Sorglose Nacht

Overview

Primary Truths was written shortly after Leibniz’s famous Discourse on Metaphysics, which places it about ten years after Freedom and Possibility, five before A New System, and almost twenty five before the mature position in the Monadology and the Principles of Nature and Grace.

This essay importantly develops at least two of Leibniz’s fundamental principles, the so-called “Predicate-in-Notion Principle” (PIN: that the notion of the predicate is in some way included in that of the subject - cf. §2.a below) and the Principle of the Identity of Indiscernables (PII), which he indicates here is derivable from combination of the Principles of Sufficient Reason (PSR) and Contradiction (PC) (cf. §4 below).

Brandon Look explains the implicit argument nicely:

1. Suppose there were two indiscernible individuals, a and b, in our world, W.
2. If this were the case, then there must also be a possible world, W^*, in which a and b are "switched".
3. But if this were the case, then God could have had no reason for choosing W over W^*.
4. But God must have a reason for acting as he does. (PSR)
5. Therefore, our original supposition must be false. There are not two indiscernible individuals in our world. (PII)

Outline

1. The primary truths are identities (A is A, everything is similar or equal to itself).
2. All other truths are reducible to these identities by resolving their definitions into their (progressively simpler) component propositions. This is called an a priori proof.
   1. Predicate in Notion Principle (PIN): Since all truths follow from primary truths, it follows that in any true proposition the predicate is always in the subject.
   2. This is the case for every (necessary or contingent) affirmative truth, and this tells us something about the nature of contingency and the challenges in thinking necessity (the fate of the free, e.g.).
3. The principle of sufficient reason
   1. Take this axiom: “There is no effect without a cause/Nothing is without reason.” (PSR, see Overview) If this were false, then there would be a truth that couldn’t be proved a priori (couldn’t resolve into identities). So, if this is false, Leibniz’s theory of truth is false. So, this follows from Leibniz’s theory of truth.
   2. This also applies to symmetries: Symmetry will follow from symmetry.
   3. Finally, there is even a reason about eternal truths. Imagine that we live in a world constituted by tiny spheres. There still needs to be a reason why they aren’t cubes.
4. The principle of the identity of indiscernibles
   1. From these considerations, it follows that in nature there can’t be two things that differ in number alone. (PII, see Overview)
   2. The basic idea in this argument seems to be that if x is identical to y in every way but in the fact that it one a second instance of the other, then there is no reason for them both to exist.
5. It also follows that there are no purely relational properties - that is, all properties are properties of things, and relational properties are grounded in non-relational ones. This, I think, is meant to follow from (2.a): Since all P’s of a given S are contained within S, it would seem to follow that if relational predicate R is attributable to S, then it would have to be contained in S, or at least in some P of S.
6. Any complete notion of a substance contains all its predicates: past, present and future. (If an S will have P, then it is now has T where T = “it is true now that it will have P”).
   1. This is a complete (perfect) notion of a substance, and from this we are meant to understand that God, who has knowledge of the possibilities for each of infinitely many potentially actual complete notions, would choose the ones that it, in its supreme wisdom, thought best.
7. Every individual substance contains in its complete notion the entire universe.
   1. For any given things x and y, there is a true proposition about how x relates to y only if they are related to each other.
   2. Since there are no purely relational predicates, both x and y must contain a predicate that explains their relationship.
   3. This must be the case for x viz. every other thing in the universe.
8. This means that all created substances are mirrors of the entire universe, which is to say, God, the universal cause. These expressions vary in perfection.
   1. This implies that every time any created substance changes, it changes all the others.
   2. However, strictly speaking, this does not mean that any created substances exercises metaphysical action or influence on anything else. This is to say that there is no inter-substance causal relationship, because each substance already contains within itself the entire universe, past, present, and future, which means that substances just harmoniously change without any sort of meaningful interaction.
   3. This theory also cleanly accounts for the correspondence of soul and body, without having to provide a medium of transport. By the nature of their complete concepts, they are simply in harmony already.
   4. Further, this implies that there is no atom (no body that could not be split). If there were atoms, there would be no cause to explain the effects of (e.g.) their size and shape. Every material thing requires smaller material things to explain its various properties.
   5. This means that every particle in the universe contains a world of infinitely many creatures.
   6. It also means that there is no determinate shape in actual things, because there is infinite complexity in any materially instantiated thing. Therefore, perfect circles, etc. exist only in our thoughts.
9. Bodies, Monads
   1. Since things have no determinate shape, this means that bodies are just extension and motion (which are “not substances, but true phenomena”)
   2. That means that something unextended is required for bodies, because material, extended stuff (as infinitely complex) can’t deliver unity. Since this can’t be atoms, all that remains is something analagous to souls.
   3. Corporeal substance comes into existence through creation (as opposed to construction) and leaves through annihilation (as opposed to dispersal), because there is no reason for them not to last forever. (Luckily, we know this argument gets better.)
   4. Therefore, animate things don’t come into or go out of existence entirely, but are merely transformed.

Bureaucratic Note

Finally, I should note that this ends my dalliance with pre-Kantian rationalism. Although I plan to come back to Spinoza at some point, for now, in order to push through to modernity, I’m going to take a step back to the roots of Kant’s other wellspring, British empiricism, and take a look at some bits of at least Locke and Hume, before finally arriving at Kant himself, who will represent the start of the period of philosophy in which I am most interested, German idealism. So, up next: John Locke.

Overview

Leibniz’s famous 1695 essay (in long form: A new system of the nature and communication of substances, and also of the union that exists between the soul and the body) was the introduction to a broad European readership of his original metaphysical ideas (many of which he had come to a decade earlier).

