, there is an internal redistribution of its forces. It bounces off the wall because of its elasticity: in springing back to its original shape, it pushes itself off the wall in the reverse direction.


The ability to act is characteristic of substance. That this ability is missing from Cartesian extended substance, was, Leibniz believed, an over-reaction to the medieval abuse of the notion of a substantial form. Admitting that appeal to a form can be vacuous, he proposed that this notion nonetheless has a proper use in metaphysics. The form is what provides the unity of substance, which is the only true being. A heap or aggregation is not a unity and clearly not a substance. A machine falls short of substantial unity as well, as its parts are related externally to one another, analogously to an army. On the other hand, an organism manifests true unity and can be called a substance. (Here Leibniz departed from Descartes's reduction of non-human animals to robots.)

One difficulty in understanding Leibniz's position (a difficulty noted by Arnauld) lies in Leibniz's description of the rehabilitated notion of a substantial form. As Leibniz described Arnauld's objection, "our body and soul are two really distinct substances; therefore it seems that the one is not the substantial form of the other" (Letter of December 8, 1696, text p. 78). The form of a body ought to be something in the body, but the soul is not. Leibniz first responded that the body is not a substance at all, but only a "being by aggregation." He then appealed to Church doctrine that asserts that the soul is the substantial form of the body. In the letter of April 30, 1687, he stated that:

It also seems that what constitutes the essence of a being by aggregation is only a mode of the things of which it is composed. For example, what constitutes the essence of an army is only a mode of the mn who compose it. This mode therefore presupposes a substance whose essence is not a mode of [another] substance. Every machine also presupposes some substance in the pieces of which it is made, and there is no plurality without true unities.
So insofar as the body is an aggregate, it is composed of "pieces" which are substances. Leibniz goes on to claim that he introduced "these substantial forms, or rather these corporeal substances endowed with a true unity" in order to account for "the force which is the cause of motion and which is in corporeal substance."

One of the fascinating features of Leibniz's philosophy is that he found the whole universe full of life. An organic body is composed of substances which themselves are unities of substances, and so on. A peculiar feature of this view is that in each case, there is a single substance which unifies the rest into a system. This "seed" or "dominant" substance is preserved through the generation and destruction of the rest of the organism.

Leibniz hypothesized that every living being has a seed which has existed from the creation of the universe. When the organized substance ceases to be through death, the seed of the substance remains, perhaps to become the kernal of another animal. This change or metamorphosis is like a change of clothing. Leibniz liked to use the example of the transformation of a caterpiller into a butterfly to illustrate change of form. Metamorphosis must be contrasted with metempsychosis, in which a separately existing soul is associated with a different body.

Living things, and only living things, are composite substances. Leibniz claimed that an composite, substance or aggregate, must be composed of substances. And if there is a composite, there must be something which is not composite, something which is simple. The simple beings of which all things are composed must themselves be substances, that is, something real. Otherwise, the composite itself is not real, but only an appearance, like a rainbow.

But what are the simple substances? The ancient Greeks, as well as a number of seventeenth century philosophers, held that they are atoms: indivisible, extended particles. Leibniz maintained that atoms are impossible, because an extended thing is by its very nature capable of division. No volume is so small that it cannot be subdivided into smaller volumes. Mathematical points are not extended, and hence are indivisible, but they are only abstractions, not anything real. So the simple substances populating the created universe must be understood in some other way.

We can look at Leibniz's positive characterization of monads as a response to two further problem with conventional atomism. First, since an atom is said to be simple and lacking parts, how can one atom be distinguished from another? It could not be by their size, since a larger extended thing has more parts than a smaller one, and to have a different shape requires differently shaped parts. Since all atoms would be qualitatively identical, they would all be quantitatively identical (the same thing), given Leibniz's principle of the identity of indiscernibles. So simple substances must have some basis for qualitative difference. Extension cannot be that basis.

The second problem with extended atoms is that their lack of parts makes them incapable of reflecting the states of other atoms. This conflicts with Leibniz's holistic thesis that in each thing is an expression of the states of all other things. A simple substance must have a basis for the reflection of the rest of the universe.


