Sorglose Nacht

Overview

The Enquiry is Hume’s concise rendering of his philosophical position (”moderate skepticism”). It consists primarily of statements of his methodological and epistemological views, along with his accounts of free will and religious knowledge.

In Stephen Buckle’s introduction to the first Enquiry, he describes its unified argument as such: “After Section 1 makes its case for serious philosophizing, Sections 2-6 put in place the basic account of human psychological functioning, and this account is then put to work in Sections 7-11.” I’ve taken a cue here and split the outline into two sections (1-6 and 7-11).

On a bureaucratic note, I’ve changed my outline numbering system. The reason I’ve done this is because anymore these texts are getting long, and marking numbered paragraphs alphabetically seems counter-intuitive at best. Here, I’ll try using the capitalized roman numerals (I) to represent chapters, and standard numerals (1) to represent numbered paragraphs.

Outline

1. On the different species of philosophy
   1. Moral philosophy (the study of human nature and action, contra natural philosophy - the study of the world) has two common manners of treatment.
      1. The first manner is designed to influence people to be virtuous by “excit[ing] and regulat[ing] our sentiments…[to] bend our hearts to the love of probity.”
   2. The second is more concerned with cultivating our understanding rather than our manners. Cartesian rationalism is a good example of this type of philosophy, which is “unintelligible to the common man.”
   3. It is certain that the “easy and obvious philosophy” will always receive the common person’s preference over the “accurate and abtruse.” The former may also be more useful in daily life.
   4. In this graph he makes a series of consistently wrong assumptions about which philosophers posterity will remember, choosing Cicero over Aristotle, La Bruyere over Malebranche, and Addison over Locke.
   5. Society types in particular like the easy philosophy, by whose writings “virtue becomes amiable, science agreeable, company instructive, and retirement entertaining.”
   6. Contra certain obsessive rationalists, Hume admonishes “be a philosopher, but…be still a man.” (Here, as many places, Hume is more enjoyable when read to oneself in a Scottish accent.)
   7. However, too much of a good thing (here, Epicurianism) is not the answer either. Perhaps there is something worth considering in the metaphysical endeavor.
   8. For one, accuracy-obsessed philosophy does so in the service of the humane pursuits. By analogy, Hume considers the painter’s debt to the anatomist: “Accuracy is,” he notes, “in every case, advantageous to beauty, and just reasoning to delicate sentiment.”
   9. Secondly, most human progress in understanding comes from the kind of enquiry of the metaphysicians, or “a spirit of accuracy…carries [all human pursuits] nearer their perfection.”
   10. While the important task of making this slow and arduous progress will seem dry to most, some minds “require severe exercise.”
   11. However, the justest exception to be taken with metaphysical philosophy is that these deep folk claim to “penentrate into subjects utterly inaccessible to the understanding.”
   12. This fact should not condemn the deep philosophical enterprise, though. On the contrary, the “only method of freeing learning…from these abstruse questions, is to enquire seriously into the nature of human understanding, and show…that it is by no means fitted for such remote and abstruse subjects.”
   13. There would be considerable other advantages to such an enquiry, the least of which might be a delineation of the distinct parts and powers of the mind.
   14. Skepticism against such an effort ostensibly entails skepticism about the ability of all speculation whatsoever, and of action. One cannot doubt that the mind is endowed with several distinct powers.
   15. There’s thus no reason to despair of such an effort of categorization.
   16. Hume modestly writes that even a small accomplishment in this endeavour would be ample reward for his effort.
   17. “Happy, if we can unite the boundaries of the different species of philosophy, by reconciling profound enquiry with clearness, and truth with novelty!”
2. Of the origin of ideas
   1. Objects of imagination and memory pale in force and vivacity to those of sensation.
   2. Similarly with emotions: A man in a fit of anger “is actuated in a very different manner” than one who merely thinks about anger.
   3. This indicates that we can divide all perceptions into two classes, distinguished by force: ideas (those “less lively”) and impressions (those more).
   4. At first blush, thinking seems unbounded (it is unconstrained by time and space, e.g.).
   5. Upon reflection, however, we realize that thought cannot really invent anything, rather it can merely compound, transpose, augment or diminish the objects we receive from our impressions.
   6. Two arguments to prove this. First, any of our ideas, when subjected to appropriate scrutiny, resolve themselves into simple ideas (received from impressions - very Lockean).
   7. Second, when a person has a defect of some sense (say, he is blind), he is likewise defective in his ability to comprehend its correspondent ideas (here, e.g. color).
   8. There is one phenomenon that contradicts this, for which Lock proposes the following thought experiment:
