Metaphysics VIII, Reading 2: Substantial Form Compared with Accidental Form, and Why Proportions Matter

Orientation #

He says he is beginning the second reading of Metaphysics Book VIII, following the previous meeting’s treatment of matter and the proportion by which first matter is known (prev. lecture). At the close he announces that the third reading, next time, will treat substantial form, “and it’s going to be a very interesting way he does this.” The next class takes up that third reading, on form compared with Plato’s separated species and with numbers.

The class, in order #

1. Why he now turns to form (“it remains to say what is the substance as act”) #

Point: all earlier thinkers agreed matter is in some sense substance, because the underlying subject of change is obvious; substance as form is more hidden. So Aristotle now begins from the acts or forms more known to us, i.e. sensible, accidental forms, and will reach substantial form proportionally — just as first matter was reached by proportion to an actual substance underlying accidental change.

2. Democritus’s three differences (“shape, or in position or in order”) #

Democritus’s underlying body is the atoms, all more or less the same, differing only in shape (straight/curved), position (upside down, on the side), and order (before and after). Aristotle’s reply: there seem to be many other differences besides these.

3. The catalogue of accidental differences (“some things are said by the mode of composition”) #

Each kind of accidental difference with its example:

• Composition (ratio) of the matter: honey water; water as H₂O, two to one — aside: one-to-one is a bad ratio (carbon monoxide vs. CO₂); a Manhattan is two to one, so is a stinger.
• Bound together: a bundle — Thomas (and “the physician”) on a woman’s hair bound together.
• Glued together: a book (“I don’t know what the books were like in those days”).
• Nailed together: a wooden box (or screwed).
• Position: threshold and lintel — same wood, differing only as below and above, not by order or shape.
• Time: dinner and breakfast — possibly the same fish, differing by morning or evening.
• Sensible qualities undergone: hard/soft, dense/rare, dry/wet — generally by excess and defect. Consequence he stresses: by reason of these, a thing is said to be what it is — a chair is a chair more by its shape than by its matter; by matter it is a chair only in ability. So “what it is” is said in as many ways: a threshold is such because placed thus; ice is what it is by having been solidified in a certain way (“very primitive science”). Some things are defined by several at once — a chair by shape of parts, by being screwed together, and by arrangement, all necessary. He then notes (a paragraph ahead) that some accidental differences can be reduced to the most fundamental: shapes back to straight and curved (a semicircle involves both), smooth and rough.

4. Digression: “substance” and “nature” — different origins, overlapping senses (“if you look at it in the fifth book of wisdom”) #

Natura comes from natus, birth (nativitas); carried over to the source of the baby in the mother, then generalised to an intrinsic source of any change. Hence Physics II: nature is the beginning and cause of motion and rest in that in which it is; then he shows nature is matter, then that it is form, and form more than matter — by matter a thing is a natural thing only in ability, by form it is this or that natural thing in act. The parallel he draws: “substance” (from standing under) and “nature” are not synonyms, since each has many senses, but they overlap in three — matter, form, and what a thing is (this last especially close to form). The order is the same in both, and it is a reverse order: matter is known to be substance/nature before form, but form is more substance and more nature than matter. Hence Aristotle’s plan: having established that both are there, he treats form first (third reading), matter after. Aside: immaterial substances are like form without matter, and so “much more substantial than we are.” A man once asked him whether angels really exist; he answered, “They’re more real than you are.” His teacher Kasurik: you meet your guardian angel after death and take him for God; and you never count angels, since each is a wholly new creature, not two of a kind.

5. The proportion that yields substantial form (“Yet it is the proportional in each”) #

None of the accidental forms listed is substance, even joined with matter; yet the proportional is found in each. He puts the proportion on the board:

first matter : man and lion :: clay : sphere and cube

Argument:

1. Clay is able to be a sphere and able to be a cube (not at once).
2. It is not a sphere by being clay, nor a cube by being clay.
3. Therefore there is something else by which the clay is actually a sphere, and something else again for the cube or pyramid — an (accidental) form.
4. Likewise first matter is able to be man, lion, dog, cat, tree, stone, but is none of them by being first matter.
5. Therefore something else makes first matter actually a man rather than a lion.
6. This we call form too — not because “form” means the same thing, but because it is proportional, so not purely equivocal: a substantial form as opposed to an accidental form.

Student question: “What was the definition of substantial form again?” — His answer: he is not defining it; you must know it by how it is proportional to accidental form, and he runs the proportion through again.