Outline

1. This paper is published in a scholarly journal - it is not written in the popular style.
2. Physics needs more than the concept of matter (”extended mass”), it also needs an operative concept of force.
3. At first, Leibniz favored an idea of matter and empty space (because it gives us a physics we can always “picture”).
   1. The matter itself, he realized, doesn’t yield any real unities. Because matter, by its nature is always divisible into smaller matter, and thus never a unity per se.
   2. Likewise, he thinks, geometrical points can’t yield existential unities, because points aren’t real extant stuff.
   3. In order to get a unity (a thing that’s deep down really just one thing), he needed a “real and living” point.
      1. These points, he realized, must be something like our idea of a soul - must be a force - that is, like appetition (desire and its low-grade analogs) and sentiment (belief, feeling).
      2. We can use these substantial forms to solve general (not particular) problems in natural science. Indeed, they are what Aristotle calls ‘first entelechies’.
      3. Leibniz calls them ‘basic forces’ for intelligibility, and because they involve actuality and activeness.
4. These forms and souls had to be indivisible.
   1. However, since this is the case, it also had to be the case that they were created and annihillated (rather than assembled/dismantled).
   2. This means that all substances were created with the universe, survive its duration, and will die with it.
5. There are at least two types of simple substances, though: rational souls (minds) and other souls. Compared with the latter, our minds are “like little Gods.”
   1. So, where God has imposed an order on matter, minds have special laws that raise them above that, or that matter works for minds (the punishment of the wicked, and the happiness of the good).
6. Since we are saying that souls (rather than atoms) last forever, one might be disposed to imagine that they pass from body to body. Because of microscopic observation, Leibniz is rather inclined to conclude that the animal simply begins and then just adds on other bits to itself in growth and development.
7. But what about the end of the animal, then? Since it is unreasonable to assume that souls just occupy a chaotic material station after death, the only tenable position is that not merely the soul but the animal is conserved (albeit in much smaller form) after death.
   1. This entails that rather than a transporting of souls, there is merely a continuous transforming, and that there is no death in a metaphysical sense.
8. God, however, has provided for rational souls so well that nothing can ever make them lose the “moral qualities of their personhood”.
   1. Thus it can be said that everything tends to not merely the perfection of the universe in general, but of these creatures in particular (who are destined to reach such a high degree of happiness that it affects the universe as a whole!)
9. Leibniz now attributes something like this view (that things don’t die, just appear and disappear) to Hippocrates, Parmenides, and Melissus.
10. The moderns take there to only be a quantitative difference - i.e. large and small - between the machines of nature and of humans, rather than a qualitative one. This is too far.
    1. For Leibniz the machines of nature and of humans differ not only by degree, but in kind. He isolates three differences:
       1. Nature’s machines are so well equipped as to never succumb to accidental destruction.
       2. Nature’s machines have a truly infinite number of parts.
       3. Nature’s machines remain the same, although they are (beautiful here:) “folded together differently.”
11. Furthermore, the soul is a true unity (which is what we call the ‘I’). Where human machines are more like armies of parts, and thus require unified parts somewhere.
    1. Since these unified parts clearly can’t be material (which for Leibniz is infinite in its compositional complexity). Rather we need something like “atoms of substance” (contra atoms of matter).
    2. These atoms of substance are:
       1. the sources of activity
       2. the basic reason for the composition of things (the explanation for material unities)
       3. the ultimate elements in the analysis of substantial things
    3. They might be called metaphysical points. They are not merely mathematical points because they have something alive in them (a kind of perception).
    4. So where material points seem indivisible but are not, and mathematical points are indivisible but are not things, only forms or souls/metaphysical points are both exact and real.
12. This generates a problem viz the soul’s communion with the body. The Cartesian/Malebranchean position is that senses and the motor behind actions is that God manually coordinates our activity/sensation with our volition, as well as causality in general.
13. Leibniz thinks that this is motivated right (its negative argument is good), but that its positive argument is wrong.
    1. In other words, it’s right that one created thing has no real influence on another and that all things are continually produced by the power of God, but relying on a deus ex machina is ostensibly the same as relying on miracles.
    2. Leibniz wants to explain how God coordinates causality.
14. Leibniz thinks that this happens because God initially created each soul to be spontaneous (aka. not causally affected by other monads), but meanwhile to just be in perfect conformity to things outside it.
    1. This entails that the internal perceptions of our souls are purely mental phenomena. The constitution of the soul “gives the substance a representative nature”: or, each substance reflects the entire universe in itself according to its particular point of view.
    2. Thus, the interaction of the body and the soul works by means of a universal spontaneous coordination that is the property of every substance.
    3. This theory has the charm of explaining how the soul resides in the body: e.g. in the same way that a unity is in a multitude.
15. Why couldn’t souls be like formal, free automatons? (This question will turn out not to answer itself.)
    1. Since the soul represents the entire universe (although with differing degrees of clarity), conversely, the body is adpated to the soul, and this gives us the sense of causal mind-body interaction.
16. It also has the advantage of showing that we are not susceptible to any kind of material causal determinism.
    1. Every mind is like a world apart: self-sufficient, independent of every other created thing, involving the infinite, and expressing the universe.
    2. It is also meant to be another proof of God that so many interacting substances do so harmoniously, a fact which implies that they share a common cause.
17. This system finally also allows us to understand “x acted on y and z” as “A change occurred in x which intelligibly explains changes in y and z, in such a way that we can conclude that when God was decreeing what substances were to exist he chose y and z so as to fit with the already chosen x.”
    1. That is, if matter is not substance, then something like this story is the only coherent way to explain the appearance of material causality.
18. This will prove useful in physics, despite its metaphysical character.

Overview

The Principles is among the last philosophical texts of Leibniz. It provides a short summary written in lay style of his philosophy. Taken together with the Monadology, Theodicy and the New System, Leibniz found it to be a coherent and comprehensive statement of his philosophy. (cf. Pauline Phemister, Leibniz and the Natural World pp. 7-8)

