Sorglose Nacht

Overview

1. The Two Systems

There are actually two sets of Categories articulated in the Categories. The first (2.b) is four-fold, and the second is ten-fold (4.a). It is notable that there is considerable debate about the subject matter of the second system of classification (aka. whether it is a classification of (1) words or of (2) objects in the world, or as classifying (3) linguistic predicates in so far as they are related to the world in semantically significant ways).

2. A Metaphysical Note about the Second System

That there are highest kinds (categories) can be motivated by noticing the fact that the ordinary objects of our experience fall into classes of increasing generality. Consider, for instance, a maple tree. It goes something like ‘maple trees’ -> ‘trees’ -> ‘plants’ -> ‘living things’ -> and so on. Now, quite naturally any good Aristotelian will tell you that this increase in generality or extension cannot go on ad infinitum. We seem to require, then, a highest kind. The obvious appeal here is to Being.

The class that contains all and only beings must be the class with the greatest possible extension. However, in the Metaphysics, however, Aristotle argues that being is not a genus. Why? According to Aristotle, every genus must be differentiated by some differentia that falls outside that genus. Hence, if being were a genus, it would have to be differentiated by a differentia that fell outside of it. In other words, being would have to be differentiated by some non-being, which, according to Aristotle, is a metaphysical absurdity. This can generalize to any proposal for a single highest kind.

Hence, he does not think that there is one single highest kind. Instead, he thinks that there are ten.

3. The Structure of the Categories

In the Pre-Predicamenta (1-4), Aristotle discusses a number of semantic relations (1,3), gives a division of beings into four kinds (2), and then presents his canonical list of ten categories (4). In the Predicamenta (5-9) Aristotle discusses in detail the categories of substance (5), quantity (6), relatives (7), and quality (8), and provides a cursory treatment of the other categories (9). And finally, in the Post-Predicamenta, he discusses a number of concepts relating to modes of opposition (10-11), priority and simultaneity (12-13), motion (14), and ends with a brief discussion of having (15).