6. Likenesses and differences of the two forms (“simply without qualification”) #

Likenesses: both are act as opposed to ability; by both, something is in some way. Differences:

• By substantial form something is simply, without qualification; by accidental form only in a qualified sense. Health is not responsible for my being but for my being healthy; geometry is not that by which I am, but that by which I am a geometer. When I was generated I came to be; when I studied Euclid I came to be a geometer. If I forget my geometry I cease to be a geometer, not to be; when I die, I cease to be.
• Substantial form comes to a subject that is only ability, so actuality is in the form before its subject. Accidental form comes to a subject that is already an actual substance, so actuality is in the subject first — which is why some accidental forms are taken for the substance of the thing.
• (Physics I, end) In substance matter is for the sake of form; but accidental forms are for the sake of the subject, because of the imperfection of the substance. From being a man I do not understand even what a square is, so I need accidents to perfect me; God from being God understands geometry and everything else, is universally perfect, lacking in nothing — “the man who’s got everything”; His justice is nothing added to Him. He ties the labour of seeing this to the tools of dialectic: the third tool is seeing differences, the fourth seeing likenesses; Aristotle says seeing a proportional likeness exercises the mind more than a likeness of two things of the same kind, because it is more distant, just as seeing the difference between things close together exercises it more.

Illustrations of “simply” vs. “in a qualified way”:

• Classroom threat: “If you leave this classroom, you will cease to be” — to the judge he could plead he meant “cease to be in the room”, but no one would understand him so; unqualified, it means die. Conversely, walking in, you came to be in the classroom, and you must add it.
• Language lengthens likewise: Anne / Annette (little Anne — a woman he knew wanted “Anne” as she got older), dad / daddy.
• Secundum quid vs. simply. Aside on the soul in heaven: De Koninck’s audience with Pius XII before the definition of the Assumption — if Mary’s body was not assumed, Mary is not in heaven. “St. Peter is in heaven” is a synecdoche; your soul is most of all you, but not the whole of you; strictly you are in heaven after the last judgment, with your body back.

7. Digression: the power of proportion (“discoveries are made in physics by seeing a proportion”) #

Pierre Duhem — working physicist (thermodynamics), then profound historian of science, then writer on the nature of science; the 1950 edition has a preface by Louis de Broglie, who himself began in medieval history — says the commonest way discoveries are made in physics is by seeing a proportion. Einstein, in The Evolution of Physics, says of de Broglie’s own theory (built on a proportion) that “we’ve seen this more than once” in the history of physics. Euclid: books I–IV go together, book V is the theory of proportions, and with it book VI shows the Pythagorean theorem true not only of squares but of any similar rectilinear figures — “you realize the power.” Scripture and theology: “Render to Caesar what is Caesar’s, and to God what is God’s” states a proportion, and the Fathers extend it — what bears Caesar’s image goes to Caesar, what bears God’s image, the soul, goes to God. “The Lord is my shepherd.” The Our Father: as God forgives me, so I to my neighbour — a proportion with three terms, as 9:6 :: 6:4, using me twice (the unforgiving debtor parable). Once in senior seminar he made each philosophy major take a book of Aristotle and bring out its proportions. Plato: the Republic — book I seems finished, then at the start of book II Socrates is asked whether he wants to seem to convince them or really convince them; the whole work grows from one proportion, soul’s parts to city’s parts, the city being easier to see, so he blows it up. Also: reason is to the emotions as a man to a horse — the horse tries to throw him, he can give up or keep remounting until it obeys. Aristotle’s proportion: should reason rule the emotions as master rules slave, or as father rules son? As father rules son — the master rules for his own good, the father for the son’s; so reason rules the emotions for the good of the emotions. Seen in good family life: children under discipline are emotionally happier than those with none, who wear themselves out with no restraint. Proportion is also how words are carried over: “before” in being (this can be without that, not vice versa) carried over to “before” in knowing — plane geometry before solid geometry, as bricks before a brick wall.

8. Form is responsible for being what it is (“the eye of a dead man is no more an eye”) #

As accidental form makes something actually a chair or table, substantial form makes it be a man, lion or dog; when the soul is gone the body is no longer a man. Aristotle’s comparison: the eye of a dead man is no more an eye than the eye of a statue — it sees no more; it is not really an eye anymore.

