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There is no question that Leibniz introduced a spirited and powerful position into the age-old philosophical debate concerning free will. Which position is "metaphysically incoherent," however, remains under debate. For more on the philosophical debate of free will, see " Free Will ".

Leibniz's approach to the classic problem of evil is similar. The problem of evil, for Leibniz, can be put in the following way: If God is supremely good, and the creator or author of the best possible universe, then why is there so much pain and sin in the world? Leibniz claims that this apparent paradox is not a real problem.

Leibniz coined the term "theodicy" to refer to an attempt to reconcile God's supremely benevolent and all-good nature with the evil in the world. However, his thoughts on the issue are to be found spread over many texts. To judge it full of misery on this small fraction is presumptuous.

Between and , at the request of Caroline, Princess of Wales, a series of long letters passed between Leibniz and the English physicist, theologian, and friend of Newton, Samuel Clarke. It is generally assumed that Newton had a hand in Clarke's end of the correspondence. They were published in Germany and in England soon after the correspondence ceased and became one of the most widely read philosophical books of the 18th Century.

Leibniz and Clarke had several topics of debate: the nature of God's interaction with the created world, the nature of miracles, vacua, gravity, and the nature of space and time. Although Leibniz had written about space and time previously, this correspondence is unique for its sustained and detailed account of this aspect of his philosophy. It is also worth pointing out that Leibniz and after him Kant continues a long tradition of philosophizing about space and time from the point of view of space, as if the two were always in a strict analogy.

Newton, and after him Clarke, argued that space and time must be absolute that is, fixed background constants and in some sense really existent substances in their own right at least, this was Leibniz's reading of Newton. The key argument is often called the "bucket argument. With linear motion, the frame does not matter as far as the mathematics are concerned, it does not matter if the boat is moving away from the shore, or the shore is moving away from the boat ; even linear acceleration changing velocity but not direction can be accounted for from various frames of reference.

However, acceleration in a curve to take Newton's example, water forced by the sides of a bucket to swirl in a circle, and thus to rise up the sides of the bucket , could only have one frame of reference. For the water rising against the sides of the bucket can be understood if the water is moving within a stationary universe, but makes no sense if the water is stationary and the universe is spinning.

Such curved acceleration requires the postulation of absolute space which makes possible fixed and unique frames of reference. Similar problems made Einstein's General Theory of Relativity so much more mathematically complicated than the Special Theory. 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.

But Leibniz's most famous arguments for his theory of space and time stem from the principle of sufficient reason the principle that everything which happens has, at least in principle, an explanation of why it happened as it did and not otherwise. Leibniz is fond of using leaves as an example. Two leaves often look absolutely identical. Leibniz's support for the principles of the identity of indiscernibles primarily derives from his commitment to the principle of sufficient reason in the following way. 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.

Note that Leibniz's argument relates to a scholastic debate centered on the notion of "Buridan's Ass. 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. Thus, absolute space is absurd, because it violates the principle of sufficient reason see "Correspondence with Clarke," Leibniz's Fourth Paper. Analogous problems are thought to result from a conception of absolute time. That is the negative portion of Leibniz's argument. 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. 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. Leibniz's view has two major implications. 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. It is sometimes convenient to think of space and time as something "out there," over and above the entities and their relations to each other, but this convenience must not be confused with reality. Space is nothing but the order of co-existent objects; time nothing but the order of successive events.

Take the analogy of a virtual reality computer program. Within the computer's memory are just numbers and ultimately mere binary information linked together. These numbers describe in an essentially non-spatial and temporal way a virtual space and time, within which things can "exist," "move" and "do things. This, in turn, is linked to four further numbers representing three dimensions of space and one of time--that is, the bird's position.

Suppose further the computer contains also the number one, corresponding to the viewer and again linked to four further numbers for the viewer's position, plus another three giving the direction in which the viewer's virtual eyes are looking. The bird appears in the viewer's headset, then, when the fourth number associated with the bird is the same as the viewer's fourth number they are together in time , and when the first three numbers of the bird its position in virtual space are in a certain algebraic relation to the number representing the viewer's position and point of view.