Outline

1. Equivocations, univocations, and derivatives.
   1. Equivocations (homonyms) are things sharing a name but with different meanings. His example is a real man and a figure in a picture are called “animals”.
      1. Such words are applicable to various items in the world in virtue of the fact that those items all bear some type of relation to some one thing or type of thing.
      2. A second example of such a homonym is “healthy”: A regimen is healthy because it is productive of health; urine is healthy because it is indicative of health; and Socrates is healthy because he has health. In this case, a regimen, urine and Socrates are all called ‘healthy’ not because they stand under some one genus, namely healthy things, but instead because they all bear some relation to health.
   2. Univocations (synonyms) are things that mean the same thing and are applied to different things. His example is a man and an ox; both are “animals”. That is, they all stand under a genus; in this case, “animals”.
   3. Derivatives are things that derive their meanings from other things. His example is the way a courageous man derives his name (as such, “courageous man”) from the word “courage”.
2. Kinds of things qua predication
   1. Simple and composite expressions.
      1. Simple forms of speech are either a single subject or predicate: ox, man, wins, runs.
      2. Composite forms of speech are subject/predicate expressions: The ox runs. The man wins.
   2. Things (a) predicable of the subject, (b) present in a subject, (c) both predicable of, and present in, a subject, (d) neither predicable of, nor present in, a subject.
      1. Qua (2.b.a): ‘Man’ is predicable of the individual man, and is never present in a subject. Presence here means “contained in”.
      2. Qua (2.b.b): Think of a particular piece of grammatical knowledge. It is present (”contained”) in the mind, but is not predicable of minds (or anything?) in general. (Try also the particular whiteness of Socrates; even if some other white is qualitatively different that Socrates’, it is numerically distinct. This is what we mean by a nonsubstantial particular.)
      3. Qua (2.b.c): While knowledge in general is present in the human mind, it is predicable of grammar. Again, whiteness provides a somewhat more intuitive example. The universal whiteness is said-of many primary substances but is only accidental to them.
      4. Qua (2.b.d): These are individuals. An individual man or horse.
   3. Irritatingly, this set of distinctions rests on a circular definition (of what “present in” means) and a missing definition (”said of” or predication). Apparently, most scholars conclude that beings that are said-of others are universals, while those that are not said-of others are particulars. Beings that are present-in others are accidental, while those that are not present-in others are non-accidental. Now, non-accidental beings that are universals are most naturally described as essential, while non-accidental beings that are particulars are best described simply as non-accidental.
   4. Putting all that good work of interpretation together, we can gather that we have
      1. Essential universals (2.b.a)
      2. Accidental particulars (2.b.b)
      3. Accidental universals (2.b.c)
      4. Non-accidental particulars (2.b.d): Primary substances, individuals.
3. The Transitive property of predication and its effects
   1. That which is predicable of the predicate is predicable of the subject.
      1. ‘Man’ is predicated of an individual man. ‘Animal’ is predicated of ‘Man’. Thus, the individual man is ‘Animal’.
   2. The differentiae of species in one genus are not the same as those in another, unless one genus is included in the other.
      1. E.g. The genera ‘Animal’ has differentiae (internally-differentiating characteristics), e.g. ‘with feet’, ‘two-footed’, ‘winged’, ‘aquatic’.
      2. These differentiae do not arbitrarily apply to all genera, e.g. ‘Knowledge’.
      3. They may, however, apply, to subordinate genera, as the parent genus will be predicated of the child.
4. The eight categories of objects under thought.
   1. The (ten-fold) categories (substance, quantity, quality, relation, place, time, position, state, action, affection) are signified by simple expressions.
      1. E.g.: Substance - ‘man’, ‘the horse’
      2. E.g.: Quantity - ‘two feet long’
      3. E.g.: Quality - ‘white’, ‘grammatical’
      4. E.g.: Affection - ‘to be cauterized’. Etc.
   2. No one of these terms involves an affirmation. Positive and negative statements arise only by combination.
5. Substance
   1. Primary and secondary substance.
      1. Primary substance is that which is neither predicable of a subject nor present in a subject (2.b.iv), aka. an individual man, horse.
      2. Secondary substances are the species and genera into which primary substances fit; in the case of a man, the species ‘man’ and the genus ‘animal’ are both secondary substances.
      3. An interesting proposed secondary substance tree from the SEP:
         1. Immobile Substances - Unmoved Mover(s)
         2. Mobile Substances - Body
            1. Eternal Mobile Substances - Heavens
            2. Destructible Mobile Substances - Sublunary bodies
