Because of his young age, however, he was refused the degree. This caused Leibniz to leave the University of Leipzig and earn the degree the following year at the University of Altdorf, whose faculty were so impressed with Leibniz that they invited him to become a professor despite his youth. Leibniz, however, declined and opted instead to pursue a career in public service.
In , Leibniz entered the service of the Elector of Mainz, who tasked him to help revise the Corpus Juris —or body of laws—of the electorate. During this time, Leibniz also worked to reconcile Catholic and Protestant parties and encouraged Christian European countries to work together to conquer non-Christian lands, instead of waging war on each other. In , Leibniz went to Paris to discuss these ideas more, staying there until While at Paris, he met a number of mathematicians like Christiaan Huygens , who made many discoveries in physics, mathematics, astronomy, and horology.
He quickly advanced in the subject, figuring out the core of some of his ideas on calculus, physics, and philosophy. Indeed, in Leibniz figured out the foundations of integral and differential calculus independently from Sir Isaac Newton. In , Leibniz also made a diplomatic trip to London, where he showed a calculating machine that he had developed called the Stepped Reckoner, which could add, subtract, multiply, and divide.
In London, he also became a fellow of the Royal Society, an honor awarded to individuals who have made substantial contributions to science or math. In , upon the death of the Elector of Mainz, Leibniz moved to Hanover, Germany, and was placed in charge of the library of the Elector of Hanover. It Hanover—the place that would serve as his residence for the rest of his life—Leibniz wore many hats. For instance, he served as a mining engineer, an advisor, and a diplomat.
As a diplomat, he continued to push for the reconciliation of the Catholic and Lutheran churches in Germany by writing papers that would resolve the views of both Protestants and Catholics. Leibniz died in Hanover on November 14, He was 70 years old.
Leibniz never married, and his funeral was only attended by his personal secretary. Leibniz was considered a great polymath and he made many important contributions to philosophy, physics, law, politics, theology, math, psychology, and other fields.
He may be most well known, however, for some of his contributions to math and philosophy. When Leibniz died, he had written between , to , pages and more than 15, letters of correspondence to other intellectuals and important politicians—including many notable scientists and philosophers, two German emperors, and Tsar Peter the Great.
Leibniz invented the modern binary system, which uses the symbols 0 and 1 to represent numbers and logical statements. According to Leibniz, the mind is always active, for there are always perceptions present to it, even if those perceptions are minute and do not rise to such a level that we are cognizant of them.
Thus, even in a deep and dreamless sleep, the mind is active, and perceptions are in the mind. Moreover, if Descartes really did advocate the perfect transparency of the mind, then it should be clear that Leibniz allows for a subtler picture of mental contents: there are many things in the mind that are confused and minute and to which we do not always have complete access.
Leibniz, however, does not simply disagree with Locke about the nature of the mind and the possibility of innate ideas. It is also Leibniz's contention that human beings are capable of knowledge in a way that Locke had clearly denied.
As shown above, Leibniz is convinced that our knowledge of necessary truths has a completely different foundation from that for which Locke argues. Similarly, Leibniz holds that we can have genuine knowledge of the real essences of things, something called into question by Locke.
Leibniz, however, holds that we can know certain things not only about individuals but also about their species and genera. It would seem, then, that Leibniz has something like the following in mind: experience informs us of a certain consistent set of sensible properties in, for example, gold; that is, a certain set of properties is compossible.
And, more important, we ought to be able to assert with certainty that if some object has the greatest ductility, then it also has the greatest weight. Like most of his great contemporaries Descartes, Spinoza, Malebranche , Leibniz developed a number of arguments for the existence of God.
But they have long histories in Leibniz's thought. Yet, unlike Descartes and Spinoza at least, Leibniz also expended great efforts in explaining and justifying God's justice and benevolence in this world. In other words, Leibniz was keen to answer the problem of evil. His work on this subject led to his thesis, so roundly mocked in Voltaire's Candide , that we live in the best of all possible worlds. Leibniz made an important contribution to the history of the ontological argument.
His reflections on this form of argument go back to the s, and we know that he shared his thoughts on this matter with Spinoza when Leibniz visited him on the way to Hanover. According to Leibniz, the argument that Descartes gives implicitly in the Fifth Meditation and explicitly in the First Set of Replies is faulty. Descartes had argued that God is a being having all perfections, existence is a perfection, therefore, God exists.
