Metaphysics VIII, Reading 1: Summing Up Book VII, Change, and Knowing First Matter by Proportion

Orientation #

He says this class covers the first and second readings of Metaphysics Book VIII; the whole of next week’s class will be the third reading (on substantial form), with the fourth and fifth perhaps the week after. He refers back to what “we were saying last time” about the definition of substance not having to bring anything else in (prev. lecture). The handout is “Aristotle, Metaphysics, Book Eight, Reading One”, pp. 1–2.

The class, in order #

1. Opening prayer and the title of St. Thomas (“Lumen Ecclesiae — Light of the Church”) #

The English “light for the Church” tones down the Latin Lumen Ecclesiae, “Light of the Church” — not as strong as what the Pope says. Christ is the light of the unenlightened.

2. Cause, beginning, element are not synonyms (“the causes and the beginnings and the elements”) #

Book VIII opens by recalling that the causes, beginnings and elements of substances are sought. Book IV had said wisdom is about being as being; but being has many meanings, the chief is substance, accidents are something of substance — so it is chiefly substance one studies.

• The three words are treated in Book V in the order beginning, cause, element, because beginning is more general than cause: every cause is a beginning in some way, not every beginning is a cause. The point is the beginning of a line, the edge of the desk the beginning of the table — neither is a cause.
• Theological use: one may say the Father is in some sense the beginning of the Son, since the Son proceeds from him; Father and Son together one beginning of the Holy Spirit. One should not speak of a cause there.
• Cause is more general than element: element is said strictly of the first things in the order of material cause — not the very first matter, which is pure ability, but the first forms of matter.
• As Thomas explains, the words get appropriated: element to material cause, beginning to the mover or maker, cause to form and end. Aristotle mentions causes first because form and end matter most to the wise man — the end is cause of the other causes and most of all appropriates the first cause, and form is the cause of being, and this is the science of being as being. The material cause is least important, being cause only of material things.

3. Which substances are agreed upon (“some substances are agreed upon by all”) #

All agree on natural, material substances: fire, earth, water, air (which the Greeks took for elements, perhaps not as simple as they thought), the other simple bodies, plants and their parts, animals and their parts, and last the heavens and their parts, thought to be unchanging except in place. The Platonists hold privately that forms and mathematical things are substances too.

• Why Plato posited them: he had answered yes to the central question — there is truth — and was convinced of truth in mathematics because it is most certain, and, through Socrates, that definitions are the way to know for sure. A definition is known universally, apart from singulars; in mathematics sphere and cube are known apart from sensible and changeable matter. If truth requires that the way we know be the way things are, then there must really be separate mathematical things answering to geometry and arithmetic, and separate universal forms answering to Socratic definitions. Aristotle takes these up in Books XIII and XIV — the final laying to rest of his teacher of twenty years. (Aside: sometimes Aristotle says “we Platonists,” as if one of them.)

4. Substance as “what a thing is” (“logos tēs ousias — ratio substantiae”) #

A second, more logical division of the word. Substance often means what a thing is, the nature: in the old translation of the Nicene Creed, “consubstantial” means having the same nature.

• The ten categories are distinguished by the way something can be said of individual substances: by reason of what they are (substance), by how big or how much (quantity), by how they are (quality), and so on.
• Evidence: in the Categories and in the book on places [Topics] he lists the same ten in the same order, except that the Categories calls the first ousia, substance, while the book on places calls it ti esti, what it is.
• “What it is” carries over to other categories (what virtue is, what the size is), but primarily belongs to substance — shown by the fact that the definition of a substance need bring nothing else in, whereas the definition of an accident must bring in that of which it is an accident (prev. lecture).
• Some thought genus and species, the universals, are more substances — that goes back to holding the forms to be substances.