Outline

1. Substances
   1. A substance is a being that is capable of action.
   2. Substances can be simple (having no parts) or composite (collection of simple substances, monads).
   3. Simple substances = unities; Composite substances = multiplicities
   4. Lives, souls, and minds are simple substances, and therefore where there is simple substance there is life.
   5. Since the whole world is built out of simple substances, life is everywhere in nature.
2. Monads
   1. Because monads have no parts, they can’t be made/unmade.
   2. They also cannot come into or go out of existence. They last as long as the universe does.
   3. They can’t have shapes or sizes (since for this they would need parts).
   4. Therefore, they must be distinguished by their qualities (perceptions) or actions (appetitions).
   5. A simple substance can be in many states at once since these states match up with its various relations to things outside it. (E.g. a geometrical point is simple, but is at the center of infinitely many angles.
3. Causes
   1. Nature is totally full of simple substances, which are separated by their actions, and in a constant state of change relative to one another.
   2. A body is an infinite number of monads clustered around a central monad.
      1. If we can think this, then we can think that the central monad corresponds with the states of the body.
      2. This means that a body is a collection of progressively complex machines, a natural automaton.
      3. In turn, this means that every monad is a living mirror which represents the universe in accordance with its own point of view.
      4. “Living” refers to a monad’s being its own source of activity.
      5. Deleuze loves this bit.
   3. A monad’s perceptions arise out of its other perceptions by the laws of appetites (the final causes) just as changes in bodies arise from the laws of movement (the laws of efficient causes). [Note: formal and efficient causes in the Aristotelian sense.]
4. Animals, Subconscious Perceptions
   1. Since every organism is made up of smaller forms of life (less complex monads, say, organs), and so are these, and so on, then not only is life everywhere, but there are “infinite levels of life.”
   2. A sufficiently complex (?) lifeform is called an animal, and its (central?) monad is called its soul.
   3. Non-reasonable animals (”bare life”) have unelevated monads for souls. They don’t have distinct enough perceptions to be remembered.
      1. Here’s a distinction between perception (say, mere perception or sentience) and awareness (say, reflective knowledge or sapience).
      2. Awareness is not given to all souls and no soul has it all the time.
      3. Here’s where Cartesians went wrong - they didn’t grok le petit perceptions (we now say: subconscious perception).
5. Minds
   1. Animals have interconnected perceptions in a way that is not quite by reason. (A dog remembers a stick with which it has been beaten.)
      1. This is to say that it is grounded only in the memory of effects, without knowledge of causes.
   2. The kinds of animals that can understand causes (and therefore other analytic principles) are rational animals. Their soul-monads are called minds. Minds are capable of reflective acts (self-knowledge, science).
6. Death
   1. The ancients believed that life emerged from chaos, but we now know that it comes from organized systems (seeds), and therefore from other forms of life.
   2. Since this is the case, since animals do not emerge out of nowhere when they are born, it is unlikely that they disappear completely when they die. There is no metempsychosis, rather merely metamorphosis.
7. Since nothing comes about without sufficient reason, and since things do exist, we should be able to give a reason why there being something is preferable to there being nothing.
8. God
   1. The sufficient reason for the existence of the universe can’t be found in the order of contingent things (bodies and their representations in souls).
      1. It can’t be in bodies because there’s never a reason in matter for its own motion. The material reasons for the motion of matter are causal, and as we know, if we follow this chain, we regress infinitely.
   2. Therefore the sufficient reason for the universe must lie outside of the causal chain. It must be something that exists necessarily and without cause.
   3. This is called God.
9. God’s Perfection
   1. This simple, primal substance must have in a higher form the perfections of those things derivative from it.
   2. Directly this means that God has perfect power (omnipotence), knowledge (omniscience), and will (is supremely good). From this follows perfect justice (goodness + omniscience).
   3. Whatever imperfections earthly stuff has, they don’t derive from God, but rather from their own limits as created things.
10. The Most Perfect Universe
    1. Since God is perfect, it follows that he chose the best design for the universe. One with:
       1. The greatest variety and orderliness.
       2. The best arranged time and place (and terrain).
       3. The maximum effect produced by the simplest means.
       4. The highest levels of power, knowledge, happiness and goodness in created things that the universe allowed.
    2. This all follows since things must lay claim to existence where their claim is in direct proportion to their perfections.
11. The Most Perfect Physics
    1. God’s perfection is also exemplified in the laws of motion, which hang together the best and are the most comprehensible to metaphysical reasoning.
    2. Leibniz, who himself discovered some laws of nature, notes that these cannot be justified merely by means of (efficient) causality, and rather require appeal to final causes, a fact which provides yet another evident proof of God.
12. The Harmony of the Monads
    1. From the perfection of the universe (by way of the perfection of its author) it follows that every living mirror (monad/substantial center) must have its perceptions and appetitions ordered in the most perfect way qua compatibility with the rest of the monads.
13. The Fold
    1. So monads are ordered in perfect harmony with one another. This implies a serious kind of determinism (Leibniz nicely says “The present is big with the future, the future could have been read in the past, and distant things are expressed in what is nearby.”)
    2. If we could unfold any individual soul, we could see the beauty of the entire universe.
    3. But, since most of a soul’s perceptions are confused, and since the soul can only know its clear and distinct perceptions, which are /much/ fewer, individual souls know very little of the universe at a given time. Only God can have distinct perceptions of everything.
    4. Leibniz is obviously getting romantic here. He waxes poetical that in the roar of the ocean, he has many confused perceptions of distinct waves.
14. Imperfect Works and the Mirror of the Creator
    1. A rational soul is not merely a mirror of the universe, but also a likeness of its creator.
    2. It not only perceives God’s works, it can reproduce something like them on a smaller scale.
15. The City of God
    1. This means that all minds, entering into a kind of harmony with God, are members of the City of God - the most perfect and judicious state, with many fine characteristics:
       1. no crime without punishment
       2. no good deed goes unrewarded
       3. “as much virtue and goodness as possible”
    2. God achieves this City by means of a pre-established harmony between the kingdoms of nature and of grace, between God as the architect and God as the monarch.
    3. Nature leads on to grace, while grace perfects nature while at the same time making use of it.
16. Love of God
    1. Reason can’t tell us about the next life, but it can assure us that things have been done in a perfect way.
    2. In loving God, we can take pleasure in his perfections, which are … perfect … and so love for God must give us the most pleasure of which we are capable.
17. Pleasure without Sensory Input
    1. It is easy to love this God. There is nothing mysterious about taking pleasure from something imperceivable. Supporting arguments:
       1. People get pleasure from honors.
       2. Martyrs show the power of the pleasures of the mind in going happily to their deaths.
       3. The pleasures of the senses, in the end, are intellectual pleasures. Their sensory character is just our confusion (the real pleasure of music is in the numbers, e.g.).
       4. Again, very poetic Leibniz: “We are not aware of the numbers of these beats, but our soul counts them all the same!”)
18. The Pursuit of Happiness
    1. Loving God is its own reward, and gives us a foretaste of our future happiness.
    2. Finally, since God is infinite, and thus never knowable in its entirety, our happiness in loving it won’t ever consist in a mind-numbing complete enjoyment with nothing left to desire, but rather in “a perpetual progression towards new pleasures and new perfections.”

Overview

This early (1680) paper by Leibniz details a two-pronged theory of truth. Certain truths are necessary because their contraries are self-contradictory, and certain (existential) truths are necessary because of a free choice of God for the more perfect existence.

This theory seems to be meant to address a problem of freedom and determinism (or, as Leibniz calls it “future contingents”) - namely, because of the latter kind of truth, God can have future directed omniscience without future events being analytically necessary.