Both problems can be solved, accrording to Leibniz, if we attribute to monads states of perception. Different perceptions are not of the nature of parts, but they are a basis for distinguishing different substances. Moreover, perceptions are by their very nature representative, making them a suitable basis for expressing the rest of the universe. Most other things are perceived very confusedly, like the roar of a wave that is a blending of many sounds.

Since the entire universe is composed of monads, everything is perceptive. Leibniz recognized that this doctrine flies in the face of Cartesianism, according to which extended things (with the possible exception of the human body) are unthinking. But this doctrine is really a reductio ad absurdum of the whole Cartesian position. The false assumption made by the Cartesians is that every perception is itself perceived; in Leibnizian terms, that every perception is apperceived.

Leibniz advanced the revolutionary doctrine that there are perceptions ("little perceptions") of which a perceiver is not conscious. Thus we need not worry (as do the Cartesians) about the status of a person in a coma. Such a person does not apperceive, and so there is some question for the Cartesians whether a mind even exists at that point, since it is not thinking. But for Leibniz, such an individual may be perceiving very confusedly.

Most monads perceive only in the most confused way, like a person in a coma. Non-human animals, on the other hand, perceive in a more sophisticated manner. There is an order to their perception when they remember facts. Leibniz used the example of a dog that runs away when it sees a stick with which it has been beaten. The dog's memory recollects the pain suffered during previous beatings, and the pain is associated with the stick. This connection is one of facts only, not being concerned with the causes involved. But Leibniz noted that "three-fourths" of human action is based on this kind of experience. (Spinoza had also noted the tendency of humans to behave in this way, and Hume would later argue that all so-called "causal" reasoning is nothing more than habitual association.)

Another distinguishing features of the souls of animals is the way in which they represent things through their sense organs. On Leibniz's scheme, the sense organs represent the world outside them, and the state of these organs is in turn represented by the soul. So sense perception is indirect representation, available only to those beings with specialized parts capable themselves of representing the world in a relatively sophisticated way.


What distinguishes the soul of humans, which we call "mind," from that of animals and lower creatures, is the ability to form notions or conceptions of things. Through these notions we can grasp the nature of ourselves: true self-knowledge. And based on knowledge of ourselves, we understand the nature of God and other immaterial things. In general, we are able to know necessary truths, which would is impossible on the basis of mere experiential association.

The ability to use general notions to represent the world allows for action according to motives. A sufficient reason for undertaking an action is that it would tend to bring about the apparent good. Being able to act for the apparent best is what finite minds have in common with God. (Note that for God, the motive is to bring about what really is good.) Leibniz conceived of God as the monarch of a "kingdom of grace," composed of all created minds. The actions of minds are harmonious with the actions of bodies in the "kingdom of nature." This implies that there is a harmony between final causes and efficient causes, respectively.

More needs to be said about the nature of actions. We have already seen that for Leibniz, action is generated internally with no outside influence. Yet there is the appearance of interaction, in which an active being (agent) affects a passive being (patient). Leibniz attempted to explain the relation in terms of the relative perfection of the agent and patient. Action is an increase in perfection and passion a diminution. The only aspect of a substance which can be quantified with respect to perfection is the clarity of its perceptions, its ability to express the state of the universe. Changes occur when God conceives the state of the world to be created in accordance with the perfection of the things in them.

Human Action

Leibniz's model for action and passion is the relation between the human mind and its body. If the perceptions in the mind are clear, the mind is more perfect relative to the body, and the perferences of the mind are reflected in the state of the body. On the other hand, if the perceptions in the mind are confused, the body's state is more perfect and the result is that the mind is swayed by the demands of the body. "For in so far as the soul has perfection and distinct thoughts, God has accommodated the body to the soul, and has arranged beforehand that the body is impellect to execute its orders. And in so far as the soul is imperfect and as its perceptions are confused, God has accommodated the soul to the body, in such sort that the soul is swayed by the passions arising out of corporeal representations. This produces the same effect and same appearance as if the one depended immediately upon the ohter, and by the agency of a physical influence" (Theodicy, Section 66).