               1. Unensouled Destructible Mobile Substances - Elements
               2. Ensouled Destructible Mobile Substances - Living things
                  1. Incapable of Perception - Plants
                  2. Capable of Perception - Animals
                     1. Irrational - Non-Human Animals
                     2. Rational - Humans
   2. Difference in the relation subsisting between essential and accidental attributes and their subject.
      1. Essential: Predicating secondary substances of primary substances entails that the primary substance is predicated by both the name and the definition of the secondary substance. (Both “man” and “bipedal animal” - or whatever - are predicated of a man by the predication of the former).
      2. Accidental: Predicating accidental characteristics of substances of the substances themselves, however, does not entail that the substance contain the definition of its attribute. (E.g. you can say, “the man is white,” but that doesn’t mean that “the man is [the definition of whiteness]”).
      3. In overview, this model entails a twofold manner of predication, one is a definitional/essential predication-relation (used by species and genera) and the other is an accidental relation (e.g. “the man is white”).
   3. All that which is not primary substance is either an essential or an accidental attribute of primary substance.
      1. Everything except primary substances is predicable (in the sense of definition) of a primary substance, or is present in a primary substance (is an accidental attribute).
   4. Of secondary substances, species are more truly substance than genera.
      1. A more convincing account of a primary substance can be given via species than via genus.
      2. The same predication-relation that exists between primary substances and everything else also exists between species and genera. [ species:genus :: subject:predicate ]
   5. All species, which are not genera, are substance in the same degree, and all primary substances are substance in the same degree.
   6. Nothing except species and genera is secondary substance: These alone convey knowledge of primary substance.
   7. The relation of primary substance to secondary substance and to all other predicates is the same as that of secondary substance to all other predicates. [E.g. a man -> “skilled in grammar” implies “man” -> “skilled in grammar”.]
   8. Substance is never an accidental attribute; e.g. a secondary substance is never “present” in a primary substance.
   9. The differentiae of species are not accidental attributes. [’two-footed’ is not in ‘man’ (remember that /in/ here is the container definition: (2.b))].
   10. Species, genus, and differentiae, as predicates, are ‘univocal’ with their subject.
       1. This means that when you predicate any one of them, they are related both in definition and name to the children of that which is predicated of them.
       2. In other words, this means specifically that there’s an inheritance effect if you enter into one of these /specific/ chain of predication:
          1. individual (primary substance) <- species <- genus <- differentiae
          2. individual (primary substance) <- species <- differentiae
   11. Primary substance is individual; secondary substance is the qualification of that which is individual.
       1. A secondary substance is a class that can be predicated of individuals.
       2. Species and genus signify substance qualitatively differentiated.
   12. No substance has a contrary.
   13. No substance can be what it is in varying degrees.
       1. If you’re a man, you’re a man all the way, contra, say, your whiteness, which admits of variation in time.
   14. The distinctive mark of substance is that contrary qualities can be predicated of it.
       1. For any other term, contraries cannot be predicated. Later (6a:0-3) we find that nothing can admit contraries at the same time.
   15. Contrary qualities cannot be predicated of anything other than substances, not even propositions and judgments.
       1. Interestingly, he admits statements and opinions as an exception here, although he argues that it is not they themselves that undergo modification, but things external to them which retroactively modify their truth values.
       2. Hence, it is distinctive that substances seem to be internally-modifiable in a way that admits contrary qualities.
6. Quantity
   1. Discrete and continuous quantity.
      1. Discrete quantities are things like number and speech. They share no “common boundary”.
      2. Continuous quantities are things like lines, solids, time, and place.
   2. Division of quantities, i.e. number, the spoken word, the line, the surface, the solid, time, place, into these two classes.
      1. Numbers and speech are constituted by discrete packets of information.
      2. Lines are constituted by continuous points, surfaces by continuous lines, solids by continuous planes.
      3. Time, past, present, and future, forms a continuous whole.
      4. Space, likewise, is a continuous quantity, as its parts share a common boundary (this is evidenced by the fact that space can be occupied with solids: cf. (6.b.ii)).