Outline

1. Premises
   1. In God everything is spontaneous.
   2. It can “hardly be doubted” that people have free will.
   3. A volition is a conscious attempt to act, and an act necessarily follows from the will and ability to do it.
   4. If the conditions pro and con for an action exist, a volitional equilibrium is reached, and thus, a person won’t act.
2. Analytic Propositions
   1. In every true proposition there is a connection between the subject and the predicate (”S is P”) and so every true proposition can be proved a priori.
   2. There are two primary propositions/truths:
      1. Necessary ones: whatever implies a contradiction is false. All truths of metaphysics (and logic, geometry, etc.) are necessary.
      2. Contingent ones: Whatever is more perfect or has more reason to be true.
   3. This cashes out to the idea that the principle of necessary truths is the principle that applies to essences, and the principle of contingent truths applies to existences.
3. Modality into Freedom
   1. God is the only being whose existence is not contingent. Which is to say that his existence is analytically entailed by his essence.
   2. For most contingent things (x), x’s definition shouldn’t explain its existence, because if it did, its nonexistence would be a contradiction.
   3. Contingent things that exist do so because they are more perfect than the possible rivals for existence. Now, if x’s nonexistence is a contradiction, then it could not be the case that there are other competing possibilities qua existence.
   4. This means that we need a notion of possibility according to which some things are not necessary and do not actually exist.
   5. If this kind of possibility exists, it implies a certain freedom on the part of a free mind to choose one thing rather than another (for its perfection, as God does, or from our imperfection).
4. Modality, God’s Actions and Existence
   1. God’s Free and Necessary Actions (God must have two types of actions)
      1. Example of a necessary action: God loves himself. This can be demonstrated from the definition of God.
      2. Example of a free action: God makes whatever is most perfect. There’s nothing contradictory in the contrary proposition (if it were, non-existent possibles would in fact be impossible).
   2. A similar conclusion (about modality) derives from the nature of existence:
      1. Take A and B. Only one of these can exist. Assume A is more perfect than B.
      2. Now, A exists because of this, and this fact can be demonstrated, or rendered certain by the nature of the case.
      3. If being certain were the same as being necessary, we’re in trouble.
      4. But, A’s existence has merely a hypothetical necessity. This means that it is necessary that if God always chooses what is most perfect, then A exists.
      5. This is to be distinguished from the (absolutely necessary-type) proposition that it is necessary that A exists.
      6. Again, if A were absolutely necessary, B would be impossible.
   3. So we must hold that:
      1. What has some degree of perfection is possible.
      2. What is more perfect than its opposite actually exists. (Perfection is an “urge for existence.”)
   4. This means that extant things are products of God’s will rather than of necessity.
   5. But: Does god will by necessity (because of his nature) or freely (because of his will)?
      1. It must be by necessity, since if he has to will to will something, this entails an infinite regress.
      2. Does this demean God? With Augustine: Such necessity is blessed.
5. Possible Things
   1. So, things are possible even if God does not will them into existence, because they are not in themselves contradictions.
   2. Or, a possible thing is “something with some essence or reality, that is, something that can be clearly understood.”
   3. This means that if there is never an instantiation of a perfect circle, a circle is still possible, but just possesses less perfection (i.e. less reality) than the things that do exist.
   4. So that “No perfect circle ever did or will exist” is a necessary proposition is true, but “No perfect circle exists” (the timeless proposition) is a necessary proposition is false.
      1. This is so because Leibniz denies that the timeless proposition can be demonstrated.
      2. Basically, Leibniz wants to distinguish between propositions that cannot be solved because they are self-contradictory (e.g. find x where x^2=9 and x+5=9) and where they are merely possible/imaginary (e.g. find x where x^2 + 9 = 3x).
6. Future Contingents
   1. This is meant to remove the problem about the foreknowledge of future contingents.
   2. God can formulate propositions about future contingents that are:
      1. necessary, given the state of the world that has “been settled once and for all”
      2. necessary, given the harmony of things.
   3. But future contingents are not necessary in the analytical sense. This lets God have foreknowledge of them even though they are not necessary.
   4. This entails that it is possible for the imperfect rather that the more perfect to exist. This is fine since we can accept “what God doesn’t will to exist doesn’t exist” without asserting the necessity of this proposition.
   5. [Near the end of this paper Leibniz has an incomplete sentence which he probably meant to turn into something saying:] The only existential proposition that is absolutely necessary is God exists.

Overview

The Monadology the most comprehensive and succinct statement of Leibniz’s mature philosophy. It is ninety points, which I’ve grouped into the following subsets (following George MacDonald Ross): Simple substances, Change, Perception and appetition, Unconscious perceptions, Animals, Reason, Contingent truths, The existence and nature of God, Causality, Possible worlds, Interconnectedness, Soul and body, Infinite divisiblity, Birth and death, Soul and body, the City of God.

It should further be indicated that many of the notes emerged or were directly copied from the very helpful (and freely available) commentary of George MacDonald Ross, and many thanks are due to him for making this text comprehensible for me. Of course, any failings in my reading are in spite of his excellent commentary and not attributable to it. Indeed, his commentary is a significantly better pedagogy, and I can’t imagine why you’d read mine, unless you’re me. Please don’t confuse that admonition with scholarly modesty: I am almost certain his will make better sense to you.