The Best Possible World

The harmony between nature and grace plays out on even a grander scale. The best possible world is one in which justice is served: the wicked are punished and the virtuous rewarded. Good and bad lie in the provence of the kingdom of grace. For the requisite rewards and punishments to take place, a course of developments in the kingdom of nature is required. This requisite development of events in the physical world takes place because they are a component of the best possible world. Human minds do not have enough knowledge of that world to determine how things tend toward the best, and due to our ignorance we think that it is possible that the world be better. But this is comparable to judging the quality of a vast painting by observing the characteristics of a very small part of it. What may seem disorderly is required for the overall effect.

The Kingdom of Nature

The relation of body to body is explained otherwise than by reference to a conception of the apparent good. In the kingdom of nature, all explanations must be mechanical only. Descartes had described the nature of bodies as extended only, and mechanical change was said to be a function of the modes of extension: the bulk, figure and motion of extended things. Leibniz held that extension cannot be the nature of bodies, since it is dependent on there being something which is diffused or spread out. Moreover, something else besides modes of extension is needed to explain mechanical change.

The missing element is force. Leibniz's account of the dynamical properties of bodies is quite complicated, and the treatment given here will be far from complete. In the first place, there is a distinction between active forces which initiate change and passive forces which merely conserve the present state of a thing. There are two kinds of passive forces, impenetrability and inertia. A force spread out over a space will resist the intrusion on its space by any other body, and the motion or rest of a body will continue until some other force intervenes. Leibiniz identified passive forces with the matter of a body.

Active force is identified with form and involves an effort or striving by the body. Leibniz conceived of active force, therefore, both metaphysically as the dynamical principle that is the soul, and mechanically as something quantifiable that accounts for the motions of bodies. He held that Descartes had confused force with mere quantity of motion, which mistake allowed him to conceive the physical world wholly in terms of modes of extension.

Extension is unsuitable as the nature of body for another reason, having to do with its infinite divisibility. Because any part of an extended thing is infinitely subdividable, Leibinz contended, an extended thing has no determinate shape or size. The line or surface which would seem to mark the limit of a thing is a mathematical abstraction, not a physical reality. The diffusion of force has no definite boundary. So to the representation of things as extended is merely appearance: extension is to substance as a rainbow is to the drops of rain from which it results. Space and time themselves are only relations between substances. Space is the order of their co-existence and time of the succession of their states.

Leibniz on his Contemporaries

This concludes the overview of Leibniz's metaphysics. We now turn to some criticisms Leibniz made of his contemporaries. In most cases, they amount to simple denials of their views, but in some cases we can get from them additional insight into Leibniz's system.


We begin with Thomas Hobbes, and specifically with his nominalism. Hobbes had maintained that there are no real "essences" or "natures," but only words that are used in a general way. This nominalism leads to conventionalism, the view that since definitions, are assigned arbitrarily, what is true and what is false is a matter of how we use language. Leibniz agreed that the choice of language may be arbitrary, but that the activity of thinking need not be. The patterns of reasoning about the language we use is invariant, indicating a correspondence with realities. Whether we do arithmetic in binary, decimal or hexadecimal mode, there is a congruence between the results of our calculations. In fact, Leibniz invented the rudiments of a universal symbolic language to express the relations among possibilities.

In one version of Leibniz's calculus, there are simple notions and composite ones built up from them, all represented by numbers. Truth is determined by arithmetic calculations. An impossible proposition is one whose subject term and predicate term each have a number, one positive, and one negative, divisible by a common number. ("A pious person is wretched" is represented by +10 -3 for the subject and +14 -5 for the predicate.) Thus a contradiction in a composite notion involves negation, which itself is a composite notion. If a notion were composed entirely of simple notions, there would be no negation and hence no way for it to contain a contradiction. From all of this it follows that if God's notion is composed only of simple notions, there could be no contradiction in it.


In this way, Leibniz thought he could repair a defect in Descartes's philosophy: that Descartes had neglected to prove God's possibility. As mentioned earlier, Leibniz maintained that there might be a contradiction harbored in it, as with the notion of a fastest motion. One could hardly maintain that the latter notion does not contain any negation in it: a slower thing is not as fast as a faster one. But in the notion of God is that of an unlimited being, and hence can contain no negation ("Monadology," Section 45).