Space and time are reduced to non-spatial and non-temporal numbers. This, however, raises a serious logical problem for Leibniz. Recall Leibniz's theory of truth as the containedness of a predicate in a subject. This seemed acceptable, perhaps, for propositions such as "Caesar crossed the Rubicon" or "Peter is ill. This includes time, as well as relations such as "the sister of" or "is angry at. Modern logicians often see this as the major flaw in Leibniz's logic and, by extension, in his metaphysics. 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. Around the end of the Seventeenth Century, Leibniz famously began to use the word "monad" as his name for substance.

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. The easiest to understand is perhaps that while atoms are meant to be the smallest unit of extension out of which all larger extended things are built, monads are non-extended recall that space is an illusion on Leibniz's view.

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.

So, relatedly, the monad must not only exhibit properties, but contain within itself "virtually" or "potentially" all the properties it will exhibit in the future, as well as contain the "trace" of all the properties it did exhibit in the past. 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. Just as in the analysis of space and time Leibniz argues that all relational predicates are actually interior predicates of some complete concept, so the monad's properties include all of its relations to every other monad in the universe.

A monad, then, is self-sufficient. Having all these properties within itself, it doesn't need to be actually related to or influenced by another other monad. 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.

Thus, just like space and time, cause and effect is a "well-founded" illusion. 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.

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But metaphysically, Leibniz argues, it makes no difference which way around the relation is understood, because the relation itself is not real. Thus, in strict metaphysical precision, we have no more reason to say that the ship pushes the water to produce this large number of circles 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. 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.

On Leibniz's view, every monad is like a clock, behaving independently of other monads. 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. It is fair to say that Leibniz's attempt to account for what happens to "souls" before the birth of body, and after its death, lead him to some colorful, but rather strained, speculations. We will examine briefly four important implications of Leibniz's account of substance: first, the distinction between metaphysical truth and phenomenal description; second, the idea of little perceptions; third, the infinitely composite nature of all body; and fourth, innate ideas.

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. Science's object is the latter, which is an illusion, but in which nothing happens that is not based upon what really happens in the metaphysical level that is, the illusion is "well-founded". Berkeley borrows this idea, see especially his "De Motu," and Kant produces a highly original version of it.

Indeed, Leibniz believes, following Descartes and many other materialists, that all such laws are mechanical in nature, exclusively involving the interaction of momenta and masses--hence his accusation that Newton's idea of gravity is merely "occult. Not surprisingly, then, Leibniz's own contributions to physical science were in the fields of the theory of momentum and engineering.

A serious error would arise only if one took the "objects" of science matter, motion, space, time, etc. Consider the following analogy: in monitoring a nation's economy, it is sometimes convenient to speak of a retail price index, which is a way of keeping track of the average change in the prices of millions of items. 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.

Science, in order to be possible for finite minds, involves that kind of simplification or "abbreviation" see, for example, "Letter to Arnauld," 30 April Leibniz is one of the first philosophers to have analyzed the importance of that which is "unconscious" in one's mental life. That a monad is a "mirror" of the whole universe entails that one's soul will actually have an infinite number and complexity of perceptions. Leibniz argues that this is a major error on Descartes' part.

Leibniz's analogy is of the roar of the waves of the beach: the seemingly singular sound of which one is conscious is in fact made up of a vast number of individual sounds of which one is not conscious--droplets of water smacking into one another. 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.

The principle of continuity is very important for Leibniz's physics see "Specimen Dynamicum" and turns up in Leibniz's account of change in the monad see below. Second, little perceptions explain the acquisition of innumerable minor habits and customs, which make up a huge part of one's distinctiveness as an individual personality. Such habits accumulate continuously and gradually, rather than all at once like decisions, and thus completely bypass the conscious will. Further, these little perceptions account for one's pre-conscious connection with the world.

For Leibniz, one's relation with the world is not one just of knowledge, or of apperceived sensation.

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An individual's relation with the world is richer than either of these, a kind of background feeling of being-a-part-of. Thus, a thorough-going skepticism, however plausible at a logical level, is ultimately absurd. Finally, Leibniz's idea of little perceptions gives a phenomenal rather than metaphysical account for the impossibility of real indiscernibles: there will always be differences in the petite perceptions of otherwise very similar monads.

