Sorglose Nacht

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

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.

Overview

The first six books of Aristotle’s metaphysics serve to give the problem of being its historical and theoretical context. Book I discusses the definition and purposes of philosophy, and gives a short recapitulation of its history. Book II seeks to address in advance concerns about Aristotle’s metaphysics, by making the argument against the possibility of an infinite regress. Later in the Metaphysics, this will be developed into the famous argument for God. Book III provides a sketch of the main problems of philosophy. Book IV details a few additional premises of Aristotle’s argument, namely the arguments for the principles of non-contradiction and the excluded middle. Book V is a philosophical lexicon, giving the meanings of 30 key philosophical terms. Book VI, finally, leads into the main argument (given in parts VII-IX), by excluding two of the senses of Being detailed in Book V as the proper object of study for metaphysics.

1. BOOK I/BIG ALPHA

   1. The advance from sensation through memory, experience, and art, to theoretical knowledge.
      1. Since we all desire to know, we rejoice in our senses. Particularly in sight.
      2. Sensation gives some animals memory, and those which have memory and hearing can be taught.
      3. Humans also have art and reasoning.
      4. Art arises when from many notions gained by experience, one universal judgment may be made (not particular, e.g. medicine good for all people with symptom n, not just Socrates).
      5. Nonetheless, it must be remembered that art can only be applied to particulars (aka. one cures Socrates, not disease y).
      6. Wisdom, though, is in knowing why the thing is so, and not simply in knowing that it is.
      7. Hence, Wisdom is knowledge about certain principles and causes.
   2. Characteristics of ‘wisdom’ (philosophy).
      1. Generally wise people: can know many things (although not necessarily in detail), can know hard things to know, can teach well, etc.
      2. Things far from the senses are hardest for men to know. Knowing these universals is a good indicator of wisdom.
      3. The most worthy of knowing among these are the first principles and causes. This is philosophy.
      4. There is no doubt straightaway that this is not “a science of production”, but rather a slow, arduous process of uncovering.
      5. There may also be some concern that philosophy’s objectives are either beyond human means or that their achievement would make God jealous.
         1. Not so: “God is thought to be among the causes of all things and to be a first principle…”
         2. Not so: “such a science either God alone can have, or God above all the others.”
   3. The successive recognition by early philosophers of the material, efficient, and final causes.
      1. Causes are spoken of in four senses:
         1. The essence/substance
         2. Matter or substratum
         3. The source of the change
         4. The purpose and the good
      2. The first philosophers identified material constituting the essential part of all things (c.i.ii above) as causal: The essence of Socrates constitutes Socrates whether he is being beautiful, or musical, or not.
         1. Ancient philosophers are generally materialists (aka. one or some combination of the four elements): Yet they don’t agree on the number or nature of these principles.
      3. For those among the ancients who abide multiple causes, we have things like fire as having independent essences (c.i.i above).
      4. But /why/ do these materials form things? And how do elements cause things like beauty? Anaxagoras talked of a /reason/ throughout nature (c.i.iii?).
   4. Inadequacy of the treatment of these causes.
      1. As an exemplar for someone who had an idea, but didn’t carry it out systematically, Aristotle poses Empedocles as the first to mention the bad and the good as principles (c.i.iv?). He was also the first to pose four material elements (though he treaded them as two: fire and its opposites).
      2. But, generally (and there are some specifics here), their treatment of the causes was quite inadequate.
   5. The Pythagorean and Eleatic schools; the former recognizes vaguely the formal cause.
      1. The Pythagoreans were the first to take up mathematics; they thought that all things (justice, soul, reason, etc) were expressible numerically. Numbers were their first principle.
         1. This gives way to a principle where even and odd are two causes, and from one springs all numbers. This in turn gives way to binary cognates: even/odd, male/female, one/many, left/right, good/bad.
         2. From this we can learn that the contraries are the principles of things.
         3. Notably (later, 987:13) unique to Pythagoreans, also, is the thought that finitude and infinity are not attributes of other things, but are themselves the substance of the things of which they are predicated.
      2. In particular, what’s germane to Aristotle is Parmenides’ conception of the One:
         1. Seeing as being is everything that exists and nothing that doesn’t, it is one.
         2. But our senses show us many things.
         3. Parmenides then gives us a two-cause/principle system: hot/cold qua existent/nonexistent.
   6. The Platonic philosophy; it uses only the material and formal causes.
      1. Socrates was busying himself about ethical matters, but in seeking the universal in these, fixed his thought for the first time on definitions.
      2. Since sensible things are always changing, any common definition could not be of them, and must rather be of an Idea. Sensible things are “named after these” in virtue of their participation in them.
         1. Note: Objects of mathematics apparently fit somewhere between sensible things and Forms, since they are eternal and also many.
         2. The participation relationship as such, provides the possibility of a unique /separation/ between the one and the many.
         3. Yet, what /happens/ appears to be contrary to this, since (i.e.) a man who makes tables applies the form, and though he is one, makes many tables. (What is the argument here?)
      3. So Plato recognized two types of causes:
         1. Essential: The Forms are the essences of things, and the One is the essence of the Forms
         2. Material
   7. The relation of the various systems to the four causes.
      1. Almost everyone gets the matter causes: be it fire and water, the infinite, atoms, the great and the small.
      2. Some others have mentioned the source of movement, e.g. friendship and strife, or reason, or love.
      3. No one has expressed the essence (i.e. substantial reality) distinctly. Plato hints at it with the Forms.
      4. The good as a cause is both said and unsaid in the philosophers of movement’s causes. For those who say that the One or the existent is the good, and that it is the cause of substance, but not that is for the sake of this. It is not then a cause qua good, but only incidentally.
   8. Criticism of pre-Platonic philosophers.
      1. One cause (ie. fire or water or air) is not a tenable position, because it gives no account of movement, or essence, etc. Similarly, multiple material elements.
      2. Anaxagoras has an interestingly modern position, but is still part of a camp that deals only with the sensible, and thus, cannot offer us a compellingly complete account of ontology.
      3. The Pythagoreans, who now deal with things visible and invisible (including numbers), still only deal with the physical world, implying that they actually agree with the physical philosophers that the real is constituted by only perceptible, sensible things.
   9. Criticism of the doctrine of ideas.
      1. The Forms are nefariously difficult to prove.
         1. There’s no convincing way to prove that they exist in the first place.
         2. Further, of the more accurate arguments, some lead to Ideas of relations, of which we may say there is no independent class, and other introduce the ‘third man’ (infinite regress of forms: F1:[a,b,c]->F2[F1,a,b,c]->…)
         3. How could the substance and that of which it is the substance exist apart?
      2. The Forms are not even that beneficial if they exist
         1. The doctrine of the Forms seems to necessitate as many Forms as there are things in the world. Apparently, this will also require Forms for the negations of things.
         2. Given (j.i) and (j.ii.i) it seems entirely unclear what exactly the Forms are contributing to either ontology or epistemology.
      3. A second thread, a participation relation tells us nothing about causation.
         1. How do sensible things come into existence given the existence of the Forms?
         2. Numbers cannot be Forms because Platonists speak of the One has homogeneous.
         3. How would a theory of Forms account for (e.g.) points on a line? [What’s the argument here?]
      4. The overview
         1. There’s no convincing account of the causes of movement from a theory of Forms.
         2. The proofs of oneness show not the oneness of all things, but the existence of a One in itself, which requires us to grant a lot of assumptions.
         3. It’s unclear how things combine to allow things like points, lines, and planes from numbers: These aren’t Forms, nor intermediates, nor perishable things. They seem to be a fourth class.
         4. How could we /learn/ the Forms of all things (contra Socrates’ recollection model)? How can we know “straightness” outside of straight things?
         5. Finally how can we comprehend sense-primitives with Formal concepts? (He doesn’t say this, but it’s Kant’s left-right intuition from the Prolegomena.)
   10. The history of philosophy reveals no causes other than the four.

