An Outline of Metaphysics Z

Chapter 1

Being (or 'is'?) is said in many ways (pollachôs legetai). [This might mean: many different kinds of things are called beings. Or it might mean: 'being' is ambiguous, i.e., has many different senses.] 'Being' is said in a different way in each of the categories. But it used primarily of substances (ousiai), and the being of everything else (quantities, qualities, etc.) is dependent on the being of substances. For a quality (or quantity) to exist is for it to be a quality (or quantity) of some substance.

Substance is primary in every sense of the word 'primary': (a) in formula, (b) in order of knowledge, and (c) in time. For (c) only substances can exist in their own right - nothing in any of the other categories can do this; (b) the formula (= definition?) of each thing must contain the formula of a substance; (a) we know a thing most fully when we know what it is (i.e., when we know its substance, not its quantity or quality or location).

So the ancient and perennial question "What is being?" becomes, for us, the question "what is substance?"

Chapter 2

There have been various opinions on our question:

  1. Bodies (animals, plants, their parts, earth, air, fire, water)
  2. Sun, moon, stars, etc.
  3. Surface, line, point, unit (= the limits of body)
  4. Eternal, non-sensible entities:
    1. Plato: Forms and mathematical entities (ta mathematika)
    2. Speusippus: the One, etc.

We must deal with various questions about these views. First: what is the nature of substance?

Chapter 3

There are four candidate criteria for substance-hood:

  1. Essence
  2. Universal
  3. Genus
  4. Subject (hupokeimenon)

    The remainder of this chapter considers candidate (D). Three different things might be counted as hupokeimenon (and hence as substance according to the subject-criterion):

    1. Matter
    2. Form
    3. The compound of matter and form

Pushing hard on the subject-criterion (interpreted now as demanding that a substance must be an ultimate subject of predication) seems to yield the result that matter is substance. But this can't be right, for matter lacks separability and this-ness. So much for (1).

(3) is also rejected: "The compound may be dismissed, for it is posterior and its nature is obvious."

This leaves us with (2), form, as the only remaining candidate for substance according to the subject-criterion. This will require further inquiry, "for this is the most perplexing kind of substance."

We'll start with the case of sensible substances; these are generally counted as substances, and they're the simplest cases (= "more knowable to us"). We can then proceed [as recommended in An. Post.] to the cases that are more knowable by nature.

Chapter 4

A second candidate: essence (to ti ên einai, lit., "the what it was to be").

  1. Essence is linked to
    1. per se (Gk. kath' hauto, lit., "in respect of itself", or "in its own right") predication:
      1. The essence of x (the what it was for x to be) is what is predicated per se of x (1029bl4).

        [Lines 1029bl6-19 show that the sense of 'per se predication' Aristotle has in mind is the first (but not the second) of the two that he distinguishes at An. Post. 73a35ff, viz.:

      2. x is predicated per se of y iff (1) x is predicated of y, and (2) x is part of the definition of y.]
    2. definition (logos, horismos):
      1. The formula (logos) of the essence of x is a formula in which x itself does not appear but which "expresses" (legonti = defines?) x (1029bl9-20).
      2. The essence of x is precisely (hoper) what x is (1030a3). [Gloss: "precisely what x is" designates a species of which x is a genus. If y is a species of the genus x, then y is precisely what (some) x is (y is hoper x, Aristotle would say). Cf. Furth, Aristotle: Metaphysics VII-X, p. 108.]
      3. When one thing is predicated [sc. accidentally] of another, this is not precisely what some "this" is (hoper tode ti): e.g., 'pale man' is not precisely what some "this" is. [Gloss: pale man is not a species of man.]
      4. "Therefore there is an essence of just those things whose formula (logos) is a definition (horismos)" (1030a6).

        [A definition thus seems to be a formula which states an essence: The definition of x is the formula which states the essence of x.]

  2. Not every formula is a definition.
    1. To be a definition, a formula must be of something primary; and primary things are those which do not imply (legetai) that one thing is predicated of another (1030a7-11).