5. What Book VII settled: definition, per se, speech, parts (“definition is speech signifying what a thing is”) #

• Definition: either there is definition only of substance, or “definition” of an accident is used in an extended sense. The etymology supports this — definition has the idea of limiting; the limits of a body are a tight fit. But to say what health is, one must bring in the body of which it is the good disposition, going outside its limits.
• Because he treated definition he treated through itself [per se], touched on in Book IV. All reasoned-out knowledge is about what belongs to a subject as such. What pertains to the definition belongs through itself; properties in the strict sense belong through itself. It belongs to two through itself to be a number; in another but real sense of through itself, to be half of four, a property falling upon it. The Posterior Analytics is full of this (kata to per se): the subject of a science must have parts and properties belonging to it through itself — geometry never discusses a green triangle.
  • Example: with plumbing trouble you call a plumber, not a pianist. Even if the plumber is a pianist, it is not through being a pianist that he repairs the plumbing. Likewise the housebuilder who is a pianist builds not as pianist but through the art of housebuilding.
• A definition is a speech. A name is vocal sound signifying by human agreement, no part of which signifies by itself; a speech is vocal sound signifying by agreement, having at least two parts that signify by themselves. “White man” is speech, “animal” a name; statements and definitions are speeches. So, as Thomas says in the Book VII commentary, a definition is never one name. A synonym is not a definition — “drying up” for “desiccation” is a synonym; a definition makes the thing more distinct. “Equilateral and right-angled quadrilateral” makes much more distinct what a square is than “square” can, and each of the three names brings out something.
• Since a definition is a speech and a speech has parts, Book VII had to consider what are parts of the substance and what are not, and whether the parts of the definition and of the thing are the same. Also that neither the universal nor the genus is really a substance.

6. Separated substances, and the plan of Book VIII (“but let us now go through the substances which are agreed upon”) #

Aristotle turns to the agreed-upon sensible or material substances; immaterial substances the philosophers call separated substances — separated from matter. We say “angels” because in Scripture they are sent to us as messengers (angel = messenger); they are called ministers and angels. (Joke: “I don’t invoke my separated substance” — “my guardian dear”; the TV show would be My Separated Substance.)

• Plan of Book VIII: readings one and two show that in material substance there are the two, matter and form — reading one chiefly that there is matter (more known to men), reading two that there is form, substantial form. Reading three treats form (act) in the genus of substance; reading four, matter; reading five, the composition of the two. Compare Peri Hermeneias: noun, verb, then their combination in a statement.

7. The three senses of substance in sensible things (“what is not this something in act”) #

All sensible substances have matter. (1) Matter is substance: what is not a this-something in act, but is a this-something only in ability (in potency). (2) Substance as the thought of what it is, the form, which being a this-something is separated in thought. (3) What is from these, of which alone there is generation and corruption, and which is without qualification separated as one reality from another. For the most part matter and form do not exist by themselves; only the composite does — but the two can be distinguished in it, and, as Thomas insists, we know this only through the fact of substantial change, first seen in natural philosophy, in Book I of Natural Hearing [ed.: Physics].

• On “some forms separable, some not”: Thomas says Aristotle may have at least two things in mind — forms definable without matter, considered in geometry; or the strange form you and I have, which can exist apart from matter (begun in the Phaedo, more fully in On the Soul III); and there are the separated substances, like pure form without matter. From the text you cannot say which he means to emphasize.

8. Heraclitus and Parmenides: change and contradiction (“day becomes night, and night becomes day”) #

• Heraclitus scandalously said Hesiod did not even know day and night — thinking them two things, when they are one and the same.
• Everyone explaining change explains it by contraries (Physics I): the Chinese of his time did, and the moderns do — Einstein said Helmholtz tries to explain all change by attraction and repulsion between unalterable particles.
• People speak as if one contrary becomes the other: day becomes night, hard becomes soft, healthy becomes sick. Grammar: becomes = comes to be; so the hard would be soft, day would be night. Yet if the sick did not become healthy, the sick would always be sick.
• Parmenides: you are admitting something both is and is not; impossible; therefore change is illusion. Heraclitus: change is real, most real of all — but then day is night, hard is soft, the awake are asleep.
• He asks the class whom they would follow; a student answers Parmenides. He notes most students, and most of history, follow Heraclitus — Hegel, Marx insist on change, development, evolution and admit contradiction (Hegel: there is a contradiction in becoming, something both is and is not). People follow Heraclitus because change most strikes the senses, which is the beginning of our knowledge.
• On the other side: in the Parmenides Plato has Socrates call him a man to be reverenced, to be feared, and represents Parmenides teaching the young Socrates the Socratic method by questioning him into contradictions. Whether historical no one knows (the dates are unsure) — but beside the point: the Socratic method of testing whether ideas contradict rests on what Parmenides insisted upon.
• The decisive argument: when two men disagree they can only go forward by going back to something they have in common — as two scientists with rival hypotheses can devise an experiment where the predictions differ. Here the two seem to have nothing in common; but what they share is that one must choose between the impossibility of contradiction and the reality of change. Why must one choose? Because change involves a contradiction and so contradicts the impossibility of contradiction. So what they have in common is the principle of contradiction — “the ball game is over. Parmenides has won.”
• Further: Heraclitus does not even save what he wanted. If day and night are the same thing there is no change from day to night; if healthy and sick are the same there is no change of health into sickness. He gives up the obvious and saves nothing.
• Aside: people who run into an apparent contradiction in their studies start saying the axiom about being and non-being is not true — but they say it is not true because it is true, because something contradicts it. Absurd attack.
• Aristotle agrees the Parmenidean axiom is the natural beginning of all axioms, most known of all: every statement is either affirmative or negative, says it is so or it is not so, never both; so every statement presupposes it is not both. But it is absurd to deny change. Therefore there must be a way of understanding change that does not involve contradiction.