If this is so, then and only then an ens perfectissimum can be said to exist. And with this definition in hand, Leibniz is then able to claim that there can be no inconsistency among perfections, since a perfection, in being simple and positive, is unanalyzable and incapable of being enclosed by limits.
Therefore, it is possible that any and all perfections are in fact compatible. And, therefore, Leibniz reasons, a subject of all perfections, or an ens perfectissimum , is indeed possible. But this argument by itself is not sufficient to determine that God necessarily exists.
Leibniz must also show that existence is itself a perfection, so that a being having all perfections, an ens perfectissimum , may be said to exist. More exactly, Leibniz needs to show that necessary existence belongs to the essence of God. In other words, if it is the case that a necessary being is the same thing as a being whose existence follows from its essence, then existence must in fact be one of its essential properties. In short, Leibniz's argument is the following:.
As we have seen, the Principle of Sufficient Reason is one of the bedrock principles of all of Leibniz's philosophy. In the Monadology , Leibniz appeals to PSR, saying that even in the case of contingent truths or truths of fact there must be a sufficient reason why they are so and not otherwise. In the Theodicy , Leibniz fills out this argument with a fascinating account of the nature of God. First, insofar as the first cause of the entire series must have been able to survey all other possible worlds, it has understanding.
Second, insofar as it was able to select one world among the infinity of possible worlds, it has a will. Third, insofar as it was able to bring about this world, it has power. And, fifth, insofar as everything is connected together, there is no reason to suppose more than one God. Thus, Leibniz is able to demonstrate the uniqueness of God, his omniscience, omnipotence, and benevolence from the twin assumptions of the contingency of the world and the Principle of Sufficient Reason.
Leibniz's account of the nature of possible worlds is dealt with in a separate entry. Here the following simple question will be addressed: How can this world be the best of all possible worlds? After all, as Voltaire brought out so clearly in Candide , it certainly seems that this world, in which one finds no short supply of natural and moral horrors, is far from perfect — indeed, it seems pretty lousy. Certainly only a fool could believe that it is the best world possible.
But, Leibniz speaks on behalf of the fool, with an argument that has essentially the following structure:. In other words, Leibniz seems to argue that, if one is to hold the traditional theistic conception of God and believe that one can meaningfully assert that the world could have been other than it is, then one must hold that this world is the best possible. Naturally, this argument is simply the Christian retort to the Epicurean argument against theism.
But what are the criteria by which one can say that this world is the best? It should be clear that Leibniz nowhere says that this argument implies that everything has to be wonderful. Indeed, Leibniz is squarely in the tradition of all Christian apologists going back to Augustine, arguing that we cannot have knowledge of the whole of the world and that even if a piece of the mosaic that is discoverable to us is ugly the whole may indeed have great beauty.
Still, Leibniz does offer at least two considerations relevant to the determination of the happiness and perfection of the world. So, is this world of genocide and natural disaster better than a world containing only one multifoliate rose? Yes, because the former is a world in which an infinity of minds perceive and reflect on the diversity of phenomena caused by a modest number of simple laws. To the more difficult question whether there is a better world with perhaps a little less genocide and natural disaster Leibniz can only respond that, if so, God would have brought it into actuality.
And this, of course, is to say that there really is no better possible world. The editors would like to thank Sally Ferguson for noticing inaccuracies in a claim and in a quote attributed to Leibniz.
Life 1. Overview of Leibniz's Philosophy 3. Some Fundamental Principles of Leibniz's Philosophy 3. Metaphysics: A Primer on Substance 4. Metaphysics: Leibnizian Idealism 5. Epistemology 6. Philosophical Theology 7. Life Leibniz was born in Leipzig on July 1, , two years prior to the end of the Thirty Years War, which had ravaged central Europe.
Overview of Leibniz's Philosophy Unlike most of the great philosophers of the period, Leibniz did not write a magnum opus ; there is no single work that can be said to contain the core of his thought. He writes: …I have tried to uncover and unite the truth buried and scattered under the opinions of all the different philosophical sects, and I believe I have added something of my own which takes a few steps forward.
The circumstances under which my studies proceeded from my earliest youth have given me some facility in this. I discovered Aristotle as a lad, and even the Scholastics did not repel me; even now I do not regret this. But then Plato too, and Plotinus, gave me some satisfaction, not to mention other ancient thinkers whom I consulted later. After finishing the trivial schools, I fell upon the moderns, and I recall walking in a grove on the outskirts of Leipzig called the Rosental, at the age of fifteen, and deliberating whether to preserve substantial forms or not.