      [Gloss: 'x = ABC' is a definition only if x is primary, i.e., if the relation of A, B, and C to one another (or, perhaps, to x) is not that of two distinct items which happen to coincide. Thus, 'pale man' (to choose one of Aristotle's favorite examples) cannot state the essence of anything (i.e., 'x = pale man' can't be a definition) because the entity pale man is not primary; rather, two items - pale and man - happen to coincide. On this reading, an entity will not be primary if it is an accidental unity. Cf. Z.12, where Aristotle directly confronts the problem of the "unity of definition," i.e., the problem of what makes the referent of a (complex) definiendum a unitary thing in a way in which the referent of other complex formulae (e.g., 'pale man') is not a genuine unity.]

    2. Therefore, only species of a genus have an essence (1030a11-12).
    3. Perhaps definition (horismos), like ti esti, is said in many ways.
    4. If so, then like being, they are said primarily of substances, and secondarily of items in other categories (cf. Top. A.9).
    5. "But this is evident: definition and essence are primarily (protôs) and without qualification (haplôs) of substances" (1030b4-6).

Chapter 5

A problem: if, in general, the coupling of two terms is not a definition (and so not a formula of an essence), how can entities like snub be defined? For snubness is not just concavity - a quality - but concavity in a nose. But if 'pale man' has no essence, why should 'snub' - i.e., 'concave nose' - have one? For in both cases, we have:

a thing (a substance, or part of one) + an attribute.

[Why is this a problem for Aristotle? If 'pale man' does not have an essence (in the primary sense) it would seem that 'snub' also lacks one. In both cases, we have an accidental unity: the man only happens to be pale, the nose only happens to be concave. But 'snub nose' has some important logical features in common with formulae that Aristotle is willing to count as definientia, e.g., 'rational animal' or 'two-footed animal': noses aren't all snub, but nothing but a nose can be snub; animals aren't all two-legged, but nothing but an animal can be two-legged. Cf. also Z.11 for more on 'snub', Z.12 on the unity of definition.]

Chapter 6

Is it the case that

  1. Each thing is the same as its essence (i.e., x = the essence of x) or are they different? This will help us in our inquiry into substance, because:
  2. Each thing is the same as its substance (i.e., x = the substance of x), and
  3. The essence of a thing is its substance (i.e., the essence of x = the substance of x).

[Puzzle: what relation is Aristotle asserting among (a), (b), and (c)? If he is asserting (b) and (c), he already has the answer to his question, since (a) follows from (b) and (c). A more plausible suggestion: Aristotle puts (b) forward as uncontroversial, and suggests that we inquire into the truth of (a). This will be relevant to our inquiry ("What is [the] substance [of x]?"), since (a) and (b) entail (c). If (a) is true, then, the answer to our question is: [the] substance [of x] = [the] essence [of x].] The answer seems to be: for entities that are primary (prôta) and spoken of per se (kath' hauta legomena), (a) is true. For other entities (e.g., accidental unities such as 'pale man') (a) is false.

[No additional detail in the present draft on the rest of this very difficult chapter. Its topic is taken up again at Z.10.]

Chapter 7

[Z.7-9 are generally thought to be an interpolation: a connected sequence of genuine Aristotelian text put (by a later hand) out of context here. These three chapters have a topical unity but are not closely linked to the surrounding discussion (Z.4-6, 10-12). They will be treated only very sketchily in this outline.]

The generation of substances. Among the topics discussed: the difference between natural and artificial production; the roles of form and matter in these productions; the ways in which form and matter of what is generated exist prior to its generation; whether there is reference to matter in formulae (logoi).

Chapter 8

What is produced in the generation of substances? Matter? Form? The compound of matter and form?

We do not produce the matter (to suppose that we do leads to an infinite regress) nor do we produce the form (we put it into something, but we don't produce it - what could we make it out of?). We put the form into the matter, and produce the compound.

Platonic Forms, as separate "this-es," are useless in describing generation; the man you need to produce a man is not the Platonic Form autoanthrôpos. What you need is just another matter/form compound of the same kind, for "man begets man."

