1. Section 7. We are further told that the monads lack windows.

L thinks that there is only one thing other than a substance, and this is an accident.  Accidents are modifications of substances: they are ways that that substance is.  If I am a substance, then my blueeyedness is an accident, as is my being a philosopher and so on.  Considered in this way, an accident is tightly bound to its substance.  One cannot take my blueeyedness and give it to someone else.  Even if my eyes were stolen and implanted somewhere else, then it would be that person who is blue-eyed, not I, and so it would become his blueeyedness, not mine.   It wouldn’t be my blueeyedness--the accident--that would be doing the traveling, but the eyes--the part.  Thus, Leibniz says picturesquely, an accident of mine cannot somehow leave me and go into you in such a way that by means of this accident something happens in you.  So, I can only cause effects in myself and you can only cause effects in yourself.

•   Presumably the person who claims we just directly act on someone else will think this to be question-begging.  Perhaps the argument is to be understood along the lines of the intuitions grounding a contact physics, supplemented with the idea that there can’t really be contact between monads.  First of all, the monads don’t have parts, and so they can’t touch.  Could we maybe have two monads at the same place at the same time?  But I think L doesn’t want to say that monads are literally spatial beings.  Or maybe we should think of the mutual independence of the monads.

•   There is an exception here: God.  If one exception, why not more?  But God’s causality is different.  It’s not that God affects monads once they’re created.  Rather, he just creates them at the start to act like He wants them to.

2. We get some arguments for the immateriality of the soul.  The first argument invokes the image of a mill.  Suppose that we could think without souls.  Well, we’d be thinking machines.  Imagine blowing us up so that our parts would be as big as the parts of a mill.  Where would perception be?

• A more powerful argument is the mechanism argument: “If in that which is organic there is nothing but mechanism, that is, bare matter, having differences of place, magnitude and figure, nothing can be deduced and explained from it, except mechanism, that is except such differences as I have just mentioned.” (p. 86)

• Can’t get something for nothing.  From a proposition of the form “There is a machine in which x pushes against y, y pushes against z, x has such-and-such shape…” one cannot derive a proposition of the form “The machine is conscious.”
• Is this a good argument?  Couldn’t someone say: “But can’t you say likewise that from the fact that molecules are doing such-and-such you can’t derive the fact that the material is hot?”
• But there is a disanalogy there.  Consciousness seems to be a radically different kind of property from mechanical properties, while heat does not.  Consciousness is, after all, a property that can only be perceived by the one who has it, unlike mechanical properties which can be perceived by all human beings.  If it is such a radically different kind of property then it is plausible that it is not derivable from the properties of matter in the way that heat is derivable.

3. What makes something one thing is the interrelation of monads, and their hierarchical relation to the central monad.

• The interrelation consists in nothing other than mutual representation.
• One can scientifically study the body while ignoring the soul and vice versa.

4. The Pre-Established Harmony ensures that all the perceptions of the different monads are coordinated.  The perceptions present phenomena or appearances to the monads.  The interrelation of these phenomena will be interrelated in such a way as to satisfy the criteria set forth in “On the method of distinguishing…”, an early essay of L’s.  These criteria are vividness, complexity and internal coherence.