Outline

1. Simple Substances (1-9)
   1. §1: Monads are nothing other than simple substances (without parts) which make up compounds.
      1. How are monads are supposed to make up, or “enter into” compounds?
      2. Either (a) they are literally the smallest parts of compound bodies (literal) or (b) compound bodies are constructed out of the perceptions of monads (metaphorical).
   2. §2: There must be simple substances since there are compounds (which by definition are aggregates of simples).
      1. Later, the distinction between mere compounds and organic bodies - which are also compounds, but such that the whole is more than just the sum of its parts - will become crucial.
      2. Leibniz’s argument is that since a (non-organic) compound is the sum of its parts, it is only real in so far as its parts are real. But the same is true of the parts of the parts.
   3. §3: Extension, shape, and divisibility are possible only where there are parts. So these monads are the genuine atoms of Nature, and (in a word) the elements of things.
      1. Here we learn that monads are ultimate entities which do not have the properties of matter - this is to escape the infinite regress of material atomism.
   4. §4: There is no conceivable way in which a simple substance could be broken up or naturally cease to exist.
      1. “naturally” = in accordance with the laws of mechanics.
   5. §5: There is no conceivable way in which a simple substance could naturally come into being, since it could not be “built” (mechanically).
   6. §6: Summary: Monads come into being only by creation, and go out of being only by annihilation. Compounds come in our out of being through their parts.
   7. §7: This is two arguments: (1) there is no way of explaining how a monad could be internally altered or changed by some other created being, and (2) monads have no windows to let anything in or out by.
      1. First: The only type of influence we can conceive of is when one piece of matter is moved by another piece of matter in accordance with the laws of motion. In compounds this will - or at least can - cause some internal change. In monads it cannot, as they have no parts.
      2. Second: One of the ways in which one substance might be influenced by another is by perceiving it. The problem here is the question about how sense-data might enter the soul and influence it. The brain may have windows, but the soul doesn’t.
      3. In the second argument, we also note that Leibniz was in complete agreement with Descartes, Hobbes, and Spinoza, in that accidents are modes of substances, and cannot exist independently of them.
   8. §8: On the other hand, monads must have some qualities (cf. 1.c: they have no quantitative differences), insofar as they (a) are beings, (b) the compound things they make up are differentiable (cf. 1.h.i below).
      1. Note that Leibniz makes a caveat here about his belief that there’s no empty space. If there were, things could be differentiable by being encoded with monads and empty space (note also here is Leibniz figures out you can encode data in binary).
   9. §9: It is even necessary for every monad to be different from every other monad.
      1. This is qua Leibniz’s Principle of the Identity of Indiscernibles (PII), although his argument is pretty flabby. In this passage he both fails to account for both:
         1. the fact that even though no two macroscopic objects are identical, they might still be made out of a small set of identical sets of microscopic objects.
         2. the fact that we are regularly confronted with indistinguishable objects (take, e.g. this: eeee).
      2. Elsewhere, he provides two main arguments for PII:
         1. (1:1) In the Leibnizian double-aspect (body/soul) program, the soul is the only genuine unity (and therefore the only fully real part).
         2. (1:2) Hence, its individual existence cannot depend on its body or matter. It is thus like an Aquinan angel: there cannot be two with exactly the same set of properties.
         3. (2:1) Space and time are ultimately nothing other than relations.
         4. (2:2) Therefore, they must be defined in terms of the things they relate, not the other way around.
         5. (2:3) This means that you can’t distinguish one monad from another by holding one in your left hand and one in your right hand.
2. Change (10-13)
   1. §10: Every created being (including every monad) is subject to change, and this change is continuous in each of them.
      1. Note that now, not only are the qualities of one monad different from those of every other monad at any given time, but the qualities of the same monad are different from one moment to the next.
      2. Also note that the change is /continuous/ as well as continual.
   2. §11: These natural changes to which monads are subject come from an internal principle (following 1.g.i).
   3. §12: In addition to the source of change, there must be something which specifies precisely what all those changes are going to be. This precise specification (or complete concept, cf. 2.c.i below) which makes each monad different from every other monad.
      1. Elsewhere Leibniz tells us that this is the complete concept of the monad, which includes all the predicates it will ever have.
   4. §13: A unitary simple substance must contain multiplicity (i.e. a multiplicity of qualities): Given that monads change, and given that the change is gradual, there must be some continuity between one state and the next. In other words, some aspects must remain the same while others change.
      1. Note that this argument is invalid for a given monad with one quality. That’s probably okay, though, as this really just recapitulates (1.h).
3. Perception and apperception (14-17)
   1. §14: These affections and relations are perceptions. By definition, perceptions are representations of a multiplicity within the unity of a simple substance.
      1. Note: It was only in the 17th century that people started using the word “consciousness” in the modern sense. To fill the gap in the French language, Leibniz coined the term apperception.
      2. Leibniz then criticises Descartes for failing to recognise the existence of unconscious perceptions. This isn’t wholly fair, since Descartes did recognise the existence of images in the brain of which we might not be conscious. But Leibniz’s point is that the soul can have unconscious as well as conscious perceptions.
      3. He also details his departure from the Cartesian schemata for souls, which included only humans and angels. Leibniz admits three kinds of souls, which are sharply distinct:
         1. Spirits: Have self-consciousness and reason;
         2. Animals: Have sensation, emotion, and motivation;
         3. Monads and entelechies (cf. 4.a): merely express the universe confusedly, and have an appetition towards a better state.
      4. Finally he eludes to his later point that the “folk” (and Descrates) are wrong to think of death as a complete separation of the immaterial soul from the body, since it is not separable from the body. For Leibniz, what we call “death” is a prolonged period of unconsciousness in a smaller body.
   2. §15: The transition from one perception to another can be called appetition. Appetition is directedness towards greater perfection, and while no monad can completely acheive perfection (of perception), but every appetition makes some progress.
   3. §16: We should have no difficulty over the concept of multiplicity within a simple substance (i.e. despite the fact that it has no parts), since every time we have a thought, we are conscious of variegation in what we are thinking about, and our souls are simple substances.
   4. §17: Perceptual states - caused by appetition (cf. 3.a.i) - cannot be caused by mechanical causation in matter.
      1. This is because if you imagine a walking around inside a big brain machine, you cannot imagine seeing a perception being produced by its parts.
      2. Secondly, Leibniz asserts, there is “nothing to be found in simple substances, apart from perceptions and their changes.”
4. Unconscious perceptions (18-24)
   1. §18: “Entelechy” is an alternate word for monad. It comes from the Greek meaning “they have perfection” or “completeness”, in the sense of “self-sufficiency”. They only have a certain perfection, otherwise they would be God. But leaving aside their dependence on God, they are self-sufficient in that they act entirely independently of all other beings.
   2. §19: Here Leibniz amplifies the distinction he made in (3.a), between animal souls and bare monads. All monads (i.e. spirits, animal souls, and bare monads) can be called “souls” in that they all have perception and appetite, but it is less misleading to distinguish between bare monads, which have “simple” perceptions, and animal souls which have “sensations.”
   3. §20: When we have a dreamless sleep or we faint, our soul is not distinguishable from a bare monad; it is still different, nonetheless, in its capacity to leave that state.
      1. Leibniz’s purpose here is to explain how we can conceive of what bare perception is like, by analogy with our conscious experience.
   4. §21: Recap (2.a, 1.h): Simple substances must have a continued existence, but they cannot exist unless they are characterised by some affections, i.e. perceptions.