An individual is a form in matter. Different individuals (of the same species) differ in matter, but not in form.

Chapter 9

Kinds of Generation

  1. Spontaneous vs. artistic generation:
    1. Some things can be produced in either of these ways (e.g., health); others can only be produced by art, never spontaneously (e.g., a house). Why is this?
    2. The reason is to be found in the matter involved. Where the matter is capable of setting itself in motion, there can be spontaneous generation; where the matter is incapable of this, an external mover is required to inform the matter.
    3. When something is produced artificially, in a way (tina tropon) the thing doing the producing has the same form as the product. [Cf. the discussion of natural generation in Z.8: "man begets man." Here it is clear that (where 'F' is a term for a form) the production of an F begins with something that is an F. Aristotle is here trying to stretch the point to cover non-natural generation.] E.g., a house is produced "from a house, qua by the mind; for the art <of housebuilding> is the form." [Presumably, the point is that for a house to be produced there must be someone who has in mind a house; the form that gets put into the matter was previously found in the mind of the builder.]
  2. Natural generation:
    1. Likened to artistic production: the efficient cause (in this case the seed) has the form potentially; product and producer are the same in form.
    2. An exception: the formula 'An F produces an F' does not always hold. Thus, the parent of a mule is not a mule. These are cases in which the offspring is an imperfect form.
  3. What comes to be is the compound, not the matter or the form; the brazen sphere, not the sphere nor the brass.
  4. Whenever an F comes to be, some (at least potential) F must pre-exist. But it is a peculiarity of substances that when a substance F comes to be, "there must exist beforehand in complete reality (entelecheia, actuality) another substance [sc., another F which produces it."

Chapter 10

[This is a long and complex chapter. What follows is only a capsule summary.]

Every definition (horismos) is a formula, and every formula (logos) has parts. As the logos of x is to x, so any part of the logos of x is to some part of x. [Call this "the correspondence thesis."]

The question thus arises: if y is a part of x, is the logos of y a part of the logos of x?

We seem to get different answers in different cases. A semi-circle is part of a circle, but the logos of a circle does not include that of a semi-circle. [In defining circle, you don't mention semi-circle; to suppose so would threaten an infinite regress.] On the other hand, the formula for a syllable would include the formulae of its component letters.

Perhaps 'part' is said in many ways. But never mind: let's raise our question for the case where x is a substance: if x is a substance and y is a part of x, is the logos of y a part of the logos of x?

The answer is this: if y is the matter (or part of the matter) of x, then the logos of y is not a part of the logos of x. But if y is the form (or part of the form) of x, then the logos of y is a part of the logos of x.

The idea seems to be that the parts of a logos are somehow prior to the logos itself, whereas a whole (physical) substance seems to be prior to its parts. And this asymmetry threatens the parallel between a thing and its definition that Aristotle is eager to establish.]

The compound of matter and form, the individual, has no definition. This is because it contains matter, which is in itself unknowable. (Matter may be either perceptible or intelligible.)

Chapter 11

This leads naturally to our next question: when is a part of x a part of the form of x, and when a part of the compound of matter and form?