The differences may not be observable at the moment, but will "unfold in the fullness of time" into a discernible difference New Essays on Human Understanding , According to Leibniz, everything one perceives which is a unified being must be a single monad. For example, I take up a marble, and I find it to be a red, round, hard, single body. We call the redness, the roundness, the hardness, and the singleness, [] "qualities" of the marble; and it sounds, at first, the height of absurdity to say that all these qualities are modes of our own consciousness, which cannot even be conceived to exist in the marble.

But consider the redness, to begin with. How does the sensation of redness arise? The waves of a certain very attenuated matter, the particles of which are vibrating with vast rapidity, but with very different velocities, strike upon the marble, and those which vibrate with one particular velocity are thrown off from its surface in all directions. The optical apparatus of the eye gathers some of these together, and gives them such a course that they impinge upon the surface of the retina, which is a singularly delicate apparatus connected with the termination of the fibres of the optic nerve.

The impulses of the attenuated matter, or ether, affect this apparatus and the fibres of the optic nerve in a certain way; and the change in the fibres of the optic nerve produces yet other changes in the brain; and these, in some fashion unknown to us, give rise to the feeling, or consciousness of redness. If the marble could remain unchanged, and either the rate of vibration of the ether, or the nature of the retina, could be altered, the marble would seem not red, but some other colour.

There are many people who are what are called colour-blind, being unable to distinguish one colour from another. Such an one might declare our marble to be [] green; and he would be quite as right in saying that it is green, as we are in declaring it to be red. But then, as the marble cannot, in itself, be both green and red, at the same time, this shows that the quality "redness" must be in our consciousness and not in the marble. In like manner, it is easy to see that the roundness and the hardness are forms of our consciousness, belonging to the groups which we call sensations of sight and touch.

If the surface of the cornea were cylindrical, we should have a very different notion of a round body from that which we possess now; and if the strength of the fabric, and the force of the muscles, of the body were increased a hundredfold, our marble would seem to be as soft as a pellet of bread crumbs. Not only is it obvious that all these qualities are in us, but, if you will make the attempt, you will find it quite impossible to conceive of "blueness," "roundness," and "hardness" as existing without reference to some such consciousness as our own.

It may seem strange to say that even the "singleness" of the marble is relative to us; but extremely simple experiments will show that such is veritably the case, and that our two most trustworthy senses may be made to contradict one another on this very point. Hold the marble between the finger and thumb, and look at it in the ordinary way. Sight and touch agree [] that it is single. Now squint, and sight tells you that there are two marbles, while touch asserts that there is only one. Next, return the eyes to their natural position, and, having crossed the forefinger and the middle finger, put the marble between their tips.

Then touch will declare that there are two marbles, while sight says that there is only one; and touch claims our belief, when we attend to it, just as imperatively as sight does. But it may be said, the marble takes up a certain space which could not be occupied, at the same time, by anything else. In other words, the marble has the primary quality of matter, extension. Surely this quality must be in the thing and not in our minds?

But the reply must still be; whatever may, or may not, exist in the thing, all that we can know of these qualities is a state of consciousness.

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What we call extension is a consciousness of a relation between two, or more, affections of the sense of sight, or of touch. And it is wholly inconceivable that what we call extension should exist independently of such consciousness as our own. Whether, notwithstanding this inconceivability, it does so exist, or not, is a point on which I offer no opinion.

Thus, whatever our marble may be in itself, all that we can know of it is under the shape of a bundle of our own consciousnesses. Nor is our knowledge of anything we know or [] feel more, or less, than a knowledge of states of consciousness. And our whole life is made up of such states. Some of these states we refer to a cause we call "self;" others to a cause or causes which may be comprehended under the title of "not-self.

They are not immediately observed facts, but results of the application of the law of causation to those facts. Strictly speaking, the existence of a "self" and of a "not-self" are hypotheses by which we account for the facts of consciousness. This, in my judgment, is the ultimate issue of Descartes' argument; but it is proper for me to point out that we have left Descartes himself some way behind us.

He stopped at the famous formula, "I think, therefore I am. In the first place, the "therefore" has no business there. The "I am" is assumed in the "I think," which is simply another way of saying "I am thinking. The first of these is, "something called I exists;" the second is, "something called thought exists;" and the third is, "the thought is the result of the action of the I.

Now, it will be obvious to you, that the only one of these three propositions which can stand the Cartesian test of certainty is the second. It cannot be doubted, for the very doubt is an existent thought. But the first and third, whether true or not, may be doubted, and have been doubted.