2. BOOK II/LITTLE ALPHA

   1. General considerations about the study of philosophy.
      1. Philosophy is the attempt to attain knowledge of truth. The (eternal) truth which causes all other truths is the sublime object of philosophy.
   2. There cannot be an infinite series, an infinite variety of kinds, of causes.
      1. There is a first principle, and the causes of things are neither (b.i.i) an infinite series nor (b.i.ii) infinitely varied in kind.
         1. Cause itself necessitates that the series of causes be bounded. If (a) every (temporal) events is caused, and (b) there is no beginning of this series, then (c) every event is an intermediate event (requiring a causal agent that precedes it), and therefore (d) nothing causes anything else. Better:
            1. A contingent being exists (a contingent being is such that if it exists, it can not-exist)
            2. This contingent being has a cause or explanation of its existence.
            3. The cause or explanation of its existence is something other than the contingent being itself.
            4. What causes or explains the existence of this contingent being must either be solely other contingent beings or include a non-contingent (necessary) being.
            5. Contingent beings alone cannot cause or explain the existence of a contingent being.
            6. Therefore, what causes or explains the existence of this contingent being must include a non-contingent (necessary) being.
            7. Therefore, a necessary being (a being which, if it exists, cannot not exist) exists.
         2. If the kinds of causes are infinite, then knowledge (this seems to mean, “complete knowledge”) is impossible, because we cannot account for/abstract from infinite types causes in finite time.
   3. Different methods are appropriate to different studies.
      1. Getting knowledge (ontology) and getting the way of attaining knowledge (epistemology) are two different things, and require different modes of discourse.

3. BOOK III/BETA

   1. Sketch of the main problems of philosophy.
   2. Fuller statement of the problems: -
      1. Can one science treat of all the four causes?
      2. Are the primary axioms treated of by the science of substance, and if not, by what science?
      3. Can one science treat of all substances?
      4. Does the science of substance treat also of its attributes?
      5. Are there any non-sensible substances, and if so, of how many kinds?
      6. Are the genera, or the constituent parts, of things their first principles?
      7. If the genera, is it the highest genera or the lowest?
      8. Is there anything apart from individual things?
      9. Is each of the first principles one in kind, or in number?
      10. Are the principles of perishable and of imperishable things the same?
      11. Are being and unity substances or attributes?
      12. Are the objects of mathematics substances?
      13. Do Ideas exist, as well as sensible things and the objects of mathematics?
      14. Do the first principles exist potentially or actually?
      15. Are the first principles universal or individual?