  1. We must answer this question to be able to define anything, since a definition is of the universal, i.e., the form. [According to the correspondence thesis (Z.10) the parts of a definition will correspond to the parts of the form. So we have to know which of x's parts are parts of the form of x in order to know how to construct the definition of x.]
  2. Some easy cases: things found in many different kinds of matter, e.g., circles, which may be of wood, bronze, stone, etc. It's obvious that none of these materials is part of the essence of circle, since it is separable from them (dia to chorizesthai autôn). [I.e., no particular kind of matter is peculiar to circles.]
  3. A harder case: things found in only one kind of matter, e.g., men, who are always made of flesh and bones and the like. Here it's tempting to think that flesh-and-bones is part of the form, but that would be wrong. It's rather as if all the circles there have ever been were made out of bronze: in this case, it would be hard not to think of a circle as made of bronze. Still, bronze would be no part of the form.
  4. But one must not fly to the opposite extreme of treating parts of the form as if they were matter.
    1. Some people treat lines as if they were the matter of triangles, so that there would be no reference to lines in the definition of a triangle. "They reduce everything to numbers, and say that the formula of line is that of two." [Aristotle evidently has the Pythagoreans in mind.]
    2. "Those who assert the Ideas" [Aristotle no doubt means the Platonists] make a similar move. Some of them say 'two is the Line-Itself'; others say 'two is the form of the line'. These people have a problem: for in some cases, x is the same as the form of x, and in other cases, it is not. (Thus, they say 'two is the form of two' and also 'two is the form of the line'.) "It follows that there is one form for many things whose form is evidently different."
    3. This same conclusion also confronts the Pythagoreans.
  5. Still, one can't "reduce everything to form, and eliminate matter. For some things are surely a particular form in a particular matter, or particular things in a particular state." (1036b22-24)

    [This is an important, but inconclusive, passage with respect to the issue of whether Aristotle countenances particular or individual forms or essences. Literally, he says that some things are a "this in that" (tod' en tôide) or "these being thus" (hodi tadi echonta). But what he doesn't make clear is whether "some things" means, e.g., Socrates, Callias, et al. or man, horse, et al. If he means the latter, his point is that some kinds, such as man, require certain kinds of matter, such as flesh-and-bones. From this nothing follows about a form or essence that is peculiar to an individual man that is not shared by other men.]

  6. Question [and possible counter-example?]: what about mathematical objects? [They aren't material, so presumably their parts are parts of a form, rather than a compound of matter and form. And a semi-circle is part of a circle. So,] why isn't the formula of semi-circle included in the formula of circle?

    Answer: there is matter even in mathematical circles. "For there is matter in everything that is not an essence and a bare form but a 'this'." It is, however, intelligible (not perceptible) matter. [Thus, the two semi-circles composing a circle can be considered its intelligible matter.]

  7. Souls and substances.
    1. It is also clear that:
      1. soul (psuchê) is primary substance (protê ousia)
      2. body (sôma) is matter
      3. "man or animal is the compound of the two taken universally (hôs katholou, literally, 'as universal')."
    2. [The discussion in (1) concerned universals; the case of individuals may seem different.] "If, indeed, [it's right to say, as some people do, that] Socrates is a soul)," then names for individuals, like 'Socrates' and 'Coriscus', have a double reference. Each applies to
      1. a soul
      2. a compound
    3. But if [one of these proper names applies] without qualification (haplôs) to this soul and this body, then the case of the particular (to kath' hekaston) is like that of the universal (to katholou).

      [I.e., as the universal man is a compound of soul (form) and body (matter), so the particular man (e.g., Socrates) is a compound of this soul and this body. This is an important passage for those who hold that there are particular (i.e., non-universal) forms in Aristotle's Metaph. But it is important to note that the assertion of a particularized form (e.g., Socrates' soul) is contained in an 'if' clause. Given that Aristotle holds that there is matter in every 'this' (1037a2), he would have the problem, on this line, of saying what the matter in this soul is. (He would presumably say that it is intelligible matter.) The alternative interpretation would take Aristotle's view to be this:

      1. Man (a universal) is a compound of soul (a universal form) and body (a universal: a kind of matter)
      2. This man (a particular) is a compound of soul (a universal form) and this body (a particular: an instance of a kind of matter).

        This line fits in better with the view - often attributed to Aristotle - that it is matter that individuates.]

  8. We will postpone consideration of whether there is another kind of substance and another kind of matter [sc. than perceptible substances and their matter]. It's for their sake that we're investigating sensible substances, which are in a way the province of physics, i.e., second philosophy [as opp. to metaphysics, or first philosophy].

  9. We still have the problem of definitions: what is the relation between a a definition and its parts? On account of what is a definition one formula (logos)? Clearly the thing [defined] is one, even though it has parts; but what makes it one? We've got to look into this later. [Aristotle takes up the problem of the unity of definitions in Z.12 and H.6.]