It was over the nature of God that Leibniz clashed most forcefully with Descartes. To be sure, he criticized Descartes in many petty ways, even accusing him of having set himself up as the leader of a cult. Much of his criticism was directed against Descartes' skill as a scientist. But the most objectionable feature of Descartes's scheme was that his God was no more than a power, not acting from the good. In this way, it resembles the God of Spinoza, who is no God at all. As a consequence, Leibniz concludes, Descartes gives the pagan counsel of resignation rather than the Christian counsel of hope. (Leibniz leveled this criticism at Spinoza as well.)


Leibniz's criticisms of Spinoza come at different levels. At the highest, he claimed that there is only one essence (that of God) which exists necessarily. Other essences exist contingently if they do at all. Those which do not exist are possible but not actual, so the range of possibility extends beyond the actual, contrary to Spinoza's assertion. Perhaps Leibniz believed this because of his very permissive logical conception of possibility, i.e., that which does not contain a contradiction in its own concept (whether or not its existence is compatible with God's nature).

Turning to the attributes, we find Leibniz criticizing Spinoza for claiming that extension can be an attribute of a substance, since what is extended is divisible, while substance is unitary. So only composites are extended, but composites are not substances. Leibniz found it absurd that Spinoza recognized the indivisibility of substance while maintaining that extension is an attribute of God.

Leibniz claimed that Spinoza badly misconstrued the nature of thought. Ideas and the minds composed of them are said to be modes of the attribute of thinking. Given the unity of substance, there is an idea corresponding to each body, so that some mode of thought corresponds even to incorporeal things. Leibniz countered that although each substance has perception, not all have thought, which is a property of minds alone. Moreover, minds are not modes of thinking, but the reverse is true: thoughts are modes of minds, which themselves are substances.

This said, there are major areas of agreement between Spinoza and Leibniz. Most importantly, Leibniz adapted Spinoza's view that the properties of substance are all consequences of its essence. The only difference is that Leibniz allowed for a number of substances, whose non-existence (except for that of God) is possible.

The second area of agreement is related to the first: there can be no interaction between mind and body. For Spinoza, the reason is that mind and body are modes of a single thing. Leibniz maintained that it is a mistake to think that a single thing has a mind and a body; instead a mind has a body associated with it. Nonetheless, the unfolding of the states of the mind and the unfolding of the states of the body occur in parallel, just as the Spinoza's "modes of thought and extension" develop in parallel causal chains.


Leibniz had interesting things to say about his other contemporaries, such as Berkeley and Malebranche. Time does not permit a discussion of his relations to those philosophers. There is much to say about the dispute with Newton, but that must wait for the development of Newton's views in the next set of notes .


John Locke (1632-1704) was a renowned English philosopher whose chief work in metaphysics and theory of knowledge was An Essay concerning Human Understanding (1690). [ Click here for lecture notes on Locke's Essay. ] The book was translated into French in 1700, after which Leibniz undertook to write an extensive reply to it. He nearly finished the work in 1709, but did not publish it, stating, "I dislike to publish refutations of dead authors, although they might appear during their lifetime and be communicated to the authors themselves" (Letter to Remond, March 14, 1714). The book, New Essays concerning Human Understanding, was finally published in 1765.

Locke himself was heavily influenced by other English philosophers, especially Newton. He shared with Newton the belief that the physical world is composed of small, solid bodies he called "corpuscles." The existence of these bodies he treated as only a hypothesis, as with Newton. Moreover, Locke was highly skeptical about the prospects of human knowledge about the corpuscles and the way in which they act. He thought, unlike Leibniz, that we can gain no knowledge of nature a priori, but must instead rely solely on sensory experience, which is feeble at best.