      1. Suppose a person is acquainted by experience with all but one particular shade of blue.
      2. When shown a gradient of color, he will be aware that there is a jump between the shade preceding the shade he has not experienced, and the one following it.
      3. This means, despite having never experienced that shade, he can infer that it should be there.
      4. However, Hume chalks up this example to complete anomaly.
   9. On the main, this is very useful as a heuristic device for analyzing philosophical argumentation. If you suspect that some philosopher’s terminology has no referent (apparently a big problem in Hume’s time), you can ask yourself, “from what impression is that supposed to be derived?”
3. Of the association of ideas
   1. It is evident that the different thoughts of our mind are always somehow connected to one another.
   2. Hume proposes that this principle of connection takes only three forms: resemblance, contiguity in time or place, and cause and effect.
   3. That these principles serve to connect ideas will not be doubted. That the three of them are exhaustive may justly be doubted. Hume will try to evidence his taxonomy’s exhaustiveness by showing that it applies to a wide variety of examples (following Hutcheson, he will immediately discuss aesthetics, qua the relationship between history and poetry).
   4. People’s actions are directed at ends. We seldom speak or think without purpose or intention.
   5. All compositions of genius therefore must arise at least in the first place from some aim or intention.
   6. Since this is always the case, there always must be some thread which relates the events of a narrative.
   7. The connecting principle may be different, depending on the designs of the poet or historian. Ovid’s Metamorphoses operates connectively by resemblance.
   8. A historian, however, may be influenced by contiguity in time and place.
   9. However, the most usual form of connection in poetic and historical narratives is cause and effect. For a historian, this seems obvious, as the more perfect the chain of causal links, the more perfect is the historical account.
   10. The same is true of a narrative about an individual, but from a narrative standpoint, this degree of detail can be boring. History and poetry thus differ in their “unity of action” not in kind, but merely in degree.
   11. He here gives us the example that it may not be necessary, as in the Iliad to let the reader know “each time the hero buckles his shoes.” If an epic poet does this, the reader’s imagination will doubtless flag.
   12. Secondly, he notes that the epic poet must not trace the causes to any great distance - again, the reader will lose interest.
   13. The same rule in dramatic poetry - introducing an actor only tangentially related to the main characters is just confusing. The author must, again, select which elements she will admit onto the stage, at the clear expense of providing a full accounting of the causal nexus which determines the plot.
   14. Paragraph 14 recaps 7-13: the relation of cause and effect is the same in history and poetry, where the latter’s concern is the imagination and passions of its readers.
   15. Since the difference is only measured by degrees, it will be difficult to separate history from epic poetry cleanly.
   16. Here a brief discussion of the role of narrative contrast in unifying Achilles’ anger in the death of Hector and his anger which “produced so many ills to the Greeks.”
   17. Here an analysis of Paradise Lost that suggests that the connective structure of this poem is not necessary causal, but rather resemblance (of miraculous events) and contiguity (of events in Christian metaphysical time).
   18. The full empirical review of the exhaustiveness of this taxonomy would lead us into reasonings too copious for this enquiry.
4. Sceptical doubts concerning the operations of the understanding
   1. (Part I) All objects of human reason may be divided into (1) relations of ideas and (2) matters of fact. The former are propositions which are independent of the actually existing stuff of the universe.
   2. The latter (matters of fact) are, on the contrary, just states of affairs in the really existing universe. Their contrary states don’t imply contradictions, and we cannot prove their contraries demonstratively false.
   3. It might be worth our time, then, to figure out something about what exactly assures us of any matter of fact, beyond the “present testimony of our senses.”
   4. Outside of that present testimony, everything we have to say about matters of fact seems to be founded on the relation of cause and effect. (It is supposed that there is some causal relation between the present fact and whatever we infer from it.)
   5. Therefore, we’d better look at how we arrive at the knowledge of cause and effect.
   6. Hume affirms that the knowledge of this relation arises entirely from experience. No object, considered in itself, ever reveals by its sensory qualities, the causes that produced it or the effects that will arise from it.
   7. It thus will be admitted that causes and effects are discoverable only by experience (not by reason) with regards to objects.
   8. However, it may not be so self-evident that this is the case when we consider events.