  10. Summary (1037a21-b7) of points made so far in Z.4-11. [Note omission of any reference to Z.7-9, confirming the suggestion in first comment on Z.7.] We have said:
    1. what essence is, and how it is "itself by itself" (auto kath' hauto) [ = independent?] (Z.4)
    2. why the logos of the essence of some things, but not of others, contains [reference to] the parts of the thing defined (Z.10)
    3. that the material parts of a substance are not present in the logos of that substance (Z.10)
      1. such parts belong to the compound, not to the substance
      2. of the compound, in a way there is a logos and in a way there is not (Z.10-11):
        1. there is no logos of it with its matter, "for this is indefinite (aoriston)"
        2. there is a logos of it with respect to its primary substance (protê ousia), e.g., in the case of man the logos of soul
    4. that substance is the form within [a compound], and it is from form and matter [that we get] the so-called compound substance.
      1. An example [of such a form] is concavity: from it and a nose [matter] we get (esti) a snub nose, and snubness (Z.5)
      2. but in a compound substance, such as a snub nose, or Callias, there is matter present.
    5. that in some cases a thing (hekaston) and its essence are the same, and in some cases not (Z.6)
      1. They are the same in the case of primary substances, e.g. curvature and the essence of curvature, if this is primary. (In Z.4, Aristotle says that by primary he means "what is not spoken of as one thing being said of another" - 1030a10.)
      2. They are not the same in the case of things that are
        1. "as matter, or as compounded with matter"
        2. one per accidens, e.g., Socrates and the musical.

        [The text for (b) is difficult. The outline above is based on Ross's text, which contains an emendation not found in any MSS. Without this emendation, the text would most plausibly be construed as follows:]

      3. But things that are "as matter, or as compounded with matter"
        1. are not the same as their essences
        2. are not even per accidens one, in the way that Socrates and the musical [are accidentally one].

What follows is a preliminary and incomplete draft of an outline of chapters 12-17:

Chapter 12

The Unity of Definition

What does the unity of a substance consist in? Look at the definition of a substance, e.g.:

man  =df  two-footed animal

Why does 'two-footed animal' pick out a unity in a way that 'pale man' does not? Pale man is an accidental unity; why isn't two-footed animal like that?

[Aristotle presents the problem as one involving the definiens (two-footed animal): what makes this compound a unity? But another way of putting what's at issue here is this: what makes the definiendum (man) a substance? What makes the formula above a definition, a statement of something's essence?
Recall the discussion of pale man in Z.4: suppose the word 'cloak' (himation) meant pale man. Then would the formulae

  1. a cloak is a pale man
  2. a man is a two-footed animal

be on equal footing? Why is (ii), but not (i), a definition? We'd like to say that man is a unity in a way that pale man is not. But the fact that we use a simple expression in one case and a compound one in the other makes our task seem easier than it is. For (ii) licenses the replacement of 'man' with 'two-footed animal'; and although there is no simple expression that stands to 'pale man' in the way that 'man' stands to 'two-footed animal', we can always suppose that there were such a word, in the manner of (i). Now the two cases seem much more difficult to pry apart.

Aristotle's solution does not emerge until H6: the relation between matter and form is not like that between substance and accident. Whereas a pale man may be considered an "accidental unity" of substance and accident, a two-footed animal (or a rational animal, or whatever is the correct definition of man) is not an accidental unity of matter and form. The form is the actuality of which the matter is the potentiality. In some such way, matter and form are supposed to be one in a way that substance and accident are not. But Aristotle's solution is less than crystal-clear.]

Chapter 13

Universals are not Substances

[This chapter returns to the four candidate criteria for substance-hood set out in Z.4, mentions that essence and subject have been discussed, and proceeds to universal. What happened to genus, the fourth candidate from Z.4?

One possibility: genus, for Aristotle, can be treated either as matter or as universal. Matter was discussed in Z.3, and the present chapter will take care of universals. So genus is, in effect, covered.]

Universals are common, i.e., belong to more than one thing. But the substance of a thing is supposed to be peculiar to it, not common to many. So no universal can be a substance.