4. BOOK IV/LAMBDA

   1. Our object is the study of being as such.
      1. In order to grasp first causes/principles, we need to study being as being. We arrive at this conclusion because it must be something about being as such that is /necessary/ to the existence of things.
   2. We must therefore study primary being (viz. substance), unity and plurality, and the derivative contraries, and the attributes of being and of substance.
      1. All things that are said to be refer to a single “thing”, namely, substance.
         1. “Substance” is the stuff of being, it seems, because things are said to be insofar as they are related to (are, or are qualities of, or are negations of, etc.) substance.
         2. Hence, substance is the subject of philosophy.
      2. Now, there are as many parts of philosophy as there are kinds of substance. What we are detailing here is “first philosophy” (here, ontology).
         1. Being and unity have a strict causal relationship (”one being” parses out to the same content as “being”). This means that the study of unity is part of the study of being, and hence falls under first philosophy’s domain. (Entails sameness, etc.)
         2. Likewise, as difference is simply the negation or privation of unity, this too must fall under the domain of our first science. Which entails of course unlikeness, otherness, contrariety, etc.
         3. Also, the history of philosophy tells us that all things are either contraries or composed thereof (hot/cold, love/strife, limited/unlimited), and hence in this way too we can see that first philosophy entails a study of being as sameness and otherness.
         4. So our first philosophy will examine being qua being, and also the attributes that belong to it qua being: prior/posterior, genus/species, whole/part, etc.
   3. We must study also the primary axioms, and especially the law of contradiction.
      1. Truths that hold good for everything there is (axioms) doubtless also belong to the domain of first philosophy. The reason is that what unites these axioms is being itself, so they are axioms that hold good for all things qua being.
      2. And here Aristotle introduces, as the fundamental axiom, the law of non-contradiction.
         1. Remember, this is a term logic: “the same attribute cannot at the same time belong and not belong to the *same subject* and in the same respect.” (My emphasis: Not subject/predicate-combo [proposition]).
   4. Fatal difficulties involved in the denial of this law.
      1. This law is so solid that no educated person should ever demand its demonstration.
      2. We can however demonstrate it negatively:
         1. Reasoning is possible because words at least one meaning. (E.g. Men are ‘two-footed animals’.)
            1. If they had several, we could create new words for each of the meanings.
            2. If they had infinite meanings, reason would be impossible. Likewise if they had none.
         2. So, if a name has one and only one meaning. This entails that “being a man” cannot mean “not being a man”.
         3. Any confusion of the signifier/signified relationship is just that: confusion. It doesn’t point to the possibility that words have multiple meanings.
      3. Given that, we understand that non-contradiction is necessary. (E.g. a man can not both be and not be a two-footed animal.)
      4. Further, this incontradictable “manness” is the very substance/essence of what it is to be a man.
         1. So, attributes are not essential (e.g. against the view that not-manness could be an attribute of a man, I suppose) because this would entail infinite predication:
            1. An accident is of a subject, not another accident: The white is not musical, the man is white and musical.
            2. But, in “Socrates is musical” both terms are “accidental to something else.” So, two senses:
               1. White is accidental to Socrates, and Socrates the white has not yet another accident.
               2. White cannot have musicality.
            3. On overview: Sense (d.iv.i.i) reduces to sense, and (d.iv.i.ii), in this an infinite number of accidents combined together is impossible; there must be substance somewhere.
         2. The end result of this is you’re just talking about infinite indeterminate subjects, all of which must be predicated by the affirmation and negation of every attribute.
            1. We say x is y.
            2. We say z is b.
            3. We say x is not z qua b. This entails x is not b.
            4. Without N/c we say x is b.
            5. This entails in turn that x is in fact z, and every other subject, etc.
      5. Two arguments in conclusion
         1. Nicely summed up: “If it is true that a thing is a man and a not-man, evidently also it will be neither a man nor a not-man.”
         2. Either N/c is true of everything, or else of nothing. If it were true of something, then the possible predicates of that would be subject to it, and so on…
      6. Two more tempered arguments
         1. Practically, we don’t see people walking off cliffs all the time, so they must be capable of some kind of judgements, and hence telling the difference between good and not-good.
         2. Additionally, there seems to be “more truth” in thinking that 4 is 5 than there is in thinking that it’s 1000. In other words, he admits of some “degree” of attributes that’s possible in things (terms). [Again, this would appear to be contra propositional logic.]
   5. The connexion of such denial with Protagoras’ doctrine of relativity; the doctrine refuted.
      1. Nonetheless, we see contradictions cropping up everywhere - aka. two men will have contradictory opinions on what is good. This can lead to a certain relativism, that all opinions are right!
      2. This is due first to a confusion about two senses of “be”: namely, something can potentially at the same time two contraries, but not actually.
      3. Secondly this confusion arises as entailed by a confusion about from whence truth comes. Namely, some think that truth arises from the sensual appearances. (Aka. they think that since things become, they are neither being nor non-being exactly, or rather both.)
         1. There’s an appeal here that things are changing only in quantity, not in quality.
            1. Note generally that the required product is to show that there’s something changeless.
         2. Not all appearances are true; people (e.g. doctors) and senses (e.g. sight) have different degrees of authority on various objects of appearance. But the appearance of (e.g.) sweetness as such will never be changed (sweetness will always be sweet).
   6. Further refutation of Protagoras.
      1. If not all things are relative, and some are self-existent (e.g. the objects of sensation), not everything that appears will be true.
      2. If a thing is one, this entails that it is in relation to either one or a definite number of things; that “that which thinks” is in relation to infinite things is impossible. (This is an argument against solipsism.)
   7. The law of excluded middle defended.
      1. There cannot be an intermediate between contradictories. If there was, saying “it is” or “it isn’t” is bankrupt of its content.
      2. Another regress: If there is a term B which is neither A nor not-A, there will be a new term C which is neither B nor not-B.
      3. So, if (4.e.iii) then everything is true, and if (4.g.i) then everything is false.
   8. All judgements are not true, nor are all false; all things are not at rest, nor are all in motion.
      1. Any of this requires us to postulate the notion of “meaning”. Namely, that we know what it is for something to be true or false.
      2. Hence, given (4.c.ii) and (4.h.i), some judgements must be true and some must be false.
      3. This dictates also that there are both motion and rest.
         1. Admitting that there is some truth in (4.e.i), and that some propositions can be true and false at different times, there must be movement.
         2. And, if everything is constantly in motion, nothing can be true. We can be assured that the former clause of the previous sentence is false by appeal to (2.b.i) [among other things].