9. The underlying subject (“there must be a third thing”) #

Take the apparent contradictions one by one:

• Health itself never becomes sickness; the good condition of the body could never be the bad condition; health itself cannot be sick. So there is something besides health and sickness — the underlying subject, the body. The body is not the same as its health (else it could never be sick) nor as its sickness; but health or sickness can be in it, not both at once. The body is able to be healthy and able to be sick, not both at the same time.
• Hardness does not become softness; that whereby things are hard is not itself soft. So a third thing — butter: not the same as its hardness or its softness but the subject of both; able to be both, not at once; actually hard, still able to be soft, and becoming soft it loses hardness.
• Spherical shape does not become cubical. Third thing: clay, subject of both shapes, never both at once.
• So: the underlying subject, and its ability toward two opposites. This unties the apparent contradiction.
• Why then do we say “the healthy becomes sick”? Because being healthy happens to what becomes sick — as a pianist built my house, not as pianist but because being a pianist happens to the housebuilder. We speak by happening, not through itself; it is the body as such that becomes sick.
• When the ignorant come to know, ignorance does not become knowledge; the third thing is the mind, able to be ignorant and able to know, not both in the same way at once.
• All these are accidental changes: health and sickness are quality (first species), hard and soft the third species, shape the fourth.

10. First matter and the proportion (“suppose we feed Boethius to the lions”) #

If a man becomes a lion — not figuratively — the change is between two substances. Aristotle says in Physics I that the subject underlying man and lion, the very first matter, is knowable by a proportion, in the Euclidean sense: a likeness of ratios. First matter is to man and lion as clay is to sphere and cube.

• But likeness is a slippery thing (Plato in the Sophist; Aristotle in the book on mistakes in thinking, the Sophistical Refutations — apparent but not real refutations), and likeness is the cause of deception: poisonous mushrooms that look edible; the boyhood piece of metal that looked like spilled ink on mother’s white tablecloth; salt in the sugar bowl discovered in the coffee.
• Arithmetical drill on where a likeness lies: 4 is to 6 as 2 is to 3 — not because an even is to an odd (4 and 6 are both even), not as prime to prime (4 and 6 are composite), not odd to even. The likeness: 4 is the same parts of 6 that 2 is of 3 — think of 4 as two twos and 6 as three twos, so 4 is two of the three parts of 6.
• Apply it: clay is an actual substance, first matter is not — it is substance in ability. Sphere and cube are two accidents, man and lion two substances. So in those respects they are unlike. In what way alike? Just as clay is able to be sphere or cube but not both at once, and being actually one remains able to be the other, and becoming the other ceases to be the former — so first matter is able to be man or lion, not both at once, and so on. That is where the likeness consists.
• Why proportion at all: first matter is pure ability considered by itself, hence not knowable by itself; ability is known only in comparison. Everything else in the proportion has some actuality. To try to know first matter by itself is to try to know the unknowable. Thomas says explicitly in his exposition that Aristotle indicates we come to know first matter through the fact of substantial change.
• Modern confirmation: in high-energy experiments modern physics comes very close to first matter; Heisenberg compares what they do there with Aristotle’s first matter, since those experiments seem to reveal the complete mutability of matter. Student question: are the “elements” of modern physics a stepping-? — His answer: the experiments seem to reveal that no form of matter is permanent; if first matter were an actual substance it would be some eternal form of matter. And since nothing comes from nothing, one is forced to the idea that the underlying matter is substance only in ability, never isolated by itself, always under some form. This shows why the early Greeks and early moderns thought first matter some actual substance.
• Substantial form too will be known by a proportion, since it can be neither sensed nor imagined — only accidental forms can. As clay is actually a sphere through this form and a cube through that, so first matter is actually a man through this form and a lion through that: a substantial form, because man and lion are substances. The differences between substantial and accidental form come later; reading three, on substantial form, is the most interesting part of Book VIII.