Substances are not predicable of a subject, but universals are predicable. So, again, universals aren't substances.

But even if a universal can't be the whole essence of a thing, it may be part of an essence. Thus, animal is part of the essence of man and part of the essence of horse, but it is not the essence of anything all by itself.

This is presumably because there's no such thing as being an animal without being a particular kind of animal (cf. 1038b33). Every animal belongs to some species or other

If x is a substance and y is a part of the essence of x, then y is not the substance of anything (1038b31-32).

A universal is a such, but not a this.

But this leaves us with a problem: if a universal is a such, and not a this, how can a substance be composed of universals? How can a bunch of suches add up to a this?] If a substance isn't composed of universals, and isn't composed of substances either (as has just been shown), "every substance would be incomposite, so that there would not even be a formula of any substance." But if substances can't be defined, nothing can be; so we get the result that nothing is definable.

[The inference to the incompositeness of substances seems a non-sequitur: why should universals and substances exhaust the field of possible candidates for being parts of substances? But the second inference seems secure: if something is incomposite, then it cannot have a definition, given that the definiens will always be a complex formula, and that there is always a one-to-one correspondence between the parts of the formula and the parts of the thing.]

Chapter 14

An argument against the Platonists

They make universals (their Forms or Ideas) substances, and allow them to be "separate" [and presumably what Aristotle would call "thises"]. From this, Aristotle attempts to draw absurd consequences. The argument is complex, but the drift is this: if the Platonic form animal is a this, then what kind of animal is it? A horse? A man? Is it both two-legged and four-legged? It can't be both; and if it were just two-legged, say, then horses wouldn't be animals (since they aren't two-legged). So it is neither: presumably it has no definite number of legs. Then how can it be a this?

Chapter 15

There are two kinds of substance:

  1. the compound [of matter and form]
  2. the formula [not compounded with matter].

(A) are generated and destroyed; (B) are not.

Sensible individual substances are not definable, nor do they figure in demonstrations, because they have matter. No individual can be defined, not even [presumably immaterial] Platonic Forms. A definition is general and applies in principle to more than one thing.

An individual which is eternal and unique, e.g. the sun, may seem to be definable, but it isn't. Its formula is general. [I.e., what is defined is a kind that has only one member. But it is the kind, not the individual that happens to be its only member, that is defined.]

Chapter 16

Most so-called substances are really only potencies: e.g., the parts of animals, or earth, air, and fire.

A substance must be one, i.e., have unity, and not just be a heap.

Still, the parts of living things may seem more than potencies, but have complete actuality: they have a source of movement within them. Thus, some animals can live when divided. [Lines 1040bl4-16 seem to suggest that even if, say, the front half of an earthworm is capable of growing into a complete earthworm if it should be severed from the rear half, it doesn't count as an actual substance while it's still just a part of the whole.]

'One', like 'being', is said in many ways. So neither is the substance of anything. Both may seem more substantial than 'principle', 'element', or 'cause', but none of them is substance, because nothing that is common is substance.

What about [Platonic] Forms? Their proponents say that a Form is (1) separate and (2) a One over Many [i.e., a universal]. If Forms are substances, they are separate; but if they are universals, they aren't separate. [Clearly, Aristotle thinks that the Platonists are placing incompatible requirements on the Forms.]


Chapter 17

A new beginning [a very brief summary of this important chapter]

Substance is a principle (archê) and a cause (aitia). We appeal to substance when we explain why something is thus-and-so.

'Why' questions always ask why one thing attaches to another [i.e., why some predicate belongs to some subject].

Our answer mentions the essence; we state "the cause, i.e., the form, by reason of which the matter is some definite thing." (E.g., why are these bricks and boards a house? Why are these flesh and bones a man?)

Essence, or form - which is what we have finally discovered substance to be - is not one of the elements in a compound (of matter and form). Rather, it is a cause of the elements combining in the way that they are combined in the compound. [I.e., form or essence is a principle of organization.]

"Substances are formed

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