Mechanism finally prevailed and led me to apply myself to mathematics…. But when I looked for the ultimate reasons for mechanism, and even for the laws of motion, I was greatly surprised to see that they could not be found in mathematics but that I should have to return to metaphysics. This led me back to entelechies, and from the material to the formal, and at last brought me to understand, after many corrections and forward steps in my thinking, that monads or simple substances are the only true substances and that material things are only phenomena, though well founded and well connected.
Of this, Plato, and even the later Academics and the skeptics too, had caught some glimpses… I flatter myself to have penetrated into the harmony of these different realms and to have seen that both sides are right provided that they do not clash with each other; that everything in nature happens mechanically and at the same time metaphysically but that the source of mechanics is metaphysics.
As he puts it in the New Essays , although time and place i. Thus, although diversity in things is accompanied by diversity of time or place, time and place do not constitute the core of identity and diversity, because they [sc. To which it can be added that it is by means of things that we must distinguish one time or place from another, rather than vice versa.
Briefly, one way to sketch the argument is this: 1 Suppose there were two indiscernible individuals, a and b , in our world, W. PSR 5 Therefore, our original supposition must be false.
There are not two indiscernible individuals in our world. PII Now, it was said above that Leibniz excludes purely extrinsic denominations or relational properties from the kinds of properties that are constitutive of an individual. Metaphysics: A Primer on Substance I consider the notion of substance to be one of the keys to the true philosophy. PII 2 A substance can only begin in creation and end in annihilation.
Bodies act according to the laws of efficient causes or of motions. And these two kingdoms, that of efficient causes and that of final causes, are in harmony with each other.
For God, so to speak, turns on all sides and in all ways the general system of phenomena which he finds it good to produce in order to manifest his glory, and he views all the faces of the world in all ways possible, since there is no relation that escapes his omniscience.
The result of each view of the universe, as seen from a certain position, is a substance which expresses the universe in conformity with this view, should God see fit to render his thought actual and to produce this substance. Epistemology Leibniz's reflections on epistemological matters do not rival his reflections on logic, metaphysics, divine justice, and natural philosophy in terms of quantity. Philosophical Theology Like most of his great contemporaries Descartes, Spinoza, Malebranche , Leibniz developed a number of arguments for the existence of God.
In short, Leibniz's argument is the following: 1 God is a being having all perfections. Definition 2 A perfection is a simple and absolute property.
Definition 3 Existence is a perfection. But, Leibniz speaks on behalf of the fool, with an argument that has essentially the following structure: 1 God is omnipotent and omniscient and benevolent and the free creator of the world.
Definition 2 Things could have been otherwise—i. Premise 3 Suppose this world is not the best of all possible worlds. God lacked foreknowledge ; or God did not wish this world to be the best; or God did not create the world; or there were no other possible worlds from which God could choose.
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Jalabert, Jacques, Jauernig, Anja, Jolley, Nicholas, Leibniz , New York: Routledge. Jolley, Nicholas ed. Kauppi, Raili, Kulstad, Mark A. Leduc, Christian, Levey, Samuel, Lin, Martin, Lodge, Paul, a.
Lodge, Paul ed. Lodge, Paul, and Marc Bobro, Look, Brandon C. Martin, Gottfried, Mates, Benson, McDonough, Jeffrey K. McRae, Robert, Mercer, Christia, Mercer, Christia, and Robert C. Sleigh Jr. Jolley ed. Mondadori, Fabrizio, Mugnai, Massimo, Such curved acceleration requires the postulation of absolute space which makes possible fixed and unique frames of reference. Leibniz, however, has a completely different understanding of space and time. In short, an empty space would be a substance with no properties; it will be a substance that even God cannot modify or destroy.
From this principle, together with the law of non-contradiction, Leibniz believes that there follows a third: the principle of the identity of indiscernibles , which states that any entities which are indiscernible with respect to their properties are identical.
Leibniz is fond of using leaves as an example. Two leaves often look absolutely identical. So, it must be the case that no two leaves are ever exactly alike.
If any objects are in every way the same, but actually distinct, then there would be no sufficient reason that is, no possible explanation for why the first is where and when it is, and the second is where and when it is, and not the other way around.
If, then, one posits the possible existence of two identical things things that differ in number only—that is, one can count them, but that is all , then one also posits the existence of an absurd universe, one in which the principle of sufficient reason is not universally true. Leibniz often expresses this in terms of God: if two things were identical, there would be no sufficient reason for God to choose to put one in the first place and the other in the second place.