5. BOOK V/DELTA: PHILOSOPHICAL LEXICON

   1. Beginning
      1. The ways in which it is spoken of.
         1. The first point or the best point at which to start.
         2. The immanent (a house’s foundation) or non-immanent (parents to child) start of something.
         3. The mover/changer of something.
         4. The condition of knowability of something.
      2. What these ways have in common.
         1. They are the first point from which a thing comes to be (known).
   2. Cause
      1. The ways in which it is spoken of.
         1. The material stuff (bronze:statue) or the pattern (or essence) of something.
         2. Both the beginning (5.a.ii) and the end of something (one walks for health).
      2. What follows
         1. There are several causes of one thing.
         2. Causes and effects usually play both roles reciprocally (excercise is a cause of good health, which causes exercise).
         3. Contraries are usually causes for contrary effects (the presence and privation of the steersman:safety and shipwreck).
      3. Four senses of causes: Material substrata, essences, sources of change, ends.
      4. Genus and accident:
         1. Causes as either the individual, or the genus, or as the accidental, or as the genus that includes the accidental.
         2. Genus-causes are also inherited from parent objects (the sculpture is caused by Ron, and man, and animal, and living thing, etc.).
         3. Accidental causes are “accidentally” inherited from individuals (the sculpture is caused by Ron, who is musical, so the musical caused the statue).
      5. What these ways have in common.
         1. They may all be taken as acting or having a capacity, although this works in different ways.
   3. Element
      1. The ways in which it is spoken of.
         1. The (indivisible) primary component(s) immanent in a thing.
         2. Indivisible primary things that are useful for many purposes (aka. atoms) - cf. /elemental/.
      2. What these ways have in common.
         1. The element of each thing is the first component immanent in each.
   4. Nature
      1. The ways in which it is spoken of.
         1. The genesis, the cause of genesis (seed), and the source of the primary movement of growing things (mother:baby).
         2. (a) The primary material out of which an object is made (wood:bed), or (b) the essence of a natural object.
         3. By extension of (5.d.i.ii.b), every essence in general.
      2. What these ways have in common.
         1. The essence of things which have in themselves a source of movement.
   5. Necessary
      1. The ways in which it is spoken of.
         1. (a) That without which a thing cannot live (breathing, food) and (b) that without which good cannot come (medicine).
         2. The compulsory and compulsion (doing one’s taxes).
      2. What these ways have in common.
         1. That which cannot be otherwise than it is.
   6. One, Many
      1. The ways in which it is spoken of.
         1. One by accident (Coriscus is musical and just; musical:just)
         2. One by its own nature (continuous things: straight lines are more “one” than bent lines).
         3. One by virtue of homogenous substratum.
         4. One by virtue of participation in a genus ([horse, man, dog] qua “animal”).
         5. One by indistinguishability (Leibniz’s identity of indiscernables).
         6. Generally, one by continuity, form, or definition. (qua form: Circle is more “one” than straight line.)
         7. Beginning in number.
      2. What these ways have in common.
         1. Oneness by (a) number by essence, (b) species by definition, (c) genus by shared figures of predication, (d) analogy by relation to a third or fourth thing.
      3. “Many” will be the opposite of these.
   7. Being
      1. The ways in which it is spoken of.
         1. Accidentally. By unessential attributes: musical, white.
         1. Synthetic predication: Both belong to the same thing, and this is.
         2. The subject of which the attribute is predicated is.
         3. The attribute which is predicated on a subject is.
      2. Essentially: By their own nature.
         1. By the categories (inc. analytic/tautological predication).
      3. A statment that is true. (”Socrates is musical.”)
      4. That which is potentially and actually (the half line is in the line, we still call the first corn sprouts corn).
   8. Substance
      1. The ways in which it is spoken of.
         1. The simple bodies (earth, fire, water, etc); everything else is predicated on them.
         2. That which, being a subject’s unpredicated attribute (e.g. an animal’s soul) and its cause.
         3. The enabling condition of an individual, the loss of which would entail the loss of the individual (e.g. plane to line).
         4. The essence or definition of a thing.
      2. What these ways have in common.
         1. The ultimate substratum.
         2. The separable nature of the shape or form of each thing.
   9. The same, Other, Diffferent, Like, Unlike
      1. The ways in which it is spoken of.
         1. The same as accidental (coincidence of attributes in an individual). Aka. the musical man is the same as the musical.
         2. The same by their nature: Sameness as a unity of treating many as one (these Warhols) or one as many (my “self” qua mind/body dualism).
         3. Different: (a) things which though other are the same in some respect, (b) those whose genus is other, to contraries, etc.
         4. “Like” things have the same attributes in every respect, or many same attributes, those whose quality is one, sharing in the most salient attribute(s).
   10. Opposite, Contrary, Other in species, The same in species
       1. The ways in which it is spoken of.
          1. Contradictories and contraries, relative terms, qua privation and possession.
          2. Contrary:
             1. Attributes differening in genus that can’t belong at the same time to the same subject
             2. The most different of things in the same genus
             3. The most different of attributes/things in the same subject/faculty
             4. The most different absolutely or in genus or in species.
             5. Things which being in the same genus have a difference (”man and horse” via animals).
   11. Prior, Posterior
       1. The ways in which it is spoken of.
          1. Empirically
             1. Prior: Some things because they are nearer to some (absolute, natural or referential) beginning.
             2. Posterior, because they are farther.
             3. Beginnings can be spatial, temporal, qua movement (boy:man) or power, or in arrangement.
          2. Qua Knowledge: Prior in definition (e.g. universals).
          3. The attributes of prior things are prior: Straightness (attribute of line) is prior to smoothness (attribute of plane).
          4. Metaphysically: E.g. for Plato, this Forms would have been prior to concrete particulars.
       2. What these ways have in common.
          1. Generally, prior things can exist without posterior things but not vice versa. (And again, in some ways, the same things may alternately occupy prior and posterior positions in relation to each other.)
   12. Potency, Capable, Incapacity, Possible, Impossible
       1. The ways in which it is spoken of.
          1. The (a) intrinsic or extrinsic source of movement or change, (b) the condition of possibility for (a) - its capability, (c) the capability of performing /well/ [white men can’t jump], (d) the states in virtue of which something is unchangeable.
          2. Capacity is the intrinsic ability of something for (a)-(d) above, and incapacity is its opposite.
          3. The possible is that which is not of necessity false, and the impossible is that which is (of necessity false).
   13. Quantum
       1. The ways in which it is spoken of.
          1. That which is divisible into two or more constituent parts, each of which is “one” and “this”.
          2. This can be either a plurality if it numerable, or a magnitude if it is measurable.
             1. Plurality: divisible into non-continuous parts.
             2. Magnitude: divisible into continuous parts.
          3. This can, like most of these things, be essential or accidental (that to which musicality and whiteness belong is a quantum).
   14. Quality
       1. The ways in which it is spoken of.