   9. Imagine two billiard balls, a first moving towards a second, making contact. Motion in the second is quite a distinct event from motion in the first.
   10. We of course think that when the first hits the second, the second will move. But we can conceive many other outcomes rationally. The first could stop, or be deflected in some other direction. There is never an a priori reason, then, that grounds our preference that the second will move on contact.
   11. Since every effect is distinct from its cause, and therefore cannot be discovered in the cause. Therfore, it is in vain that we should try to rationally infer an effect from a cause.
   12. While elasticity, gravity, etc. are probably the ultimate causes we shall ever discover in nature, “the most perfect philosophy of the natural kind only staves off our ignorance a little longer,” and “the observation of human blindless and weakness is the result of all philosophy.”
   13. Neither can geometry account for the law of motion, since the latter relies on the real existential world, for which we can only experimentally suppose the efficacy of the former.
   14. (Part II) Since the foundation of all our reasoning is experience, we need to ask, what is the foundation of all conclusions from experience?
   15. Even after we have experience of cause and effect, our conclusions from that experience are not founded on any process of the understanding. Explaining this is what follows.
   16. The main question to answer is why our experience of the behavior of one object should be extended to predictions about the behavior of other objects, however similar, at different times. Even when we allow that this inference is just, we need to know what the “medium” between the single experience and the expectation of similar experiences in the future.
   17. Just because we haven’t figured out this intermediate step yet doesn’t mean we never will. This means the negative proof isn’t good enough, and we need to endeavor to enumerate all the branches of human knowledge, and that none of them can afford such an intermediate step.
   18. There are two kinds of reasonings: demonstrative (that reasoning which concerns ideas) and moral reasoning (that reasoning that concerns fact and existence. That there are no demonstrative arguments to provide the intermediary step seems evident, since it doesn’t imply a contradiction that the course of nature may change sometime in the future.
   19. If we are going to be persuaded by any arguments to continue to expect future behaviors based on past experience, these arguments are going to be probable only.
   20. From causes which appear similar we expect similar effects, but even though there is “nothing so like as eggs,” no one “expects the same taste and relish in all of them.”
   21. If someone is to infer that some bundle of qualities (x) implies some causal power (y), based on his past experience that all x’s have the power y, of what nature is this inference? It’s neither demonstrative nor intuitive, and to say that it’s experimental is begging the question.
       1. Hume also makes the point here that regardless of the fact that as an agent he is satisfied to act based on inferences from experience, as a philosopher, he remains curious as to the nature of these inferences.
   22. Now Hume is going to give us some arguments that will prove that he hasn’t merely /missed/ some argument for the foundation of this inference.
   23. Imagine a child who puts her hand by a candle. The flame burns her, and in the future, she will be careful not to put her hand near the candle again. If you assert that the child develops this conclusion by rational means, and that the means are so evident that an infant can deploy them, this means that any valid explanation of the rational process can’t be more complex than those deployed by an infant. Since this is true, Hume thinks it likely that some philosopher would already have been able to explain it. Indeed, if he’s missing it, he would be “a very backward scholar; since I cannot now discover an argument which, it seems, was perfectly familiar to me long before I was out of my cradle.”
5. Sceptical solution of these doubts
   1. (Part I) One school of philosophy doesn’t lead us to the kind of hyper-rational selfishness in which philosophers are known to indulge. Academic (that is, post-Platonic, contra Pyrrhonian) Scepticism: suspending judgment, and renouncing speculation about things outside the limits of common life and practice.
   2. Though we must conclude (viz. the previous chapter) that there is a step taken by the mind which is not supported by a rational argument, there is no danger that this lack of argument will threaten all the knowledge (which is almost all of it) which it grounds.
   3. To an alien, there is no reason to conclude that simply because one event precedes another that the first is the cause and the second the effect.
   4. Now imagine that our alien has a little more experience. Though he now finds himself determined to draw the inference that one thing causes another, he still has no rational justificatin for doing so. But there must be some principle which makes him form this conclusion.
   5. That principle is custom or habit. It is by habit that we associate, e.g. heat and flame. There is a long footnote here that suggests that this experiential justification for reason underlies not only our knowledge of objects, but our views on civil government, moral conduct, the law, etc.