• Vividness.
• Complexity: Reality is inexhaustible for Leibniz.  Indeed, one might say that this is one of the major differences between reality and irreality.  Consider Winston Churchill.  There is an infinitude of facts about Churchill.  How many hairs did he have at a given time and date?  What was his weight to the microgram?  What did he have for breakfast on September 17, 1932?  Exactly how many molecules of water did he consume on January 15, 1911?  What did he dream the night before?  There are well-defined answers to all of these questions, though some of the answers are no longer available to us.  On the other hand, consider Sherlock Holmes.  How many hairs did he have on a given date?  What was his weight to the microgram?  What did he have for breakfast on some date that Arthur Conan Doyle did not see fit to describe?  We not only do not have answers to these questions, but there are no answers to them.  It’s not merely due to the limitations in our knowledge that there are no answers.  The reality of Churchill is inexhaustible.  But basically there is nothing more to Sherlock Holmes than what is found in the writings of Arthur Conan Doyle.  Reality thus exhibits a depth of complexity that fiction lacks. 
• Admittedly, this depth of complexity we may not always perceive.  However, with the little perceptions of Leibniz, we do perceive them.  It is Leibniz’s contention that we have perceptions of all of reality, though in confused form.  Compare the fact that this piece of chalk is gravitationally affected by everything in the universe.  Maybe if we figured out exactly the various physical forces affecting the piece of chalk, we could know a lot about the universe.
• Internal coherence: Basically, this means that reality is amenable to scientific investigation.  Behind various complex phenomena there are relatively simple laws of nature.  Planets, moons, galaxies—they all move in their different ways, but they do so under the influence of a simple force of gravitation.  (Relativity theory complicates only to simplify: It treats gravity and electromagnetism in a unified way.)  According to L., the most evident way that this criterion is to be applied is in prediction.  If we can predict future states from past ones—presumably by using simple laws of nature—then this gives one very good reason to think we are talking of reality.  Note that the coherence criterion will include the concurrence of other people.
• These are epistemic criteria as given in the essay, and as L. notes they do not prove that something is real, but they do make it very likely.  If all of the conditions are met, then very likely the phenomenon in question reflects reality.
• However, at the end of the essay, L. considers the possibility that God has put us in a life-long dream where we perceive things according to these conditions—think of the Matrix.  He doesn’t say—as Kant would—that under that supposition these phenomena are in fact real: that a dream having vividness, complexity and coherence would be real.  But he does say that God wouldn’t count as a deceiver if God put us in such a dream—for we can only conclude that it is probable that what we se is there, and we cannot go from probability to certainty (if I buy a lottery ticket and win, I was not deceived when I earlier thought I would lose)—and in saying this he makes one less sure whether in fact we are in such a dream or not.  (Descartes’ argument for the reality of our perceptions was based on the idea that God wouldn’t deceive us.)  He also says that in a dream the phenomena proceed from an inner source—from ourselves—but that the same is true in reality.  Indeed, in L.’s system it is so in reality: the pre-established harmony is such that we produce phenomena on appropriate occasions.
• So what more do we have in reality than in the dream?  Well, first of all, there is correlation between the phenomena that all the monads have.  When I see a horse and you are looking in the same direction, you too see a horse.  Moreover, our perceptions are coordinated in such a way that there is a precise relation between the angle at which the horse you see appears and the angle at which the horse I see appears.  This is also coordinated with the unconscious perceptions that the monads in the horse’s hoof and in the Andromeda Galaxy have.  In a vivid and coherent dream there is no coordination between my phenomena and yours—if there is, we think a miracle or a great coincidence has occurred—although obviously when I dream I think there is such a coordination.
• Is this all there is to it?  Are we all simply dreaming well-coordinated dreams?  Is this all reality is?  Sort of.  There is a little more here.  The phenomena I have do represent how things are outside me.  For instance, when I see you with eyes turned towards a horse, I do in fact learn real things about you from what I see.  I learn, for instance that you are having a conscious perception of a horse (assuming I know you’re not blind or distracted).  I also know something about the monads making up the horse: they are having perceptions—perhaps unconscious—of you.  So in fact the phenomena do give me a true knowledge of external reality.  The phenomena do present other monads to me, albeit in an indistinct way.
• Bodies are purely phenomenal: all there really are are the monads and their internal states.  However, we have phenomena of bodies.  I perceive your body, and your body is unified in my perception.  It is also unified in your perception, and in various ways in the perceptions of the monads making it up.  So, what we have are not mere phenomena but what we can call well-grounded phenomena.

5. A different story is given in the letter to Des Bosses.  Leibniz’s ecumenical scheme was that Catholics and Protestants would see that they could both accept Leibniz’s system, and hence would see that their disagreements aren’t so great.

• Transubstantiation: Bread and wine change into the body of Jesus at Mass.  Leibniz did not believe in transubstantiation, but he wants to show how he could accommodate it in his system if he had to.
• He gives more than one account.  The first is the troublesome one.  He says that in addition to the interrelations of monads there is a substantial bond or chain.  This is what makes an aggregate be a genuine unified substance.  Here, L abandons the idea that the central monad is what unifies an organism, and supposes there is a substantial bond that does this.  This lets one say that the body is a genuine unity, over and beyond just a bunch of interrelated monads, but at the cost of introducing a new item into his system.
• Once one has the item, the transubstantiation is accounted for as follows.  The bread, if it has a substantial bond of its own, loses its substantial bond, though its monads remain.  The monads then become united to the substantial bond that constitutes the body of Jesus.
• Theologically unacceptable to Catholics because it means that the bread and wine become a part of the body of Christ rather than that the whole body of Christ becomes present instead of bread and wine.
• Although L. argues to the contrary, it seems that idea of the monads of bread and wine remaining is a theologically dubious one that pushes one in the direction of Luther’s doctrine of consubstantiation rather than the Catholic doctrine of transubstantiation.
• Possible that L. is simply being diplomatic.  Or he may be thinking: Philosophy can’t tell us if there is a substantial bond or not.  If faith requires us to accept one, then this is not contrary to reason but merely above reason—an important distinction for Leibniz.  It’s possible he might need a substantial bond or something like it to explain the Incarnation.
• Leibniz’s official philosophical story doesn’t include substantial bonds.  In fact, the official story claims that substances other than monads are nothing but well-founded phenomena, i.e., appearances.  Since it is a part of the doctrine of the transubstantiation that the appearances remain the same, it at first seems like he can’t have any story to tell.  If the appearances don’t change and appearances constitute bodies, then nothing has changed.  But actually the imperceptible appearance has changed.  The microscopic constitution has changed to be that of Jesus’s body and blood, and we perceive this, but only by means of the little perceptions.  The gross perceptions are not like this. 
• This wouldn’t really satisfy a Catholic theologian because it makes the presence of Jesus be primarily a matter of appearance.
• Why doesn’t L. just say that the monads of bread and wine cease to exist and the monads of Christ’s body and blood come to exist in their place, existing in two places at once?  He doesn’t say this because what makes them be the monads of Jesus’s body is that they appear interconnected, and they wouldn’t thus appear interconnected if they were not seen as such.  But he could insist that what makes them be the monads of Jesus’s body is not that they appear interconnected to us, but that they do so to Jesus’s central monad.