      1. Leibniz then introduces, without explanation, the expression “little perceptions,” which will mean “perceptions of which we are unconscious.” (Unconsciousness is, by definition, a state in which everything is confused. For us to be conscious, we have to be conscious of something. If everything is confused, we are not conscious of one thing rather than another.)
   5. §22: Since monads cannot be influenced by other monads, their whole history must be determined by their internal law of change. At any given time, their present state is completely determined by their immediately preceding state, and any future state can be deduced from it.
   6. §23: Since (4.e) and the fact that when you wake up, you become conscious of your perceptions, it follows that you must have been perceiving before too (albeit in an unconscious way). the natural course of events,
      1. Here: A perception can only arise from a previous perception.
      2. Elsewhere: You can’t be woken up by something, unless you perceive it before you wake up. Consequently, it must have been perceived unconsciously.
   7. §24: Recap (3.a.iii,4.b): Bare monads have no sensations, since nothing is distinguished from anything else.
5. Animals (25-28)
   1. §25: The perceptual state of animals differs from that of bare monads because their sense organs concentrate information (like the lens of a camera to film). In an aside, Leibniz makes the suggestion that there may be senses of which we are unaware.
   2. §26: In addition to sensation, animals have something analogous to reasoning in humans. It is some association of an image with a memory: some whip equals pain (Hobbes, Hume).
   3. §27: Associations are established more quickly if the images make more of an impression.
   4. §28: Most of the time, people are motivated by an animal-like (e.g. habitual, brute-associative) reasoning to behave certain ways. His example is the difference between the folk and astronomical flavors of the knowledge that the sun will rise tomorrow.
6. Reason (29-35)
   1. §29: It is knowledge of necessary and eternal truths which distinguishes us from mere animals. This is what in us is called the “rational soul,” or spirit.
   2. §30: It is also through the knowledge of necessary truths that we are capable of reflection. Thinking of ourselves, being, substance, monads, etc. we attain the objects of our reasonings.
      1. Descartes didn’t really distinguish reason from self-consciousness; there was just a faculty of human beings which contained abstract and universal ideas, and it did not concern itself with individual existences.
      2. Leibniz, on the other hand, makes a clear distinction between knowledge of eternal truths on the one hand, and self-consciousness on the other (and remember that he had to /invent/ the word “apperception” for this purpose).
      3. This point is about order of discovery. For Descartes, we first had to strip away our preconceptions till we arrived at pure knowledge of the thinking self, and then build everything up in the order: self, God, eternal truths, the material world. Leibniz, on the other hand, sees no need to doubt that we perceive individual things (even if they are not as they seem), and that we have knowledge of eternal truths.
      4. Leibniz even seems to imply that we could get by without self-consciousness at all: we could navigate round the world of experience using our senses, and we could do mathematics, by concentrating our whole attention on eternal truths, and what can be deduced from them.
   3. §31: Our reasoning is grounded on two great principles. “One is the principle of contradiction, by virtue of which we judge false anything which involves a contradiction, and true anything which is the opposite or contradictory of the false.”
      1. Note 1: Leibniz is about to distinguish between “truths of reasoning” and “truths of fact”; but before he has explained the distinction, he introduces the two great principles by which we establish them. The principle of contradiction is what we use to establish truths of reasoning.
      2. Note 2: His definition of the Principle of Contradiction is rather awkward, it merges what we now call the principle of non-contradiction ((p && !p)==false) and the law of the excluded middle (if it’s not p, it’s not-p, and vice versa).
   4. §32: The other is the principle of sufficient reason: an event cannot occur unless there is a sufficient cause; and by “sufficient” he means a complete and fully determinate set of preconditions, such that if they are present, it is inconceivable that the event should not occur.
   5. §33: There are also two sorts of truths: those of reasoning (necessary) and those of fact (contingent). You can break down necessary truths into smaller and smaller ones, until you reach primary ones.
      1. Fun fact: One of Leibniz’s big projects (called the “universal characteristic”) was to list all the primary concepts, and devise a notation for all complex concepts which would make explicit how they were derived from the primary ones. Once that had been achieved, all reasoning would become a matter of straight calculation, which could be done by a machine.
   6. §34: He now claims that the geometrical method of Euclid is the same as the process of analysis he has just described. Note that if so, axioms and postulates would not be necessary. -GMR
   7. §35: Finally, there are simple ideas which cannot be defined and there are also axioms and postulates - in a word, primary principles - which cannot be proved (and do not need to, as they are assertions of identity).
      1. Again, assuming there are simple (primary) ideas, and we know what they are, it is difficult to see what role there can be for primary principles, or axioms. If they are explicit assertions of identity, they will all be of the form A=A, where A is any primary idea. -GMR
7. Contingent truths (36-37)
   1. §36: The principle of sufficient reason (6.d) applies to contingent truths as well. Reasoning is analysis, and what is being analyzed is the complete concept of an individual (he doesn’t explicity say this here), which is infinite.
      1. This is what is meant by Leibniz’s doctrine (not mentioned herein) that all truth is analytic (that in every true proposition the concept of the predicate is contained in the concept of the subject). While it seems paradoxical to claim that contingent truths are analytically true, what Leibniz means is that if we had the complete concept of an individual, then every truth about that individual would be analytically true. Or, if we already knew everything, we would have nothing new to learn. Meanwhile, only a tiny proportion of possible complete concepts have been actualised, and it cannot be proved, even by an infinite analysis, whether a concept has been actualised or not.
   2. §37: Since any sequence of contingent things is infinite, it is never possible to arrive at the sufficient reason for anything within this sequence.
8. The existence and nature of God (38-48)
   1. §38: This is why the ultimate reason for things must lie in a necessary substance (one who’s existence is not contingent on anything else), ‘God’. However, in this God-substance, “the detail of changes exists only eminently”: the sufficient reason for the changes in a created monad lies in the monad itself, but there is something different and superior in God, which is the source of the principle of change within the monad.
      1. This is a strategy to distance himself from Spinoza, for whom the cause of change was within God himself.
   2. §39: If this God-substance is a sufficient reason for all the changes in all the stuff in the created universe, and all this stuff and all these causal chains are interconnected, “there is only one God, and this God is sufficient.”
   3. §40: Since all that stuff is dependent on God, it follows that none of it could restrict him in any way, and hence he is infinite.
      1. Secondly, Leibniz argues that God must be incapable of having any limits. This actually depends on an argument below (8.g).
      2. Finally, God must contain absolutely as much reality as is possible. This is true if we grant Leibniz the unstated metaphysical assumption (which he did believe) that possibility strives to existence, and will become actual unless something prevents it.
   4. §41: And, since God is infinite positive reality, God is perfect. Perfection = infinite positive reality.
   5. §42: God gives created things what perfection (=reality, being) they have. Their imperfection (=lack of reality, nothingness) comes from their own nature as created things.
   6. §43: Like Spinoza, Leibniz regards God as the source of essences (ideas, concepts, possibilities) - insofar as they are real* - as well as of existences.
      1. * The concept of something possible isn’t real in the way that something which actually exists is real. Nevertheless, it must have some sort of reality, otherwise there would be no possibility of the thing.
      2. Similarly, there can’t be any eternal truths unless the concepts they involve have some reality. (This is all pretty Cartesian.)
   7. §44: If essences have any reality, this reality must be grounded in something which actually exists (an essence or a possibility is not a self-subsistent entity, a substance). But in the case of contingent beings, their actual existence depends on the realisation of their essence or possibility = essences are logically prior to existences. Consequently, essences cannot be grounded in any contingent being, but must be grounded in a necessary being.