9. Corollary: this form belongs to this matter (“not just any form is in any matter”) #

Form and matter are like relatives; you cannot have just any form with any matter. Chair: you shape this part and screw it to that. But making a Manhattan you do not get out the screws for the whiskey and vermouth — that is not the form. Consequences:

• Soul: no transmigration, the soul of a man into a dog’s body. Organic body means, in Greek, a body composed of tools; that would be the art of the cook passing into the tools of the carpenter or tailor. Each art has its own tools, each soul its own body.
• Pleasure (Ethics X): pleasure is not something the same that you sprinkle on everything like sugar or salt; the pleasure of hearing Mozart differs from that of seeing a painting — it arises from the activity itself.
• Politics: not just any form of government can be realised in any people. He recalls the State Department trying to plant an American form of government where a people is not ready, and African countries after the Second World War given an American or British form — in practice rubber-stamp republics, like the Soviet under the Communists.

10. Definition by matter, by form, or by both (“By both, you’re going to be complete”) #

A complete definition gives both; giving only one is an imperfect definition.

• “What is water?” — H₂O gives the matter and does not say how hydrogen and oxygen are united: incomplete. Saying “two to one” gives the form without the matter.
• “What is the Pythagorean theorem?” — students answer a² = b² + c², which tells you nothing: no right triangle, no squares; it could be just three numbers. Some form, but not the matter.

11. Summing up sensible substance (“this is as matter, this as form and act”) #

Aristotle’s own summary: it is clear what sensible substance is and how it is — one as matter, one as form and act, and the third the composite of the two. Much more is still to be said, especially about form; the third reading, next time, takes up substantial form.

His words #

• “ability” — what a thing can be, as opposed to act [ed.: potency].
• “Natural Hearing” — Aristotle’s Physics.
• “the fifth book of wisdom” — Metaphysics V, where the senses of substance and nature are set out.
• “first matter” — the subject of substantial change, knowable only by proportion [ed.: prime matter].
• “simply” / “without qualification” vs. “in a qualified sense” — the two ways of being, by substantial and accidental form.
• secundum quid — his Latin for “in a qualified way.”
• “the third and the fourth tools of dialectic” — seeing differences; seeing likenesses, especially proportional ones.
• “organic body” — “in Greek a body composed of tools.”
• “universally perfect” — Thomas’s expression for God’s lacking in nothing.
• “proportional likeness” — likeness of ratios, the kind needed when things are far apart.

Texts #

Read in class

• Aristotle, Metaphysics VIII, reading two — handout “Aristotle, Metaphysics, Book Eight, Reading One,” pp. 2–3: the opening on matter agreed as substance; Democritus’s three differences; the catalogue of other differences; “none of these is substance, even joined with matter, yet it is the proportional in each”; the corollary that act and form differ as their matter differs; definition by matter and/or form; the closing summary of sensible substance.

Mentioned

• Aristotle, Physics II (nature defined; nature as matter, then as form, form more nature); Physics I, end (matter for the sake of form).
• Aristotle, Metaphysics V (senses of substance and nature); chapter on perfection (God lacking in nothing).
• Aristotle, Nicomachean Ethics X (pleasure proper to each activity); the proportion of master/slave and father/son for reason and emotions.
• Aristotle, Topics — third and fourth tools of dialectic (inferred).
• Euclid, Elements I–VI, esp. V (proportion) and VI (generalised Pythagorean theorem).
• Plato, Republic I–II; the man-and-horse image for reason and emotions.
• Pierre Duhem on the nature of science, 1950 ed. with preface by Louis de Broglie; Einstein, The Evolution of Physics.
• Scripture: “Render to Caesar…”; “The Lord is my shepherd”; the Our Father; the parable of the unforgiving debtor.
• Charles De Koninck’s audience with Pius XII before the definition of the Assumption.

His questions #

• Is the clay a sphere or a cube by being clay? No; by being clay it is only able to be either, so something else makes it actually one.
• Is first matter a man or a lion by being first matter? No; it is all of these in ability, so there must be a substantial form whereby it is this rather than that.
• What is a chair by — its matter or its shape? More by its shape; by its matter it is a chair only in ability.
• Why is one piece of wood a threshold and another a lintel? By position only — one below, one above — not by order or shape.
• When I studied Euclid, did I come to be? Only in a qualified sense: I came to be a geometer; if I forget geometry I do not cease to be.
• Should reason rule the emotions as a master rules a slave, or as a father rules a son? As a father rules a son, for the good of the emotions themselves, not tyrannically.
• Is “H₂O” a complete answer to “What is water?” No; it gives the matter without saying how the elements are united, so the definition is imperfect.
• What was the definition of substantial form again? (student) He gives none: it is known only through its proportion to accidental form.