   6. “Custom, then, is the great guide of human life.” Without custom, we wouldn’t know anything about anything but what our sense experience and memory deliver us. This means that we wouldn’t know how to adjust means to make ends we want, and this would be the end “at once of all action, as well as the chief part of speculation.”
   7. Also, it is prudent to note that though our conclusions can carry us beyond memory and sense, some fact must always be present to sense or memory to provide a starting point to draw a conclusion.
   8. In conclusion, all beliefs about matters of fact are derived from some present object and a customary conjuction between that object and some other object.
   9. From here, then, we need to examine the nature of that belief and of the customary conjunctions from which it is derived.
   10. (Part II) What’s the difference, cognitively speaking, between a belief and something we just imagine?
   11. The difference lies in some sentiment or feeling that gets conjoined to beliefs (by force of custom) that doesn’t get joined up with fictions. Since there’s no logical contradiction in the idea of a red ocean, it is just some sentiment that forces us to understand an image of one as fiction, whereas to one of a blue ocean we attribute facticity.
   12. Defining this sentiment is hard, but describing it might not be so bad. We can call a belief “something felt by the mind, which distinguishes the ideas of judgment from the fictions of the imagination. It gives them more weight and influence…and renders them a governing principle of our actions.”
   13. On summary, “…belief is nothing but a conception more intense and steady than what attends the mere fictions of the imagination, and…this manner of conception arises from a customary conjunction of the object with something present to the memory or senses.”
   14. We will also remember that the principles of that conjunction are resemblance, contiguity and causation. Does it happen, Hume now asks, that “when one of the objects is presented to the sense or memory, the mind is not only carried to the conception of the correlative, but reaches a steadier and stronger conception of it than what otherwise it would have been able to attain?” He finds that in the case of cause and effect, this is indeed the case. The question is now whether it is generally the case.
   15. He argues that it is the case for the resemblance connection as well, using the example of viewing a picture of an absent friend.
   16. Further evidence for the power of resemblance comes in the form of Roman Catholic rituals that use idols (of the crucifixion of Jesus, e.g.).
   17. He argues then that it is also the case for the contiguity relation, using this example: when walking hear his home, the things that he passes remind him of his (absent) home more acutely than do similar things hundreds of miles away.
   18. Finally, “no one can doubt” that causation works similarly. His (strange) example here is the desire for religious types to have relics of saints, which he suggests are effects close to the cause (the holy person).
   19. Another, still weird example, is that in seeing the son of our dead friend, we remember him more acutely. The implication here is that the son is the effect, and the father the cause.
   20. Finally, all three connective types require that the correlative object is presupposed. It would have no effect if, e.g. we didn’t believe the father, or Jesus, or the saint, or our home, or our absent friend actually existed.
   21. This paragraph seems a little strange at first blush, because he suggests that custom is the principle by which “a kind of pre-established harmony between the course of nature and the succession of our ideas” (an obvious reference to Liebniz) and he ends up talking about final causes (in reference to Aristotle). It’s actually kind of nice, though, when you understand these problems in terms of paragraph 6 above: if custom didn’t unite our thoughts with our past experience of nature, we wouldn’t know how to act to bring about ends, and hence both moral action and knowledge would be impossible.
   22. Finally, there’s a practical analogy: we use our instinct for inferring future behavior from past experience in the same way we use our legs. We don’t have to understand the way the muscles and nerves work together to walk.
6. Of probability
   1. Although our world is causally determined, our ignorance of the real cause of any event means that our future-directed knowledge for real events and objects always takes the form of a belief or opinion.
   2. This opinion is based on probability.
   3. Now recall that a belief is just a stronger conception of some object than that which we have of some correspondent object of fiction in our imaginations.
   4. We can now understand that probability begets belief (and degree of belief). Since fire has always burned throughout our experience, it is incredibly probable that it will again. Therefore, we believe with high assurance that we’ll be burned if we touch a fire. In short, Hume thinks that when we project our experience of past events onto our beliefs about the future, those beliefs acquire a degree of assurance proportional to the consistency of our past experience in similar situations.

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.