11. The last paragraph: the heavenly bodies (“he complains about the distance”) #

Aristotle held that sun, moon and stars undergo no substantial change, no alteration, growth or death — only change of place. A body can have change of substance (as we do in death) and also change of place; but perhaps not the reverse: what changes place need not change quality or substance. Maybe we know better now, and they have the same kind of matter. Aristotle complains of the distance between himself and the heavens; in the biological works he says he wanted to know them better but they are not accessible — he could cut animals open and do anatomy, but had no telescope or subtler instrument. Thomas, aware we are not altogether sure about the heavens, says perhaps a change there takes longer than the lives of many men. He says we need not dwell on this paragraph. Break here.

His words #

• Light of the Church — Lumen Ecclesiae; stronger than the translation “light for the Church”.
• Beginning / cause / element — beginning widest, cause narrower, element narrowest (first things in the order of material cause).
• Ability — [ed.: potency]; “sometimes just the Latin words, in potency”.
• Logos tēs ousias / ratio substantiae — the definition of what a thing is.
• Ti esti — “what it is”; the name of the first category in the book on places.
• Book on places [ed.: Topics].
• Through itself — kata to per se; belonging to a subject as such, opposed to “by happening”.
• Name — vocal sound signifying by human agreement, no part of which signifies by itself.
• Speech — vocal sound signifying by agreement, having at least two parts signifying by themselves.
• Natural Hearing [ed.: Physics].
• Separated substances — the philosophers’ name for immaterial substances; “angels” is the scriptural name, from angel = messenger.
• This something in act — what matter is not; matter is a this-something only in ability.
• Proportion — in the Euclidean sense, a likeness of ratios; how first matter and substantial form are known.
• Book on mistakes in thinking [ed.: Sophistical Refutations] — apparent but not real refutations.

Texts #

Read in class

• Aristotle, Metaphysics VIII, reading one — handout pp. 1–2 (recapitulation of Book VII; “all sensible substances have matter”; the three senses of substance; final paragraph on the heavenly bodies).
• Aquinas, commentary on that text (his exposition of how we come to know first matter).
• Aristotle, Physics I, on first matter known by proportion (with Aquinas’s commentary, lectio 13 — inferred).

Mentioned

• Aristotle, Metaphysics IV (being as being; through itself), V (beginning, cause, element), VII (definition, per se, parts, universal and genus), XIII–XIV (Plato’s forms and mathematicals).
• Aristotle, Categories; Topics; On Interpretation; Posterior Analytics; Sophistical Refutations; On the Soul III; the biological works.
• Plato, Phaedo; Parmenides; Sophist.
• Heraclitus, Hesiod, Parmenides, Socrates, Democritus-era Greeks; Hegel, Marx, Einstein on Helmholtz, Heisenberg.
• The Nicene Creed (“consubstantial”, old translation).

His questions #

• Is every beginning a cause? — No; the point is the beginning of a line but not its cause.
• Why did Plato posit mathematicals and separate forms? — Because he held truth requires that the way we know be the way things are, and we know mathematics and definitions apart from sensible matter.
• Is there definition of accident? — Either not at all, or in an extended sense, since one must go outside the thing’s limits.
• If your plumbing breaks, do you call a pianist? — No; even if the plumber is a pianist, it is not as pianist that he plumbs.
• Whom would you follow, Parmenides or Heraclitus? — Parmenides: what the two have in common is the principle of contradiction, so “the ball game is over.”
• Does health itself become sickness? — No; therefore there must be a third thing, the underlying subject, able to be both but not at once.
• In what way is 4 to 6 as 2 is to 3? — In that 4 is the same parts of 6 that 2 is of 3.
• How is first matter like clay, since clay is an actual substance? — Only in this: able to be either of two, not both at once, and losing the one in becoming the other.
• Can first matter be known by itself? — No; it is pure ability, knowable only by proportion, through the fact of substantial change.
• Do the sun, moon and stars change substantially? — Aristotle says no, only in place; “maybe we know better than that now” — left open, with Thomas’s suggestion that such change may take longer than many men’s lives.