          1. The differentia of essence (e.g. man is an animal of a certain quality).
          2. In mathematics: E.g. factors of a number. (”6″ is the quality of six, where “2×3″ and “3+3″ are some of its quantitative attributes.
          3. All the modifications of substances that move (E.g. hot or cold, white or black) which, when changed, alter the substance.
       2. What these ways have in common.
          1. Properly: The differentia of the essence.
          2. Vulgarly: The modifications of things that move.
   15. Relative
       1. The ways in which it is spoken of.
          1. Reciprocal relations to a common term. E.g. As 1/2:2 or 1/3:3 qua 1.
             1. This can be definite (qua above) or indefinite (e.g. “many times n”).
             2. All these relations refer to unity/likeness/sameness.
          2. Active to passive. E.g. As that which can heat to that which can be heated.
          3. “…as the measurable to the measure, and the knowable to knowledge, and the perceptible to perception.
       2. What these ways have in common.
          1. (5.p.i) & (5.p.ii): Something’s very essence (thing that heats, half of one) includes a reference to something else.
          2. (5.p.iii): Something else’s essence (an inch) includes a reference to it (measurability, knowability).
       3. Finally, this all works by extension: Medicine is relative because its genus, science, is.
          1. And this extension can be accidental (white is relative if the same thing happents to be double [a relative term] relative term) or essential (equality).
   16. Complete
       1. The ways in which it is spoken of.
          1. That outside of which it is impossible to find any of its parts.
          2. That which cannot be improved upon.
          3. Things which have attained their end.
   17. Limit
       1. The ways in which it is spoken of.
          1. The last point of each thing; the first point beyond which it is not possible to find any part, and the first point within which every part is.
          2. The form of a special magnitude (e.g. in a thing that has magnitude).
          3. The end, substance, or essence of each thing (the limit of an object is equivalent to the limit of its knowability).
   18. That in virtue of which, In virtue of itself
       1. “In virtue of which…”
          1. The form or substance of each thing (a man is good in virtue of the good itself).
          2. The proximate subject in which it is the nature of an attribute to be found (color in a surface).
          3. For what end? (”In virtue of what has he come?”)
          4. What is the cause? (”In virtue of what has he wrongly inferred…”)
          5. In reference to position (e.g. ‘at which he stands’ or ‘along which he walks’)
       2. “In virtue of itself”
          1. The essence of each thing (”Callias is in virtue of himself Callias”).
          2. Whatever is present in the thing (”Callias is in virtue of himself an animal”).
          3. Whatever attribute a thing receives in itself directly or in one of its part (”The surface is white in virtue of itself”).
          4. That which has no cause other than itself (”Man is man in virtue of himself”).
          5. Whatever attributes belong to a thing alone.
   19. Disposition
       1. The ways in which it is spoken of.
          1. The arrangement of that which has parts, in respect of either place or potency or kind.
   20. Having or habit
       1. The ways in which it is spoken of.
          1. “Having”: The relationship between the haver and the had. Evidently, we cannot have this having, in virtue of an infinite regress.
          2. A disposition of one who is (well or ill) disposed (e.g. “a health habit”).
          3. A portion of such disposition.
   21. Affection
       1. The ways in which it is spoken of.
          1. A quality in respect of which a thing can be altered (white, sweet, etc.)
          2. The one of these alterations actually accomplished.
          3. Especially, injurious alterations actually accomplished.
          4. And hence, misfortunes in general.
   22. Privation
       1. The ways in which it is spoken of.
          1. Something none of the attributes a thing might naturally have (even if the thing would not naturally have it). “The plant is deprived of eyes.”
          2. A special case of (5.y.i) where the thing would naturally have it (a blind man vs. a mole).
          3. The violent taking away of something.
   23. Have or hold, Be in
       1. Have or hold, to be in something
          1. To treat a thing according to one’s own nature (”fever has him”).
          2. When something is present in something receptive of it (”the bronze has the form of a statue”, “he has a disease”).
          3. The container of something (”the casks hold the wine”).
          4. Something that hinders something else from moving or acting (”the pillars hold up the roof”).
   24. From
       1. The ways in which it is spoken of.
          1. As from matter: (a) from the higest genus (all meltable things come from water), (b) a statue comes from bronze.
          2. As from the first moving principle (fight from abusive language).
          3. As a part from a whole (a verse from the Illiad), or the whole from a part (words from letters).
          4. Something comes from something insofar as it comes from a part of it (”Plants come from the earth”).
          5. Following in time (night comes from day).
   25. Part
       1. The ways in which it is spoken of.
          1. That into which a quantum can in any way be divided.
          2. Of the parts in (5.bb.i.i) only those which measure a whole.
          3. The elements into which a kind might be divided apart besides quantity (species are parts of genus).
          4. The elements into which a whole is divided (as “bronze cube” and “statue” are to “bronze”).
          5. The elements in a definition (the genus now as part of the species).
   26. Whole, Total, All
       1. The ways in which it is spoken of.
          1. That from which is absent none of its natural parts.
          2. That which contains things and these things form a unity:
             1. The whole of living things includes [man, horse, god].
             2. Something is whole by nature (a tree, I suppose).
          3. Quanta to which position makes a difference are wholes (say, a person), those to which it does not are totals (water). See (dd) below.
   27. Mutilated
       1. Totals (qua [5.cc.i.iii] above) cannot be mutilated. You can’t mutilate water, or six, or fire.
       2. Wholes, on the other hand, can. You can chop off a man’s arm, and he ceases to be “whole”.
   28. Race or genus, Other in genus
       1. The ways in which it is spoken of.
          1. A continuous generation of formally similar things (the race of men).
          2. The thing which first brought things into existence (Hellenes come from Hellen, they are her race).
          3. The extensional concept (e.g. ‘plane’ to all planar figures).
          4. The substratum of the qualities; the part of the definition whose differentiae gives the qualities of a participating particular.
   29. False
       1. A false thing:
          1. Cannot be put together (is non-existent).
             1. Always: “the diagonal of a square is = its side”
             2. Sometimes: “I am done taking notes on Aristotle”
          2. Representations (a sketch, a dream) that are not the things the appearance of which they produce in us.
       2. A false account:
          1. “A false account is not an account of anything, except in a qualified sense.”
          2. A true account attains to the essence or accidental qualities of a thing. A false account is the opposite of this.
       3. A false man:
          1. A person who is fond of false accounts (5.ff.ii) for their own sake.
   30. Accident
       1. The ways in which it is spoken of.
          1. That which can be asserted of something (S) but is neither necessary nor usually part of S.
             1. Accidents thus have indefinite or chance causes.
          2. All that attaches to each thing in virtue of itself but is not its essence.
             1. E.g. that a triangles’ add up to 180 degrees. (Spurious, I know, but that’s what he says.)
             2. Hence this type of accident may be eternal, but no accident of the other sort can ever be.