   3. The parts of some quantities have a relative position, those of others have not. Division of quantities into these two classes.
      1. Either a quantity’s parts have a relative position, each to each, or they do not.
      2. Quantities that do: Lines (their parts are distinguishable and relative to their other parts), and hence planes, solids, and space.
      3. Quantities that don’t: Numbers, time, speech do not because they don’t have “an abiding existence”. One might say they have a relative order, but not a relative position.
   4. Quantitative terms are applied to things other than quantity, in view of their relation to one of the aforesaid quantities.
      1. E.g. A white wall is large in terms of length (solid), a speech is long in terms of time, etc.
   5. Quantities have no contraries.
      1. Terms such as ‘great’ and ’small’ are relative, not quantitative, and moreover cannot be contrary to each other (because of their reliance on a third party or external standard).
      2. That which is most reasonably supposed to contain a contrary is space. But this seems to fall apart because of a confusion of contrariness and extreme difference of degree (the weight of the universe is not the contrary of the weight of a dust mite). Interesting that he should say this and still call sickness and health contrary.
   6. No quantity can be what it is in varying degrees: Just because n is bigger than m, it doesn’t make n /more of a number/.
   7. The peculiar mark of quantity is that equality and inequality can be predicated of it.
   8. Question: “Perhaps the most interesting question concerns the fact that some of the species in quantity appear to be quantified things rather than quantities themselves. Consider, for instance, body. In its most natural sense, ‘body’ signifies bodies, which are not quantities but rather things with quantities. The same is true of line, surface, place and arguably speech. Of course, there are quantities naturally associated with some of these species. For instance, length, breadth and depth are associated with line, body and surface. But Aristotle does not list these as the species under quantity. So, in the first instance, we can ask: does Aristotle intend his division of Quantity to be a division of quantities or quantified things?”
7. Relation
   1. First definition of relatives: Relatives are explained by reference to some other thing. (E.g. “superior” implies superiority over something else.)
   2. Some relatives have contraries (e.g. virtuous/depraved) but not all (e.g. “double”).
   3. Some relatives are what they are in varying degrees (e.g. likeness or unlikeness).
   4. A relative term has always its correlative, and the two are interdependent (e.g. slave->master, double->half, greater->lesser).
   5. The correlative is only clear when the relative is given its proper name, and in some cases words must be coined for this purpose.
      1. This is a little convoluted, basically he seems to be talking about something like this:
      2. Call the condition of being a ruddered thing “rubob”. Call the opposite condition “belbob”. Something is rubob in virtue of its rudder and relative to something belbob.
      3. E.g. a “slave” is not usefully defined with reference to bipedalism. The correct correlative of a relative term (a) is what remains after all incidental attributes are removed from (a).
   6. Most relatives come into existence simultaneously; but the objects of knowledge and perception are prior to knowledge and perception.
      1. True, e.g.: Doubleness and halfness are mutually dependent immediately.
      2. False, e.g.: The objects of knowledge/perception.
   7. No primary substance or part of a primary substance is relative.
   8. Revised definition of relatives, excluding secondary substances.
      1. The fact that a thing is explained with reference to something else does not make it essentially relative. (This is the argument against ‘head’ and ‘hand’ as candidates for categorization as relative.)
         1. Question: How do we distinguish between those things about which we are just confused and need new terminology (7.e) and the case when something that requires something external in its explanation is actually not relative?
      2. There’s an appeal to intuition now, (if a man knows something is beautiful, he knows that than which it is more beautiful). I frankly don’t see how this is a helpful criterion though, given the whole “rudder” problematic.
   9. It is impossible to know that a thing is relative, unless we know that to which it is relative.
      1. He concludes that no substance is relative in character, but again I am still stuck up on rudders.
   10. Overview: “Perhaps the most straightforward reading of Aristotle’s discussion is the following. He noticed that certain predicates in language are logically incomplete - they are not used in simple subject/predicate sentences of the form ‘a is F’ but rather require some type of completion. To say ‘three is greater’ is to say something that is incomplete - to complete it requires saying what three is greater than. Nonetheless, Aristotle accepted a doctrine according to which properties in the world always inhere in a single subject. In other words, although Aristotle countenanced relational predicates, and though he certainly thought that objects in the world are related to other objects, he did not accept relations as a genuine type of entity. So, Aristotle’s category of relatives is a kind of halfway house between the linguistic side of relations, namely relational predicates, and the ontological side, namely relations themselves.”