I deny not but that a man, accustomed to rational and regular experiments, shall be able to see further into the nature of bodies, and guess righter at their yet unknown properties, than one that is a stranger to them: but yet, as I have said, this is but judgment and opinon, not knowledge and certainty. This way of getting and improving our knowledge in substances only by experience and history, which is all that the weakness of our faculties in this state of mediocrity which we are in in the world can attain to, makes me suspect that natural philosophy is not capable of being made a science. (Essay, Book IV, Chapter XII, "Of the Improvement of our Knowledge," Section 10)
Leibniz replied that although "physics as a whole will never be a perfect science among us," physical science is still possible, in cases in which "physicists by means of certain principles of experience give a reason for a multitude of phenomena and can indeed prove them in practice."

Another conclusion of Locke's was highly controversial in his time and bears on comments of Demaris Cudworth described below. Locke had claimed that although in its own nature matter could not, through some sort of organization, think, it is in God's power to "superadd" the power of thought to matter (Essay, Book IV, Chapter III, "Of the Extent of Human Knowledge," Section 6). This conclusion had drawn the wrath of Bishop Stillingfleet, with whom Locke engaged in a sharp correspondence. Against Stillingfleet's charge that it is, on Locke's principles, "possible that it may be a material substance that thinks in us." Locke protested there that he did not claim that we humans are material thinking substances; in fact, it "will prove in the highest degree probable" that we are immaterial substances.

Leibniz's response was to allow that Locke's conclusion is not unreasonable given confused notions of matter and thought; but once they are clearly understood, the conclusion is unsupportable. Matter is only a mass, which is the resultant of real unities, immaterial substances. So God cannot give thought to matter.

Leibniz and Damaris Cudworth

We shall conclude with a discussion of the exchange of letters between Leibniz and Damaris Cudworth, Lady Masham. Cudworth was the daughter of a well-known English philosopher, Ralph Cudworth, and close friend of Locke, who lived out his final days on her estate. One can see the obvious influence of both these men on her thinking, but she struck an independent course.

Cudworth's interest lay mainly in the issue of how living organisms are related to matter. This issue was widely debated after Descartes's proclamation that aside from human beings, all living things are robotic, behaving according to strictly mechanical principles. An opposing view had been offered by one Hieronymus Rorarius, who wrote a book attempting to show that other animals are more rational than human beings. The Frenchman Pierre Bayle devoted a chapter, "Rorarius," of his Historical and Critical Dictonary to the topic. Here he criticized Leibniz's view among others.

Leibniz had offered a view very much opposed to Descartes's. All living things are so by virtue of a soul, endowed with perceptions, which is associated with their bodies. Ralph Cudworth's scheme was not so extreme. He wished to deny reasoning and knowledge to animals but explain how they could behave in an apparently knowing manner. To this end, he posited "plastic natures" which operate unconsciously according to God's ends, which are ideas in the mind of God. His daughter defended this view against Bayle's charge that they would operate in accord with no ideas at all, or else under God's direct guidance. But she did not endorse her father's view, contenting herself with the observation that it is of no help to the atheist.

Cudworth professed great puzzlement over Leibniz's notion of the soul. She noted that he had refered to it variously as a form and as a kind of force. It is unclear how it could be all these things, and unclear which of them it should be said to be. Moreover, the soul is something unextended which nevertheless is united to the body, which is an extended thing. Cudworth proposed, on the contrary, that there are two kinds of extended substance, solid and non-solid, and that thought is annexed to non-solid extension. Still, she allowed as possible Locke's suggestion that God could add the power of thinking to solid extended substance.

I clearly conceive an extension without solidity, and a solid extension: to some system of which last if it should be affirmed that God did annex thought, I see no absurdity in this from there being nothing in extension and impenetrablility or solidity, from whence thought can naturally, or by a train of causes be derived; the which I believe it demonstrable it cannot be. (Sixth Letter to Leibniz, August 8, 1704)
The reason it is not absurd to suppose that a solid substance thinks is found in Locke's view (which is not attributed to him here) that substance is "unknown" and hence might support both solidity and thought. Ultimately, Cudworth concluded that we humans probably do not know how God did dispose the world: even if he does so in the simplest way, "I am very apt to believe that God's ways are past our finding out, in this sense."

[ Previous Lecture Notes | Next Lecture Notes | Lecture Notes Menu | Philosophy 22 Home Page ]