6. BOOK VI/EPSILON

   1. Distinction of ‘theology’, the science of being as such, from the other theoretical sciences, mathematics and physics.
      1. Most sciences (wissenshaft) “bracket” the question of being in total, and deal with on particular aspect of being.
         1. The natural/physical sciences are “theoretical” sciences, and focused on one particular sort of being. Namely, the concrete stuff of nature/the world, or stuff as it is embedded in concrete particulars.
         2. Mathematics is also theoretical, but whence its objects are to be categorized (qua existence/being) is still unclear.
            1. That said, it is clear that some mathematical theorems consider things eternal/unmoveable/etc., but A wonders if that shouldn’t more properly be the domain of another science.
            2. Some part of maths also deals with things that are eternal but which are nonetheless embedded in concrete particulars (he appeals to the movements of the planets).
         3. The third theoretical philosophy is theology. This will be the most important of the three, assuming that there is some kind of immovable substance. If there is, “theology” will be first philosophy.
   2. Four senses for ‘being’. Of these (i) accidental being is the object of no science.
      1. Recapitulating, Being is (a) accidental, (b) true (’non-being’ being the false), (c) figures of predication, (d) potential or actual existence.
      2. Accidental being (6.b.i.a, 5.g.i.i) cannot be treated scientifically.
         1. Accidents are those things which are not always or for the most part so.
         2. Science is either of that which is always or is for the most part. How else would it be learnable/teachable?
   3. The nature and origin of accident.
      1. Accidental things exist, for otherwise everything that is will be necessary (aka. it would be necessary that Socrates is musical). I think this is basically done by the law of the excluded middle.
      2. I think that what happens here is that he says that in one sense (contra 6.c.i) everything will happen of necessity, because of the causal deterministic nature of the world. So accidents have first causes too, although determining these causes is a sticky wicket.
   4. (ii) Being as truth is not primary being.
      1. Being as truth and falsity (6.b.i.b, 5.g.i.iii) is not the subject of philosophy either. Truth and falsity are determined in thought, and thus being in this sense is a distinctly second-stage type of being.
      2. For the record, though these notes stop here, we are now prepared to consider “being qua being”, obviously either in terms of (6.b.i.c) or (6.b.i.d).