   8. §45: Leibniz now gives us three arguments for the existence of God.
      1. The Ontological Argument (a priori): Only the necessary being (God) must exist if he is possible (8.g). Since nothing can prevent the possibility of an unlimited being (8.c), we know God exists.
      2. The Cosmological Argument (a posteriori): The created universe exists, it must have been created by God.
      3. The Argument from the Middle (a priori*): Eternal truths exist (8.f); hence God exists (8.g). * Eternal truths seem to be co-existent with God’s nature, and therefore belong to the cause rather than to the effect.
   9. §46: Eternal truths depend on God but are not arbitrarily determined by his will, they are the internal objects of his understanding. On the other hand, contingent truths do depend on his will, since his understanding can /entertain/ alternative possibilities; that they are chosen as they are is for his purpose of a harmonious universe.
      1. Note that this toes the line between Descartes (all truths depend on God’s will) and Spinoza (none do).
   10. §47: God is the unity or original simple substance (he has no parts). He creates all monads and, just like Descartes thinks, continually re-creates them moment to moment. In other words, for the state of the universe at any given instant (p): God brings (p) into existence. The the reason for (p) is the immediately preceding state of the universe (p’).
       1. Because monads are finite, they are “bounded” in what they can receive from God.
   11. §48: God has power, knowledge, and will. Monads mirror these faculties in substance (b/c created by God’s power?), perception, and appetition. The faculty-to-faculty relationship is infinite:imitation of the infinite.
9. Causality (49-52)
   1. §49: Given that there is no direct interaction between monads, a monads can act insofar as their perceptions are distinct (active, spiritual aspect, Leibniz here says “have perfection”) and be acted upon insofar as their perceptions are confused (passive, material aspect).
      1. Basically one acts when one has intention. If I run up behind you and yell boo, I am acting. Your confused reaction is your being acted upon.
      2. The relationship between the active, spiritual power of monads and action is unclear, but it’s nonetheless there in the text.
   2. §50: Moreover, it’s not merely that one monad has more distinct perceptions than another, it provides the a priori explanation of what happens in the other. Of course, not being God, no monad’s perceptions are /perfectly/ clear.
   3. §51: But these inter-monad influences are not “real”: only God can have a real influence on things. The gist of this seems to be that when God was creating the universe (remember that there is no contingency to the eye of God for Leibniz), and selecting which monads would exist, he picked them in proportion to their “harmony.” Their perfection is in their ability for coordination, harmony. Therefore, given that God decided to include me in the best possible universe, he organized in advance that when my monad yelled “Boo”, your monad would have the simulataneous perception of being yelled at.
      1. Again, the parallels between Leibniz’s universe and the one that you can program on your computer are completely remarkable.
   4. §52: Every action is an interaction: When I yell, and you jump, your jump causes a reaction in me in turn.
10. Possible worlds (53-55)
    1. §53: God chose our world out of an infinity of possible ones, and there had to be a reason for his choice. (Hence, the set of possible universes required that each member be unique. E.g. Choose the best “1″: [1,4,203,1]. You can’t do it.)
    2. §54: This reason can be found only in harmony, or the degrees of perfection which these worlds contain.* Thus nothing is entirely arbitrary.
       1. * Confusing: If degree of perfection is the amount of positive reality (8.d), and also the amount of distinct perception (9.a). Harmony is the accommodation of the perceptions of monads to each other (9.c).
       2. So, for example, the universe would have more perfection if the person I yelled at had a distinct rather than a confused perception of the event; but it would be less harmonious, since their passivity has to be accommodated to my activity. Cf. (11.c) for the fix.
    3. §55: So God must choose the best universe out of the goodness of his will.
11. Interconnectedness (56-61)
    1. §56: The perceptions of monads are expressions of their relations to every other; this must be the case because of the harmony of the universe. Although monads don’t really have any causal influence on each other, it is just as if they did. (Like gravity, which Leibniz didn’t believe in.)
       1. In reflecting every other, each monand is a permanent living mirror of the universe.
    2. §57: If we consider monadic perceptions, there are infinitely many universes (insofar as there are infinitely many perspectives on the universe), although these are each only a representation of the one universe.
       1. Although Leibniz doesn’t go into this here, the concept of a monad’s unique point of view is crucial to his account of space: Space is a logical construction out of monadic perceptions. Monads are not in space, but space is in them. However, one can talk of monads as if they were in space, since their point of view gives them a unique position in relation to all other monads.
    3. §58: This is the means for obtaining as much variety as possible, but with the greatest order as possible. In other words, it is the means for obtaining as much perfection as possible. This is a new definition of perfection: maximum variety (which includes quantity of reality as well as differentness), together with the maximum order (or harmony).
    4. §59: Leibniz now claims that his hypothesis does the most justice to God. Potential rivals followed by their problem:
       1. Descartes: too capricious
       2. Spinoza: no goodness or freedom
       3. Malebranche: too much miraculous interference
       4. Newton: too hands off. (God built the clock, but has to wind it up from time to time since he wasn’t clever enough to make it go on for ever.)
    5. §60: An apriori argument for universal harmony, proceeding from cause (God’s creative act) to effect (the created universe), and not from effect to hypothetical cause.
       1. Since monads are by nature representative, nothing can restrict them from representing everything. (This depends on two additional premises:)
          1. Whatever exists in essence is actualised unless something prevents it (again, a classical Leibnizian assumption). So since monads are essentially representative, they will represent everything unless stopped.
          2. Nothing (apart from God) can influence the inside of monad. Consequently, nothing can block a monad’s representations (except God, who’s goodness - expressed as a desire for harmony - would have prevented him from doing so, cf. [10.c]).
       2. However, it is a common sense that we don’t actually perceive everything. Leibniz suggests that we do in fact, but not distinctly (a very, very large percentage of our total perceptions are “little perceptions” cf. [4.d.i]).
          1. Hence, the subset of clear perceptions is both very small and distinct on a per-monad basis (I suppose insofar as monads are “positioned”, and have a certain perceptual filter which responds to the proximity and size of other monads).
       3. Hence, what distinguishes us from God is that only some of our perceptions are distinct; and what distinguishes us from each other is the variations in our distinct perceptions.
    6. §61: Total conservation of information
       1. The universe is full of matter (note that he assumes this, but his argument might go): In the material universe, the interconnectedness of everything is mediated by one piece of matter pushing against its neighbours in accordance with the laws of motion. If there were any gaps, the causal chains would be broken, and the universe wouldn’t be interconnected. Consequently, there cannot be a vacuum.
       2. If the universe is full of matter, and obeys the laws of mechanics, then every motion in it is transmitted between monads in every direction. The force of the shock wave diminishes with distance as it spreads more widely. But given that there are no smallest quantities in Nature, the wave will spread to infinity.
       3. Hence, a sufficiently detached and intelligent observer could read the entire state of the universe off any given monad.
12. Soul and body (62-64)
    1. §62: What makes my body my body is that it is represented more distinctly than surrounding bodies. Then it seems like he says that the soul represents the whole universe only because it represents its body, which represents the whole universe.
       1. GMR: I’m sure this is inconsistent with what he said earlier about the creation of monads, especially if monads are logically prior to bodies in space. What he should be saying is that the two go hand in hand: that there is a one-to-one correspondence between the distinct and confused representations of the whole universe in the soul, and the infinitely complex motions in the body.
    2. §63: Following (12.a), a body belongs to either an entelechy (in a living being) or, more specifically, a soul in an animal.
       1. Note that he has defined dead matter out of existence: the only real beings are living beings.