For the assertor may be asked, How do you know that thought is not self-existent; or that a given thought is not the effect of its antecedent thought, or of some external power? And a diversity of other questions, much more easily put than answered. Descartes, determined as he was to strip off all the garments which the intellect weaves for itself, forgot this gossamer shirt of the "self"; to the great detriment, and indeed ruin of his toilet when he began to clothe himself again.

But it is beside my purpose to dwell upon the minor peculiarities of the Cartesian philosophy. It is enough for all the practical purposes of human existence if we find that our trust in the representations of consciousness is verified by results; and that, by their help, we are enabled "to walk surefootedly in this life. Thus the method, or path which leads to truth, indicated by Descartes, takes us straight to the Critical Idealism of his great successor Kant. But it is also that Idealism which refuses to make any assertions, either positive or negative, as to what lies beyond consciousness.

It accuses the subtle Berkeley of stepping beyond [] the limits of knowledge when he declared that a substance of matter does not exist; and of illogicality, for not seeing that the arguments which he supposed demolished the existence of matter were equally destructive to the existence of soul. And it refuses to listen to the jargon of more recent days about the "Absolute" and all the other hypostatised adjectives, the initial letters of the names of which are generally printed in capital letters; just as you give a Grenadier a bearskin cap, to make him look more formidable than he is by nature.

I repeat, the path indicated and followed by Descartes, which we have hitherto been treading, leads through doubt to that critical Idealism which lies at the heart of modern metaphysical thought. The early part of the seventeenth century, when Descartes reached manhood, is one of the great epochs of the intellectual life of mankind. At that time, physical science suddenly strode into the arena of public and familiar thought, and openly challenged not only Philosophy and the Church, but that common ignorance which often passes by the name of Common Sense.

The assertion of the [] motion of the earth was a defiance to all three, and Physical Science threw down her glove by the hand of Galileo. It is not pleasant to think of the immediate result of the combat; to see the champion of science, old, worn, and on his knees before the Cardinal Inquisitor, signing his name to what he knew to be a lie.

And, no doubt, the Cardinals rubbed their hands as they thought how well they had silenced and discredited their adversary.

But two hundred years have passed, and however feeble or faulty her soldiers, Physical Science sits crowned and enthroned as one of the legitimate rulers of the world of thought. As a ship, which having lain becalmed with every stitch of canvas set, bounds away before the breeze which springs up astern, so the mind of Descartes, poised in equilibrium of doubt, not only yielded to the full force of the impulse towards physical science and physical ways of thought, given by his great contemporaries, Galileo and Harvey, but shot beyond them; and anticipated, by bold speculation, the conclusions, which could only be placed upon a secure foundation by the labours of generations of workers.

Let us try to understand how Descartes got into this path, and why it led him where it did. The mechanism of the circulation of the blood had evidently taken a great hold of his mind, as he describes it several times, at much length.

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But if this apparently vital operation were explicable as a simple mechanism, might not other vital operations be reducible to the same category? Descartes replies without hesitation in the affirmative. Hence they pass into the nerves and are distributed to the muscles, causing contraction, or relaxation, according to their quantity. Cherie rated it liked it Mar 15, Ron Potter rated it it was amazing Jun 05, Talia rated it it was amazing Dec 30, Lee Adams rated it liked it Feb 09, Ms rated it it was amazing Nov 22, Shane Lynch rated it liked it May 24, Matthew Tuxford rated it liked it Oct 17, Emma marked it as to-read Mar 13, Amanda marked it as to-read Mar 20, Mark marked it as to-read May 15, Neil marked it as to-read Jun 29, Khadija marked it as to-read Jul 07, Robyn marked it as to-read Oct 04, Alma marked it as to-read Nov 15, Randall marked it as to-read Dec 15, Manish Singh marked it as to-read Feb 08, Soham added it Mar 04, Freexii added it Mar 09, Spencer Marlen-starr added it Jul 23, Hyle Daley added it Nov 11, Richard Heggie marked it as to-read Nov 30, Rebecca Kon is currently reading it Feb 21, Kara Van is currently reading it Apr 16, Jay Kim is currently reading it Jun 29, Mark Flory added it Oct 12, Richard Ohlrogge added it Oct 28, Becky added it Nov 06,

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