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”.