Overview

In the Timaeus, Plato presents an elaborately wrought account of the formation of the universe. Plato is deeply impressed with the order and beauty he observes in the universe, and his project in the dialogue is to explain that order and beauty. The universe, he proposes, is the product of rational, purposive, and beneficent agency.

As Plato tells it, the beautiful orderliness of the universe is not only the manifestation of Intellect; it is also the model for rational souls to understand and to emulate. Such understanding and emulation restores those souls to their original state of excellence, a state that was lost in their embodiment.

Background

Despite some critical bickering, it is generally accepted that the Timaeus was written in the “late” period.

1. THE SETUP

   1. SOCRATES first recapitulates the main points he made the previous day (similar to those in “The Republic”, but unrecorded) to all present’s satisfaction. Apparently, today, Socrates was to listen, and CRITIAS and TIMAEUS were to tell.
   2. Critias suggests that he tell a lost story - and he swears it is factual - of the old Athenians. Socrates’ (unrecorded) account of perfect governance had brought it to his mind. In order for this story to be told, however, Critias will require a fairly long wind-up from Timaeus, which constitutes the entirety of this dialogue.
      1. Timaeus (an astronomer) will begin with the generation of the world and go up to the creation of men (inclusive, it turns out). Critias will take it from there, which he does in the next (eponymous) dialogue.
   3. In his prefatory remarks Timaeus describes the account he is about to give as a “likely account” (eikôs logos). This apology is clearly meant to lower our expectations: the account is no more than likely. It will take place it three substantive parts.
      1. The first two seem to actually be two separate accounts of the causes of the way the universe is: the divine and necessary causes, respectively.
      2. Finally, we will get an account of how this all comes to constitute the human.

2. THE ACHIEVEMENTS OF THE INTELLECT, PART 1: THE TELEOLOGICAL UNIVERSE

   1. Timaeus begins with a (now familiar) account of “what is and never becomes” (that which is apprehended by reason - the Forms, or the pattern) and vice versa (apprehended by opinion).
   2. Overview: The achievements here are those of the creation of the world, and “the intellect” here is God. Here is an overview of the argument for God:
      1. Some things always are, without ever becoming (27d6).
      2. Some things become, without ever being (27d6-28a1).
      3. If and only if a thing always is, then it is grasped by understanding, involving a rational account (28a1-2).
      4. If and only if a thing becomes, then it is grasped by opinion, involving unreasoning sense perception (28a2-3).[16]
      5. The universe is a thing that has become (28b7; from 5a-c, and 4).
         1. The universe is visible, tangible and possesses a body (28b7-8).
         2. If a thing is visible, tangible and possesses a body, then it is perceptible (28b8).
         3. If a thing is perceptible, then it has become (28c1-2; also entailed by 4).
      6. Anything that becomes is caused to become by something (28a4-6, c2-3).
      7. The universe has been caused to become by something (from 5 and 6).
      8. The cause of the universe is a Craftsman, who fashioned the universe after a model (28a6 ff., c3 ff.; apparently from 7, but see below).
      9. The model of the universe is something that always is (29a4-5; from 9a-9e).
         1. Either the model of the universe is something that always is or something that has become (28a5-29a2, also implied at 28a6-b2).
         2. If the universe is beautiful and the Craftsman is good, then the model of the universe is something that always is (29a2-3).
         3. If the universe is not beautiful or the Craftsman is not good, then the model of the universe is something that has become (29a3-5).
         4. The universe is supremely beautiful (29a5).
         5. The Craftsman is supremely good (29a6).
      10. The universe is a work of craft, fashioned after an eternal model (29a6-b1; from 8 and 9).
   3. Given familiar Platonic doctrines and assumptions, the argument up to the intermediate conclusion that the universe has a cause of its becoming (7) presents no particular difficulties. But 7 by itself gives only partial support to 8. Here it helps to anticipate 9d as a fundamental premise in Timaeus’ reasoning; it is not just the generation of any world, but that of a supremely beautiful one that Timaeus’ reasoning here - and in fact throughout the discourse - attempts to explain. That a world as beautiful as ours might be the effect of an unintelligent cause is a possibility that does not so much as cross Plato’s mind.
   4. The one-world entailment:
      1. If everything must have a cause, and hence the world was created (vi-iix) and
      2. since the artificer is good, it was created from the model of the eternal [note that this is a criterion for the goodness of God, and the alternative is blasphemy] (ix-x), then:
      3. Since it is created on the model of the beautiful (form), which is whole, the world is whole. Hence, there cannot be many worlds, but only one: ours.