Similar considerations apply to Newtonian absolute space. The first concerns the violation of the principle of the identity of indiscernibles. Suppose that space is absolute.
Since every region of space would be indiscernible from any other and spatial relations would be construed as extrinsic, it would be possible for two substances to be indiscernible yet distinct in virtue of being in different locations. But this is absurd, Leibniz argues, because it violates the principle of the identity of indiscernibles. The second reductio concerns the violation of the principle of sufficient reason. Leibniz argues that there would then be no sufficient reason for why the whole universe was created here instead of two meters to the left because no region of space is discernible from any other.
Analogous problems are thought to result from a conception of absolute time. But what does all this say about space? For Leibniz, the location of an object is not a property of an independent space, but a property of the located object itself and also of every other object relative to it. This means that an object here can indeed be different from an object located elsewhere simply by virtue of its different location, because that location is a real property of it.
That is, space and time are internal or intrinsic features of the complete concepts of things, not extrinsic. Let us return to the two identical leaves. All of their properties are the same, except that they are in different locations. But that fact alone makes them completely different substances.
To swap them would not just involve moving things in an indifferent space, but would involve changing the things themselves.
That is, if the leaf were located elsewhere, it would be a different leaf. A change of location is a change in the object itself, since spatial properties are intrinsic similarly with location in time. First, there is no absolute location in either space or time ; location is always the situation of an object or event relative to other objects and events. Second, space and time are not in themselves real that is, not substances.
Space and time are, rather, ideal. Space and time are just metaphysically illegitimate ways of perceiving certain virtual relations between substances.
They are phenomena or, strictly speaking, illusions although they are illusions that are well-founded upon the internal properties of substances. Thus, illusion and science are fully compatible. For God, who can grasp all at once complete concepts, there is not only no space but also no temptation of an illusion of space. Space is nothing but the order of co-existent objects; time nothing but the order of successive events.
This is usually called a relational theory of space and time. Take the analogy of a virtual reality computer program. What one sees on the screen or in a specially designed virtual reality headset is the illusion of space and time. Space and time are reduced to non-spatial and non-temporal numbers. For Leibniz, God in this analogy apprehends these numbers as numbers , rather than through their translation into space and time.
This, however, raises a serious logical problem for Leibniz. Leibniz has to argue that all relational predicates are in fact reducible to internal properties of each of the three substances.
Furthermore, Leibniz must provide a response to the Newtonian bucket argument. Indeed, Leibniz thinks that one simply needs to provide a rule for the reduction of relations. For linear motion the virtual relation is reducible to either or both the object and the universe around it. For non-linear motion, one must posit a rule such that the relation is not symmetrically reducible to either of the subjects bucket, or universe around it.
Rather, non-linear motion is assigned only when, and precisely to the extent that, the one subject shows the effects of the motion. Perhaps it seems strange that the laws of nature should be different for linear as opposed to non-linear motion. It sounds like an arbitrary new law of nature, but Leibniz might respond that it is no more arbitrary that any other law of nature; people have just become used to the illusion of space and time as extrinsic relations of entities that they are not used to thinking in these terms.
We are now, finally, ready to get a picture of what Leibniz thinks the universe is really like. It is a strange, and strangely compelling, place. These are the fundamental existing things, according to Leibniz.
His theory of monads is meant to be a superior alternative to the theory of atoms that was becoming popular in natural philosophy at the time. Leibniz has many reasons for distinguishing monads from atoms. We must begin to understand what a monad is by beginning from the idea of a complete concept.
As previously stated, a substance that is, monad is that reality which the complete concept represents. A complete concept contains within itself all the predicates of the subject of which it is the concept, and these predicates are related by sufficient reasons into a vast single network of explanation. Furthermore, the network of explanation is indivisible; to divide it would either leave some predicates without a sufficient reason or merely separate two substances that never belonged together in the first place.
Correspondingly, the monad is one, simple and indivisible. A monad, then, is self-sufficient. So if I were capable of considering distinctly everything which is happening or appearing to me now, I would be able to see in it everything which will ever happen or appear to me for all time.
According to Leibniz, causation is to be account for by saying that one thing, A, causes another, B, when the virtual relation between them is more clearly and simply expressed in A than in B. But metaphysically, Leibniz argues, it makes no difference which way around the relation is understood, because the relation itself is not real. Leibniz goes on to insist that the first direction of explanation is much simpler, since the second would involve leaping directly to the action of God to explain the extraordinary action of so many individual bits of water.