8. Quality
   1. Definition of qualities: “that in virtue of which people are said to be such and such.”
   2. Different kinds of quality.
      1. Habits and dispositions
         1. Habits are more lasting and firmly established than dispositions.
         2. Knowledge and virtue, e.g., are habits.
         3. On the other hand, heat and cold, disease and health are dispositions.
         4. Habits are dispositions, but not vice versa.
      2. Capacaties
         1. Capacities are predicated of a person in virtue capacity (nice). E.g. being a good runner or boxer.
         2. There is also a kind of health that is less a disposition (e.g. I am healthy at the moment), and more of a capacity towards health (e.g. I am a healthy person generally).
      3. Affective qualities (distinction between affective qualities and affections)
         1. Affective qualities and affections are like: sweetness, bitterness, whiteness, blackness, heat and cold.
         2. Affective qualities are actually capacities to produce affections “in the way of perception.” These are things like sweetness and heat, which are capable of producing affections in the senses.
         3. Contrarily, affections are like pallor and flushing (in skin). This is again reliant on a more permanent/less permanent distinction. Affections are caused by affectors (shame/fear). So the white of Socrates when he sees a ghost is an affection, and the white of my walls is an affective quality.
         4. There are also affective qualities and affections of the soul. Of the former: temper, insanity, irascibility as constitutional. Of the latter: the same list as a temporary state. We can say that affective qualities are pathologies of affections.
      4. Shape, etc. (Rarity, density, etc. are not qualities)
         1. Straightness, curvedness, triangularity or octagonality are qualities.
         2. Rarity and density, roughness and smoothness because these are actually composite attributes: roughness is due to the unevenness of an array of parts, sparseness because of the distance between parts, etc. These are not intrinsic, and thus not qualities.
   3. Adjectives are generally formed derivatively from the names of the corresponding qualities (e.g.: the quality ‘whiteness’ nominates the adjective ‘white’).
      1. The alternative to that is when things derive names from sciences (e.g. the ‘boxer’ derives his name from the science of ‘boxing’, as the innate capacity for boxing, as a quality, has no name).
   4. Most qualities have contraries
      1. Usually: justice/injustice, whiteness/blackness
      2. Not always: Red, yellow
      3. If of two contraries one is a quality, the other is also a quality.
   5. A quality can in most cases be what it is in varying degrees.
      1. In the case where it is debatable whether it can (e.g. justice), we can at least say that subjects can possess most qualities in varying degrees.
      2. Qualities of shape are an exception to both of these rules (8.e, 8.e.i).
   6. The peculiar mark of quality is that likeness and unlikeness is predicable of things in respect of it.
   7. Habits and dispositions as genera are relative; as “individuals”/(species?), qualitative.
      1. While knowledge, e.g., as a genera is relative (to something) - knowledge is always knowledge of something, a particular branch of knowledge (say, musicology) is not relative to anything.
      2. Furthermore, if something should happen to be both a quality and a relation, this wouldn’t really hurt anything.
9. Action and affection and the other categories described.
   1. Action and affection both admit of contraries and of variation of degree (heating/cooling, being glad/being vexed).
   2. Position we understood back in (7.d-e), when we “stated that such terms derived their names from those of the corresponding attitudes.”
   3. Time, place (’in the Lyceum’), state (’shod’, ‘armed’) are easily intelligible.
10. Four classes of opposites.
    1. Correlatives: ‘Double’ and ‘half’.
       1. Correlatives are defined in reference to each other: A double is two times its half, knowledge is grasping an object.
    2. Contraries: ‘Good’ and ‘bad’. (Some contraries have an intermediate, and some have not)
       1. Tautologically defined: The ‘good’ is not ‘the good of the bad’ (qua 10.b), but ‘the contrary of the bad.’
       2. There are some contraries that are mutually exclusive (odd, even) and some that aren’t (blackness, whiteness).
    3. Positives and privatives: ‘Blindness’ and ’sight’.
       1. Positives and privatives reference the same subject (blindness and sight reference the eyes).
       2. Also, it is “a universal rule” that positives are the “natural” state of things. We don’t refer to blind chairs, because they are not missing sight in any significant sense.