3. THE ACHIEVEMENTS OF THE INTELLECT, PART 2: DIVINE PHYSICS

   1. Once the conclusion that the universe is teleologically structured is settled, the explanatory methodology of the discourse changes accordingly. The question can now be: Given that the world as a whole is the best possible one within the constraints of becoming and of Necessity, what sorts of features should we expect the world to have?
   2. Divine Physics: The world is created of several elements:
      1. Fire: Since visibility is a necessity for a world.
      2. Earth: Since tangibility is a necessity for a world.
      3. Air & Water: Because we need two more means to get three dimensions, which we need because the model of the world is three-dimensional.
      4. These four elements comprise a universe that is fashioned as a globe. A globe is the perfect form, as it is entirely self-sufficient.
      5. Finally, the universe gets a soul.
   3. The actual material creation of the universe was created by god using a pretty standard series of arithmetic means and exponential series of twos and threes [1,2,4,8]&[1,3,9,27].
      1. Once the matter of the universe is created, god sets it into motion, thus creating time (day and night, months, years).
      2. God then creates gods, who he charges to create air-things, water-things, and land-things.
      3. The gods, thus charged, fashioned bodies, and (per the teachings of meta-God) laid souls into the bodies. This embodiment confuses the souls (another familiar Platonic theme), anodyne to which we have sight, which, when combined with souls, allows philosophy.

4. AN ACCOUNT OF THE EFFECTS OF NECESSITY

   1. Overview: In addition to the divinely motivated creation of the universe, there seem to be some necessary causes. These are part and parcel to a (heretofore unmentioned) third ingredient of existence.
      1. Recall that the first two are the pattern on which it is fashioned and the things themselves which imitate the pattern. This is precisely the being/becoming distinction.
      2. In addition to these two, we also have “the receptacle”: namely, space itself, with whatever pre-deistically/rationally-ordered properties it has.
      3. Thus the thing that appears as fire here and now is not fire in its own right: its fieriness is only a temporary characterization of it. What, then, is that thing in its own right? In a difficult and controversial passage Timaeus proposes a solution: In its own right it is (part of) a totally characterless subject that temporarily in its various parts gets characterized in various ways. This is the receptacle - an enduring substratum, neutral in itself but temporarily taking on the various characterizations. The observed particulars just are parts of that receptacle so characterized.
      4. Think of the receptacle as filled space. As space, its role is to provide both three-dimensional extension and a specific location for any observable particular to be “in” at a given time: for any particular to be, it must be occupy some spatial location, though not necessarily the same one throughout. On the other hand, as the filling of that space, it serves as the neutral underlying substratum from which a particular, once characterized in some way, is constituted.
      5. An observable particular, then, is a bit of extended, localizable stuff that may be variously characterized at various times and in various places. It appears that the receptacle is intended to serve both as the matter from which observable particulars are constituted and as the spatial field or medium in which they subsist.
   2. The complete metaphysical position of the Timaeus is summed up here as (i) the eternal and unchanging forms, the “model,” or “father”; (ii) the copies of the model or “offspring” of the father and the mother (on our account, the observable particulars); and (iii) the receptacle, or “mother.”
   3. Now, the four elements (fire, earth, water, and air) are cyclical, one is always changing into the other, and so goes the world.
      1. There appears to be a question about whether these essences exist as such, or just structure existence. As soon as that is brought up, though, we are into describing the essences geometrically.
      2. I think the play here is that when God gives the world reason and measure, these substances are formalized (so to speak) into their correct geometries.
      3. On a side point, above we said that these elements are cyclically. But it is a misapprehension that they are cyclically generated. In fact, they all come from triangles.
   4. The geometries of the four substances:
      1. Fire: Tetrahedron (four triangular faces)
      2. Earth: Cube (six square faces)
      3. Water: Icosahedron (20 triangular faces)
      4. Air: Octahedron (eight triangular faces)
   5. If (a-c) constitute the discussion of matter, then what follows is the discussion of motion. This (like the above) ultimately is less interesting than what Plato is trying to do with all this (dated) speculation.
      1. Suffice it to say that the shapes infuse the interstices between each other and combine to form the media of all the senses: sight, touch, taste and hearing are discussed.
      2. In addition to filling the interstices, they can also break each other, for whatever that’s worth.

5. HOW INTELLECT AND NECESSITY COOPERATE TO PRODUCE THE CONSTITUTION OF HUMAN BEINGS: ETHICS

   1. This generally takes the form of how the elements combine to form the body (organs, bones, sinews, limbs, and so on) of the human person. Then the converse, from whence imbalances arise (diseases), and then on to what one should do to care for one’s soul.
   2. The stated thematic purpose of Timaeus’ discourse - sandwiched as it is between those of Socrates and Critias - is to provide an account of human nature (in the context of the nature of the universe as a whole) that, conjoined with Socrates’ previous account of education (à la Republic), will provide the basis for Critias’ forthcoming account of human virtue in action, as displayed by the deeds of the ancient Athenians.
      1. If we take this stated purpose seriously, we will expect the entire cosmological account to culminate in human psychology and ethics. And that is indeed what we find.
   3. In the passage that may fairly be taken as the climax of Timaeus’ discourse, human beings are urged to devote their utmost attention to the cultivation and preservation of the well being of their immortal, rational souls.
   4. The whole thing ends up somewhat anticlimactically with some fairly serious misogynist rhetoric: Women are presumed to have been created in the second generation of men - those who were cowards or led unrighteous lives were changed into women. Hence, perhaps, the conflation “to get fucked.”

A quick note: This ends our series of outlines of Platonic Dialogues. Next up: Aristotle.