But that simplicity is hardly the same as truth. So, instead of cause and effect being the basic agency of change, Leibniz is offering a theory of pre-established harmony sometimes referred to as the hypothesis of concomitance to understand the apparently inter-related behavior of things.
Consider the common analogy of two clocks. The two clocks are on different sides of a room and both keep good time that is, they tell the same time. When two things behave in corresponding ways, then it is often assumed without any real evidence that there is causation occurring. But another person who knew about clocks would explain that the two clocks have no influence one on the other, but rather they have a common cause for example, in the last person to set and wind them.
Since then, they have been independently running in sync with one another, not causing each other. Nevertheless, every monad is synchronized with one another by God, according to his vast conception of the perfect universe. We must be careful, however, not to take this mechanical image of a clock too literally. Not all monads are explicable in terms of physical, efficient causes. In accordance with his theory of pre-established harmony, Leibniz argues that monads do not affect one another and that each monad expresses the entire universe.
Furthermore, since a monad cannot be influenced, there is no way for a monad to be born or destroyed except by God through a miracle—defined as something outside the natural course of events. All monads are thus eternal. The primary, most fundamental level of reality is the metaphysical level , which includes only monads, their perceptions, and their appetitions no causality, no space, no time—at least as ordinarily understood—each monad spontaneously unfolding according to the kind of thing that it is.
The phenomenal or descriptive level involves what appears to be happening from the finite, imperfect perspective of human minds things cause one another in space and time. Therefore, the laws of physics are perfectly correct, as a description.
But there is nothing for sale anywhere which costs just that amount. As a measure it works well, provided one does not take it literally. Obviously, however, one does not apperceive that is, one is not conscious of all these little perceptions , as Leibniz calls them. Thus, perception for Leibniz does not mean apperception.
Further, where one is conscious of some perception, it will be of a blurred composite perception. For Leibniz, little perceptions are an important philosophical insight. This follows, Leibniz believes, from the principle of sufficient reason together with the idea of the perfection of the universe consisting of something like plenitude.
But the idea of little perceptions allows Leibniz to account for how such continuity actually happens even in everyday circumstances. Such habits accumulate continuously and gradually, rather than all at once like decisions, and thus completely bypass the conscious will. Thus, a thorough-going skepticism, however plausible at a logical level, is ultimately absurd. According to Leibniz, everything one perceives which is a unified being must be a single monad.
Everything else is a composite of many monads. A coffee cup, for example, is made of many monads an infinite number, actually. In everyday life, one tends to call it a single thing only because the monads all act together. Leibniz thus says that, at least for living things, one must posit substantial forms , as the principle of the unity of certain living composites.
Furthermore, according to Leibniz, such composite bodies must be made of an infinite number of other inanimate as well as animated monads. Perhaps Leibniz was understandably impressed by the different levels of magnitude being revealed by relatively recently invented instruments like the microscope and telescope. Every portion of matter can be thought of as a garden full of plants, or as a pond full of fish. But every branch of the plant, every part of the animal, and every drop of its vital fluids, is another such garden, or another such pool.
Note: Although there is an extraordinary sublimity of such an image, Leibniz is often accused of making rather too much of an inadequate conception of the infinite. The substantial form is thus a unified explanation of bodily form and function. A mere chunk of stuff has, of course, an explanation, but not a unified one—not in one monad, the soul.
Leibniz thus distinguishes four types of monads : humans, animals, plants, and matter. An innate idea is any idea which is intrinsic to the mind rather than arriving in some way from outside it. During this period in philosophy, innate ideas tended to be opposed to the thorough-going empiricism of Locke. Like Descartes before him—and for many of the same reasons—Leibniz found it necessary to posit the existence of innate ideas.
In general, at least any relation in space or time will appear in this way. Thus, one could imagine Leibniz being a thorough-going empiricist at the phenomenal level of description.
This would amount to the claim that the metaphysically true innateness of all ideas is epistemologically useless information. Leibniz finds it necessary, therefore, to advance the following arguments in favor of phenomenally innate ideas:. But it is impossible to derive universal necessity from experience. Note that this argument is hardly new to Leibniz. By using rational principles of physics, for example, one can analyze a situation and predict the outcome of all the masses and forces, even without ever having experienced a similar situation or outcome.
Thus, at the phenomenal level, Leibniz can distinguish between innate and empirical ideas. An empirical idea is a property of a monad which itself expresses a relation to some other substance or which arises from another internal property that is the expression of an external substance. Although the difference between empirical and innate is in fact an illusion, it does make a difference, for example, to the methodology of the sciences.
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