       3. The terms expressing possession and privation (’being blind’) are not the positive and the privative (’blindness’), though the former are opposed each to each in the same sense as the latter.
       4. Similarly the facts which form the basis of an affirmation or a denial are opposed each to each in the same sense as the affirmation and denial themselves.
       5. Positives and privatives are not opposed in the same sense in which correlatives (10.a.i) nor contraries (10.b.i) are opposed.
       1. Viz. contraries: (1) Positives/privatives are not like contraries with no intermediates because in the case of the latter, one or the other has to be present in the “subject in which they naturally persist.”
          1. His examples are health/sickness and odd/even. You get odd/even: Every number has to be either odd or even entirely. His argument is that there exists a subject who has not advanced to the state in which sight is natural, and thus is neither seeing nor blind in the sense set forth in (10.c.ii).
       2. (2) They are not like contraries which have intermediates because in the latter, only one of the two contraries need be in a subject which is constituted by that quality (e.g. fire must be hot, and hence not cold. Otherwise, things can be in the middle of the hot/cold spectrum.)
          1. The appeal here is that - while it is not necessary per se for a given subject - once said subject has reached a stage in which sight is natural, it will either see or be blind.
          2. This contra contraries with intermediate stages, for which (a) it is never necessary that one or the other be inherent in a subject, and that (b) in the special cases, if one or the other should be present, it will not admit of its intermediate or its contrary.
       3. Also contra contraries, there can be no change from one state (e.g. privation) to its opposite.
11. Affirmation and negation: ‘He sits’, ‘he does not sit’.
    1. These are distinguished by from other contraries by the fact that one is always false and the other true.
       1. Opposite affirmations seem to possess this mark, but they do not. Eg. [”Socrates is ill”, “Socrates is well”] will always contain only one true and only one false statement if Socrates exists.
       2. Contra (10.d.i), the set [”Socrates is ill”,”Socrates is not ill”] always contains one true and one false statement, regardless of the existential status of Socrates.
12. Contraries further discussed
    1. Evil is generally the contrary of good, but sometimes two evils are contrary (e.g. defect, excess).
    2. When one contrary exists, the other need not exist (when “Socrates is well” then manifestly not “Socrates is ill”).
    3. Contrary attributes are applicable within the same species or genus (whiteness and blackness require a body, disease and health, a living body).
    4. Contraries must themselves be within the same genus (white and black->color), or within opposite genera (justice,injustice->virtue,vice), or be themselves genera (good and evil).
13. The word ‘prior’ is applicable:
    1. To that which is previous in time.
    2. To that on which something else depends, but which is not itself dependent on that something else.
    3. To that which is prior in arrangement.
    4. To that which is better or more honorable (he’s “first in my book”).
    5. To that one of two interdependent things which is the cause of the other and not the other way around. (The being of j:The truth of the proposition “J is.”)
14. The word ’simultaneous’ is used:
    1. Of those things which come into being at the same time. (”Double/half” cf. 7.f)
    2. Of those things which are interdependent, but neither of which is the cause of the other. (”Double/half”, cf. 10.a.i)
    3. Of the different species of the same genus (’animal’: ‘winged’,'terrestrial’,'aquatic’).
15. Motion is of six kinds: Generation, destruction, increase, diminution, alteration, and change of place.
    1. It is obvious that five of the six are distinct kinds; the exception is alteration. One may feel like alteration implies other types of movement.
       1. This is not the case, apprarently, insofar as a square can increase but not alter (qua square). Hence it is does not directly alteration or diminution, which it seemed to initially.
    2. Rest is the contrary of motion generally, but the contraries of the specific kinds have their contraries in other kinds (e.g.: generation/destruction, diminution/increase).
       1. The contrary of change seems to be either rest in place or change in the reverse direction.
       2. The contrary of alteration seems to be either stability of quality (rest) or change of quality in the reverse direction.
16. The meanings of the term ‘to have’.
    1. With reference to a habit or disposition (”he has a pleasant temperment”).
    2. With reference to quantity (”he has a height of six feet”).
    3. With regard to possessions and parts (”he has a coat”, “he has two hands”).
    4. With regard to content (”the jar has wine”).
    5. With regard to a wife/husband, which Aristitotle concludes is the most remote meaning of “having”, since it really parses out to “lives with”.