    3. §64: The organic body of a living being is a divine machine. The difference between a divine machine and one of ours is that divine machines’ parts are manufactured at a single source, whereas we may make a cog, but we don’t make the parts that make the cog.
       1. For Leibniz, divine machines are organic machines from top to bottom: Organic bodies have organs (heart, lungs), which are themselves organic bodies with organs (cells); and they in turn have an organic structure (nuclei, cell walls), and their parts have an organic structure (chromosomes). He didn’t know these things specifically, but was pretty sure it was turtles all the way down.
13. Infinite divisibility (65-69)
    1. §65: The material world is built up out of infinitely small parts. If it weren’t, “it would be impossible for each portion of matter to express the whole universe.”
       1. What are the parts? As we saw in Spinoza, matter cannot be constructed out of mathematical points, since infinitely many mathematical points are still at one point.
    2. §66: “From this you can see that there is a world of created things…in the smallest part of matter.” This is the “universe-in-every-electron” idea, which seems fanciful, but is nonetheless a logical consequence of infinitely divisible matter coupled with the assumption that the laws of nature are the same everywhere.
    3. §67: Leibniz waxes poetical: “Each portion of matter can be conceived as like a garden full of plants, or like a pond full of fish.”
    4. §68: If you were to probe deep enough, you would find that ultimately there was no intervening dead matter at all, and everything would be full of living bodies. (The water in the pond contains the fish, Leibniz says.)
    5. §69: Things seem inert or chaotic because our perception is confused: When we have a distinct perception of anything, we can see that it is composed of tiny living organisms.
14. Birth and death (70-77)
    1. §70: Each living body has a “dominant entelechy,” a soul. (Monads can’t be parts of each other, so the relationship is one of dominance.) In other words, my soul dominates the monads which are the principles of the unity of the organs of which my body is composed. They in turn dominate the monads which are the principles of the unity of the parts of their bodies; and so on to infinity.
       1. He doesn’t actually say what this dominance consists in, but GMR conjectures that the dominant monad is the more active partner in a given interaction.
    2. §71: There is no particular piece of matter to which a monad is permanently attached. (He echos the principle of Heraclitus that “everything flows,” like a river, so that bodies [organic and inorganic?] are constantly losing and gaining particles.)
       1. What he doesn’t say explicitly is that when a subordinate organism joins or leaves a larger organism, it must be somehow transformed. E.g. when I eat food, it becomes part of me.
    3. §72: Souls gradually lose parts of their body, but are never completely deprived of a body. This is contra to two popular theories of the immortality of the soul:
       1. Platonic/Pythagorean: That the soul leaves the body (rendering it dead) and moves to another, theretofore soulless body.
       2. Cartesian: That the soul can survive without the body.
    4. §73: As such, (a) death is not the annihilation of the soul, and (b) birth is not its creation. Generation/birth is “unfolding and growth”, and death is “infolding and shrinkage.”
    5. §74: Not merely that there is a seed before the generation or conception of the new animal, but the animal itself (body plus soul) pre-exists in it. On conception, the infolded form or soul becomes dominant,
    6. §75: Just as only a tiny proportion of acorns become oaks, so only a tiny proportion of spermatozoa are “chosen” to pass through to a “larger theatre.”
    7. §76: Now on to death: At death, the animal is transformed back into a seminal animal, or something similar.
    8. §77: So it’s not merely that the soul or monad is immortal (on the apriori grounds that it is a mirror of the indestructible universe); the animal itself is immortal: It always has /some/ body.
15. Soul and body (78-81)
    1. §78: The soul and the body each follow their own laws, and they coincide by virtue of the pre-established harmony between all substances (since they are all representations of one and the same universe).
       1. Elsewhere, Leibniz gives the analogy of two clocks which keep perfect time. The perfect clockmaker made them so well that neither of them ever goes wrong.
    2. §79: The laws for souls and bodies:
       1. “Souls act in accordance with the laws of final causes” - they are constantly striving for greater perfection.
       2. “Bodies act in accordance with the laws of efficient causes” - e.g. with the laws of mechanics, and are pushed from behind by blind forces acting on them.
       3. God has brought it about that the two are in perfect harmony.
    3. §80: Cartesian mechanics
       1. Leibniz gives a clever explanation of how Descartes might have thought that the soul could influence the body without contravening the laws of mechanics.
       2. Descartes believed in a law of conservation of “motion,” so that its quantity in nature could be neither increased nor diminished.
       3. If the soul could make a particle of matter in the brain move faster, this would contravene the law.
       4. On the other hand, if it merely deflected the particle, so that it travelled into a different nerve ending, the total quantity of motion would be conserved.
       5. What Descartes couldn’t understand was that what is conserved is motion in a given direction, and that it requires an input of energy to change the direction of motion of a particle.
    4. §81: “This system means that bodies act as if there were no souls…and that souls act as if there were no bodies; and that the two act as if there were an influence of the one upon the other.”
16. The City of God (82-90)
    1. §82: Existentially, humans are in the same position as other living beings: from the creation of the universe they have existed with body and soul, and they will continue to do so to eternity.
       1. During the periods when they are not actual, living human beings, but only seminal animals, they have distinct perceptions (like other sensing animals), but it is only when they become actual human beings through the act of conception that they become rational souls (reasoning, spiritual).
    2. §83: Among the characteristics already specified (in 6.a-b) - knowledge of necessary truths, self-consciousness, a concept of God - and whereas all monads are images of the created universe, human souls are also images of God.
    3. §84: Since humans are images of God himself, they can have a kind of social or personal relationship with him: He is not just their creator, but he is also like their king (in respect of his power) and father (in respect of his love).
    4. §85: “From this it is easy to conclude that the congregation of all spirits must constitute the City of God (Augustine), the most perfect state possible under the most perfect of monarchs.”
    5. §86: Introducing the moral dimension
       1. God couldn’t be glorious without the City of God, since otherwise there wouldn’t be any creatures capable of glorifying him.
       2. If God had merely created a huge machine of a universe, you could admire his cleverness and power, but the machine would be morally neutral. God needs rational and moral beings in order to manifest goodness (justice, mercy, and so on).
    6. §87: Like the perfect harmony between the realms of efficient and final causes, there is also a perfect harmony between the physical realm of nature and the moral realm of grace. Here is the contrast between humans (moral organisms, rational souls) and the rest of Nature.
    7. §88: The purely mechanical laws of Nature will bring about a destruction of the earth, exactly when the moral laws of the City of God require some people to be punished, and others rewarded.
       1. Leibniz seems to eqivocate between his Platonism and his Christianity here:
       2. Plato believed the universe is cyclical, so that there is a succession of holocausts followed by a new beginning.
       3. Christians believe here will be a single Last Judgment, when the world is overturned, and sinners die a second death. The world will then be restored, and the elect will live in eternal bliss under Christ’s reign.
       4. Leibniz seems to believe that the earth will be destroyed periodically, but each period will be better than the previous one, because the universe is becoming ever more perfect.
    8. §89: God doles out rewards and punishments, which will be felt by our living bodies in a continuation of the present universe, and not by disembodied souls in some extra-terrestrial heaven or hell.
    9. §90: The best of all possible worlds
       1. As with Spinoza, virtue consists in the pure and disinterested love of God.
       2. Also like Spinoza, Leibniz holds the view that we should be indifferent to our own sufferings, and see them as contributing to the good of the whole, governed by a divine providence.
       3. Provided that we align ourselves with the will of God, we will find that this is not only the best possible world in general, but that it is the best possible for ourselves in particular.