6. The identity of indiscernibles says that we cannot have two different objects that have the same CIC.

• L. argues for the principle of identity of indiscernibles on the basis of the Principle of Sufficient Reason.  Samuel Clarke was a disciple of Newton, and Newton believed in an absolute space-time.  L. argues that then there is no reason why the universe isn’t moved over in time or space.  L.’s own view of space-time is that it is relational and phenomenal: it consists of nothing but the perceived relations between things.  When the universe is “moved over” these relations do not change and hence in reality there is no change.  This is an argument for the identity of indiscernibles in a special case: Newton believed in indiscernible places, whereas there aren’t any by this argument.
• What of other things?  Well, suppose A and B are indiscernible.  Then, there can’t be a reason as to why A is playing the role it is whereas B is playing the role it is. 
• This seems to be actually a shaky argument.  After all, if they are indiscernible, if they have the same CIC, they are playing the very same role!  And so the supposition that they might switch is a null-hypothesis. 
• But perhaps we can see L. as arguing against a position that holds that two things that are indiscernible internally could play different external roles, and could in fact swap their external roles.  Imagine the two iron spheres in an asymmetric universe.  People who don’t believe in indiscernibles tend to think this is a meaningful assumption, and they tend to think that things would be different if one swapped the two spheres.  But if they would be different, then PSR would be violated.
• Clarke says: But maybe the reason for things being as they are—the universe being created when it is, say—is to be found in God’s free will.
• L. answers: Yes, but God must have a reason for his choice, and no reason can be given here.
• This shows L.’s basic commitment to a controversial notion of free will that involves always having a reason for choosing as one does.  We will examine this more closely later.

7. The identity of indiscernibles says that we cannot have two different objects that have the same CIC.

• L. argues for the principle of identity of indiscernibles on the basis of the Principle of Sufficient Reason.  Samuel Clarke was a disciple of Newton, and Newton believed in an absolute space-time.  L. argues that then there is no reason why the universe isn’t moved over in time or space.  L.’s own view of space-time is that it is relational and phenomenal: it consists of nothing but the perceived relations between things.  When the universe is “moved over” these relations do not change and hence in reality there is no change.  This is an argument for the identity of indiscernibles in a special case: Newton believed in indiscernible places, whereas there aren’t any by this argument.
• What of other things?  Well, suppose A and B are indiscernible.  Then, there can’t be a reason as to why A is playing the role it is whereas B is playing the role it is.  Letters to Clarke, IV.3, p. 327.
• This seems to be actually a shaky argument.  After all, if they are indiscernible, if they have the same CIC, they are playing the very same role!  And so the supposition that they might switch is a null-hypothesis. 
• But perhaps we can see L. as arguing against a position that holds that two things that are indiscernible internally could play different external roles, and could in fact swap their external roles.  Imagine the two iron spheres in an asymmetric universe.  People who don’t believe in indiscernibles tend to think this is a meaningful assumption, and they tend to think that things would be different if one swapped the two spheres.  But if they would be different, then PSR would be violated.
• Clarke says: But maybe the reason for things being as they are—the universe being created when it is, say—is to be found in God’s free will.
• L. answers: Yes, but God must have a reason for his choice, and no reason can be given here.
• This shows L.’s basic commitment to a controversial notion of free will that involves always having a reason for choosing as one does.  We will examine this more closely later.

• What about Black’s intuitions? The world consisting of only two items or a symmetric world? Well, Leibniz says that two indiscernibles are one thing counted twice. Maybe these worlds need to be thought of as worlds with space looped over.