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.

Overview

A Stranger, a student of Parmenides, will set out to define the Sophist. Upon reaching the conclusion that the Sophist is one who sells the appearance of wisdom, he will announce that in order to prove this conclusion, an investigation into the nature of non-Being will be required. This will be approached by an investigation into Being itself, which will be divided into five great kinds. By analyzing these, he will prove that the negation of not-being operates on the predicate being, not the subject. Further, negation simply implies difference, not opposition.

Background

This is a late Platonic Dialogue. After criticizing the Middle Period conception of the forms (the theory of separate, immaterial forms) in Parmenides. The Sophist and Statesman show the author’s increasing interest in mundane and practical knowledge.

The Setup

SOCRATES asks an Eleatic STRANGER to help him define the terms “statesman”, “sophist”, and “philosopher”. They start with Sophist. Socrates, remembering the method employed in Parmenides by its’ namesake, asks whether the stranger would like to proceed by Q&A. The Stranger indicates that he would, if someone would not give him a lot of sass-back, but just acquiesce to his points (qua young Aristoteles in Parmenides). Socrates proposes that THEAETETUS will do just that.

1. DIAIRESIS: Since Sophists are slippery to define, the Stranger suggests that they begin by using their proposed method on something easier; say, an angler.
   1. Str. defines two classes of arts: productive (or creative) and acquisitive. Anglers belong to the acquisitive class, which can itself be separated into two: exchange and conquest. Conquest may be further separated into hunting and fighting. Hunting can be divided into animal hunting and the hunting of lifeless things. Animal hunting can be divided into by-land and by-water. By-water into fowling and fishing. Fishing into enclosure (fishing by nets) and striking (by spear). Striking into firing (by night) and barbing (by day). Barb-fishing into spearing and angling (by hook).
   2. This method of definition-finding is called diairesis. Now we’re going to try this method on the Sophist.
   3. The Sophist is acquisitive, and further is a hunter. And a by-land hunter at that.
      1. Hunting on land has two divisions: Hunting tame and wild animals.
      2. Tame animals into hunting with violence [piracy, tyranny], and hunting with persuasion [lawyer, orator].
      3. Persuasion into public and private.
      4. Private into receiving hire and bringing gifts (lovers).
      5. For hire into those whose reward is virtue and whose is money. The latter of these is the Sophist.
   4. Alternatively the Sophist could follow the path of exchange. Exchange divides into giving and selling.
      1. Selling into the sale of one’s own productions (retailers), the sale of others’ (merchants).
      2. Merchants into those who provide food for the body, and for the soul (music, paintings, marionette playing, knowledge).
      3. Food for the soul -> display and (n). (n) -> sale of knowledge of virtue and sale of other kinds of knowledge (art-seller). The former is the Sophist.
   5. A third alternative is that the Sophist follows the path of the fighting arts. This into competitive and pugnacious.
      1. Pugnacious into violent (bodily strength) and controversy (words). Controversey into forensic and disputation. Disputation into without rules and by rules (argumentation). Argumentation into wasting and making money. The later of which is Sophistry.
   6. Fourth, we run down this line: Let’s start with the arts of discernment. This can be split into a) arts that split like from like and b) those that split better from worse.
      1. The latter is called purification, which can be split into purification of living things and of inanimate objects. The former can be split into purification of bodies and souls. The latter can be split into: the purification of vice and of ignorance. (Alternatively the former can be split into gymnastic and medicine.)
      2. The purification of ignorance requires instruction, which can be split into admonition (resolves stupidity - ignorance which thinks it’s knowledgeable), and the dialectical remedy for plain ignorance. The latter of these is the domain of the Sophists.
   7. Thus the Sophist is determined to be:
      1. A paid hunter after wealth and youth (c).
      2. A merchant in the goods of the soul, a retailer of these wares (and one who manufactures them) (d).
      3. A hero of debate (e).
      4. A purger of souls, clearing away notions obstructive to knowledge (f).
2. COMBINATION: With five definitions in hand, they set out to find the common elements of contained within the five.
   1. The Sophist is a disputer, and teaches disputation. That is, the art of argumentation about anything. This means that the Sophists (otherwise they would be bankrupt) are assumed to have knowledge about everything. Thus, Sophists are in possession of a conjectural, non-truthful knowledge of all things.
   2. Sophists thus imitate wisdom, he is like a juggler. And the imitative art, like anything, can be split: a) likeness-making (painters) and b) appearance-making (that is, where one could not get a broad enough perspective on the reality to even understand if there is a likeness or not.
   3. And now, if the essence of the sophist is that he produces appearances, and more precisely false appearances. He imitates the wise man (Sophist 268b-c). But how can we make sense of this appearing but not being, this stating things but not true things? We have to contend once again with Parmenides’ old doctrine: “He who says that falsehood exists has the audacity to assert the being of not-being.”
3. THE RETURN OF PLATO’S BEARD:
   1. To define the sophist as an expert in deception, as someone who produces false appearances by means of statements, the Stranger needs to show that Parmenides was wrong; he needs to demonstrate that it is possible to say and to think that things that are not are, and to do so without contradiction.
      1. We can’t say “things which are not” nor “what is not” because in doing so we attribute singularity or plurality to non-Being, which is inapplicable.
      2. This is the basic Quinean position on Plato: by admitting things that aren’t, you are already contradicting yourself. (Note that this is what propositional logic theoretically resolves - contra term logic - via bound variables.)
   2. Parricide?
      1. We can’t make the “image”/non-being analogy, because the Sophist will show that
         by defining images, we predicate non-being.
      2. False opinion seems to think that things are not are, or vice versa.
      3. Hence, the Stranger will be forced to test the philosophy of Parmenides.
   3. Investigating Being: Number
      1. First of all, all previous theories of being may have taken the concept of “being” as lightly as Theaet. used to take non-being. Thus, let us investigate being first.
      2. Both the concepts of multiplicity and unity run into problems when you assert them of being. Starting with unity, we go through the standard Purity-F regimen:
         1. If Being is one then it is both being and one, and hence not one.
         2. Being can’t parts (a beginning, end).
         3. Yet, if being is not one, it lacks unity, and hence is not whole (everything). Etc.
      3. Hence, maybe we need to throw away the idea that Being is either one or two.
   4. Investigating Being II: Essence
      1. Let’s appeal to various notions of essence (essentially: materialist and Platonic notions).
      2. Starting with the materialists, Str. wants to suggest that being is that which has any power to affect another. Now the appeal is that given bodies (changing) and souls (unchanging; essential).
      3. Further, Being must contain both the movable (insofar as it contains mind, life, and soul) and unmovable (insofar as it contains sameness, etc).
      4. Which is a bit like the problems of (c) above, insofar as both rest and motion require predication, which is thus a third term.
      5. But if the many cannot be one, and the one cannot be many, how again will we attribute being to motion or to rest? In other words, we need an account of how one thing can be called by many names.
   5. Return to Participation: To show that one thing can be called by many names and that some names specify the object but mis-describe it, the Stranger introduces some machinery. He proposes that some kinds can partake of other kinds (these terms appear to be synonyms and to introduce an asymmetrical relation between an object and a property it has), whereas some kinds cannot blend with each other.
      1. Further, there are great kinds that enable the blending of kinds, much as vowels enable consonants to fit together. Even as some expertise is required to determine which letters can associate with which, so dialectic is required to determine which kinds blend and which do not, and which kinds hold everything together and make them capable of blending, and which are causes of division.
      2. The Stranger announces that there are five great kinds. He will ask two questions about them: (1) what are they like? and (2) what capacity do they have to associate with each other? The kinds to be discussed are: motion, rest, being, sameness and difference. Note that these five are not claimed to be exhaustive of all great kinds. Presumably, there are others, such as are discussed in the second part of Parmenides.
4. THE FIVE GREAT KINDS: TWO QUESTIONS
   1. The Stranger addresses question (1): What is each of the great kinds like? He distinguishes each of the five kinds from one another, starting with being, motion, and rest.
      1. Motion and rest, as opposites, do not associate with each other; but being associates with both, since both of them are. Being must be a third thing distinct from them:
      2. Similarly, sameness and difference are distinct from motion and rest. Furthermore, being is distinct from sameness. They have to be different, because if they were not, when we say that motion and rest both are, we could substitute the same, and motion would be the same as rest.
      3. Finally, the Stranger distinguishes difference from being. This argument introduces a crucial distinction between two modes of predication.
      4. Difference is distinct from being, because difference is always in relation to other things (pros alla) and more precisely in relation to something different (pros heteron), whereas being is both itself by itself (auto kath hauto) and in relation to other things (pros alla).
   2. Question (2): The Blending of Kinds
      1. The Stranger carries out the analysis for one great kind, motion, and argues very systematically that motion is non-identical with each of the other four kinds (motion is not rest, not the same, and so on), but partakes of three of the four - all but rest.
      2. The whole analysis is implemented with two relations: non-identity (F is not G, because F partakes of difference from G), and positive predication (F is G, because F partakes of G). Note that this leaves out negative predication - which is what one would think Plato would want to use to handle the problem of false statement.
5. NEGATION
   1. The Stranger made a serious mistake about negation in the last two (constructive) puzzles about not-being earlier in the dialogue. The mistake was to suppose that the negation in “not-being” indicates the opposite of being (opposites are polar incompatibles, and these include polar contraries, like black and white, which have some intermediate between them, and polar contradictories, like odd and even, and motion and rest, which do not).
      1. The opposite of being (its polar contradictory) is nothing. Parmenides was right to object that we cannot speak or think about nothing. If any speaking or thinking is going on, we are speaking or thinking about something. The Stranger showed in the first three (destructive) puzzles about not-being that any attempt to refer to nothing fails.
      2. But Parmenides was wrong to suppose that all talk about what is not is attempted talk about nothing.
      3. The problem of not-being is solved by recognizing two things: (1) the negation operates on the predicate, not the subject; (2) the negation need not specify the opposite of the item negated but only something different from it.
      4. Now, the negation appears to specify part of a wider kind which is determined by the positive term (e.g. large) that is negated (in this case size). Like varieties of applied mathematics, whose content is supplied by the domain to which the knowledge is applied, there are kinds of difference whose content is supplied by the objects differentiated.
      5. A kind of difference (say size) contains two parts, which are opposites (polar contradictories), such as large and not-large. Let us call this kind an incompatibility range.
   2. The Stranger distinguishes between names and verbs. A verb is a sign that is set over actions (or properties); a name is a sign that is set over the things that perform the actions (or have the properties). There cannot be a sentence that is simply a string of names or a string of verbs. A statement must fit a name together with a verb.
      1. The central idea is very simple. Statements are structured.
      2. For instance, “Theaetetus is sitting” is true, because “sitting” specifies something that is about Theaetetus, who is currently sitting. “Theaetetus is flying” is false, because “flying” specifies something different from what is about Theaetetus.
      3. As noted above (§4.b.ii), we need negative predication to explain the false statement: If “Theaetetus is flying” is false, it is false because the negative predication “Theaetetus is not flying” is true.
      4. The analysis of negative predication (as distinct from non-identity) is complex. This is what scholars of the Sophist talk about; which is a lot more detailed than we care to be.
6. MUTATIS MUTANDIS…
   1. The Sophist was left closed in the imitative art, which was a kind of creation. But now, we’re going to go back and note that creation is of two kinds: human and divine.
      1. Inside the human kind of creation, we have a split (again) between representational creation and appearance-based creation. Now, from above we remember that the latter was to partake of falsehood, it it could be shown that falsehood was a part of real being. We have now accomplished this, and thus, it is so.
      2. This diairesis continues until we come to our definition of a Sophist: “he…who…is an imitator of appearance, and is separated from the class of phantastic which is a branch of image-making into that further division of creation, the juggling of words, a creation human, and not divine-any one who affirms the real Sophist to be of this blood and lineage will say the very truth.”